# Properties

 Label 630.2.m.a.323.1 Level 630 Weight 2 Character 630.323 Analytic conductor 5.031 Analytic rank 0 Dimension 4 CM no Inner twists 2

# Learn more about

## Newspace parameters

 Level: $$N$$ $$=$$ $$630 = 2 \cdot 3^{2} \cdot 5 \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 630.m (of order $$4$$, degree $$2$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$5.03057532734$$ Analytic rank: $$0$$ Dimension: $$4$$ Relative dimension: $$2$$ over $$\Q(i)$$ Coefficient field: $$\Q(\zeta_{8})$$ Coefficient ring: $$\Z[a_1, a_2]$$ Coefficient ring index: $$1$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

## Embedding invariants

 Embedding label 323.1 Root $$-0.707107 - 0.707107i$$ of $$x^{4} + 1$$ Character $$\chi$$ $$=$$ 630.323 Dual form 630.2.m.a.197.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-0.707107 - 0.707107i) q^{2} +1.00000i q^{4} +(-2.00000 - 1.00000i) q^{5} +(-0.707107 + 0.707107i) q^{7} +(0.707107 - 0.707107i) q^{8} +O(q^{10})$$ $$q+(-0.707107 - 0.707107i) q^{2} +1.00000i q^{4} +(-2.00000 - 1.00000i) q^{5} +(-0.707107 + 0.707107i) q^{7} +(0.707107 - 0.707107i) q^{8} +(0.707107 + 2.12132i) q^{10} +0.585786i q^{11} +(4.00000 + 4.00000i) q^{13} +1.00000 q^{14} -1.00000 q^{16} +(0.585786 + 0.585786i) q^{17} -2.82843i q^{19} +(1.00000 - 2.00000i) q^{20} +(0.414214 - 0.414214i) q^{22} +(4.82843 - 4.82843i) q^{23} +(3.00000 + 4.00000i) q^{25} -5.65685i q^{26} +(-0.707107 - 0.707107i) q^{28} +0.828427 q^{29} +1.75736 q^{31} +(0.707107 + 0.707107i) q^{32} -0.828427i q^{34} +(2.12132 - 0.707107i) q^{35} +(6.24264 - 6.24264i) q^{37} +(-2.00000 + 2.00000i) q^{38} +(-2.12132 + 0.707107i) q^{40} -3.17157i q^{41} +(6.07107 + 6.07107i) q^{43} -0.585786 q^{44} -6.82843 q^{46} +(9.24264 + 9.24264i) q^{47} -1.00000i q^{49} +(0.707107 - 4.94975i) q^{50} +(-4.00000 + 4.00000i) q^{52} +(-2.58579 + 2.58579i) q^{53} +(0.585786 - 1.17157i) q^{55} +1.00000i q^{56} +(-0.585786 - 0.585786i) q^{58} +2.82843 q^{59} -9.89949 q^{61} +(-1.24264 - 1.24264i) q^{62} -1.00000i q^{64} +(-4.00000 - 12.0000i) q^{65} +(8.41421 - 8.41421i) q^{67} +(-0.585786 + 0.585786i) q^{68} +(-2.00000 - 1.00000i) q^{70} +1.17157i q^{71} +(7.07107 + 7.07107i) q^{73} -8.82843 q^{74} +2.82843 q^{76} +(-0.414214 - 0.414214i) q^{77} -5.65685i q^{79} +(2.00000 + 1.00000i) q^{80} +(-2.24264 + 2.24264i) q^{82} +(-0.828427 + 0.828427i) q^{83} +(-0.585786 - 1.75736i) q^{85} -8.58579i q^{86} +(0.414214 + 0.414214i) q^{88} +3.17157 q^{89} -5.65685 q^{91} +(4.82843 + 4.82843i) q^{92} -13.0711i q^{94} +(-2.82843 + 5.65685i) q^{95} +(-4.58579 + 4.58579i) q^{97} +(-0.707107 + 0.707107i) q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4q - 8q^{5} + O(q^{10})$$ $$4q - 8q^{5} + 16q^{13} + 4q^{14} - 4q^{16} + 8q^{17} + 4q^{20} - 4q^{22} + 8q^{23} + 12q^{25} - 8q^{29} + 24q^{31} + 8q^{37} - 8q^{38} - 4q^{43} - 8q^{44} - 16q^{46} + 20q^{47} - 16q^{52} - 16q^{53} + 8q^{55} - 8q^{58} + 12q^{62} - 16q^{65} + 28q^{67} - 8q^{68} - 8q^{70} - 24q^{74} + 4q^{77} + 8q^{80} + 8q^{82} + 8q^{83} - 8q^{85} - 4q^{88} + 24q^{89} + 8q^{92} - 24q^{97} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/630\mathbb{Z}\right)^\times$$.

 $$n$$ $$127$$ $$281$$ $$451$$ $$\chi(n)$$ $$e\left(\frac{3}{4}\right)$$ $$-1$$ $$1$$

## Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −0.707107 0.707107i −0.500000 0.500000i
$$3$$ 0 0
$$4$$ 1.00000i 0.500000i
$$5$$ −2.00000 1.00000i −0.894427 0.447214i
$$6$$ 0 0
$$7$$ −0.707107 + 0.707107i −0.267261 + 0.267261i
$$8$$ 0.707107 0.707107i 0.250000 0.250000i
$$9$$ 0 0
$$10$$ 0.707107 + 2.12132i 0.223607 + 0.670820i
$$11$$ 0.585786i 0.176621i 0.996093 + 0.0883106i $$0.0281468\pi$$
−0.996093 + 0.0883106i $$0.971853\pi$$
$$12$$ 0 0
$$13$$ 4.00000 + 4.00000i 1.10940 + 1.10940i 0.993229 + 0.116171i $$0.0370621\pi$$
0.116171 + 0.993229i $$0.462938\pi$$
$$14$$ 1.00000 0.267261
$$15$$ 0 0
$$16$$ −1.00000 −0.250000
$$17$$ 0.585786 + 0.585786i 0.142074 + 0.142074i 0.774567 0.632492i $$-0.217968\pi$$
−0.632492 + 0.774567i $$0.717968\pi$$
$$18$$ 0 0
$$19$$ 2.82843i 0.648886i −0.945905 0.324443i $$-0.894823\pi$$
0.945905 0.324443i $$-0.105177\pi$$
$$20$$ 1.00000 2.00000i 0.223607 0.447214i
$$21$$ 0 0
$$22$$ 0.414214 0.414214i 0.0883106 0.0883106i
$$23$$ 4.82843 4.82843i 1.00680 1.00680i 0.00681991 0.999977i $$-0.497829\pi$$
0.999977 0.00681991i $$-0.00217086\pi$$
$$24$$ 0 0
$$25$$ 3.00000 + 4.00000i 0.600000 + 0.800000i
$$26$$ 5.65685i 1.10940i
$$27$$ 0 0
$$28$$ −0.707107 0.707107i −0.133631 0.133631i
$$29$$ 0.828427 0.153835 0.0769175 0.997037i $$-0.475492\pi$$
0.0769175 + 0.997037i $$0.475492\pi$$
$$30$$ 0 0
$$31$$ 1.75736 0.315631 0.157816 0.987469i $$-0.449555\pi$$
0.157816 + 0.987469i $$0.449555\pi$$
$$32$$ 0.707107 + 0.707107i 0.125000 + 0.125000i
$$33$$ 0 0
$$34$$ 0.828427i 0.142074i
$$35$$ 2.12132 0.707107i 0.358569 0.119523i
$$36$$ 0 0
$$37$$ 6.24264 6.24264i 1.02628 1.02628i 0.0266387 0.999645i $$-0.491520\pi$$
0.999645 0.0266387i $$-0.00848036\pi$$
$$38$$ −2.00000 + 2.00000i −0.324443 + 0.324443i
$$39$$ 0 0
$$40$$ −2.12132 + 0.707107i −0.335410 + 0.111803i
$$41$$ 3.17157i 0.495316i −0.968847 0.247658i $$-0.920339\pi$$
0.968847 0.247658i $$-0.0796610\pi$$
$$42$$ 0 0
$$43$$ 6.07107 + 6.07107i 0.925829 + 0.925829i 0.997433 0.0716040i $$-0.0228118\pi$$
−0.0716040 + 0.997433i $$0.522812\pi$$
$$44$$ −0.585786 −0.0883106
$$45$$ 0 0
$$46$$ −6.82843 −1.00680
$$47$$ 9.24264 + 9.24264i 1.34818 + 1.34818i 0.887640 + 0.460537i $$0.152343\pi$$
0.460537 + 0.887640i $$0.347657\pi$$
$$48$$ 0 0
$$49$$ 1.00000i 0.142857i
$$50$$ 0.707107 4.94975i 0.100000 0.700000i
$$51$$ 0 0
$$52$$ −4.00000 + 4.00000i −0.554700 + 0.554700i
$$53$$ −2.58579 + 2.58579i −0.355185 + 0.355185i −0.862035 0.506849i $$-0.830810\pi$$
0.506849 + 0.862035i $$0.330810\pi$$
$$54$$ 0 0
$$55$$ 0.585786 1.17157i 0.0789874 0.157975i
$$56$$ 1.00000i 0.133631i
$$57$$ 0 0
$$58$$ −0.585786 0.585786i −0.0769175 0.0769175i
$$59$$ 2.82843 0.368230 0.184115 0.982905i $$-0.441058\pi$$
0.184115 + 0.982905i $$0.441058\pi$$
$$60$$ 0 0
$$61$$ −9.89949 −1.26750 −0.633750 0.773538i $$-0.718485\pi$$
−0.633750 + 0.773538i $$0.718485\pi$$
$$62$$ −1.24264 1.24264i −0.157816 0.157816i
$$63$$ 0 0
$$64$$ 1.00000i 0.125000i
$$65$$ −4.00000 12.0000i −0.496139 1.48842i
$$66$$ 0 0
$$67$$ 8.41421 8.41421i 1.02796 1.02796i 0.0283621 0.999598i $$-0.490971\pi$$
0.999598 0.0283621i $$-0.00902914\pi$$
$$68$$ −0.585786 + 0.585786i −0.0710370 + 0.0710370i
$$69$$ 0 0
$$70$$ −2.00000 1.00000i −0.239046 0.119523i
$$71$$ 1.17157i 0.139040i 0.997581 + 0.0695201i $$0.0221468\pi$$
−0.997581 + 0.0695201i $$0.977853\pi$$
$$72$$ 0 0
$$73$$ 7.07107 + 7.07107i 0.827606 + 0.827606i 0.987185 0.159579i $$-0.0510137\pi$$
−0.159579 + 0.987185i $$0.551014\pi$$
$$74$$ −8.82843 −1.02628
$$75$$ 0 0
$$76$$ 2.82843 0.324443
$$77$$ −0.414214 0.414214i −0.0472040 0.0472040i
$$78$$ 0 0
$$79$$ 5.65685i 0.636446i −0.948016 0.318223i $$-0.896914\pi$$
0.948016 0.318223i $$-0.103086\pi$$
$$80$$ 2.00000 + 1.00000i 0.223607 + 0.111803i
$$81$$ 0 0
$$82$$ −2.24264 + 2.24264i −0.247658 + 0.247658i
$$83$$ −0.828427 + 0.828427i −0.0909317 + 0.0909317i −0.751109 0.660178i $$-0.770481\pi$$
0.660178 + 0.751109i $$0.270481\pi$$
$$84$$ 0 0
$$85$$ −0.585786 1.75736i −0.0635375 0.190612i
$$86$$ 8.58579i 0.925829i
$$87$$ 0 0
$$88$$ 0.414214 + 0.414214i 0.0441553 + 0.0441553i
$$89$$ 3.17157 0.336186 0.168093 0.985771i $$-0.446239\pi$$
0.168093 + 0.985771i $$0.446239\pi$$
$$90$$ 0 0
$$91$$ −5.65685 −0.592999
$$92$$ 4.82843 + 4.82843i 0.503398 + 0.503398i
$$93$$ 0 0
$$94$$ 13.0711i 1.34818i
$$95$$ −2.82843 + 5.65685i −0.290191 + 0.580381i
$$96$$ 0 0
$$97$$ −4.58579 + 4.58579i −0.465616 + 0.465616i −0.900491 0.434875i $$-0.856793\pi$$
0.434875 + 0.900491i $$0.356793\pi$$
$$98$$ −0.707107 + 0.707107i −0.0714286 + 0.0714286i
$$99$$ 0 0
$$100$$ −4.00000 + 3.00000i −0.400000 + 0.300000i
$$101$$ 17.6569i 1.75692i 0.477813 + 0.878461i $$0.341429\pi$$
−0.477813 + 0.878461i $$0.658571\pi$$
$$102$$ 0 0
$$103$$ −7.41421 7.41421i −0.730544 0.730544i 0.240183 0.970728i $$-0.422792\pi$$
−0.970728 + 0.240183i $$0.922792\pi$$
$$104$$ 5.65685 0.554700
$$105$$ 0 0
$$106$$ 3.65685 0.355185
$$107$$ −5.17157 5.17157i −0.499955 0.499955i 0.411469 0.911424i $$-0.365016\pi$$
−0.911424 + 0.411469i $$0.865016\pi$$
$$108$$ 0 0
$$109$$ 9.31371i 0.892091i −0.895010 0.446046i $$-0.852832\pi$$
0.895010 0.446046i $$-0.147168\pi$$
$$110$$ −1.24264 + 0.414214i −0.118481 + 0.0394937i
$$111$$ 0 0
$$112$$ 0.707107 0.707107i 0.0668153 0.0668153i
$$113$$ −11.3137 + 11.3137i −1.06430 + 1.06430i −0.0665190 + 0.997785i $$0.521189\pi$$
−0.997785 + 0.0665190i $$0.978811\pi$$
$$114$$ 0 0
$$115$$ −14.4853 + 4.82843i −1.35076 + 0.450253i
$$116$$ 0.828427i 0.0769175i
$$117$$ 0 0
$$118$$ −2.00000 2.00000i −0.184115 0.184115i
$$119$$ −0.828427 −0.0759418
$$120$$ 0 0
$$121$$ 10.6569 0.968805
$$122$$ 7.00000 + 7.00000i 0.633750 + 0.633750i
$$123$$ 0 0
$$124$$ 1.75736i 0.157816i
$$125$$ −2.00000 11.0000i −0.178885 0.983870i
$$126$$ 0 0
$$127$$ 7.65685 7.65685i 0.679436 0.679436i −0.280437 0.959873i $$-0.590479\pi$$
0.959873 + 0.280437i $$0.0904792\pi$$
$$128$$ −0.707107 + 0.707107i −0.0625000 + 0.0625000i
$$129$$ 0 0
$$130$$ −5.65685 + 11.3137i −0.496139 + 0.992278i
$$131$$ 16.4853i 1.44033i 0.693805 + 0.720163i $$0.255933\pi$$
−0.693805 + 0.720163i $$0.744067\pi$$
$$132$$ 0 0
$$133$$ 2.00000 + 2.00000i 0.173422 + 0.173422i
$$134$$ −11.8995 −1.02796
$$135$$ 0 0
$$136$$ 0.828427 0.0710370
$$137$$ 12.0000 + 12.0000i 1.02523 + 1.02523i 0.999673 + 0.0255558i $$0.00813555\pi$$
0.0255558 + 0.999673i $$0.491864\pi$$
$$138$$ 0 0
$$139$$ 17.6569i 1.49763i −0.662776 0.748817i $$-0.730622\pi$$
0.662776 0.748817i $$-0.269378\pi$$
$$140$$ 0.707107 + 2.12132i 0.0597614 + 0.179284i
$$141$$ 0 0
$$142$$ 0.828427 0.828427i 0.0695201 0.0695201i
$$143$$ −2.34315 + 2.34315i −0.195944 + 0.195944i
$$144$$ 0 0
$$145$$ −1.65685 0.828427i −0.137594 0.0687971i
$$146$$ 10.0000i 0.827606i
$$147$$ 0 0
$$148$$ 6.24264 + 6.24264i 0.513142 + 0.513142i
$$149$$ −8.14214 −0.667030 −0.333515 0.942745i $$-0.608235\pi$$
−0.333515 + 0.942745i $$0.608235\pi$$
$$150$$ 0 0
$$151$$ −18.8284 −1.53224 −0.766118 0.642700i $$-0.777814\pi$$
−0.766118 + 0.642700i $$0.777814\pi$$
$$152$$ −2.00000 2.00000i −0.162221 0.162221i
$$153$$ 0 0
$$154$$ 0.585786i 0.0472040i
$$155$$ −3.51472 1.75736i −0.282309 0.141154i
$$156$$ 0 0
$$157$$ −9.65685 + 9.65685i −0.770701 + 0.770701i −0.978229 0.207528i $$-0.933458\pi$$
0.207528 + 0.978229i $$0.433458\pi$$
$$158$$ −4.00000 + 4.00000i −0.318223 + 0.318223i
$$159$$ 0 0
$$160$$ −0.707107 2.12132i −0.0559017 0.167705i
$$161$$ 6.82843i 0.538155i
$$162$$ 0 0
$$163$$ 11.7279 + 11.7279i 0.918602 + 0.918602i 0.996928 0.0783260i $$-0.0249575\pi$$
−0.0783260 + 0.996928i $$0.524958\pi$$
$$164$$ 3.17157 0.247658
$$165$$ 0 0
$$166$$ 1.17157 0.0909317
$$167$$ −7.58579 7.58579i −0.587006 0.587006i 0.349814 0.936819i $$-0.386245\pi$$
−0.936819 + 0.349814i $$0.886245\pi$$
$$168$$ 0 0
$$169$$ 19.0000i 1.46154i
$$170$$ −0.828427 + 1.65685i −0.0635375 + 0.127075i
$$171$$ 0 0
$$172$$ −6.07107 + 6.07107i −0.462915 + 0.462915i
$$173$$ −11.4853 + 11.4853i −0.873210 + 0.873210i −0.992821 0.119611i $$-0.961835\pi$$
0.119611 + 0.992821i $$0.461835\pi$$
$$174$$ 0 0
$$175$$ −4.94975 0.707107i −0.374166 0.0534522i
$$176$$ 0.585786i 0.0441553i
$$177$$ 0 0
$$178$$ −2.24264 2.24264i −0.168093 0.168093i
$$179$$ 16.5858 1.23968 0.619840 0.784728i $$-0.287198\pi$$
0.619840 + 0.784728i $$0.287198\pi$$
$$180$$ 0 0
$$181$$ −19.0711 −1.41754 −0.708771 0.705439i $$-0.750750\pi$$
−0.708771 + 0.705439i $$0.750750\pi$$
$$182$$ 4.00000 + 4.00000i 0.296500 + 0.296500i
$$183$$ 0 0
$$184$$ 6.82843i 0.503398i
$$185$$ −18.7279 + 6.24264i −1.37690 + 0.458968i
$$186$$ 0 0
$$187$$ −0.343146 + 0.343146i −0.0250933 + 0.0250933i
$$188$$ −9.24264 + 9.24264i −0.674089 + 0.674089i
$$189$$ 0 0
$$190$$ 6.00000 2.00000i 0.435286 0.145095i
$$191$$ 14.3431i 1.03783i −0.854825 0.518917i $$-0.826335\pi$$
0.854825 0.518917i $$-0.173665\pi$$
$$192$$ 0 0
$$193$$ 13.4853 + 13.4853i 0.970692 + 0.970692i 0.999583 0.0288908i $$-0.00919750\pi$$
−0.0288908 + 0.999583i $$0.509198\pi$$
$$194$$ 6.48528 0.465616
$$195$$ 0 0
$$196$$ 1.00000 0.0714286
$$197$$ −10.2426 10.2426i −0.729758 0.729758i 0.240813 0.970571i $$-0.422586\pi$$
−0.970571 + 0.240813i $$0.922586\pi$$
$$198$$ 0 0
$$199$$ 4.10051i 0.290677i −0.989382 0.145339i $$-0.953573\pi$$
0.989382 0.145339i $$-0.0464271\pi$$
$$200$$ 4.94975 + 0.707107i 0.350000 + 0.0500000i
$$201$$ 0 0
$$202$$ 12.4853 12.4853i 0.878461 0.878461i
$$203$$ −0.585786 + 0.585786i −0.0411141 + 0.0411141i
$$204$$ 0 0
$$205$$ −3.17157 + 6.34315i −0.221512 + 0.443025i
$$206$$ 10.4853i 0.730544i
$$207$$ 0 0
$$208$$ −4.00000 4.00000i −0.277350 0.277350i
$$209$$ 1.65685 0.114607
$$210$$ 0 0
$$211$$ −4.00000 −0.275371 −0.137686 0.990476i $$-0.543966\pi$$
−0.137686 + 0.990476i $$0.543966\pi$$
$$212$$ −2.58579 2.58579i −0.177593 0.177593i
$$213$$ 0 0
$$214$$ 7.31371i 0.499955i
$$215$$ −6.07107 18.2132i −0.414043 1.24213i
$$216$$ 0 0
$$217$$ −1.24264 + 1.24264i −0.0843559 + 0.0843559i
$$218$$ −6.58579 + 6.58579i −0.446046 + 0.446046i
$$219$$ 0 0
$$220$$ 1.17157 + 0.585786i 0.0789874 + 0.0394937i
$$221$$ 4.68629i 0.315234i
$$222$$ 0 0
$$223$$ 7.31371 + 7.31371i 0.489762 + 0.489762i 0.908231 0.418469i $$-0.137433\pi$$
−0.418469 + 0.908231i $$0.637433\pi$$
$$224$$ −1.00000 −0.0668153
$$225$$ 0 0
$$226$$ 16.0000 1.06430
$$227$$ 1.17157 + 1.17157i 0.0777600 + 0.0777600i 0.744917 0.667157i $$-0.232489\pi$$
−0.667157 + 0.744917i $$0.732489\pi$$
$$228$$ 0 0
$$229$$ 8.24264i 0.544689i 0.962200 + 0.272345i $$0.0877990\pi$$
−0.962200 + 0.272345i $$0.912201\pi$$
$$230$$ 13.6569 + 6.82843i 0.900506 + 0.450253i
$$231$$ 0 0
$$232$$ 0.585786 0.585786i 0.0384588 0.0384588i
$$233$$ 14.8284 14.8284i 0.971443 0.971443i −0.0281608 0.999603i $$-0.508965\pi$$
0.999603 + 0.0281608i $$0.00896506\pi$$
$$234$$ 0 0
$$235$$ −9.24264 27.7279i −0.602923 1.80877i
$$236$$ 2.82843i 0.184115i
$$237$$ 0 0
$$238$$ 0.585786 + 0.585786i 0.0379709 + 0.0379709i
$$239$$ 13.6569 0.883388 0.441694 0.897166i $$-0.354378\pi$$
0.441694 + 0.897166i $$0.354378\pi$$
$$240$$ 0 0
$$241$$ −4.14214 −0.266818 −0.133409 0.991061i $$-0.542592\pi$$
−0.133409 + 0.991061i $$0.542592\pi$$
$$242$$ −7.53553 7.53553i −0.484402 0.484402i
$$243$$ 0 0
$$244$$ 9.89949i 0.633750i
$$245$$ −1.00000 + 2.00000i −0.0638877 + 0.127775i
$$246$$ 0 0
$$247$$ 11.3137 11.3137i 0.719874 0.719874i
$$248$$ 1.24264 1.24264i 0.0789078 0.0789078i
$$249$$ 0 0
$$250$$ −6.36396 + 9.19239i −0.402492 + 0.581378i
$$251$$ 26.6274i 1.68071i −0.542038 0.840354i $$-0.682347\pi$$
0.542038 0.840354i $$-0.317653\pi$$
$$252$$ 0 0
$$253$$ 2.82843 + 2.82843i 0.177822 + 0.177822i
$$254$$ −10.8284 −0.679436
$$255$$ 0 0
$$256$$ 1.00000 0.0625000
$$257$$ 8.58579 + 8.58579i 0.535567 + 0.535567i 0.922224 0.386657i $$-0.126370\pi$$
−0.386657 + 0.922224i $$0.626370\pi$$
$$258$$ 0 0
$$259$$ 8.82843i 0.548572i
$$260$$ 12.0000 4.00000i 0.744208 0.248069i
$$261$$ 0 0
$$262$$ 11.6569 11.6569i 0.720163 0.720163i
$$263$$ 7.65685 7.65685i 0.472142 0.472142i −0.430465 0.902607i $$-0.641651\pi$$
0.902607 + 0.430465i $$0.141651\pi$$
$$264$$ 0 0
$$265$$ 7.75736 2.58579i 0.476531 0.158844i
$$266$$ 2.82843i 0.173422i
$$267$$ 0 0
$$268$$ 8.41421 + 8.41421i 0.513980 + 0.513980i
$$269$$ 5.65685 0.344904 0.172452 0.985018i $$-0.444831\pi$$
0.172452 + 0.985018i $$0.444831\pi$$
$$270$$ 0 0
$$271$$ 4.10051 0.249088 0.124544 0.992214i $$-0.460253\pi$$
0.124544 + 0.992214i $$0.460253\pi$$
$$272$$ −0.585786 0.585786i −0.0355185 0.0355185i
$$273$$ 0 0
$$274$$ 16.9706i 1.02523i
$$275$$ −2.34315 + 1.75736i −0.141297 + 0.105973i
$$276$$ 0 0
$$277$$ −2.10051 + 2.10051i −0.126207 + 0.126207i −0.767389 0.641182i $$-0.778444\pi$$
0.641182 + 0.767389i $$0.278444\pi$$
$$278$$ −12.4853 + 12.4853i −0.748817 + 0.748817i
$$279$$ 0 0
$$280$$ 1.00000 2.00000i 0.0597614 0.119523i
$$281$$ 19.0711i 1.13768i −0.822447 0.568842i $$-0.807391\pi$$
0.822447 0.568842i $$-0.192609\pi$$
$$282$$ 0 0
$$283$$ −21.3137 21.3137i −1.26697 1.26697i −0.947646 0.319322i $$-0.896545\pi$$
−0.319322 0.947646i $$-0.603455\pi$$
$$284$$ −1.17157 −0.0695201
$$285$$ 0 0
$$286$$ 3.31371 0.195944
$$287$$ 2.24264 + 2.24264i 0.132379 + 0.132379i
$$288$$ 0 0
$$289$$ 16.3137i 0.959630i
$$290$$ 0.585786 + 1.75736i 0.0343986 + 0.103196i
$$291$$ 0 0
$$292$$ −7.07107 + 7.07107i −0.413803 + 0.413803i
$$293$$ 8.65685 8.65685i 0.505739 0.505739i −0.407477 0.913216i $$-0.633591\pi$$
0.913216 + 0.407477i $$0.133591\pi$$
$$294$$ 0 0
$$295$$ −5.65685 2.82843i −0.329355 0.164677i
$$296$$ 8.82843i 0.513142i
$$297$$ 0 0
$$298$$ 5.75736 + 5.75736i 0.333515 + 0.333515i
$$299$$ 38.6274 2.23388
$$300$$ 0 0
$$301$$ −8.58579 −0.494877
$$302$$ 13.3137 + 13.3137i 0.766118 + 0.766118i
$$303$$ 0 0
$$304$$ 2.82843i 0.162221i
$$305$$ 19.7990 + 9.89949i 1.13369 + 0.566843i
$$306$$ 0 0
$$307$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$308$$ 0.414214 0.414214i 0.0236020 0.0236020i
$$309$$ 0 0
$$310$$ 1.24264 + 3.72792i 0.0705772 + 0.211732i
$$311$$ 4.82843i 0.273795i −0.990585 0.136897i $$-0.956287\pi$$
0.990585 0.136897i $$-0.0437131\pi$$
$$312$$ 0 0
$$313$$ 2.24264 + 2.24264i 0.126762 + 0.126762i 0.767641 0.640880i $$-0.221430\pi$$
−0.640880 + 0.767641i $$0.721430\pi$$
$$314$$ 13.6569 0.770701
$$315$$ 0 0
$$316$$ 5.65685 0.318223
$$317$$ −24.7279 24.7279i −1.38886 1.38886i −0.827726 0.561132i $$-0.810366\pi$$
−0.561132 0.827726i $$-0.689634\pi$$
$$318$$ 0 0
$$319$$ 0.485281i 0.0271705i
$$320$$ −1.00000 + 2.00000i −0.0559017 + 0.111803i
$$321$$ 0 0
$$322$$ 4.82843 4.82843i 0.269078 0.269078i
$$323$$ 1.65685 1.65685i 0.0921898 0.0921898i
$$324$$ 0 0
$$325$$ −4.00000 + 28.0000i −0.221880 + 1.55316i
$$326$$ 16.5858i 0.918602i
$$327$$ 0 0
$$328$$ −2.24264 2.24264i −0.123829 0.123829i
$$329$$ −13.0711 −0.720631
$$330$$ 0 0
$$331$$ 18.6274 1.02386 0.511928 0.859029i $$-0.328932\pi$$
0.511928 + 0.859029i $$0.328932\pi$$
$$332$$ −0.828427 0.828427i −0.0454658 0.0454658i
$$333$$ 0 0
$$334$$ 10.7279i 0.587006i
$$335$$ −25.2426 + 8.41421i −1.37915 + 0.459718i
$$336$$ 0 0
$$337$$ 10.1716 10.1716i 0.554081 0.554081i −0.373535 0.927616i $$-0.621854\pi$$
0.927616 + 0.373535i $$0.121854\pi$$
$$338$$ 13.4350 13.4350i 0.730769 0.730769i
$$339$$ 0 0
$$340$$ 1.75736 0.585786i 0.0953062 0.0317687i
$$341$$ 1.02944i 0.0557472i
$$342$$ 0 0
$$343$$ 0.707107 + 0.707107i 0.0381802 + 0.0381802i
$$344$$ 8.58579 0.462915
$$345$$ 0 0
$$346$$ 16.2426 0.873210
$$347$$ −8.48528 8.48528i −0.455514 0.455514i 0.441666 0.897180i $$-0.354388\pi$$
−0.897180 + 0.441666i $$0.854388\pi$$
$$348$$ 0 0
$$349$$ 32.7279i 1.75189i 0.482415 + 0.875943i $$0.339760\pi$$
−0.482415 + 0.875943i $$0.660240\pi$$
$$350$$ 3.00000 + 4.00000i 0.160357 + 0.213809i
$$351$$ 0 0
$$352$$ −0.414214 + 0.414214i −0.0220777 + 0.0220777i
$$353$$ 18.3848 18.3848i 0.978523 0.978523i −0.0212513 0.999774i $$-0.506765\pi$$
0.999774 + 0.0212513i $$0.00676499\pi$$
$$354$$ 0 0
$$355$$ 1.17157 2.34315i 0.0621806 0.124361i
$$356$$ 3.17157i 0.168093i
$$357$$ 0 0
$$358$$ −11.7279 11.7279i −0.619840 0.619840i
$$359$$ 23.7990 1.25606 0.628031 0.778188i $$-0.283861\pi$$
0.628031 + 0.778188i $$0.283861\pi$$
$$360$$ 0 0
$$361$$ 11.0000 0.578947
$$362$$ 13.4853 + 13.4853i 0.708771 + 0.708771i
$$363$$ 0 0
$$364$$ 5.65685i 0.296500i
$$365$$ −7.07107 21.2132i −0.370117 1.11035i
$$366$$ 0 0
$$367$$ −10.2426 + 10.2426i −0.534661 + 0.534661i −0.921956 0.387295i $$-0.873410\pi$$
0.387295 + 0.921956i $$0.373410\pi$$
$$368$$ −4.82843 + 4.82843i −0.251699 + 0.251699i
$$369$$ 0 0
$$370$$ 17.6569 + 8.82843i 0.917936 + 0.458968i
$$371$$ 3.65685i 0.189854i
$$372$$ 0 0
$$373$$ −11.0711 11.0711i −0.573238 0.573238i 0.359794 0.933032i $$-0.382847\pi$$
−0.933032 + 0.359794i $$0.882847\pi$$
$$374$$ 0.485281 0.0250933
$$375$$ 0 0
$$376$$ 13.0711 0.674089
$$377$$ 3.31371 + 3.31371i 0.170665 + 0.170665i
$$378$$ 0 0
$$379$$ 25.7990i 1.32521i 0.748971 + 0.662603i $$0.230548\pi$$
−0.748971 + 0.662603i $$0.769452\pi$$
$$380$$ −5.65685 2.82843i −0.290191 0.145095i
$$381$$ 0 0
$$382$$ −10.1421 + 10.1421i −0.518917 + 0.518917i
$$383$$ 4.41421 4.41421i 0.225556 0.225556i −0.585277 0.810833i $$-0.699014\pi$$
0.810833 + 0.585277i $$0.199014\pi$$
$$384$$ 0 0
$$385$$ 0.414214 + 1.24264i 0.0211103 + 0.0633308i
$$386$$ 19.0711i 0.970692i
$$387$$ 0 0
$$388$$ −4.58579 4.58579i −0.232808 0.232808i
$$389$$ −9.79899 −0.496829 −0.248414 0.968654i $$-0.579909\pi$$
−0.248414 + 0.968654i $$0.579909\pi$$
$$390$$ 0 0
$$391$$ 5.65685 0.286079
$$392$$ −0.707107 0.707107i −0.0357143 0.0357143i
$$393$$ 0 0
$$394$$ 14.4853i 0.729758i
$$395$$ −5.65685 + 11.3137i −0.284627 + 0.569254i
$$396$$ 0 0
$$397$$ −0.928932 + 0.928932i −0.0466218 + 0.0466218i −0.730033 0.683412i $$-0.760495\pi$$
0.683412 + 0.730033i $$0.260495\pi$$
$$398$$ −2.89949 + 2.89949i −0.145339 + 0.145339i
$$399$$ 0 0
$$400$$ −3.00000 4.00000i −0.150000 0.200000i
$$401$$ 26.8701i 1.34183i 0.741536 + 0.670913i $$0.234098\pi$$
−0.741536 + 0.670913i $$0.765902\pi$$
$$402$$ 0 0
$$403$$ 7.02944 + 7.02944i 0.350161 + 0.350161i
$$404$$ −17.6569 −0.878461
$$405$$ 0 0
$$406$$ 0.828427 0.0411141
$$407$$ 3.65685 + 3.65685i 0.181264 + 0.181264i
$$408$$ 0 0
$$409$$ 10.0000i 0.494468i −0.968956 0.247234i $$-0.920478\pi$$
0.968956 0.247234i $$-0.0795217\pi$$
$$410$$ 6.72792 2.24264i 0.332268 0.110756i
$$411$$ 0 0
$$412$$ 7.41421 7.41421i 0.365272 0.365272i
$$413$$ −2.00000 + 2.00000i −0.0984136 + 0.0984136i
$$414$$ 0 0
$$415$$ 2.48528 0.828427i 0.121998 0.0406659i
$$416$$ 5.65685i 0.277350i
$$417$$ 0 0
$$418$$ −1.17157 1.17157i −0.0573035 0.0573035i
$$419$$ −18.6274 −0.910009 −0.455004 0.890489i $$-0.650362\pi$$
−0.455004 + 0.890489i $$0.650362\pi$$
$$420$$ 0 0
$$421$$ −40.6274 −1.98006 −0.990030 0.140860i $$-0.955013\pi$$
−0.990030 + 0.140860i $$0.955013\pi$$
$$422$$ 2.82843 + 2.82843i 0.137686 + 0.137686i
$$423$$ 0 0
$$424$$ 3.65685i 0.177593i
$$425$$ −0.585786 + 4.10051i −0.0284148 + 0.198904i
$$426$$ 0 0
$$427$$ 7.00000 7.00000i 0.338754 0.338754i
$$428$$ 5.17157 5.17157i 0.249977 0.249977i
$$429$$ 0 0
$$430$$ −8.58579 + 17.1716i −0.414043 + 0.828087i
$$431$$ 26.1421i 1.25922i 0.776910 + 0.629611i $$0.216786\pi$$
−0.776910 + 0.629611i $$0.783214\pi$$
$$432$$ 0 0
$$433$$ 18.2426 + 18.2426i 0.876685 + 0.876685i 0.993190 0.116505i $$-0.0371690\pi$$
−0.116505 + 0.993190i $$0.537169\pi$$
$$434$$ 1.75736 0.0843559
$$435$$ 0 0
$$436$$ 9.31371 0.446046
$$437$$ −13.6569 13.6569i −0.653296 0.653296i
$$438$$ 0 0
$$439$$ 3.89949i 0.186113i −0.995661 0.0930564i $$-0.970336\pi$$
0.995661 0.0930564i $$-0.0296637\pi$$
$$440$$ −0.414214 1.24264i −0.0197469 0.0592406i
$$441$$ 0 0
$$442$$ 3.31371 3.31371i 0.157617 0.157617i
$$443$$ −3.51472 + 3.51472i −0.166989 + 0.166989i −0.785655 0.618665i $$-0.787674\pi$$
0.618665 + 0.785655i $$0.287674\pi$$
$$444$$ 0 0
$$445$$ −6.34315 3.17157i −0.300694 0.150347i
$$446$$ 10.3431i 0.489762i
$$447$$ 0 0
$$448$$ 0.707107 + 0.707107i 0.0334077 + 0.0334077i
$$449$$ −16.7279 −0.789439 −0.394720 0.918802i $$-0.629158\pi$$
−0.394720 + 0.918802i $$0.629158\pi$$
$$450$$ 0 0
$$451$$ 1.85786 0.0874834
$$452$$ −11.3137 11.3137i −0.532152 0.532152i
$$453$$ 0 0
$$454$$ 1.65685i 0.0777600i
$$455$$ 11.3137 + 5.65685i 0.530395 + 0.265197i
$$456$$ 0 0
$$457$$ 2.17157 2.17157i 0.101582 0.101582i −0.654489 0.756071i $$-0.727116\pi$$
0.756071 + 0.654489i $$0.227116\pi$$
$$458$$ 5.82843 5.82843i 0.272345 0.272345i
$$459$$ 0 0
$$460$$ −4.82843 14.4853i −0.225127 0.675380i
$$461$$ 5.31371i 0.247484i −0.992314 0.123742i $$-0.960510\pi$$
0.992314 0.123742i $$-0.0394895\pi$$
$$462$$ 0 0
$$463$$ −19.7990 19.7990i −0.920137 0.920137i 0.0769016 0.997039i $$-0.475497\pi$$
−0.997039 + 0.0769016i $$0.975497\pi$$
$$464$$ −0.828427 −0.0384588
$$465$$ 0 0
$$466$$ −20.9706 −0.971443
$$467$$ −14.0000 14.0000i −0.647843 0.647843i 0.304629 0.952471i $$-0.401468\pi$$
−0.952471 + 0.304629i $$0.901468\pi$$
$$468$$ 0 0
$$469$$ 11.8995i 0.549468i
$$470$$ −13.0711 + 26.1421i −0.602923 + 1.20585i
$$471$$ 0 0
$$472$$ 2.00000 2.00000i 0.0920575 0.0920575i
$$473$$ −3.55635 + 3.55635i −0.163521 + 0.163521i
$$474$$ 0 0
$$475$$ 11.3137 8.48528i 0.519109 0.389331i
$$476$$ 0.828427i 0.0379709i
$$477$$ 0 0
$$478$$ −9.65685 9.65685i −0.441694 0.441694i
$$479$$ 19.1716 0.875972 0.437986 0.898982i $$-0.355692\pi$$
0.437986 + 0.898982i $$0.355692\pi$$
$$480$$ 0 0
$$481$$ 49.9411 2.27712
$$482$$ 2.92893 + 2.92893i 0.133409 + 0.133409i
$$483$$ 0 0
$$484$$ 10.6569i 0.484402i
$$485$$ 13.7574 4.58579i 0.624690 0.208230i
$$486$$ 0 0
$$487$$ 18.9706 18.9706i 0.859638 0.859638i −0.131657 0.991295i $$-0.542030\pi$$
0.991295 + 0.131657i $$0.0420298\pi$$
$$488$$ −7.00000 + 7.00000i −0.316875 + 0.316875i
$$489$$ 0 0
$$490$$ 2.12132 0.707107i 0.0958315 0.0319438i
$$491$$ 26.7279i 1.20621i −0.797660 0.603107i $$-0.793929\pi$$
0.797660 0.603107i $$-0.206071\pi$$
$$492$$ 0 0
$$493$$ 0.485281 + 0.485281i 0.0218560 + 0.0218560i
$$494$$ −16.0000 −0.719874
$$495$$ 0 0
$$496$$ −1.75736 −0.0789078
$$497$$ −0.828427 0.828427i −0.0371600 0.0371600i
$$498$$ 0 0
$$499$$ 23.4558i 1.05003i 0.851094 + 0.525014i $$0.175940\pi$$
−0.851094 + 0.525014i $$0.824060\pi$$
$$500$$ 11.0000 2.00000i 0.491935 0.0894427i
$$501$$ 0 0
$$502$$ −18.8284 + 18.8284i −0.840354 + 0.840354i
$$503$$ −16.5563 + 16.5563i −0.738211 + 0.738211i −0.972232 0.234021i $$-0.924812\pi$$
0.234021 + 0.972232i $$0.424812\pi$$
$$504$$ 0 0
$$505$$ 17.6569 35.3137i 0.785720 1.57144i
$$506$$ 4.00000i 0.177822i
$$507$$ 0 0
$$508$$ 7.65685 + 7.65685i 0.339718 + 0.339718i
$$509$$ −18.3431 −0.813046 −0.406523 0.913641i $$-0.633259\pi$$
−0.406523 + 0.913641i $$0.633259\pi$$
$$510$$ 0 0
$$511$$ −10.0000 −0.442374
$$512$$ −0.707107 0.707107i −0.0312500 0.0312500i
$$513$$ 0 0
$$514$$ 12.1421i 0.535567i
$$515$$ 7.41421 + 22.2426i 0.326709 + 0.980128i
$$516$$ 0 0
$$517$$ −5.41421 + 5.41421i −0.238117 + 0.238117i
$$518$$ 6.24264 6.24264i 0.274286 0.274286i
$$519$$ 0 0
$$520$$ −11.3137 5.65685i −0.496139 0.248069i
$$521$$ 42.7696i 1.87377i 0.349640 + 0.936884i $$0.386304\pi$$
−0.349640 + 0.936884i $$0.613696\pi$$
$$522$$ 0 0
$$523$$ −25.3137 25.3137i −1.10689 1.10689i −0.993557 0.113334i $$-0.963847\pi$$
−0.113334 0.993557i $$-0.536153\pi$$
$$524$$ −16.4853 −0.720163
$$525$$ 0 0
$$526$$ −10.8284 −0.472142
$$527$$ 1.02944 + 1.02944i 0.0448430 + 0.0448430i
$$528$$ 0 0
$$529$$ 23.6274i 1.02728i
$$530$$ −7.31371 3.65685i −0.317687 0.158844i
$$531$$ 0 0
$$532$$ −2.00000 + 2.00000i −0.0867110 + 0.0867110i
$$533$$ 12.6863 12.6863i 0.549504 0.549504i
$$534$$ 0 0
$$535$$ 5.17157 + 15.5147i 0.223587 + 0.670760i
$$536$$ 11.8995i 0.513980i
$$537$$ 0 0
$$538$$ −4.00000 4.00000i −0.172452 0.172452i
$$539$$ 0.585786 0.0252316
$$540$$ 0 0
$$541$$ −29.1127 −1.25165 −0.625826 0.779962i $$-0.715238\pi$$
−0.625826 + 0.779962i $$0.715238\pi$$
$$542$$ −2.89949 2.89949i −0.124544 0.124544i
$$543$$ 0 0
$$544$$ 0.828427i 0.0355185i
$$545$$ −9.31371 + 18.6274i −0.398955 + 0.797911i
$$546$$ 0 0
$$547$$ −12.5563 + 12.5563i −0.536871 + 0.536871i −0.922608 0.385738i $$-0.873947\pi$$
0.385738 + 0.922608i $$0.373947\pi$$
$$548$$ −12.0000 + 12.0000i −0.512615 + 0.512615i
$$549$$ 0 0
$$550$$ 2.89949 + 0.414214i 0.123635 + 0.0176621i
$$551$$ 2.34315i 0.0998214i
$$552$$ 0 0
$$553$$ 4.00000 + 4.00000i 0.170097 + 0.170097i
$$554$$ 2.97056 0.126207
$$555$$ 0 0
$$556$$ 17.6569 0.748817
$$557$$ 7.55635 + 7.55635i 0.320173 + 0.320173i 0.848833 0.528661i $$-0.177306\pi$$
−0.528661 + 0.848833i $$0.677306\pi$$
$$558$$ 0 0
$$559$$ 48.5685i 2.05423i
$$560$$ −2.12132 + 0.707107i −0.0896421 + 0.0298807i
$$561$$ 0 0
$$562$$ −13.4853 + 13.4853i −0.568842 + 0.568842i
$$563$$ 6.68629 6.68629i 0.281794 0.281794i −0.552030 0.833824i $$-0.686147\pi$$
0.833824 + 0.552030i $$0.186147\pi$$
$$564$$ 0 0
$$565$$ 33.9411 11.3137i 1.42791 0.475971i
$$566$$ 30.1421i 1.26697i
$$567$$ 0 0
$$568$$ 0.828427 + 0.828427i 0.0347600 + 0.0347600i
$$569$$ −14.1005 −0.591124 −0.295562 0.955324i $$-0.595507\pi$$
−0.295562 + 0.955324i $$0.595507\pi$$
$$570$$ 0 0
$$571$$ −11.0294 −0.461568 −0.230784 0.973005i $$-0.574129\pi$$
−0.230784 + 0.973005i $$0.574129\pi$$
$$572$$ −2.34315 2.34315i −0.0979718 0.0979718i
$$573$$ 0 0
$$574$$ 3.17157i 0.132379i
$$575$$ 33.7990 + 4.82843i 1.40952 + 0.201359i
$$576$$ 0 0
$$577$$ −10.7279 + 10.7279i −0.446609 + 0.446609i −0.894226 0.447616i $$-0.852273\pi$$
0.447616 + 0.894226i $$0.352273\pi$$
$$578$$ −11.5355 + 11.5355i −0.479815 + 0.479815i
$$579$$ 0 0
$$580$$ 0.828427 1.65685i 0.0343986 0.0687971i
$$581$$ 1.17157i 0.0486050i
$$582$$ 0 0
$$583$$ −1.51472 1.51472i −0.0627332 0.0627332i
$$584$$ 10.0000 0.413803
$$585$$ 0 0
$$586$$ −12.2426 −0.505739
$$587$$ 17.7990 + 17.7990i 0.734643 + 0.734643i 0.971536 0.236893i $$-0.0761290\pi$$
−0.236893 + 0.971536i $$0.576129\pi$$
$$588$$ 0 0
$$589$$ 4.97056i 0.204808i
$$590$$ 2.00000 + 6.00000i 0.0823387 + 0.247016i
$$591$$ 0 0
$$592$$ −6.24264 + 6.24264i −0.256571 + 0.256571i
$$593$$ −16.3848 + 16.3848i −0.672842 + 0.672842i −0.958370 0.285528i $$-0.907831\pi$$
0.285528 + 0.958370i $$0.407831\pi$$
$$594$$ 0 0
$$595$$ 1.65685 + 0.828427i 0.0679244 + 0.0339622i
$$596$$ 8.14214i 0.333515i
$$597$$ 0 0
$$598$$ −27.3137 27.3137i −1.11694 1.11694i
$$599$$ −15.3137 −0.625701 −0.312851 0.949802i $$-0.601284\pi$$
−0.312851 + 0.949802i $$0.601284\pi$$
$$600$$ 0 0
$$601$$ −4.14214 −0.168961 −0.0844806 0.996425i $$-0.526923\pi$$
−0.0844806 + 0.996425i $$0.526923\pi$$
$$602$$ 6.07107 + 6.07107i 0.247438 + 0.247438i
$$603$$ 0 0
$$604$$ 18.8284i 0.766118i
$$605$$ −21.3137 10.6569i −0.866525 0.433263i
$$606$$ 0 0
$$607$$ −7.31371 + 7.31371i −0.296854 + 0.296854i −0.839780 0.542926i $$-0.817316\pi$$
0.542926 + 0.839780i $$0.317316\pi$$
$$608$$ 2.00000 2.00000i 0.0811107 0.0811107i
$$609$$ 0 0
$$610$$ −7.00000 21.0000i −0.283422 0.850265i
$$611$$ 73.9411i 2.99134i
$$612$$ 0 0
$$613$$ −9.07107 9.07107i −0.366377 0.366377i 0.499777 0.866154i $$-0.333415\pi$$
−0.866154 + 0.499777i $$0.833415\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ −0.585786 −0.0236020
$$617$$ 24.0416 + 24.0416i 0.967880 + 0.967880i 0.999500 0.0316203i $$-0.0100667\pi$$
−0.0316203 + 0.999500i $$0.510067\pi$$
$$618$$ 0 0
$$619$$ 17.8579i 0.717768i −0.933382 0.358884i $$-0.883157\pi$$
0.933382 0.358884i $$-0.116843\pi$$
$$620$$ 1.75736 3.51472i 0.0705772 0.141154i
$$621$$ 0 0
$$622$$ −3.41421 + 3.41421i −0.136897 + 0.136897i
$$623$$ −2.24264 + 2.24264i −0.0898495 + 0.0898495i
$$624$$ 0 0
$$625$$ −7.00000 + 24.0000i −0.280000 + 0.960000i
$$626$$ 3.17157i 0.126762i
$$627$$ 0 0
$$628$$ −9.65685 9.65685i −0.385350 0.385350i
$$629$$ 7.31371 0.291617
$$630$$ 0 0
$$631$$ −0.201010 −0.00800209 −0.00400104 0.999992i $$-0.501274\pi$$
−0.00400104 + 0.999992i $$0.501274\pi$$
$$632$$ −4.00000 4.00000i −0.159111 0.159111i
$$633$$ 0 0
$$634$$ 34.9706i 1.38886i
$$635$$ −22.9706 + 7.65685i −0.911559 + 0.303853i
$$636$$ 0 0
$$637$$ 4.00000 4.00000i 0.158486 0.158486i
$$638$$ 0.343146 0.343146i 0.0135853 0.0135853i
$$639$$ 0 0
$$640$$ 2.12132 0.707107i 0.0838525 0.0279508i
$$641$$ 21.2132i 0.837871i −0.908016 0.418936i $$-0.862403\pi$$
0.908016 0.418936i $$-0.137597\pi$$
$$642$$ 0 0
$$643$$ −10.9706 10.9706i −0.432637 0.432637i 0.456888 0.889524i $$-0.348964\pi$$
−0.889524 + 0.456888i $$0.848964\pi$$
$$644$$ −6.82843 −0.269078
$$645$$ 0 0
$$646$$ −2.34315 −0.0921898
$$647$$ −33.2426 33.2426i −1.30690 1.30690i −0.923639 0.383264i $$-0.874800\pi$$
−0.383264 0.923639i $$-0.625200\pi$$
$$648$$ 0 0
$$649$$ 1.65685i 0.0650372i
$$650$$ 22.6274 16.9706i 0.887520 0.665640i
$$651$$ 0 0
$$652$$ −11.7279 + 11.7279i −0.459301 + 0.459301i
$$653$$ 14.2426 14.2426i 0.557358 0.557358i −0.371197 0.928554i $$-0.621052\pi$$
0.928554 + 0.371197i $$0.121052\pi$$
$$654$$ 0 0
$$655$$ 16.4853 32.9706i 0.644133 1.28827i
$$656$$ 3.17157i 0.123829i
$$657$$ 0 0
$$658$$ 9.24264 + 9.24264i 0.360316 + 0.360316i
$$659$$ −26.7279 −1.04117 −0.520586 0.853809i $$-0.674286\pi$$
−0.520586 + 0.853809i $$0.674286\pi$$
$$660$$ 0 0
$$661$$ 40.0416 1.55744 0.778719 0.627372i $$-0.215870\pi$$
0.778719 + 0.627372i $$0.215870\pi$$
$$662$$ −13.1716 13.1716i −0.511928 0.511928i
$$663$$ 0 0
$$664$$ 1.17157i 0.0454658i
$$665$$ −2.00000 6.00000i −0.0775567 0.232670i
$$666$$ 0 0
$$667$$ 4.00000 4.00000i 0.154881 0.154881i
$$668$$ 7.58579 7.58579i 0.293503 0.293503i
$$669$$ 0 0
$$670$$ 23.7990 + 11.8995i 0.919435 + 0.459718i
$$671$$ 5.79899i 0.223868i
$$672$$ 0 0
$$673$$ 3.34315 + 3.34315i 0.128869 + 0.128869i 0.768599 0.639731i $$-0.220954\pi$$
−0.639731 + 0.768599i $$0.720954\pi$$
$$674$$ −14.3848 −0.554081
$$675$$ 0 0
$$676$$ −19.0000 −0.730769
$$677$$ 15.8284 + 15.8284i 0.608336 + 0.608336i 0.942511 0.334175i $$-0.108458\pi$$
−0.334175 + 0.942511i $$0.608458\pi$$
$$678$$ 0 0
$$679$$ 6.48528i 0.248882i
$$680$$ −1.65685 0.828427i −0.0635375 0.0317687i
$$681$$ 0 0
$$682$$ 0.727922 0.727922i 0.0278736 0.0278736i
$$683$$ 24.3848 24.3848i 0.933058 0.933058i −0.0648383 0.997896i $$-0.520653\pi$$
0.997896 + 0.0648383i $$0.0206531\pi$$
$$684$$ 0 0
$$685$$ −12.0000 36.0000i −0.458496 1.37549i
$$686$$ 1.00000i 0.0381802i
$$687$$ 0 0
$$688$$ −6.07107 6.07107i −0.231457 0.231457i
$$689$$ −20.6863 −0.788085
$$690$$ 0 0
$$691$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$692$$ −11.4853 11.4853i −0.436605 0.436605i
$$693$$ 0 0
$$694$$ 12.0000i 0.455514i
$$695$$ −17.6569 + 35.3137i −0.669763 + 1.33953i
$$696$$ 0 0
$$697$$ 1.85786 1.85786i 0.0703716 0.0703716i
$$698$$ 23.1421 23.1421i 0.875943 0.875943i
$$699$$ 0 0
$$700$$ 0.707107 4.94975i 0.0267261 0.187083i
$$701$$ 40.8284i 1.54207i 0.636794 + 0.771034i $$0.280260\pi$$
−0.636794 + 0.771034i $$0.719740\pi$$
$$702$$ 0 0
$$703$$ −17.6569 17.6569i −0.665941 0.665941i
$$704$$ 0.585786 0.0220777
$$705$$ 0 0
$$706$$ −26.0000 −0.978523
$$707$$ −12.4853 12.4853i −0.469557 0.469557i
$$708$$ 0 0
$$709$$ 40.8284i 1.53334i −0.642039 0.766672i $$-0.721911\pi$$
0.642039 0.766672i $$-0.278089\pi$$
$$710$$ −2.48528 + 0.828427i −0.0932709 + 0.0310903i
$$711$$ 0 0
$$712$$ 2.24264 2.24264i 0.0840465 0.0840465i
$$713$$ 8.48528 8.48528i 0.317776 0.317776i
$$714$$ 0 0
$$715$$ 7.02944 2.34315i 0.262886 0.0876287i
$$716$$ 16.5858i 0.619840i
$$717$$ 0 0
$$718$$ −16.8284 16.8284i −0.628031 0.628031i
$$719$$ 38.6274 1.44056 0.720280 0.693684i $$-0.244013\pi$$
0.720280 + 0.693684i $$0.244013\pi$$
$$720$$ 0 0
$$721$$ 10.4853 0.390492
$$722$$ −7.77817 7.77817i −0.289474 0.289474i
$$723$$ 0 0
$$724$$ 19.0711i 0.708771i
$$725$$ 2.48528 + 3.31371i 0.0923010 + 0.123068i
$$726$$ 0 0
$$727$$ −22.6274 + 22.6274i −0.839204 + 0.839204i −0.988754 0.149550i $$-0.952218\pi$$
0.149550 + 0.988754i $$0.452218\pi$$
$$728$$ −4.00000 + 4.00000i −0.148250 + 0.148250i
$$729$$ 0 0
$$730$$ −10.0000 + 20.0000i −0.370117 + 0.740233i
$$731$$ 7.11270i 0.263073i
$$732$$ 0 0
$$733$$ −0.443651 0.443651i −0.0163866 0.0163866i 0.698866 0.715253i $$-0.253688\pi$$
−0.715253 + 0.698866i $$0.753688\pi$$
$$734$$ 14.4853 0.534661
$$735$$ 0 0
$$736$$ 6.82843 0.251699
$$737$$ 4.92893 + 4.92893i 0.181560 + 0.181560i
$$738$$ 0 0
$$739$$ 7.45584i 0.274268i −0.990553 0.137134i $$-0.956211\pi$$
0.990553 0.137134i $$-0.0437890\pi$$
$$740$$ −6.24264 18.7279i −0.229484 0.688452i
$$741$$ 0 0
$$742$$ −2.58579 + 2.58579i −0.0949272 + 0.0949272i
$$743$$ −31.1127 + 31.1127i −1.14141 + 1.14141i −0.153222 + 0.988192i $$0.548965\pi$$
−0.988192 + 0.153222i $$0.951035\pi$$
$$744$$ 0 0
$$745$$ 16.2843 + 8.14214i 0.596610 + 0.298305i
$$746$$ 15.6569i 0.573238i
$$747$$ 0 0
$$748$$ −0.343146 0.343146i −0.0125467 0.0125467i
$$749$$ 7.31371 0.267237
$$750$$ 0 0
$$751$$ 48.4853 1.76925 0.884627 0.466300i $$-0.154413\pi$$
0.884627 + 0.466300i $$0.154413\pi$$
$$752$$ −9.24264 9.24264i −0.337044 0.337044i
$$753$$ 0 0
$$754$$ 4.68629i 0.170665i
$$755$$ 37.6569 + 18.8284i 1.37047 + 0.685237i
$$756$$ 0 0
$$757$$ −23.5563 + 23.5563i −0.856170 + 0.856170i −0.990884 0.134714i $$-0.956988\pi$$
0.134714 + 0.990884i $$0.456988\pi$$
$$758$$ 18.2426 18.2426i 0.662603 0.662603i
$$759$$ 0 0
$$760$$ 2.00000 + 6.00000i 0.0725476 + 0.217643i
$$761$$ 18.9706i 0.687682i 0.939028 + 0.343841i $$0.111728\pi$$
−0.939028 + 0.343841i $$0.888272\pi$$
$$762$$ 0 0
$$763$$ 6.58579 + 6.58579i 0.238421 + 0.238421i
$$764$$ 14.3431 0.518917
$$765$$ 0 0
$$766$$ −6.24264 −0.225556
$$767$$ 11.3137 + 11.3137i 0.408514 + 0.408514i
$$768$$ 0 0
$$769$$ 41.5980i 1.50006i −0.661403 0.750031i $$-0.730039\pi$$
0.661403 0.750031i $$-0.269961\pi$$
$$770$$ 0.585786 1.17157i 0.0211103 0.0422206i
$$771$$ 0 0
$$772$$ −13.4853 + 13.4853i −0.485346 + 0.485346i
$$773$$ 34.9411 34.9411i 1.25674 1.25674i 0.304107 0.952638i $$-0.401642\pi$$
0.952638 0.304107i $$-0.0983581\pi$$
$$774$$ 0 0
$$775$$ 5.27208 + 7.02944i 0.189379 + 0.252505i
$$776$$ 6.48528i 0.232808i
$$777$$ 0 0
$$778$$ 6.92893 + 6.92893i 0.248414 + 0.248414i
$$779$$ −8.97056 −0.321404
$$780$$ 0 0
$$781$$ −0.686292 −0.0245574
$$782$$ −4.00000 4.00000i −0.143040 0.143040i
$$783$$ 0 0
$$784$$ 1.00000i 0.0357143i
$$785$$ 28.9706 9.65685i 1.03400 0.344668i
$$786$$ 0 0
$$787$$ −15.5147 + 15.5147i −0.553040 + 0.553040i −0.927317 0.374277i $$-0.877891\pi$$
0.374277 + 0.927317i $$0.377891\pi$$
$$788$$ 10.2426 10.2426i 0.364879 0.364879i
$$789$$ 0 0
$$790$$ 12.0000 4.00000i 0.426941 0.142314i
$$791$$ 16.0000i 0.568895i
$$792$$ 0 0
$$793$$ −39.5980 39.5980i −1.40617 1.40617i
$$794$$ 1.31371 0.0466218
$$795$$ 0 0
$$796$$ 4.10051 0.145339
$$797$$ 20.1716 + 20.1716i 0.714514 + 0.71451