# Properties

 Label 126.3.n.b.19.1 Level $126$ Weight $3$ Character 126.19 Analytic conductor $3.433$ Analytic rank $0$ Dimension $4$ CM no Inner twists $4$

# Learn more

## Newspace parameters

 Level: $$N$$ $$=$$ $$126 = 2 \cdot 3^{2} \cdot 7$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 126.n (of order $$6$$, degree $$2$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$3.43325133094$$ Analytic rank: $$0$$ Dimension: $$4$$ Relative dimension: $$2$$ over $$\Q(\zeta_{6})$$ Coefficient field: $$\Q(\sqrt{2}, \sqrt{-3})$$ Defining polynomial: $$x^{4} + 2 x^{2} + 4$$ Coefficient ring: $$\Z[a_1, \ldots, a_{7}]$$ Coefficient ring index: $$1$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

## Embedding invariants

 Embedding label 19.1 Root $$-0.707107 + 1.22474i$$ of defining polynomial Character $$\chi$$ $$=$$ 126.19 Dual form 126.3.n.b.73.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-0.707107 + 1.22474i) q^{2} +(-1.00000 - 1.73205i) q^{4} +(4.24264 + 2.44949i) q^{5} +(3.50000 - 6.06218i) q^{7} +2.82843 q^{8} +O(q^{10})$$ $$q+(-0.707107 + 1.22474i) q^{2} +(-1.00000 - 1.73205i) q^{4} +(4.24264 + 2.44949i) q^{5} +(3.50000 - 6.06218i) q^{7} +2.82843 q^{8} +(-6.00000 + 3.46410i) q^{10} +(8.48528 + 14.6969i) q^{11} +1.73205i q^{13} +(4.94975 + 8.57321i) q^{14} +(-2.00000 + 3.46410i) q^{16} +(-4.24264 + 2.44949i) q^{17} +(25.5000 + 14.7224i) q^{19} -9.79796i q^{20} -24.0000 q^{22} +(4.24264 - 7.34847i) q^{23} +(-0.500000 - 0.866025i) q^{25} +(-2.12132 - 1.22474i) q^{26} -14.0000 q^{28} -33.9411 q^{29} +(-10.5000 + 6.06218i) q^{31} +(-2.82843 - 4.89898i) q^{32} -6.92820i q^{34} +(29.6985 - 17.1464i) q^{35} +(23.5000 - 40.7032i) q^{37} +(-36.0624 + 20.8207i) q^{38} +(12.0000 + 6.92820i) q^{40} -68.5857i q^{41} +31.0000 q^{43} +(16.9706 - 29.3939i) q^{44} +(6.00000 + 10.3923i) q^{46} +(-72.1249 - 41.6413i) q^{47} +(-24.5000 - 42.4352i) q^{49} +1.41421 q^{50} +(3.00000 - 1.73205i) q^{52} +(38.1838 + 66.1362i) q^{53} +83.1384i q^{55} +(9.89949 - 17.1464i) q^{56} +(24.0000 - 41.5692i) q^{58} +(-72.1249 + 41.6413i) q^{59} +(-72.0000 - 41.5692i) q^{61} -17.1464i q^{62} +8.00000 q^{64} +(-4.24264 + 7.34847i) q^{65} +(15.5000 + 26.8468i) q^{67} +(8.48528 + 4.89898i) q^{68} +48.4974i q^{70} +59.3970 q^{71} +(-70.5000 + 40.7032i) q^{73} +(33.2340 + 57.5630i) q^{74} -58.8897i q^{76} +118.794 q^{77} +(-20.5000 + 35.5070i) q^{79} +(-16.9706 + 9.79796i) q^{80} +(84.0000 + 48.4974i) q^{82} +4.89898i q^{83} -24.0000 q^{85} +(-21.9203 + 37.9671i) q^{86} +(24.0000 + 41.5692i) q^{88} +(50.9117 + 29.3939i) q^{89} +(10.5000 + 6.06218i) q^{91} -16.9706 q^{92} +(102.000 - 58.8897i) q^{94} +(72.1249 + 124.924i) q^{95} -41.5692i q^{97} +69.2965 q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4 q - 4 q^{4} + 14 q^{7} + O(q^{10})$$ $$4 q - 4 q^{4} + 14 q^{7} - 24 q^{10} - 8 q^{16} + 102 q^{19} - 96 q^{22} - 2 q^{25} - 56 q^{28} - 42 q^{31} + 94 q^{37} + 48 q^{40} + 124 q^{43} + 24 q^{46} - 98 q^{49} + 12 q^{52} + 96 q^{58} - 288 q^{61} + 32 q^{64} + 62 q^{67} - 282 q^{73} - 82 q^{79} + 336 q^{82} - 96 q^{85} + 96 q^{88} + 42 q^{91} + 408 q^{94} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/126\mathbb{Z}\right)^\times$$.

 $$n$$ $$29$$ $$73$$ $$\chi(n)$$ $$1$$ $$e\left(\frac{5}{6}\right)$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −0.707107 + 1.22474i −0.353553 + 0.612372i
$$3$$ 0 0
$$4$$ −1.00000 1.73205i −0.250000 0.433013i
$$5$$ 4.24264 + 2.44949i 0.848528 + 0.489898i 0.860154 0.510034i $$-0.170367\pi$$
−0.0116258 + 0.999932i $$0.503701\pi$$
$$6$$ 0 0
$$7$$ 3.50000 6.06218i 0.500000 0.866025i
$$8$$ 2.82843 0.353553
$$9$$ 0 0
$$10$$ −6.00000 + 3.46410i −0.600000 + 0.346410i
$$11$$ 8.48528 + 14.6969i 0.771389 + 1.33609i 0.936802 + 0.349861i $$0.113771\pi$$
−0.165412 + 0.986224i $$0.552896\pi$$
$$12$$ 0 0
$$13$$ 1.73205i 0.133235i 0.997779 + 0.0666173i $$0.0212207\pi$$
−0.997779 + 0.0666173i $$0.978779\pi$$
$$14$$ 4.94975 + 8.57321i 0.353553 + 0.612372i
$$15$$ 0 0
$$16$$ −2.00000 + 3.46410i −0.125000 + 0.216506i
$$17$$ −4.24264 + 2.44949i −0.249567 + 0.144088i −0.619566 0.784945i $$-0.712691\pi$$
0.369999 + 0.929032i $$0.379358\pi$$
$$18$$ 0 0
$$19$$ 25.5000 + 14.7224i 1.34211 + 0.774865i 0.987116 0.160006i $$-0.0511512\pi$$
0.354989 + 0.934870i $$0.384485\pi$$
$$20$$ 9.79796i 0.489898i
$$21$$ 0 0
$$22$$ −24.0000 −1.09091
$$23$$ 4.24264 7.34847i 0.184463 0.319499i −0.758933 0.651169i $$-0.774279\pi$$
0.943395 + 0.331670i $$0.107612\pi$$
$$24$$ 0 0
$$25$$ −0.500000 0.866025i −0.0200000 0.0346410i
$$26$$ −2.12132 1.22474i −0.0815892 0.0471056i
$$27$$ 0 0
$$28$$ −14.0000 −0.500000
$$29$$ −33.9411 −1.17038 −0.585192 0.810895i $$-0.698981\pi$$
−0.585192 + 0.810895i $$0.698981\pi$$
$$30$$ 0 0
$$31$$ −10.5000 + 6.06218i −0.338710 + 0.195554i −0.659701 0.751528i $$-0.729317\pi$$
0.320992 + 0.947082i $$0.395984\pi$$
$$32$$ −2.82843 4.89898i −0.0883883 0.153093i
$$33$$ 0 0
$$34$$ 6.92820i 0.203771i
$$35$$ 29.6985 17.1464i 0.848528 0.489898i
$$36$$ 0 0
$$37$$ 23.5000 40.7032i 0.635135 1.10009i −0.351351 0.936244i $$-0.614278\pi$$
0.986486 0.163843i $$-0.0523889\pi$$
$$38$$ −36.0624 + 20.8207i −0.949012 + 0.547912i
$$39$$ 0 0
$$40$$ 12.0000 + 6.92820i 0.300000 + 0.173205i
$$41$$ 68.5857i 1.67282i −0.548103 0.836411i $$-0.684650\pi$$
0.548103 0.836411i $$-0.315350\pi$$
$$42$$ 0 0
$$43$$ 31.0000 0.720930 0.360465 0.932773i $$-0.382618\pi$$
0.360465 + 0.932773i $$0.382618\pi$$
$$44$$ 16.9706 29.3939i 0.385695 0.668043i
$$45$$ 0 0
$$46$$ 6.00000 + 10.3923i 0.130435 + 0.225920i
$$47$$ −72.1249 41.6413i −1.53457 0.885986i −0.999142 0.0414059i $$-0.986816\pi$$
−0.535430 0.844580i $$-0.679850\pi$$
$$48$$ 0 0
$$49$$ −24.5000 42.4352i −0.500000 0.866025i
$$50$$ 1.41421 0.0282843
$$51$$ 0 0
$$52$$ 3.00000 1.73205i 0.0576923 0.0333087i
$$53$$ 38.1838 + 66.1362i 0.720448 + 1.24785i 0.960820 + 0.277172i $$0.0893973\pi$$
−0.240372 + 0.970681i $$0.577269\pi$$
$$54$$ 0 0
$$55$$ 83.1384i 1.51161i
$$56$$ 9.89949 17.1464i 0.176777 0.306186i
$$57$$ 0 0
$$58$$ 24.0000 41.5692i 0.413793 0.716711i
$$59$$ −72.1249 + 41.6413i −1.22246 + 0.705785i −0.965441 0.260622i $$-0.916072\pi$$
−0.257015 + 0.966407i $$0.582739\pi$$
$$60$$ 0 0
$$61$$ −72.0000 41.5692i −1.18033 0.681463i −0.224237 0.974535i $$-0.571989\pi$$
−0.956090 + 0.293072i $$0.905322\pi$$
$$62$$ 17.1464i 0.276555i
$$63$$ 0 0
$$64$$ 8.00000 0.125000
$$65$$ −4.24264 + 7.34847i −0.0652714 + 0.113053i
$$66$$ 0 0
$$67$$ 15.5000 + 26.8468i 0.231343 + 0.400698i 0.958204 0.286087i $$-0.0923546\pi$$
−0.726860 + 0.686785i $$0.759021\pi$$
$$68$$ 8.48528 + 4.89898i 0.124784 + 0.0720438i
$$69$$ 0 0
$$70$$ 48.4974i 0.692820i
$$71$$ 59.3970 0.836577 0.418289 0.908314i $$-0.362630\pi$$
0.418289 + 0.908314i $$0.362630\pi$$
$$72$$ 0 0
$$73$$ −70.5000 + 40.7032i −0.965753 + 0.557578i −0.897939 0.440120i $$-0.854936\pi$$
−0.0678144 + 0.997698i $$0.521603\pi$$
$$74$$ 33.2340 + 57.5630i 0.449108 + 0.777878i
$$75$$ 0 0
$$76$$ 58.8897i 0.774865i
$$77$$ 118.794 1.54278
$$78$$ 0 0
$$79$$ −20.5000 + 35.5070i −0.259494 + 0.449456i −0.966106 0.258144i $$-0.916889\pi$$
0.706613 + 0.707601i $$0.250222\pi$$
$$80$$ −16.9706 + 9.79796i −0.212132 + 0.122474i
$$81$$ 0 0
$$82$$ 84.0000 + 48.4974i 1.02439 + 0.591432i
$$83$$ 4.89898i 0.0590238i 0.999564 + 0.0295119i $$0.00939530\pi$$
−0.999564 + 0.0295119i $$0.990605\pi$$
$$84$$ 0 0
$$85$$ −24.0000 −0.282353
$$86$$ −21.9203 + 37.9671i −0.254887 + 0.441478i
$$87$$ 0 0
$$88$$ 24.0000 + 41.5692i 0.272727 + 0.472377i
$$89$$ 50.9117 + 29.3939i 0.572041 + 0.330268i 0.757964 0.652296i $$-0.226194\pi$$
−0.185923 + 0.982564i $$0.559527\pi$$
$$90$$ 0 0
$$91$$ 10.5000 + 6.06218i 0.115385 + 0.0666173i
$$92$$ −16.9706 −0.184463
$$93$$ 0 0
$$94$$ 102.000 58.8897i 1.08511 0.626486i
$$95$$ 72.1249 + 124.924i 0.759209 + 1.31499i
$$96$$ 0 0
$$97$$ 41.5692i 0.428549i −0.976774 0.214274i $$-0.931261\pi$$
0.976774 0.214274i $$-0.0687387\pi$$
$$98$$ 69.2965 0.707107
$$99$$ 0 0
$$100$$ −1.00000 + 1.73205i −0.0100000 + 0.0173205i
$$101$$ −152.735 + 88.1816i −1.51223 + 0.873085i −0.512331 + 0.858788i $$0.671218\pi$$
−0.999898 + 0.0142971i $$0.995449\pi$$
$$102$$ 0 0
$$103$$ −25.5000 14.7224i −0.247573 0.142936i 0.371080 0.928601i $$-0.378988\pi$$
−0.618652 + 0.785665i $$0.712321\pi$$
$$104$$ 4.89898i 0.0471056i
$$105$$ 0 0
$$106$$ −108.000 −1.01887
$$107$$ 72.1249 124.924i 0.674064 1.16751i −0.302677 0.953093i $$-0.597880\pi$$
0.976741 0.214421i $$-0.0687863\pi$$
$$108$$ 0 0
$$109$$ −84.5000 146.358i −0.775229 1.34274i −0.934665 0.355528i $$-0.884301\pi$$
0.159436 0.987208i $$-0.449032\pi$$
$$110$$ −101.823 58.7878i −0.925667 0.534434i
$$111$$ 0 0
$$112$$ 14.0000 + 24.2487i 0.125000 + 0.216506i
$$113$$ −59.3970 −0.525637 −0.262818 0.964845i $$-0.584652\pi$$
−0.262818 + 0.964845i $$0.584652\pi$$
$$114$$ 0 0
$$115$$ 36.0000 20.7846i 0.313043 0.180736i
$$116$$ 33.9411 + 58.7878i 0.292596 + 0.506791i
$$117$$ 0 0
$$118$$ 117.779i 0.998131i
$$119$$ 34.2929i 0.288175i
$$120$$ 0 0
$$121$$ −83.5000 + 144.626i −0.690083 + 1.19526i
$$122$$ 101.823 58.7878i 0.834618 0.481867i
$$123$$ 0 0
$$124$$ 21.0000 + 12.1244i 0.169355 + 0.0977771i
$$125$$ 127.373i 1.01899i
$$126$$ 0 0
$$127$$ 209.000 1.64567 0.822835 0.568281i $$-0.192391\pi$$
0.822835 + 0.568281i $$0.192391\pi$$
$$128$$ −5.65685 + 9.79796i −0.0441942 + 0.0765466i
$$129$$ 0 0
$$130$$ −6.00000 10.3923i −0.0461538 0.0799408i
$$131$$ −50.9117 29.3939i −0.388639 0.224381i 0.292931 0.956133i $$-0.405369\pi$$
−0.681570 + 0.731753i $$0.738703\pi$$
$$132$$ 0 0
$$133$$ 178.500 103.057i 1.34211 0.774865i
$$134$$ −43.8406 −0.327169
$$135$$ 0 0
$$136$$ −12.0000 + 6.92820i −0.0882353 + 0.0509427i
$$137$$ −76.3675 132.272i −0.557427 0.965492i −0.997710 0.0676333i $$-0.978455\pi$$
0.440283 0.897859i $$-0.354878\pi$$
$$138$$ 0 0
$$139$$ 195.722i 1.40807i 0.710165 + 0.704035i $$0.248620\pi$$
−0.710165 + 0.704035i $$0.751380\pi$$
$$140$$ −59.3970 34.2929i −0.424264 0.244949i
$$141$$ 0 0
$$142$$ −42.0000 + 72.7461i −0.295775 + 0.512297i
$$143$$ −25.4558 + 14.6969i −0.178013 + 0.102776i
$$144$$ 0 0
$$145$$ −144.000 83.1384i −0.993103 0.573369i
$$146$$ 115.126i 0.788534i
$$147$$ 0 0
$$148$$ −94.0000 −0.635135
$$149$$ −25.4558 + 44.0908i −0.170845 + 0.295912i −0.938715 0.344693i $$-0.887983\pi$$
0.767871 + 0.640605i $$0.221316\pi$$
$$150$$ 0 0
$$151$$ −5.00000 8.66025i −0.0331126 0.0573527i 0.848994 0.528402i $$-0.177209\pi$$
−0.882107 + 0.471049i $$0.843875\pi$$
$$152$$ 72.1249 + 41.6413i 0.474506 + 0.273956i
$$153$$ 0 0
$$154$$ −84.0000 + 145.492i −0.545455 + 0.944755i
$$155$$ −59.3970 −0.383206
$$156$$ 0 0
$$157$$ 36.0000 20.7846i 0.229299 0.132386i −0.380949 0.924596i $$-0.624403\pi$$
0.610249 + 0.792210i $$0.291069\pi$$
$$158$$ −28.9914 50.2145i −0.183490 0.317814i
$$159$$ 0 0
$$160$$ 27.7128i 0.173205i
$$161$$ −29.6985 51.4393i −0.184463 0.319499i
$$162$$ 0 0
$$163$$ −43.0000 + 74.4782i −0.263804 + 0.456921i −0.967250 0.253828i $$-0.918310\pi$$
0.703446 + 0.710749i $$0.251644\pi$$
$$164$$ −118.794 + 68.5857i −0.724353 + 0.418206i
$$165$$ 0 0
$$166$$ −6.00000 3.46410i −0.0361446 0.0208681i
$$167$$ 181.262i 1.08540i −0.839926 0.542701i $$-0.817402\pi$$
0.839926 0.542701i $$-0.182598\pi$$
$$168$$ 0 0
$$169$$ 166.000 0.982249
$$170$$ 16.9706 29.3939i 0.0998268 0.172905i
$$171$$ 0 0
$$172$$ −31.0000 53.6936i −0.180233 0.312172i
$$173$$ −38.1838 22.0454i −0.220715 0.127430i 0.385566 0.922680i $$-0.374006\pi$$
−0.606281 + 0.795250i $$0.707340\pi$$
$$174$$ 0 0
$$175$$ −7.00000 −0.0400000
$$176$$ −67.8823 −0.385695
$$177$$ 0 0
$$178$$ −72.0000 + 41.5692i −0.404494 + 0.233535i
$$179$$ 4.24264 + 7.34847i 0.0237019 + 0.0410529i 0.877633 0.479333i $$-0.159121\pi$$
−0.853931 + 0.520386i $$0.825788\pi$$
$$180$$ 0 0
$$181$$ 43.3013i 0.239234i −0.992820 0.119617i $$-0.961833\pi$$
0.992820 0.119617i $$-0.0381666\pi$$
$$182$$ −14.8492 + 8.57321i −0.0815892 + 0.0471056i
$$183$$ 0 0
$$184$$ 12.0000 20.7846i 0.0652174 0.112960i
$$185$$ 199.404 115.126i 1.07786 0.622303i
$$186$$ 0 0
$$187$$ −72.0000 41.5692i −0.385027 0.222295i
$$188$$ 166.565i 0.885986i
$$189$$ 0 0
$$190$$ −204.000 −1.07368
$$191$$ −38.1838 + 66.1362i −0.199915 + 0.346263i −0.948501 0.316775i $$-0.897400\pi$$
0.748586 + 0.663038i $$0.230733\pi$$
$$192$$ 0 0
$$193$$ 143.500 + 248.549i 0.743523 + 1.28782i 0.950882 + 0.309555i $$0.100180\pi$$
−0.207358 + 0.978265i $$0.566487\pi$$
$$194$$ 50.9117 + 29.3939i 0.262431 + 0.151515i
$$195$$ 0 0
$$196$$ −49.0000 + 84.8705i −0.250000 + 0.433013i
$$197$$ 127.279 0.646087 0.323044 0.946384i $$-0.395294\pi$$
0.323044 + 0.946384i $$0.395294\pi$$
$$198$$ 0 0
$$199$$ 180.000 103.923i 0.904523 0.522226i 0.0258579 0.999666i $$-0.491768\pi$$
0.878665 + 0.477439i $$0.158435\pi$$
$$200$$ −1.41421 2.44949i −0.00707107 0.0122474i
$$201$$ 0 0
$$202$$ 249.415i 1.23473i
$$203$$ −118.794 + 205.757i −0.585192 + 1.01358i
$$204$$ 0 0
$$205$$ 168.000 290.985i 0.819512 1.41944i
$$206$$ 36.0624 20.8207i 0.175060 0.101071i
$$207$$ 0 0
$$208$$ −6.00000 3.46410i −0.0288462 0.0166543i
$$209$$ 499.696i 2.39089i
$$210$$ 0 0
$$211$$ 82.0000 0.388626 0.194313 0.980940i $$-0.437752\pi$$
0.194313 + 0.980940i $$0.437752\pi$$
$$212$$ 76.3675 132.272i 0.360224 0.623927i
$$213$$ 0 0
$$214$$ 102.000 + 176.669i 0.476636 + 0.825557i
$$215$$ 131.522 + 75.9342i 0.611730 + 0.353182i
$$216$$ 0 0
$$217$$ 84.8705i 0.391108i
$$218$$ 239.002 1.09634
$$219$$ 0 0
$$220$$ 144.000 83.1384i 0.654545 0.377902i
$$221$$ −4.24264 7.34847i −0.0191975 0.0332510i
$$222$$ 0 0
$$223$$ 41.5692i 0.186409i 0.995647 + 0.0932045i $$0.0297110\pi$$
−0.995647 + 0.0932045i $$0.970289\pi$$
$$224$$ −39.5980 −0.176777
$$225$$ 0 0
$$226$$ 42.0000 72.7461i 0.185841 0.321886i
$$227$$ 330.926 191.060i 1.45782 0.841675i 0.458920 0.888478i $$-0.348237\pi$$
0.998904 + 0.0468029i $$0.0149033\pi$$
$$228$$ 0 0
$$229$$ −70.5000 40.7032i −0.307860 0.177743i 0.338108 0.941107i $$-0.390213\pi$$
−0.645969 + 0.763364i $$0.723546\pi$$
$$230$$ 58.7878i 0.255599i
$$231$$ 0 0
$$232$$ −96.0000 −0.413793
$$233$$ −114.551 + 198.409i −0.491636 + 0.851539i −0.999954 0.00963059i $$-0.996934\pi$$
0.508317 + 0.861170i $$0.330268\pi$$
$$234$$ 0 0
$$235$$ −204.000 353.338i −0.868085 1.50357i
$$236$$ 144.250 + 83.2827i 0.611228 + 0.352893i
$$237$$ 0 0
$$238$$ −42.0000 24.2487i −0.176471 0.101885i
$$239$$ −67.8823 −0.284026 −0.142013 0.989865i $$-0.545358\pi$$
−0.142013 + 0.989865i $$0.545358\pi$$
$$240$$ 0 0
$$241$$ −396.000 + 228.631i −1.64315 + 0.948675i −0.663451 + 0.748220i $$0.730909\pi$$
−0.979703 + 0.200455i $$0.935758\pi$$
$$242$$ −118.087 204.532i −0.487962 0.845175i
$$243$$ 0 0
$$244$$ 166.277i 0.681463i
$$245$$ 240.050i 0.979796i
$$246$$ 0 0
$$247$$ −25.5000 + 44.1673i −0.103239 + 0.178815i
$$248$$ −29.6985 + 17.1464i −0.119752 + 0.0691388i
$$249$$ 0 0
$$250$$ 156.000 + 90.0666i 0.624000 + 0.360267i
$$251$$ 347.828i 1.38577i 0.721050 + 0.692884i $$0.243660\pi$$
−0.721050 + 0.692884i $$0.756340\pi$$
$$252$$ 0 0
$$253$$ 144.000 0.569170
$$254$$ −147.785 + 255.972i −0.581832 + 1.00776i
$$255$$ 0 0
$$256$$ −8.00000 13.8564i −0.0312500 0.0541266i
$$257$$ 140.007 + 80.8332i 0.544775 + 0.314526i 0.747012 0.664811i $$-0.231488\pi$$
−0.202237 + 0.979337i $$0.564821\pi$$
$$258$$ 0 0
$$259$$ −164.500 284.922i −0.635135 1.10009i
$$260$$ 16.9706 0.0652714
$$261$$ 0 0
$$262$$ 72.0000 41.5692i 0.274809 0.158661i
$$263$$ −127.279 220.454i −0.483951 0.838228i 0.515879 0.856662i $$-0.327466\pi$$
−0.999830 + 0.0184332i $$0.994132\pi$$
$$264$$ 0 0
$$265$$ 374.123i 1.41178i
$$266$$ 291.489i 1.09582i
$$267$$ 0 0
$$268$$ 31.0000 53.6936i 0.115672 0.200349i
$$269$$ 16.9706 9.79796i 0.0630876 0.0364236i −0.468124 0.883663i $$-0.655070\pi$$
0.531212 + 0.847239i $$0.321737\pi$$
$$270$$ 0 0
$$271$$ 36.0000 + 20.7846i 0.132841 + 0.0766960i 0.564948 0.825127i $$-0.308896\pi$$
−0.432107 + 0.901823i $$0.642230\pi$$
$$272$$ 19.5959i 0.0720438i
$$273$$ 0 0
$$274$$ 216.000 0.788321
$$275$$ 8.48528 14.6969i 0.0308556 0.0534434i
$$276$$ 0 0
$$277$$ 168.500 + 291.851i 0.608303 + 1.05361i 0.991520 + 0.129954i $$0.0414829\pi$$
−0.383217 + 0.923658i $$0.625184\pi$$
$$278$$ −239.709 138.396i −0.862263 0.497828i
$$279$$ 0 0
$$280$$ 84.0000 48.4974i 0.300000 0.173205i
$$281$$ 246.073 0.875705 0.437853 0.899047i $$-0.355739\pi$$
0.437853 + 0.899047i $$0.355739\pi$$
$$282$$ 0 0
$$283$$ −169.500 + 97.8609i −0.598940 + 0.345798i −0.768624 0.639700i $$-0.779058\pi$$
0.169685 + 0.985498i $$0.445725\pi$$
$$284$$ −59.3970 102.879i −0.209144 0.362248i
$$285$$ 0 0
$$286$$ 41.5692i 0.145347i
$$287$$ −415.779 240.050i −1.44871 0.836411i
$$288$$ 0 0
$$289$$ −132.500 + 229.497i −0.458478 + 0.794106i
$$290$$ 203.647 117.576i 0.702230 0.405433i
$$291$$ 0 0
$$292$$ 141.000 + 81.4064i 0.482877 + 0.278789i
$$293$$ 97.9796i 0.334401i −0.985923 0.167201i $$-0.946527\pi$$
0.985923 0.167201i $$-0.0534728\pi$$
$$294$$ 0 0
$$295$$ −408.000 −1.38305
$$296$$ 66.4680 115.126i 0.224554 0.388939i
$$297$$ 0 0
$$298$$ −36.0000 62.3538i −0.120805 0.209241i
$$299$$ 12.7279 + 7.34847i 0.0425683 + 0.0245768i
$$300$$ 0 0
$$301$$ 108.500 187.928i 0.360465 0.624344i
$$302$$ 14.1421 0.0468283
$$303$$ 0 0
$$304$$ −102.000 + 58.8897i −0.335526 + 0.193716i
$$305$$ −203.647 352.727i −0.667694 1.15648i
$$306$$ 0 0
$$307$$ 71.0141i 0.231316i 0.993289 + 0.115658i $$0.0368977\pi$$
−0.993289 + 0.115658i $$0.963102\pi$$
$$308$$ −118.794 205.757i −0.385695 0.668043i
$$309$$ 0 0
$$310$$ 42.0000 72.7461i 0.135484 0.234665i
$$311$$ 186.676 107.778i 0.600245 0.346552i −0.168893 0.985634i $$-0.554019\pi$$
0.769138 + 0.639083i $$0.220686\pi$$
$$312$$ 0 0
$$313$$ 253.500 + 146.358i 0.809904 + 0.467598i 0.846923 0.531716i $$-0.178453\pi$$
−0.0370184 + 0.999315i $$0.511786\pi$$
$$314$$ 58.7878i 0.187222i
$$315$$ 0 0
$$316$$ 82.0000 0.259494
$$317$$ 118.794 205.757i 0.374744 0.649076i −0.615544 0.788102i $$-0.711064\pi$$
0.990289 + 0.139026i $$0.0443972\pi$$
$$318$$ 0 0
$$319$$ −288.000 498.831i −0.902821 1.56373i
$$320$$ 33.9411 + 19.5959i 0.106066 + 0.0612372i
$$321$$ 0 0
$$322$$ 84.0000 0.260870
$$323$$ −144.250 −0.446594
$$324$$ 0 0
$$325$$ 1.50000 0.866025i 0.00461538 0.00266469i
$$326$$ −60.8112 105.328i −0.186537 0.323092i
$$327$$ 0 0
$$328$$ 193.990i 0.591432i
$$329$$ −504.874 + 291.489i −1.53457 + 0.885986i
$$330$$ 0 0
$$331$$ 92.5000 160.215i 0.279456 0.484032i −0.691794 0.722095i $$-0.743179\pi$$
0.971250 + 0.238063i $$0.0765125\pi$$
$$332$$ 8.48528 4.89898i 0.0255581 0.0147560i
$$333$$ 0 0
$$334$$ 222.000 + 128.172i 0.664671 + 0.383748i
$$335$$ 151.868i 0.453338i
$$336$$ 0 0
$$337$$ −359.000 −1.06528 −0.532641 0.846341i $$-0.678800\pi$$
−0.532641 + 0.846341i $$0.678800\pi$$
$$338$$ −117.380 + 203.308i −0.347277 + 0.601502i
$$339$$ 0 0
$$340$$ 24.0000 + 41.5692i 0.0705882 + 0.122262i
$$341$$ −178.191 102.879i −0.522554 0.301697i
$$342$$ 0 0
$$343$$ −343.000 −1.00000
$$344$$ 87.6812 0.254887
$$345$$ 0 0
$$346$$ 54.0000 31.1769i 0.156069 0.0901067i
$$347$$ −233.345 404.166i −0.672465 1.16474i −0.977203 0.212307i $$-0.931902\pi$$
0.304738 0.952436i $$-0.401431\pi$$
$$348$$ 0 0
$$349$$ 581.969i 1.66753i −0.552117 0.833767i $$-0.686180\pi$$
0.552117 0.833767i $$-0.313820\pi$$
$$350$$ 4.94975 8.57321i 0.0141421 0.0244949i
$$351$$ 0 0
$$352$$ 48.0000 83.1384i 0.136364 0.236189i
$$353$$ 250.316 144.520i 0.709110 0.409405i −0.101621 0.994823i $$-0.532403\pi$$
0.810731 + 0.585418i $$0.199070\pi$$
$$354$$ 0 0
$$355$$ 252.000 + 145.492i 0.709859 + 0.409837i
$$356$$ 117.576i 0.330268i
$$357$$ 0 0
$$358$$ −12.0000 −0.0335196
$$359$$ −169.706 + 293.939i −0.472718 + 0.818771i −0.999512 0.0312215i $$-0.990060\pi$$
0.526795 + 0.849992i $$0.323394\pi$$
$$360$$ 0 0
$$361$$ 253.000 + 438.209i 0.700831 + 1.21387i
$$362$$ 53.0330 + 30.6186i 0.146500 + 0.0845818i
$$363$$ 0 0
$$364$$ 24.2487i 0.0666173i
$$365$$ −398.808 −1.09263
$$366$$ 0 0
$$367$$ 133.500 77.0763i 0.363760 0.210017i −0.306969 0.951720i $$-0.599315\pi$$
0.670729 + 0.741703i $$0.265981\pi$$
$$368$$ 16.9706 + 29.3939i 0.0461157 + 0.0798747i
$$369$$ 0 0
$$370$$ 325.626i 0.880069i
$$371$$ 534.573 1.44090
$$372$$ 0 0
$$373$$ 144.500 250.281i 0.387399 0.670996i −0.604699 0.796454i $$-0.706707\pi$$
0.992099 + 0.125458i $$0.0400401\pi$$
$$374$$ 101.823 58.7878i 0.272255 0.157187i
$$375$$ 0 0
$$376$$ −204.000 117.779i −0.542553 0.313243i
$$377$$ 58.7878i 0.155936i
$$378$$ 0 0
$$379$$ 7.00000 0.0184697 0.00923483 0.999957i $$-0.497060\pi$$
0.00923483 + 0.999957i $$0.497060\pi$$
$$380$$ 144.250 249.848i 0.379605 0.657495i
$$381$$ 0 0
$$382$$ −54.0000 93.5307i −0.141361 0.244845i
$$383$$ 428.507 + 247.398i 1.11882 + 0.645949i 0.941099 0.338132i $$-0.109795\pi$$
0.177718 + 0.984081i $$0.443129\pi$$
$$384$$ 0 0
$$385$$ 504.000 + 290.985i 1.30909 + 0.755804i
$$386$$ −405.879 −1.05150
$$387$$ 0 0
$$388$$ −72.0000 + 41.5692i −0.185567 + 0.107137i
$$389$$ 114.551 + 198.409i 0.294476 + 0.510048i 0.974863 0.222805i $$-0.0715214\pi$$
−0.680387 + 0.732853i $$0.738188\pi$$
$$390$$ 0 0
$$391$$ 41.5692i 0.106315i
$$392$$ −69.2965 120.025i −0.176777 0.306186i
$$393$$ 0 0
$$394$$ −90.0000 + 155.885i −0.228426 + 0.395646i
$$395$$ −173.948 + 100.429i −0.440375 + 0.254251i
$$396$$ 0 0
$$397$$ 70.5000 + 40.7032i 0.177582 + 0.102527i 0.586156 0.810198i $$-0.300641\pi$$
−0.408574 + 0.912725i $$0.633974\pi$$
$$398$$ 293.939i 0.738540i
$$399$$ 0 0
$$400$$ 4.00000 0.0100000
$$401$$ 46.6690 80.8332i 0.116382 0.201579i −0.801950 0.597392i $$-0.796204\pi$$
0.918331 + 0.395813i $$0.129537\pi$$
$$402$$ 0 0
$$403$$ −10.5000 18.1865i −0.0260546 0.0451279i
$$404$$ 305.470 + 176.363i 0.756114 + 0.436543i
$$405$$ 0 0
$$406$$ −168.000 290.985i −0.413793 0.716711i
$$407$$ 797.616 1.95975
$$408$$ 0 0
$$409$$ −361.500 + 208.712i −0.883863 + 0.510299i −0.871930 0.489630i $$-0.837132\pi$$
−0.0119329 + 0.999929i $$0.503798\pi$$
$$410$$ 237.588 + 411.514i 0.579483 + 1.00369i
$$411$$ 0 0
$$412$$ 58.8897i 0.142936i
$$413$$ 582.979i 1.41157i
$$414$$ 0 0
$$415$$ −12.0000 + 20.7846i −0.0289157 + 0.0500834i
$$416$$ 8.48528 4.89898i 0.0203973 0.0117764i
$$417$$ 0 0
$$418$$ −612.000 353.338i −1.46411 0.845307i
$$419$$ 19.5959i 0.0467683i −0.999727 0.0233842i $$-0.992556\pi$$
0.999727 0.0233842i $$-0.00744408\pi$$
$$420$$ 0 0
$$421$$ 407.000 0.966746 0.483373 0.875415i $$-0.339412\pi$$
0.483373 + 0.875415i $$0.339412\pi$$
$$422$$ −57.9828 + 100.429i −0.137400 + 0.237984i
$$423$$ 0 0
$$424$$ 108.000 + 187.061i 0.254717 + 0.441183i
$$425$$ 4.24264 + 2.44949i 0.00998268 + 0.00576351i
$$426$$ 0 0
$$427$$ −504.000 + 290.985i −1.18033 + 0.681463i
$$428$$ −288.500 −0.674064
$$429$$ 0 0
$$430$$ −186.000 + 107.387i −0.432558 + 0.249738i
$$431$$ 80.6102 + 139.621i 0.187031 + 0.323946i 0.944259 0.329204i $$-0.106780\pi$$
−0.757228 + 0.653150i $$0.773447\pi$$
$$432$$ 0 0
$$433$$ 168.009i 0.388011i 0.981000 + 0.194006i $$0.0621480\pi$$
−0.981000 + 0.194006i $$0.937852\pi$$
$$434$$ −103.945 60.0125i −0.239504 0.138278i
$$435$$ 0 0
$$436$$ −169.000 + 292.717i −0.387615 + 0.671368i
$$437$$ 216.375 124.924i 0.495137 0.285867i
$$438$$ 0 0
$$439$$ −468.000 270.200i −1.06606 0.615490i −0.138957 0.990298i $$-0.544375\pi$$
−0.927102 + 0.374809i $$0.877708\pi$$
$$440$$ 235.151i 0.534434i
$$441$$ 0 0
$$442$$ 12.0000 0.0271493
$$443$$ −63.6396 + 110.227i −0.143656 + 0.248819i −0.928871 0.370404i $$-0.879219\pi$$
0.785215 + 0.619224i $$0.212553\pi$$
$$444$$ 0 0
$$445$$ 144.000 + 249.415i 0.323596 + 0.560484i
$$446$$ −50.9117 29.3939i −0.114152 0.0659056i
$$447$$ 0 0
$$448$$ 28.0000 48.4974i 0.0625000 0.108253i
$$449$$ 110.309 0.245676 0.122838 0.992427i $$-0.460800\pi$$
0.122838 + 0.992427i $$0.460800\pi$$
$$450$$ 0 0
$$451$$ 1008.00 581.969i 2.23503 1.29040i
$$452$$ 59.3970 + 102.879i 0.131409 + 0.227607i
$$453$$ 0 0
$$454$$ 540.400i 1.19031i
$$455$$ 29.6985 + 51.4393i 0.0652714 + 0.113053i
$$456$$ 0 0
$$457$$ −12.5000 + 21.6506i −0.0273523 + 0.0473756i −0.879378 0.476125i $$-0.842041\pi$$
0.852025 + 0.523501i $$0.175374\pi$$
$$458$$ 99.7021 57.5630i 0.217690 0.125683i
$$459$$ 0 0
$$460$$ −72.0000 41.5692i −0.156522 0.0903679i
$$461$$ 78.3837i 0.170030i 0.996380 + 0.0850148i $$0.0270938\pi$$
−0.996380 + 0.0850148i $$0.972906\pi$$
$$462$$ 0 0
$$463$$ 521.000 1.12527 0.562635 0.826705i $$-0.309788\pi$$
0.562635 + 0.826705i $$0.309788\pi$$
$$464$$ 67.8823 117.576i 0.146298 0.253395i
$$465$$ 0 0
$$466$$ −162.000 280.592i −0.347639 0.602129i
$$467$$ −190.919 110.227i −0.408820 0.236032i 0.281463 0.959572i $$-0.409180\pi$$
−0.690283 + 0.723540i $$0.742514\pi$$
$$468$$ 0 0
$$469$$ 217.000 0.462687
$$470$$ 576.999 1.22766
$$471$$ 0 0
$$472$$ −204.000 + 117.779i −0.432203 + 0.249533i
$$473$$ 263.044 + 455.605i 0.556118 + 0.963224i
$$474$$ 0 0
$$475$$ 29.4449i 0.0619892i
$$476$$ 59.3970 34.2929i 0.124784 0.0720438i
$$477$$ 0 0
$$478$$ 48.0000 83.1384i 0.100418 0.173930i
$$479$$ −759.433 + 438.459i −1.58545 + 0.915363i −0.591412 + 0.806370i $$0.701429\pi$$
−0.994043 + 0.108993i $$0.965237\pi$$
$$480$$ 0 0
$$481$$ 70.5000 + 40.7032i 0.146570 + 0.0846220i
$$482$$ 646.665i 1.34163i
$$483$$ 0 0
$$484$$ 334.000 0.690083
$$485$$ 101.823 176.363i 0.209945 0.363636i
$$486$$ 0 0
$$487$$ −63.5000 109.985i −0.130390 0.225842i 0.793437 0.608653i $$-0.208290\pi$$
−0.923827 + 0.382810i $$0.874956\pi$$
$$488$$ −203.647 117.576i −0.417309 0.240933i
$$489$$ 0 0
$$490$$ 294.000 + 169.741i 0.600000 + 0.346410i
$$491$$ −627.911 −1.27884 −0.639420 0.768857i $$-0.720826\pi$$
−0.639420 + 0.768857i $$0.720826\pi$$
$$492$$ 0 0
$$493$$ 144.000 83.1384i 0.292089 0.168638i
$$494$$ −36.0624 62.4620i −0.0730009 0.126441i
$$495$$ 0 0
$$496$$ 48.4974i 0.0977771i
$$497$$ 207.889 360.075i 0.418289 0.724497i
$$498$$ 0 0
$$499$$ 116.500 201.784i 0.233467 0.404377i −0.725359 0.688371i $$-0.758326\pi$$
0.958826 + 0.283994i $$0.0916596\pi$$
$$500$$ −220.617 + 127.373i −0.441235 + 0.254747i
$$501$$ 0 0
$$502$$ −426.000 245.951i −0.848606 0.489943i
$$503$$ 538.888i 1.07135i −0.844425 0.535674i $$-0.820058\pi$$
0.844425 0.535674i $$-0.179942\pi$$
$$504$$ 0 0
$$505$$ −864.000 −1.71089
$$506$$ −101.823 + 176.363i −0.201232 + 0.348544i
$$507$$ 0 0
$$508$$ −209.000 361.999i −0.411417 0.712596i
$$509$$ 275.772 + 159.217i 0.541791 + 0.312803i 0.745805 0.666165i $$-0.232065\pi$$
−0.204013 + 0.978968i $$0.565399\pi$$
$$510$$ 0 0
$$511$$ 569.845i 1.11516i
$$512$$ 22.6274 0.0441942
$$513$$ 0 0
$$514$$ −198.000 + 114.315i −0.385214 + 0.222403i
$$515$$ −72.1249 124.924i −0.140048 0.242571i
$$516$$ 0 0
$$517$$ 1413.35i 2.73376i
$$518$$ 465.276 0.898217
$$519$$ 0 0
$$520$$ −12.0000 + 20.7846i −0.0230769 + 0.0399704i
$$521$$ −492.146 + 284.141i −0.944619 + 0.545376i −0.891405 0.453207i $$-0.850280\pi$$
−0.0532135 + 0.998583i $$0.516946\pi$$
$$522$$ 0 0
$$523$$ 457.500 + 264.138i 0.874761 + 0.505043i 0.868927 0.494939i $$-0.164810\pi$$
0.00583355 + 0.999983i $$0.498143\pi$$
$$524$$ 117.576i 0.224381i
$$525$$ 0 0
$$526$$ 360.000 0.684411
$$527$$ 29.6985 51.4393i 0.0563539 0.0976078i
$$528$$ 0 0
$$529$$ 228.500 + 395.774i 0.431947 + 0.748154i
$$530$$ −458.205 264.545i −0.864538 0.499141i
$$531$$ 0 0
$$532$$ −357.000 206.114i −0.671053 0.387432i
$$533$$ 118.794 0.222878
$$534$$ 0 0
$$535$$ 612.000 353.338i 1.14393 0.660446i
$$536$$ 43.8406 + 75.9342i 0.0817922 + 0.141668i
$$537$$ 0 0
$$538$$ 27.7128i 0.0515108i
$$539$$ 415.779 720.150i 0.771389 1.33609i
$$540$$ 0 0
$$541$$ −167.500 + 290.119i −0.309612 + 0.536263i −0.978277 0.207300i $$-0.933532\pi$$
0.668666 + 0.743563i $$0.266866\pi$$
$$542$$ −50.9117 + 29.3939i −0.0939330 + 0.0542322i
$$543$$ 0 0
$$544$$ 24.0000 + 13.8564i 0.0441176 + 0.0254713i
$$545$$ 827.928i 1.51913i
$$546$$ 0 0
$$547$$ −658.000 −1.20293 −0.601463 0.798901i $$-0.705415\pi$$
−0.601463 + 0.798901i $$0.705415\pi$$
$$548$$ −152.735 + 264.545i −0.278714 + 0.482746i
$$549$$ 0 0
$$550$$ 12.0000 + 20.7846i 0.0218182 + 0.0377902i
$$551$$ −865.499 499.696i −1.57078 0.906889i
$$552$$ 0 0
$$553$$ 143.500 + 248.549i 0.259494 + 0.449456i
$$554$$ −476.590 −0.860271
$$555$$ 0 0
$$556$$ 339.000 195.722i 0.609712 0.352018i
$$557$$ 135.765 + 235.151i 0.243742 + 0.422174i 0.961777 0.273833i $$-0.0882915\pi$$
−0.718035 + 0.696007i $$0.754958\pi$$
$$558$$ 0 0
$$559$$ 53.6936i 0.0960529i
$$560$$ 137.171i 0.244949i
$$561$$ 0 0
$$562$$ −174.000 + 301.377i −0.309609 + 0.536258i
$$563$$ −12.7279 + 7.34847i −0.0226073 + 0.0130523i −0.511261 0.859425i $$-0.670821\pi$$
0.488654 + 0.872478i $$0.337488\pi$$
$$564$$ 0 0
$$565$$ −252.000 145.492i −0.446018 0.257508i
$$566$$ 276.792i 0.489032i
$$567$$ 0 0
$$568$$ 168.000 0.295775
$$569$$ 424.264 734.847i 0.745631 1.29147i −0.204268 0.978915i $$-0.565481\pi$$
0.949899 0.312556i $$-0.101185\pi$$
$$570$$ 0 0
$$571$$ −224.500 388.845i −0.393170 0.680990i 0.599696 0.800228i $$-0.295288\pi$$
−0.992866 + 0.119238i $$0.961955\pi$$
$$572$$ 50.9117 + 29.3939i 0.0890064 + 0.0513879i
$$573$$ 0 0
$$574$$ 588.000 339.482i 1.02439 0.591432i
$$575$$ −8.48528 −0.0147570
$$576$$ 0 0
$$577$$ −253.500 + 146.358i −0.439341 + 0.253654i −0.703318 0.710875i $$-0.748299\pi$$
0.263977 + 0.964529i $$0.414966\pi$$
$$578$$ −187.383 324.557i −0.324193 0.561518i
$$579$$ 0 0
$$580$$ 332.554i 0.573369i
$$581$$ 29.6985 + 17.1464i 0.0511162 + 0.0295119i
$$582$$ 0 0
$$583$$ −648.000 + 1122.37i −1.11149 + 1.92516i
$$584$$ −199.404 + 115.126i −0.341445 + 0.197134i
$$585$$ 0 0
$$586$$ 120.000 + 69.2820i 0.204778 + 0.118229i
$$587$$ 529.090i 0.901345i 0.892689 + 0.450673i $$0.148816\pi$$
−0.892689 + 0.450673i $$0.851184\pi$$
$$588$$ 0 0
$$589$$ −357.000 −0.606112
$$590$$ 288.500 499.696i 0.488982 0.846942i
$$591$$ 0 0
$$592$$ 94.0000 + 162.813i 0.158784 + 0.275022i
$$593$$ −907.925 524.191i −1.53107 0.883964i −0.999313 0.0370681i $$-0.988198\pi$$
−0.531758 0.846896i $$-0.678469\pi$$
$$594$$ 0 0
$$595$$ −84.0000 + 145.492i −0.141176 + 0.244525i
$$596$$ 101.823 0.170845
$$597$$ 0 0
$$598$$ −18.0000 + 10.3923i −0.0301003 + 0.0173784i
$$599$$ 322.441 + 558.484i 0.538298 + 0.932360i 0.998996 + 0.0448028i $$0.0142660\pi$$
−0.460698 + 0.887557i $$0.652401\pi$$
$$600$$ 0 0
$$601$$ 458.993i 0.763716i −0.924221 0.381858i $$-0.875284\pi$$
0.924221 0.381858i $$-0.124716\pi$$
$$602$$ 153.442 + 265.770i 0.254887 + 0.441478i
$$603$$ 0 0
$$604$$ −10.0000 + 17.3205i −0.0165563 + 0.0286763i
$$605$$ −708.521 + 409.065i −1.17111 + 0.676140i
$$606$$ 0 0
$$607$$ 910.500 + 525.677i 1.50000 + 0.866025i 1.00000 $$0$$
0.500000 + 0.866025i $$0.333333\pi$$
$$608$$ 166.565i 0.273956i
$$609$$ 0 0
$$610$$ 576.000 0.944262
$$611$$ 72.1249 124.924i 0.118044 0.204458i
$$612$$ 0 0
$$613$$ −145.000 251.147i −0.236542 0.409702i 0.723178 0.690662i $$-0.242681\pi$$
−0.959720 + 0.280960i $$0.909347\pi$$
$$614$$ −86.9741 50.2145i −0.141652 0.0817826i
$$615$$ 0 0
$$616$$ 336.000 0.545455
$$617$$ −729.734 −1.18271 −0.591357 0.806410i $$-0.701407\pi$$
−0.591357 + 0.806410i $$0.701407\pi$$
$$618$$ 0 0
$$619$$ −709.500 + 409.630i −1.14620 + 0.661761i −0.947959 0.318392i $$-0.896857\pi$$
−0.198244 + 0.980153i $$0.563524\pi$$
$$620$$ 59.3970 + 102.879i 0.0958016 + 0.165933i
$$621$$ 0 0
$$622$$ 304.841i 0.490098i
$$623$$ 356.382 205.757i 0.572041 0.330268i
$$624$$ 0 0
$$625$$ 299.500 518.749i 0.479200 0.829999i
$$626$$ −358.503 + 206.982i −0.572689 + 0.330642i
$$627$$ 0 0
$$628$$ −72.0000 41.5692i −0.114650 0.0661930i
$$629$$ 230.252i 0.366060i
$$630$$ 0 0
$$631$$ −58.0000 −0.0919176 −0.0459588 0.998943i $$-0.514634\pi$$
−0.0459588 + 0.998943i $$0.514634\pi$$
$$632$$ −57.9828 + 100.429i −0.0917449 + 0.158907i
$$633$$ 0 0
$$634$$ 168.000 + 290.985i 0.264984 + 0.458966i
$$635$$ 886.712 + 511.943i 1.39640 + 0.806210i
$$636$$ 0 0
$$637$$ 73.5000 42.4352i 0.115385 0.0666173i
$$638$$ 814.587 1.27678
$$639$$ 0 0
$$640$$ −48.0000 + 27.7128i −0.0750000 + 0.0433013i
$$641$$ 479.418 + 830.377i 0.747923 + 1.29544i 0.948817 + 0.315827i $$0.102282\pi$$
−0.200894 + 0.979613i $$0.564385\pi$$
$$642$$ 0 0
$$643$$ 760.370i 1.18254i 0.806475 + 0.591268i $$0.201372\pi$$
−0.806475 + 0.591268i $$0.798628\pi$$
$$644$$ −59.3970 + 102.879i −0.0922313 + 0.159749i
$$645$$ 0 0
$$646$$ 102.000 176.669i 0.157895 0.273482i
$$647$$ 305.470 176.363i 0.472133 0.272586i −0.244999 0.969523i $$-0.578788\pi$$
0.717132 + 0.696937i $$0.245454\pi$$
$$648$$ 0 0
$$649$$ −1224.00 706.677i −1.88598 1.08887i
$$650$$ 2.44949i 0.00376845i
$$651$$ 0 0
$$652$$ 172.000 0.263804
$$653$$ −220.617 + 382.120i −0.337852 + 0.585177i −0.984028 0.178011i $$-0.943034\pi$$
0.646177 + 0.763188i $$0.276367\pi$$
$$654$$ 0 0
$$655$$ −144.000 249.415i −0.219847 0.380787i
$$656$$ 237.588 + 137.171i 0.362177 + 0.209103i
$$657$$ 0 0
$$658$$ 824.456i 1.25297i
$$659$$ −161.220 −0.244644 −0.122322 0.992490i $$-0.539034\pi$$
−0.122322 + 0.992490i $$0.539034\pi$$
$$660$$ 0 0
$$661$$ −721.500 + 416.558i −1.09153 + 0.630194i −0.933983 0.357318i $$-0.883691\pi$$
−0.157545 + 0.987512i $$0.550358\pi$$
$$662$$ 130.815 + 226.578i 0.197605 + 0.342263i
$$663$$ 0 0
$$664$$ 13.8564i 0.0208681i
$$665$$ 1009.75 1.51842
$$666$$ 0 0
$$667$$ −144.000 + 249.415i −0.215892 + 0.373936i
$$668$$ −313.955 + 181.262i −0.469993 + 0.271351i
$$669$$ 0 0
$$670$$ −186.000 107.387i −0.277612 0.160279i
$$671$$ 1410.91i 2.10269i
$$672$$ 0 0
$$673$$ −263.000 −0.390788 −0.195394 0.980725i $$-0.562598\pi$$
−0.195394 + 0.980725i $$0.562598\pi$$
$$674$$ 253.851 439.683i 0.376634 0.652349i
$$675$$ 0 0
$$676$$ −166.000 287.520i −0.245562 0.425326i
$$677$$ −432.749 249.848i −0.639216 0.369052i 0.145096 0.989418i $$-0.453651\pi$$
−0.784313 + 0.620366i $$0.786984\pi$$
$$678$$ 0 0
$$679$$ −252.000 145.492i −0.371134 0.214274i
$$680$$ −67.8823 −0.0998268
$$681$$ 0 0
$$682$$ 252.000 145.492i 0.369501 0.213332i
$$683$$ 479.418 + 830.377i 0.701930 + 1.21578i 0.967788 + 0.251767i $$0.0810115\pi$$
−0.265858 + 0.964012i $$0.585655\pi$$
$$684$$ 0 0
$$685$$ 748.246i 1.09233i
$$686$$ 242.538 420.087i 0.353553 0.612372i
$$687$$ 0 0
$$688$$ −62.0000 + 107.387i −0.0901163 + 0.156086i
$$689$$ −114.551 + 66.1362i −0.166257 + 0.0959887i
$$690$$ 0 0
$$691$$ 1069.50 + 617.476i 1.54776 + 0.893598i 0.998313 + 0.0580674i $$0.0184938\pi$$
0.549444 + 0.835530i $$0.314839\pi$$
$$692$$ 88.1816i 0.127430i
$$693$$ 0 0
$$694$$ 660.000 0.951009
$$695$$ −479.418 + 830.377i −0.689811 + 1.19479i
$$696$$ 0 0
$$697$$ 168.000 + 290.985i 0.241033 + 0.417481i
$$698$$ 712.764 + 411.514i 1.02115 + 0.589562i
$$699$$ 0 0
$$700$$ 7.00000 + 12.1244i 0.0100000 + 0.0173205i
$$701$$ 975.807 1.39202 0.696011 0.718031i $$-0.254956\pi$$
0.696011 + 0.718031i $$0.254956\pi$$
$$702$$ 0 0
$$703$$ 1198.50 691.954i 1.70484 0.984288i
$$704$$ 67.8823 + 117.576i 0.0964237 + 0.167011i
$$705$$ 0 0
$$706$$ 408.764i 0.578986i
$$707$$ 1234.54i 1.74617i
$$708$$ 0 0
$$709$$ 553.000 957.824i 0.779972 1.35095i −0.151986 0.988383i $$-0.548567\pi$$
0.931957 0.362568i $$-0.118100\pi$$
$$710$$ −356.382 + 205.757i −0.501946 + 0.289799i
$$711$$ 0 0
$$712$$ 144.000 + 83.1384i 0.202247 + 0.116767i
$$713$$ 102.879i 0.144290i
$$714$$ 0 0
$$715$$ −144.000 −0.201399
$$716$$ 8.48528 14.6969i 0.0118510 0.0205265i
$$717$$ 0 0
$$718$$ −240.000 415.692i −0.334262 0.578958i
$$719$$ 593.970 + 342.929i 0.826105 + 0.476952i 0.852517 0.522699i $$-0.175075\pi$$
−0.0264120 + 0.999651i $$0.508408\pi$$
$$720$$ 0 0
$$721$$ −178.500 + 103.057i −0.247573 + 0.142936i
$$722$$ −715.592 −0.991125
$$723$$ 0 0
$$724$$ −75.0000 + 43.3013i −0.103591 + 0.0598084i
$$725$$ 16.9706 + 29.3939i 0.0234077 + 0.0405433i
$$726$$ 0 0
$$727$$ 427.817i 0.588468i 0.955733 + 0.294234i $$0.0950646\pi$$
−0.955733 + 0.294234i $$0.904935\pi$$
$$728$$ 29.6985 + 17.1464i 0.0407946 + 0.0235528i
$$729$$ 0 0
$$730$$ 282.000 488.438i 0.386301 0.669094i
$$731$$ −131.522 + 75.9342i −0.179920 + 0.103877i
$$732$$ 0 0
$$733$$ 34.5000 + 19.9186i 0.0470668 + 0.0271741i 0.523349 0.852119i $$-0.324682\pi$$
−0.476282 + 0.879293i $$0.658016\pi$$
$$734$$ 218.005i 0.297009i
$$735$$ 0 0
$$736$$ −48.0000 −0.0652174
$$737$$ −263.044 + 455.605i −0.356911 + 0.618189i
$$738$$ 0 0
$$739$$ 243.500 + 421.754i 0.329499 + 0.570710i 0.982413 0.186723i $$-0.0597867\pi$$
−0.652913 + 0.757433i $$0.726453\pi$$
$$740$$ −398.808 230.252i −0.538930 0.311151i
$$741$$ 0 0
$$742$$ −378.000 + 654.715i −0.509434 + 0.882366i
$$743$$ −509.117 −0.685218 −0.342609 0.939478i $$-0.611311\pi$$
−0.342609 + 0.939478i $$0.611311\pi$$
$$744$$ 0 0
$$745$$ −216.000 + 124.708i −0.289933 + 0.167393i
$$746$$ 204.354 + 353.951i 0.273933 + 0.474466i
$$747$$ 0 0
$$748$$ 166.277i 0.222295i
$$749$$ −504.874 874.468i −0.674064 1.16751i
$$750$$ 0 0
$$751$$ 272.500 471.984i 0.362850 0.628474i −0.625579 0.780161i $$-0.715137\pi$$
0.988429 + 0.151687i $$0.0484706\pi$$
$$752$$ 288.500 166.565i 0.383643 0.221496i
$$753$$ 0 0
$$754$$ 72.0000 + 41.5692i 0.0954907 + 0.0551316i
$$755$$ 48.9898i 0.0648871i
$$756$$ 0 0
$$757$$ −770.000 −1.01717 −0.508587 0.861011i $$-0.669832\pi$$
−0.508587 + 0.861011i $$0.669832\pi$$
$$758$$ −4.94975 + 8.57321i −0.00653001 + 0.0113103i
$$759$$ 0 0
$$760$$ 204.000 + 353.338i 0.268421 + 0.464919i
$$761$$ 148.492 + 85.7321i 0.195128 + 0.112657i 0.594381 0.804184i $$-0.297397\pi$$
−0.399253 + 0.916841i $$0.630730\pi$$
$$762$$ 0 0
$$763$$ −1183.00 −1.55046
$$764$$ 152.735 0.199915
$$765$$ 0 0
$$766$$ −606.000 + 349.874i −0.791123 + 0.456755i
$$767$$ −72.1249 124.924i −0.0940351 0.162874i
$$768$$ 0 0
$$769$$ 704.945i 0.916703i −0.888771 0.458352i $$-0.848440\pi$$
0.888771 0.458352i $$-0.151560\pi$$
$$770$$ −712.764 + 411.514i −0.925667 + 0.534434i
$$771$$ 0 0
$$772$$ 287.000 497.099i 0.371762 0.643910i
$$773$$ 797.616 460.504i 1.03185 0.595736i 0.114333 0.993443i $$-0.463527\pi$$
0.917513 + 0.397706i $$0.130194\pi$$
$$774$$ 0 0
$$775$$ 10.5000 + 6.06218i 0.0135484 + 0.00782216i
$$776$$ 117.576i 0.151515i
$$777$$ 0 0
$$778$$ −324.000 −0.416452
$$779$$ 1009.75 1748.94i 1.29621 2.24510i
$$780$$ 0 0
$$781$$ 504.000 + 872.954i 0.645327 + 1.11774i
$$782$$ −50.9117 29.3939i −0.0651045 0.0375881i
$$783$$ 0 0
$$784$$ 196.000 0.250000
$$785$$ 203.647 0.259423
$$786$$ 0 0
$$787$$ 396.000 228.631i 0.503177 0.290509i −0.226848 0.973930i $$-0.572842\pi$$
0.730024 + 0.683421i $$0.239509\pi$$
$$788$$ −127.279 220.454i