# Properties

 Label 950.2.e.f.501.1 Level $950$ Weight $2$ Character 950.501 Analytic conductor $7.586$ Analytic rank $0$ Dimension $2$ CM no Inner twists $2$

# Learn more

## Newspace parameters

 Level: $$N$$ $$=$$ $$950 = 2 \cdot 5^{2} \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 950.e (of order $$3$$, degree $$2$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$7.58578819202$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(\zeta_{6})$$ Defining polynomial: $$x^{2} - x + 1$$ Coefficient ring: $$\Z[a_1, a_2]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 190) Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 501.1 Root $$0.500000 - 0.866025i$$ of defining polynomial Character $$\chi$$ $$=$$ 950.501 Dual form 950.2.e.f.201.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} -1.00000 q^{7} -1.00000 q^{8} +(1.50000 - 2.59808i) q^{9} +O(q^{10})$$ $$q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} -1.00000 q^{7} -1.00000 q^{8} +(1.50000 - 2.59808i) q^{9} +5.00000 q^{11} +(1.00000 - 1.73205i) q^{13} +(-0.500000 - 0.866025i) q^{14} +(-0.500000 - 0.866025i) q^{16} +3.00000 q^{18} +(-0.500000 - 4.33013i) q^{19} +(2.50000 + 4.33013i) q^{22} +(0.500000 - 0.866025i) q^{23} +2.00000 q^{26} +(0.500000 - 0.866025i) q^{28} +(-3.00000 + 5.19615i) q^{29} +4.00000 q^{31} +(0.500000 - 0.866025i) q^{32} +(1.50000 + 2.59808i) q^{36} +11.0000 q^{37} +(3.50000 - 2.59808i) q^{38} +(4.50000 + 7.79423i) q^{41} +(3.00000 + 5.19615i) q^{43} +(-2.50000 + 4.33013i) q^{44} +1.00000 q^{46} -6.00000 q^{49} +(1.00000 + 1.73205i) q^{52} +(2.50000 - 4.33013i) q^{53} +1.00000 q^{56} -6.00000 q^{58} +(2.00000 + 3.46410i) q^{62} +(-1.50000 + 2.59808i) q^{63} +1.00000 q^{64} +(6.00000 - 10.3923i) q^{67} +(-3.00000 - 5.19615i) q^{71} +(-1.50000 + 2.59808i) q^{72} +(7.00000 + 12.1244i) q^{73} +(5.50000 + 9.52628i) q^{74} +(4.00000 + 1.73205i) q^{76} -5.00000 q^{77} +(-5.00000 - 8.66025i) q^{79} +(-4.50000 - 7.79423i) q^{81} +(-4.50000 + 7.79423i) q^{82} -14.0000 q^{83} +(-3.00000 + 5.19615i) q^{86} -5.00000 q^{88} +(3.50000 - 6.06218i) q^{89} +(-1.00000 + 1.73205i) q^{91} +(0.500000 + 0.866025i) q^{92} +(-1.00000 - 1.73205i) q^{97} +(-3.00000 - 5.19615i) q^{98} +(7.50000 - 12.9904i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2q + q^{2} - q^{4} - 2q^{7} - 2q^{8} + 3q^{9} + O(q^{10})$$ $$2q + q^{2} - q^{4} - 2q^{7} - 2q^{8} + 3q^{9} + 10q^{11} + 2q^{13} - q^{14} - q^{16} + 6q^{18} - q^{19} + 5q^{22} + q^{23} + 4q^{26} + q^{28} - 6q^{29} + 8q^{31} + q^{32} + 3q^{36} + 22q^{37} + 7q^{38} + 9q^{41} + 6q^{43} - 5q^{44} + 2q^{46} - 12q^{49} + 2q^{52} + 5q^{53} + 2q^{56} - 12q^{58} + 4q^{62} - 3q^{63} + 2q^{64} + 12q^{67} - 6q^{71} - 3q^{72} + 14q^{73} + 11q^{74} + 8q^{76} - 10q^{77} - 10q^{79} - 9q^{81} - 9q^{82} - 28q^{83} - 6q^{86} - 10q^{88} + 7q^{89} - 2q^{91} + q^{92} - 2q^{97} - 6q^{98} + 15q^{99} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$$.

 $$n$$ $$77$$ $$401$$ $$\chi(n)$$ $$1$$ $$e\left(\frac{1}{3}\right)$$

## Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0.500000 + 0.866025i 0.353553 + 0.612372i
$$3$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$4$$ −0.500000 + 0.866025i −0.250000 + 0.433013i
$$5$$ 0 0
$$6$$ 0 0
$$7$$ −1.00000 −0.377964 −0.188982 0.981981i $$-0.560519\pi$$
−0.188982 + 0.981981i $$0.560519\pi$$
$$8$$ −1.00000 −0.353553
$$9$$ 1.50000 2.59808i 0.500000 0.866025i
$$10$$ 0 0
$$11$$ 5.00000 1.50756 0.753778 0.657129i $$-0.228229\pi$$
0.753778 + 0.657129i $$0.228229\pi$$
$$12$$ 0 0
$$13$$ 1.00000 1.73205i 0.277350 0.480384i −0.693375 0.720577i $$-0.743877\pi$$
0.970725 + 0.240192i $$0.0772105\pi$$
$$14$$ −0.500000 0.866025i −0.133631 0.231455i
$$15$$ 0 0
$$16$$ −0.500000 0.866025i −0.125000 0.216506i
$$17$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$18$$ 3.00000 0.707107
$$19$$ −0.500000 4.33013i −0.114708 0.993399i
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 2.50000 + 4.33013i 0.533002 + 0.923186i
$$23$$ 0.500000 0.866025i 0.104257 0.180579i −0.809177 0.587565i $$-0.800087\pi$$
0.913434 + 0.406986i $$0.133420\pi$$
$$24$$ 0 0
$$25$$ 0 0
$$26$$ 2.00000 0.392232
$$27$$ 0 0
$$28$$ 0.500000 0.866025i 0.0944911 0.163663i
$$29$$ −3.00000 + 5.19615i −0.557086 + 0.964901i 0.440652 + 0.897678i $$0.354747\pi$$
−0.997738 + 0.0672232i $$0.978586\pi$$
$$30$$ 0 0
$$31$$ 4.00000 0.718421 0.359211 0.933257i $$-0.383046\pi$$
0.359211 + 0.933257i $$0.383046\pi$$
$$32$$ 0.500000 0.866025i 0.0883883 0.153093i
$$33$$ 0 0
$$34$$ 0 0
$$35$$ 0 0
$$36$$ 1.50000 + 2.59808i 0.250000 + 0.433013i
$$37$$ 11.0000 1.80839 0.904194 0.427121i $$-0.140472\pi$$
0.904194 + 0.427121i $$0.140472\pi$$
$$38$$ 3.50000 2.59808i 0.567775 0.421464i
$$39$$ 0 0
$$40$$ 0 0
$$41$$ 4.50000 + 7.79423i 0.702782 + 1.21725i 0.967486 + 0.252924i $$0.0813924\pi$$
−0.264704 + 0.964330i $$0.585274\pi$$
$$42$$ 0 0
$$43$$ 3.00000 + 5.19615i 0.457496 + 0.792406i 0.998828 0.0484030i $$-0.0154132\pi$$
−0.541332 + 0.840809i $$0.682080\pi$$
$$44$$ −2.50000 + 4.33013i −0.376889 + 0.652791i
$$45$$ 0 0
$$46$$ 1.00000 0.147442
$$47$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$48$$ 0 0
$$49$$ −6.00000 −0.857143
$$50$$ 0 0
$$51$$ 0 0
$$52$$ 1.00000 + 1.73205i 0.138675 + 0.240192i
$$53$$ 2.50000 4.33013i 0.343401 0.594789i −0.641661 0.766989i $$-0.721754\pi$$
0.985062 + 0.172200i $$0.0550875\pi$$
$$54$$ 0 0
$$55$$ 0 0
$$56$$ 1.00000 0.133631
$$57$$ 0 0
$$58$$ −6.00000 −0.787839
$$59$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$60$$ 0 0
$$61$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$62$$ 2.00000 + 3.46410i 0.254000 + 0.439941i
$$63$$ −1.50000 + 2.59808i −0.188982 + 0.327327i
$$64$$ 1.00000 0.125000
$$65$$ 0 0
$$66$$ 0 0
$$67$$ 6.00000 10.3923i 0.733017 1.26962i −0.222571 0.974916i $$-0.571445\pi$$
0.955588 0.294706i $$-0.0952216\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ 0 0
$$71$$ −3.00000 5.19615i −0.356034 0.616670i 0.631260 0.775571i $$-0.282538\pi$$
−0.987294 + 0.158901i $$0.949205\pi$$
$$72$$ −1.50000 + 2.59808i −0.176777 + 0.306186i
$$73$$ 7.00000 + 12.1244i 0.819288 + 1.41905i 0.906208 + 0.422833i $$0.138964\pi$$
−0.0869195 + 0.996215i $$0.527702\pi$$
$$74$$ 5.50000 + 9.52628i 0.639362 + 1.10741i
$$75$$ 0 0
$$76$$ 4.00000 + 1.73205i 0.458831 + 0.198680i
$$77$$ −5.00000 −0.569803
$$78$$ 0 0
$$79$$ −5.00000 8.66025i −0.562544 0.974355i −0.997274 0.0737937i $$-0.976489\pi$$
0.434730 0.900561i $$-0.356844\pi$$
$$80$$ 0 0
$$81$$ −4.50000 7.79423i −0.500000 0.866025i
$$82$$ −4.50000 + 7.79423i −0.496942 + 0.860729i
$$83$$ −14.0000 −1.53670 −0.768350 0.640030i $$-0.778922\pi$$
−0.768350 + 0.640030i $$0.778922\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ −3.00000 + 5.19615i −0.323498 + 0.560316i
$$87$$ 0 0
$$88$$ −5.00000 −0.533002
$$89$$ 3.50000 6.06218i 0.370999 0.642590i −0.618720 0.785611i $$-0.712349\pi$$
0.989720 + 0.143022i $$0.0456819\pi$$
$$90$$ 0 0
$$91$$ −1.00000 + 1.73205i −0.104828 + 0.181568i
$$92$$ 0.500000 + 0.866025i 0.0521286 + 0.0902894i
$$93$$ 0 0
$$94$$ 0 0
$$95$$ 0 0
$$96$$ 0 0
$$97$$ −1.00000 1.73205i −0.101535 0.175863i 0.810782 0.585348i $$-0.199042\pi$$
−0.912317 + 0.409484i $$0.865709\pi$$
$$98$$ −3.00000 5.19615i −0.303046 0.524891i
$$99$$ 7.50000 12.9904i 0.753778 1.30558i
$$100$$ 0 0
$$101$$ −5.00000 + 8.66025i −0.497519 + 0.861727i −0.999996 0.00286291i $$-0.999089\pi$$
0.502477 + 0.864590i $$0.332422\pi$$
$$102$$ 0 0
$$103$$ −13.0000 −1.28093 −0.640464 0.767988i $$-0.721258\pi$$
−0.640464 + 0.767988i $$0.721258\pi$$
$$104$$ −1.00000 + 1.73205i −0.0980581 + 0.169842i
$$105$$ 0 0
$$106$$ 5.00000 0.485643
$$107$$ 4.00000 0.386695 0.193347 0.981130i $$-0.438066\pi$$
0.193347 + 0.981130i $$0.438066\pi$$
$$108$$ 0 0
$$109$$ −2.00000 3.46410i −0.191565 0.331801i 0.754204 0.656640i $$-0.228023\pi$$
−0.945769 + 0.324840i $$0.894690\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 0.500000 + 0.866025i 0.0472456 + 0.0818317i
$$113$$ 12.0000 1.12887 0.564433 0.825479i $$-0.309095\pi$$
0.564433 + 0.825479i $$0.309095\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ −3.00000 5.19615i −0.278543 0.482451i
$$117$$ −3.00000 5.19615i −0.277350 0.480384i
$$118$$ 0 0
$$119$$ 0 0
$$120$$ 0 0
$$121$$ 14.0000 1.27273
$$122$$ 0 0
$$123$$ 0 0
$$124$$ −2.00000 + 3.46410i −0.179605 + 0.311086i
$$125$$ 0 0
$$126$$ −3.00000 −0.267261
$$127$$ −7.50000 + 12.9904i −0.665517 + 1.15271i 0.313627 + 0.949546i $$0.398456\pi$$
−0.979145 + 0.203164i $$0.934878\pi$$
$$128$$ 0.500000 + 0.866025i 0.0441942 + 0.0765466i
$$129$$ 0 0
$$130$$ 0 0
$$131$$ −0.500000 0.866025i −0.0436852 0.0756650i 0.843356 0.537355i $$-0.180577\pi$$
−0.887041 + 0.461690i $$0.847243\pi$$
$$132$$ 0 0
$$133$$ 0.500000 + 4.33013i 0.0433555 + 0.375470i
$$134$$ 12.0000 1.03664
$$135$$ 0 0
$$136$$ 0 0
$$137$$ 6.00000 10.3923i 0.512615 0.887875i −0.487278 0.873247i $$-0.662010\pi$$
0.999893 0.0146279i $$-0.00465636\pi$$
$$138$$ 0 0
$$139$$ −8.00000 + 13.8564i −0.678551 + 1.17529i 0.296866 + 0.954919i $$0.404058\pi$$
−0.975417 + 0.220366i $$0.929275\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 3.00000 5.19615i 0.251754 0.436051i
$$143$$ 5.00000 8.66025i 0.418121 0.724207i
$$144$$ −3.00000 −0.250000
$$145$$ 0 0
$$146$$ −7.00000 + 12.1244i −0.579324 + 1.00342i
$$147$$ 0 0
$$148$$ −5.50000 + 9.52628i −0.452097 + 0.783055i
$$149$$ 2.00000 + 3.46410i 0.163846 + 0.283790i 0.936245 0.351348i $$-0.114277\pi$$
−0.772399 + 0.635138i $$0.780943\pi$$
$$150$$ 0 0
$$151$$ −16.0000 −1.30206 −0.651031 0.759051i $$-0.725663\pi$$
−0.651031 + 0.759051i $$0.725663\pi$$
$$152$$ 0.500000 + 4.33013i 0.0405554 + 0.351220i
$$153$$ 0 0
$$154$$ −2.50000 4.33013i −0.201456 0.348932i
$$155$$ 0 0
$$156$$ 0 0
$$157$$ −10.5000 18.1865i −0.837991 1.45144i −0.891572 0.452880i $$-0.850397\pi$$
0.0535803 0.998564i $$-0.482937\pi$$
$$158$$ 5.00000 8.66025i 0.397779 0.688973i
$$159$$ 0 0
$$160$$ 0 0
$$161$$ −0.500000 + 0.866025i −0.0394055 + 0.0682524i
$$162$$ 4.50000 7.79423i 0.353553 0.612372i
$$163$$ −10.0000 −0.783260 −0.391630 0.920123i $$-0.628089\pi$$
−0.391630 + 0.920123i $$0.628089\pi$$
$$164$$ −9.00000 −0.702782
$$165$$ 0 0
$$166$$ −7.00000 12.1244i −0.543305 0.941033i
$$167$$ −2.50000 + 4.33013i −0.193456 + 0.335075i −0.946393 0.323017i $$-0.895303\pi$$
0.752937 + 0.658092i $$0.228636\pi$$
$$168$$ 0 0
$$169$$ 4.50000 + 7.79423i 0.346154 + 0.599556i
$$170$$ 0 0
$$171$$ −12.0000 5.19615i −0.917663 0.397360i
$$172$$ −6.00000 −0.457496
$$173$$ 0.500000 + 0.866025i 0.0380143 + 0.0658427i 0.884407 0.466717i $$-0.154563\pi$$
−0.846392 + 0.532560i $$0.821230\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ −2.50000 4.33013i −0.188445 0.326396i
$$177$$ 0 0
$$178$$ 7.00000 0.524672
$$179$$ 19.0000 1.42013 0.710063 0.704138i $$-0.248666\pi$$
0.710063 + 0.704138i $$0.248666\pi$$
$$180$$ 0 0
$$181$$ −1.00000 + 1.73205i −0.0743294 + 0.128742i −0.900794 0.434246i $$-0.857015\pi$$
0.826465 + 0.562988i $$0.190348\pi$$
$$182$$ −2.00000 −0.148250
$$183$$ 0 0
$$184$$ −0.500000 + 0.866025i −0.0368605 + 0.0638442i
$$185$$ 0 0
$$186$$ 0 0
$$187$$ 0 0
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ −18.0000 −1.30243 −0.651217 0.758891i $$-0.725741\pi$$
−0.651217 + 0.758891i $$0.725741\pi$$
$$192$$ 0 0
$$193$$ 2.00000 + 3.46410i 0.143963 + 0.249351i 0.928986 0.370116i $$-0.120682\pi$$
−0.785022 + 0.619467i $$0.787349\pi$$
$$194$$ 1.00000 1.73205i 0.0717958 0.124354i
$$195$$ 0 0
$$196$$ 3.00000 5.19615i 0.214286 0.371154i
$$197$$ −23.0000 −1.63868 −0.819341 0.573306i $$-0.805660\pi$$
−0.819341 + 0.573306i $$0.805660\pi$$
$$198$$ 15.0000 1.06600
$$199$$ −12.0000 + 20.7846i −0.850657 + 1.47338i 0.0299585 + 0.999551i $$0.490462\pi$$
−0.880616 + 0.473831i $$0.842871\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ −10.0000 −0.703598
$$203$$ 3.00000 5.19615i 0.210559 0.364698i
$$204$$ 0 0
$$205$$ 0 0
$$206$$ −6.50000 11.2583i −0.452876 0.784405i
$$207$$ −1.50000 2.59808i −0.104257 0.180579i
$$208$$ −2.00000 −0.138675
$$209$$ −2.50000 21.6506i −0.172929 1.49761i
$$210$$ 0 0
$$211$$ −6.50000 11.2583i −0.447478 0.775055i 0.550743 0.834675i $$-0.314345\pi$$
−0.998221 + 0.0596196i $$0.981011\pi$$
$$212$$ 2.50000 + 4.33013i 0.171701 + 0.297394i
$$213$$ 0 0
$$214$$ 2.00000 + 3.46410i 0.136717 + 0.236801i
$$215$$ 0 0
$$216$$ 0 0
$$217$$ −4.00000 −0.271538
$$218$$ 2.00000 3.46410i 0.135457 0.234619i
$$219$$ 0 0
$$220$$ 0 0
$$221$$ 0 0
$$222$$ 0 0
$$223$$ −11.5000 19.9186i −0.770097 1.33385i −0.937509 0.347960i $$-0.886874\pi$$
0.167412 0.985887i $$-0.446459\pi$$
$$224$$ −0.500000 + 0.866025i −0.0334077 + 0.0578638i
$$225$$ 0 0
$$226$$ 6.00000 + 10.3923i 0.399114 + 0.691286i
$$227$$ 10.0000 0.663723 0.331862 0.943328i $$-0.392323\pi$$
0.331862 + 0.943328i $$0.392323\pi$$
$$228$$ 0 0
$$229$$ 6.00000 0.396491 0.198246 0.980152i $$-0.436476\pi$$
0.198246 + 0.980152i $$0.436476\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 3.00000 5.19615i 0.196960 0.341144i
$$233$$ 5.00000 + 8.66025i 0.327561 + 0.567352i 0.982027 0.188739i $$-0.0604400\pi$$
−0.654466 + 0.756091i $$0.727107\pi$$
$$234$$ 3.00000 5.19615i 0.196116 0.339683i
$$235$$ 0 0
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 0 0
$$239$$ 16.0000 1.03495 0.517477 0.855697i $$-0.326871\pi$$
0.517477 + 0.855697i $$0.326871\pi$$
$$240$$ 0 0
$$241$$ 9.00000 15.5885i 0.579741 1.00414i −0.415768 0.909471i $$-0.636487\pi$$
0.995509 0.0946700i $$-0.0301796\pi$$
$$242$$ 7.00000 + 12.1244i 0.449977 + 0.779383i
$$243$$ 0 0
$$244$$ 0 0
$$245$$ 0 0
$$246$$ 0 0
$$247$$ −8.00000 3.46410i −0.509028 0.220416i
$$248$$ −4.00000 −0.254000
$$249$$ 0 0
$$250$$ 0 0
$$251$$ 6.00000 10.3923i 0.378717 0.655956i −0.612159 0.790735i $$-0.709699\pi$$
0.990876 + 0.134778i $$0.0430322\pi$$
$$252$$ −1.50000 2.59808i −0.0944911 0.163663i
$$253$$ 2.50000 4.33013i 0.157174 0.272233i
$$254$$ −15.0000 −0.941184
$$255$$ 0 0
$$256$$ −0.500000 + 0.866025i −0.0312500 + 0.0541266i
$$257$$ −7.00000 + 12.1244i −0.436648 + 0.756297i −0.997429 0.0716680i $$-0.977168\pi$$
0.560781 + 0.827964i $$0.310501\pi$$
$$258$$ 0 0
$$259$$ −11.0000 −0.683507
$$260$$ 0 0
$$261$$ 9.00000 + 15.5885i 0.557086 + 0.964901i
$$262$$ 0.500000 0.866025i 0.0308901 0.0535032i
$$263$$ 5.50000 + 9.52628i 0.339145 + 0.587416i 0.984272 0.176659i $$-0.0565291\pi$$
−0.645128 + 0.764075i $$0.723196\pi$$
$$264$$ 0 0
$$265$$ 0 0
$$266$$ −3.50000 + 2.59808i −0.214599 + 0.159298i
$$267$$ 0 0
$$268$$ 6.00000 + 10.3923i 0.366508 + 0.634811i
$$269$$ 14.0000 + 24.2487i 0.853595 + 1.47847i 0.877942 + 0.478766i $$0.158916\pi$$
−0.0243472 + 0.999704i $$0.507751\pi$$
$$270$$ 0 0
$$271$$ 3.00000 + 5.19615i 0.182237 + 0.315644i 0.942642 0.333805i $$-0.108333\pi$$
−0.760405 + 0.649449i $$0.775000\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 12.0000 0.724947
$$275$$ 0 0
$$276$$ 0 0
$$277$$ 2.00000 0.120168 0.0600842 0.998193i $$-0.480863\pi$$
0.0600842 + 0.998193i $$0.480863\pi$$
$$278$$ −16.0000 −0.959616
$$279$$ 6.00000 10.3923i 0.359211 0.622171i
$$280$$ 0 0
$$281$$ 7.50000 12.9904i 0.447412 0.774941i −0.550804 0.834634i $$-0.685679\pi$$
0.998217 + 0.0596933i $$0.0190123\pi$$
$$282$$ 0 0
$$283$$ −7.00000 12.1244i −0.416107 0.720718i 0.579437 0.815017i $$-0.303272\pi$$
−0.995544 + 0.0942988i $$0.969939\pi$$
$$284$$ 6.00000 0.356034
$$285$$ 0 0
$$286$$ 10.0000 0.591312
$$287$$ −4.50000 7.79423i −0.265627 0.460079i
$$288$$ −1.50000 2.59808i −0.0883883 0.153093i
$$289$$ 8.50000 14.7224i 0.500000 0.866025i
$$290$$ 0 0
$$291$$ 0 0
$$292$$ −14.0000 −0.819288
$$293$$ 21.0000 1.22683 0.613417 0.789760i $$-0.289795\pi$$
0.613417 + 0.789760i $$0.289795\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ −11.0000 −0.639362
$$297$$ 0 0
$$298$$ −2.00000 + 3.46410i −0.115857 + 0.200670i
$$299$$ −1.00000 1.73205i −0.0578315 0.100167i
$$300$$ 0 0
$$301$$ −3.00000 5.19615i −0.172917 0.299501i
$$302$$ −8.00000 13.8564i −0.460348 0.797347i
$$303$$ 0 0
$$304$$ −3.50000 + 2.59808i −0.200739 + 0.149010i
$$305$$ 0 0
$$306$$ 0 0
$$307$$ −1.00000 1.73205i −0.0570730 0.0988534i 0.836077 0.548612i $$-0.184843\pi$$
−0.893150 + 0.449758i $$0.851510\pi$$
$$308$$ 2.50000 4.33013i 0.142451 0.246732i
$$309$$ 0 0
$$310$$ 0 0
$$311$$ 4.00000 0.226819 0.113410 0.993548i $$-0.463823\pi$$
0.113410 + 0.993548i $$0.463823\pi$$
$$312$$ 0 0
$$313$$ −14.0000 + 24.2487i −0.791327 + 1.37062i 0.133819 + 0.991006i $$0.457276\pi$$
−0.925146 + 0.379612i $$0.876057\pi$$
$$314$$ 10.5000 18.1865i 0.592549 1.02633i
$$315$$ 0 0
$$316$$ 10.0000 0.562544
$$317$$ −13.5000 + 23.3827i −0.758236 + 1.31330i 0.185514 + 0.982642i $$0.440605\pi$$
−0.943750 + 0.330661i $$0.892728\pi$$
$$318$$ 0 0
$$319$$ −15.0000 + 25.9808i −0.839839 + 1.45464i
$$320$$ 0 0
$$321$$ 0 0
$$322$$ −1.00000 −0.0557278
$$323$$ 0 0
$$324$$ 9.00000 0.500000
$$325$$ 0 0
$$326$$ −5.00000 8.66025i −0.276924 0.479647i
$$327$$ 0 0
$$328$$ −4.50000 7.79423i −0.248471 0.430364i
$$329$$ 0 0
$$330$$ 0 0
$$331$$ −25.0000 −1.37412 −0.687062 0.726599i $$-0.741100\pi$$
−0.687062 + 0.726599i $$0.741100\pi$$
$$332$$ 7.00000 12.1244i 0.384175 0.665410i
$$333$$ 16.5000 28.5788i 0.904194 1.56611i
$$334$$ −5.00000 −0.273588
$$335$$ 0 0
$$336$$ 0 0
$$337$$ 3.00000 + 5.19615i 0.163420 + 0.283052i 0.936093 0.351752i $$-0.114414\pi$$
−0.772673 + 0.634804i $$0.781081\pi$$
$$338$$ −4.50000 + 7.79423i −0.244768 + 0.423950i
$$339$$ 0 0
$$340$$ 0 0
$$341$$ 20.0000 1.08306
$$342$$ −1.50000 12.9904i −0.0811107 0.702439i
$$343$$ 13.0000 0.701934
$$344$$ −3.00000 5.19615i −0.161749 0.280158i
$$345$$ 0 0
$$346$$ −0.500000 + 0.866025i −0.0268802 + 0.0465578i
$$347$$ 9.00000 + 15.5885i 0.483145 + 0.836832i 0.999813 0.0193540i $$-0.00616095\pi$$
−0.516667 + 0.856186i $$0.672828\pi$$
$$348$$ 0 0
$$349$$ −28.0000 −1.49881 −0.749403 0.662114i $$-0.769659\pi$$
−0.749403 + 0.662114i $$0.769659\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 2.50000 4.33013i 0.133250 0.230797i
$$353$$ −4.00000 −0.212899 −0.106449 0.994318i $$-0.533948\pi$$
−0.106449 + 0.994318i $$0.533948\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ 3.50000 + 6.06218i 0.185500 + 0.321295i
$$357$$ 0 0
$$358$$ 9.50000 + 16.4545i 0.502091 + 0.869646i
$$359$$ −5.00000 8.66025i −0.263890 0.457071i 0.703382 0.710812i $$-0.251672\pi$$
−0.967272 + 0.253741i $$0.918339\pi$$
$$360$$ 0 0
$$361$$ −18.5000 + 4.33013i −0.973684 + 0.227901i
$$362$$ −2.00000 −0.105118
$$363$$ 0 0
$$364$$ −1.00000 1.73205i −0.0524142 0.0907841i
$$365$$ 0 0
$$366$$ 0 0
$$367$$ −2.00000 + 3.46410i −0.104399 + 0.180825i −0.913493 0.406855i $$-0.866625\pi$$
0.809093 + 0.587680i $$0.199959\pi$$
$$368$$ −1.00000 −0.0521286
$$369$$ 27.0000 1.40556
$$370$$ 0 0
$$371$$ −2.50000 + 4.33013i −0.129794 + 0.224809i
$$372$$ 0 0
$$373$$ −31.0000 −1.60512 −0.802560 0.596572i $$-0.796529\pi$$
−0.802560 + 0.596572i $$0.796529\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ 6.00000 + 10.3923i 0.309016 + 0.535231i
$$378$$ 0 0
$$379$$ −12.0000 −0.616399 −0.308199 0.951322i $$-0.599726\pi$$
−0.308199 + 0.951322i $$0.599726\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ −9.00000 15.5885i −0.460480 0.797575i
$$383$$ 4.00000 + 6.92820i 0.204390 + 0.354015i 0.949938 0.312437i $$-0.101145\pi$$
−0.745548 + 0.666452i $$0.767812\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ −2.00000 + 3.46410i −0.101797 + 0.176318i
$$387$$ 18.0000 0.914991
$$388$$ 2.00000 0.101535
$$389$$ −13.0000 + 22.5167i −0.659126 + 1.14164i 0.321716 + 0.946836i $$0.395740\pi$$
−0.980842 + 0.194804i $$0.937593\pi$$
$$390$$ 0 0
$$391$$ 0 0
$$392$$ 6.00000 0.303046
$$393$$ 0 0
$$394$$ −11.5000 19.9186i −0.579362 1.00348i
$$395$$ 0 0
$$396$$ 7.50000 + 12.9904i 0.376889 + 0.652791i
$$397$$ 14.5000 + 25.1147i 0.727734 + 1.26047i 0.957839 + 0.287307i $$0.0927599\pi$$
−0.230105 + 0.973166i $$0.573907\pi$$
$$398$$ −24.0000 −1.20301
$$399$$ 0 0
$$400$$ 0 0
$$401$$ 9.00000 + 15.5885i 0.449439 + 0.778450i 0.998350 0.0574304i $$-0.0182907\pi$$
−0.548911 + 0.835881i $$0.684957\pi$$
$$402$$ 0 0
$$403$$ 4.00000 6.92820i 0.199254 0.345118i
$$404$$ −5.00000 8.66025i −0.248759 0.430864i
$$405$$ 0 0
$$406$$ 6.00000 0.297775
$$407$$ 55.0000 2.72625
$$408$$ 0 0
$$409$$ 5.50000 9.52628i 0.271957 0.471044i −0.697406 0.716677i $$-0.745662\pi$$
0.969363 + 0.245633i $$0.0789957\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 6.50000 11.2583i 0.320232 0.554658i
$$413$$ 0 0
$$414$$ 1.50000 2.59808i 0.0737210 0.127688i
$$415$$ 0 0
$$416$$ −1.00000 1.73205i −0.0490290 0.0849208i
$$417$$ 0 0
$$418$$ 17.5000 12.9904i 0.855953 0.635380i
$$419$$ −7.00000 −0.341972 −0.170986 0.985273i $$-0.554695\pi$$
−0.170986 + 0.985273i $$0.554695\pi$$
$$420$$ 0 0
$$421$$ 4.00000 + 6.92820i 0.194948 + 0.337660i 0.946883 0.321577i $$-0.104213\pi$$
−0.751935 + 0.659237i $$0.770879\pi$$
$$422$$ 6.50000 11.2583i 0.316415 0.548047i
$$423$$ 0 0
$$424$$ −2.50000 + 4.33013i −0.121411 + 0.210290i
$$425$$ 0 0
$$426$$ 0 0
$$427$$ 0 0
$$428$$ −2.00000 + 3.46410i −0.0966736 + 0.167444i
$$429$$ 0 0
$$430$$ 0 0
$$431$$ −6.00000 + 10.3923i −0.289010 + 0.500580i −0.973574 0.228373i $$-0.926659\pi$$
0.684564 + 0.728953i $$0.259993\pi$$
$$432$$ 0 0
$$433$$ 1.00000 1.73205i 0.0480569 0.0832370i −0.840996 0.541041i $$-0.818030\pi$$
0.889053 + 0.457804i $$0.151364\pi$$
$$434$$ −2.00000 3.46410i −0.0960031 0.166282i
$$435$$ 0 0
$$436$$ 4.00000 0.191565
$$437$$ −4.00000 1.73205i −0.191346 0.0828552i
$$438$$ 0 0
$$439$$ −4.00000 6.92820i −0.190910 0.330665i 0.754642 0.656136i $$-0.227810\pi$$
−0.945552 + 0.325471i $$0.894477\pi$$
$$440$$ 0 0
$$441$$ −9.00000 + 15.5885i −0.428571 + 0.742307i
$$442$$ 0 0
$$443$$ 18.0000 31.1769i 0.855206 1.48126i −0.0212481 0.999774i $$-0.506764\pi$$
0.876454 0.481486i $$-0.159903\pi$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ 11.5000 19.9186i 0.544541 0.943172i
$$447$$ 0 0
$$448$$ −1.00000 −0.0472456
$$449$$ −19.0000 −0.896665 −0.448333 0.893867i $$-0.647982\pi$$
−0.448333 + 0.893867i $$0.647982\pi$$
$$450$$ 0 0
$$451$$ 22.5000 + 38.9711i 1.05948 + 1.83508i
$$452$$ −6.00000 + 10.3923i −0.282216 + 0.488813i
$$453$$ 0 0
$$454$$ 5.00000 + 8.66025i 0.234662 + 0.406446i
$$455$$ 0 0
$$456$$ 0 0
$$457$$ 32.0000 1.49690 0.748448 0.663193i $$-0.230799\pi$$
0.748448 + 0.663193i $$0.230799\pi$$
$$458$$ 3.00000 + 5.19615i 0.140181 + 0.242800i
$$459$$ 0 0
$$460$$ 0 0
$$461$$ 15.0000 + 25.9808i 0.698620 + 1.21004i 0.968945 + 0.247276i $$0.0795353\pi$$
−0.270326 + 0.962769i $$0.587131\pi$$
$$462$$ 0 0
$$463$$ −37.0000 −1.71954 −0.859768 0.510685i $$-0.829392\pi$$
−0.859768 + 0.510685i $$0.829392\pi$$
$$464$$ 6.00000 0.278543
$$465$$ 0 0
$$466$$ −5.00000 + 8.66025i −0.231621 + 0.401179i
$$467$$ −34.0000 −1.57333 −0.786666 0.617379i $$-0.788195\pi$$
−0.786666 + 0.617379i $$0.788195\pi$$
$$468$$ 6.00000 0.277350
$$469$$ −6.00000 + 10.3923i −0.277054 + 0.479872i
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0 0
$$473$$ 15.0000 + 25.9808i 0.689701 + 1.19460i
$$474$$ 0 0
$$475$$ 0 0
$$476$$ 0 0
$$477$$ −7.50000 12.9904i −0.343401 0.594789i
$$478$$ 8.00000 + 13.8564i 0.365911 + 0.633777i
$$479$$ 9.00000 15.5885i 0.411220 0.712255i −0.583803 0.811895i $$-0.698436\pi$$
0.995023 + 0.0996406i $$0.0317693\pi$$
$$480$$ 0 0
$$481$$ 11.0000 19.0526i 0.501557 0.868722i
$$482$$ 18.0000 0.819878
$$483$$ 0 0
$$484$$ −7.00000 + 12.1244i −0.318182 + 0.551107i
$$485$$ 0 0
$$486$$ 0 0
$$487$$ 23.0000 1.04223 0.521115 0.853487i $$-0.325516\pi$$
0.521115 + 0.853487i $$0.325516\pi$$
$$488$$ 0 0
$$489$$ 0 0
$$490$$ 0 0
$$491$$ −13.5000 23.3827i −0.609246 1.05525i −0.991365 0.131132i $$-0.958139\pi$$
0.382118 0.924113i $$-0.375195\pi$$
$$492$$ 0 0
$$493$$ 0 0
$$494$$ −1.00000 8.66025i −0.0449921 0.389643i
$$495$$ 0 0
$$496$$ −2.00000 3.46410i −0.0898027 0.155543i
$$497$$ 3.00000 + 5.19615i 0.134568 + 0.233079i
$$498$$ 0 0
$$499$$ 19.5000 + 33.7750i 0.872940 + 1.51198i 0.858941 + 0.512074i $$0.171123\pi$$
0.0139987 + 0.999902i $$0.495544\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 12.0000 0.535586
$$503$$ −16.5000 + 28.5788i −0.735699 + 1.27427i 0.218718 + 0.975788i $$0.429813\pi$$
−0.954416 + 0.298479i $$0.903521\pi$$
$$504$$ 1.50000 2.59808i 0.0668153 0.115728i
$$505$$ 0 0
$$506$$ 5.00000 0.222277
$$507$$ 0 0
$$508$$ −7.50000 12.9904i −0.332759 0.576355i
$$509$$ −7.00000 + 12.1244i −0.310270 + 0.537403i −0.978421 0.206623i $$-0.933753\pi$$
0.668151 + 0.744026i $$0.267086\pi$$
$$510$$ 0 0
$$511$$ −7.00000 12.1244i −0.309662 0.536350i
$$512$$ −1.00000 −0.0441942
$$513$$ 0 0
$$514$$ −14.0000 −0.617514
$$515$$ 0 0
$$516$$ 0 0
$$517$$ 0 0
$$518$$ −5.50000 9.52628i −0.241656 0.418561i
$$519$$ 0 0
$$520$$ 0 0
$$521$$ 18.0000 0.788594 0.394297 0.918983i $$-0.370988\pi$$
0.394297 + 0.918983i $$0.370988\pi$$
$$522$$ −9.00000 + 15.5885i −0.393919 + 0.682288i
$$523$$ −21.0000 + 36.3731i −0.918266 + 1.59048i −0.116218 + 0.993224i $$0.537077\pi$$
−0.802048 + 0.597259i $$0.796256\pi$$
$$524$$ 1.00000 0.0436852
$$525$$ 0 0
$$526$$ −5.50000 + 9.52628i −0.239811 + 0.415366i
$$527$$ 0 0
$$528$$ 0 0
$$529$$ 11.0000 + 19.0526i 0.478261 + 0.828372i
$$530$$ 0 0
$$531$$ 0 0
$$532$$ −4.00000 1.73205i −0.173422 0.0750939i
$$533$$ 18.0000 0.779667
$$534$$ 0 0
$$535$$ 0 0
$$536$$ −6.00000 + 10.3923i −0.259161 + 0.448879i
$$537$$ 0 0
$$538$$ −14.0000 + 24.2487i −0.603583 + 1.04544i
$$539$$ −30.0000 −1.29219
$$540$$ 0 0
$$541$$ 10.0000 17.3205i 0.429934 0.744667i −0.566933 0.823764i $$-0.691870\pi$$
0.996867 + 0.0790969i $$0.0252036\pi$$
$$542$$ −3.00000 + 5.19615i −0.128861 + 0.223194i
$$543$$ 0 0
$$544$$ 0 0
$$545$$ 0 0
$$546$$ 0 0
$$547$$ −11.0000 + 19.0526i −0.470326 + 0.814629i −0.999424 0.0339321i $$-0.989197\pi$$
0.529098 + 0.848561i $$0.322530\pi$$
$$548$$ 6.00000 + 10.3923i 0.256307 + 0.443937i
$$549$$ 0 0
$$550$$ 0 0
$$551$$ 24.0000 + 10.3923i 1.02243 + 0.442727i
$$552$$ 0 0
$$553$$ 5.00000 + 8.66025i 0.212622 + 0.368271i
$$554$$ 1.00000 + 1.73205i 0.0424859 + 0.0735878i
$$555$$ 0 0
$$556$$ −8.00000 13.8564i −0.339276 0.587643i
$$557$$ −4.50000 + 7.79423i −0.190671 + 0.330252i −0.945473 0.325701i $$-0.894400\pi$$
0.754802 + 0.655953i $$0.227733\pi$$
$$558$$ 12.0000 0.508001
$$559$$ 12.0000 0.507546
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 15.0000 0.632737
$$563$$ −32.0000 −1.34864 −0.674320 0.738440i $$-0.735563\pi$$
−0.674320 + 0.738440i $$0.735563\pi$$
$$564$$ 0 0
$$565$$ 0 0
$$566$$ 7.00000 12.1244i 0.294232 0.509625i
$$567$$ 4.50000 + 7.79423i 0.188982 + 0.327327i
$$568$$ 3.00000 + 5.19615i 0.125877 + 0.218026i
$$569$$ 45.0000 1.88650 0.943249 0.332086i $$-0.107752\pi$$
0.943249 + 0.332086i $$0.107752\pi$$
$$570$$ 0 0
$$571$$ 12.0000 0.502184 0.251092 0.967963i $$-0.419210\pi$$
0.251092 + 0.967963i $$0.419210\pi$$
$$572$$ 5.00000 + 8.66025i 0.209061 + 0.362103i
$$573$$ 0 0
$$574$$ 4.50000 7.79423i 0.187826 0.325325i
$$575$$ 0 0
$$576$$ 1.50000 2.59808i 0.0625000 0.108253i
$$577$$ −32.0000 −1.33218 −0.666089 0.745873i $$-0.732033\pi$$
−0.666089 + 0.745873i $$0.732033\pi$$
$$578$$ 17.0000 0.707107
$$579$$ 0 0
$$580$$ 0 0
$$581$$ 14.0000 0.580818
$$582$$ 0 0
$$583$$ 12.5000 21.6506i 0.517697 0.896678i
$$584$$ −7.00000 12.1244i −0.289662 0.501709i
$$585$$ 0 0
$$586$$ 10.5000 + 18.1865i 0.433751 + 0.751279i
$$587$$ 6.00000 + 10.3923i 0.247647 + 0.428936i 0.962872 0.269957i $$-0.0870095\pi$$
−0.715226 + 0.698893i $$0.753676\pi$$
$$588$$ 0 0
$$589$$ −2.00000 17.3205i −0.0824086 0.713679i
$$590$$ 0 0
$$591$$ 0 0
$$592$$ −5.50000 9.52628i −0.226049 0.391528i
$$593$$ 21.0000 36.3731i 0.862367 1.49366i −0.00727173 0.999974i $$-0.502315\pi$$
0.869638 0.493689i $$-0.164352\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ −4.00000 −0.163846
$$597$$ 0 0
$$598$$ 1.00000 1.73205i 0.0408930 0.0708288i
$$599$$ 22.0000 38.1051i 0.898896 1.55693i 0.0699877 0.997548i $$-0.477704\pi$$
0.828908 0.559385i $$-0.188963\pi$$
$$600$$ 0 0
$$601$$ 21.0000 0.856608 0.428304 0.903635i $$-0.359111\pi$$
0.428304 + 0.903635i $$0.359111\pi$$
$$602$$ 3.00000 5.19615i 0.122271 0.211779i
$$603$$ −18.0000 31.1769i −0.733017 1.26962i
$$604$$ 8.00000 13.8564i 0.325515 0.563809i
$$605$$ 0 0
$$606$$ 0 0
$$607$$ −13.0000 −0.527654 −0.263827 0.964570i $$-0.584985\pi$$
−0.263827 + 0.964570i $$0.584985\pi$$
$$608$$ −4.00000 1.73205i −0.162221 0.0702439i
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 0 0
$$612$$ 0 0
$$613$$ 12.5000 + 21.6506i 0.504870 + 0.874461i 0.999984 + 0.00563283i $$0.00179300\pi$$
−0.495114 + 0.868828i $$0.664874\pi$$
$$614$$ 1.00000 1.73205i 0.0403567 0.0698999i
$$615$$ 0 0
$$616$$ 5.00000 0.201456
$$617$$ 10.0000 17.3205i 0.402585 0.697297i −0.591452 0.806340i $$-0.701445\pi$$
0.994037 + 0.109043i $$0.0347785\pi$$
$$618$$ 0 0
$$619$$ −45.0000 −1.80870 −0.904351 0.426789i $$-0.859645\pi$$
−0.904351 + 0.426789i $$0.859645\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 2.00000 + 3.46410i 0.0801927 + 0.138898i
$$623$$ −3.50000 + 6.06218i −0.140225 + 0.242876i
$$624$$ 0 0
$$625$$ 0 0
$$626$$ −28.0000 −1.11911
$$627$$ 0 0
$$628$$ 21.0000 0.837991
$$629$$ 0 0
$$630$$ 0 0
$$631$$ 11.0000 19.0526i 0.437903 0.758470i −0.559625 0.828746i $$-0.689055\pi$$
0.997528 + 0.0702759i $$0.0223880\pi$$
$$632$$ 5.00000 + 8.66025i 0.198889 + 0.344486i
$$633$$ 0 0
$$634$$ −27.0000 −1.07231
$$635$$ 0 0
$$636$$ 0 0
$$637$$ −6.00000 + 10.3923i −0.237729 + 0.411758i
$$638$$ −30.0000 −1.18771
$$639$$ −18.0000 −0.712069
$$640$$ 0 0
$$641$$ 5.00000 + 8.66025i 0.197488 + 0.342059i 0.947713 0.319123i $$-0.103388\pi$$
−0.750225 + 0.661182i $$0.770055\pi$$
$$642$$ 0 0
$$643$$ −8.00000 13.8564i −0.315489 0.546443i 0.664052 0.747686i $$-0.268835\pi$$
−0.979541 + 0.201243i $$0.935502\pi$$
$$644$$ −0.500000 0.866025i −0.0197028 0.0341262i
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 3.00000 0.117942 0.0589711 0.998260i $$-0.481218\pi$$
0.0589711 + 0.998260i $$0.481218\pi$$
$$648$$ 4.50000 + 7.79423i 0.176777 + 0.306186i
$$649$$ 0 0
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 5.00000 8.66025i 0.195815 0.339162i
$$653$$ 25.0000 0.978326 0.489163 0.872192i $$-0.337302\pi$$
0.489163 + 0.872192i $$0.337302\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ 4.50000 7.79423i 0.175695 0.304314i
$$657$$ 42.0000 1.63858
$$658$$ 0 0
$$659$$ 7.50000 12.9904i 0.292159 0.506033i −0.682161 0.731202i $$-0.738960\pi$$
0.974320 + 0.225168i $$0.0722932\pi$$
$$660$$ 0 0
$$661$$ −12.0000 + 20.7846i −0.466746 + 0.808428i −0.999278 0.0379819i $$-0.987907\pi$$
0.532533 + 0.846410i $$0.321240\pi$$
$$662$$ −12.5000 21.6506i −0.485826 0.841476i
$$663$$ 0 0
$$664$$ 14.0000 0.543305
$$665$$ 0 0
$$666$$ 33.0000 1.27872
$$667$$ 3.00000 + 5.19615i 0.116160 + 0.201196i
$$668$$ −2.50000 4.33013i −0.0967279 0.167538i
$$669$$ 0 0
$$670$$ 0 0
$$671$$ 0 0
$$672$$ 0 0
$$673$$ −16.0000 −0.616755 −0.308377 0.951264i $$-0.599786\pi$$
−0.308377 + 0.951264i $$0.599786\pi$$
$$674$$ −3.00000 + 5.19615i −0.115556 + 0.200148i
$$675$$ 0 0
$$676$$ −9.00000 −0.346154
$$677$$ −27.0000 −1.03769 −0.518847 0.854867i $$-0.673639\pi$$
−0.518847 + 0.854867i $$0.673639\pi$$
$$678$$ 0 0
$$679$$ 1.00000 + 1.73205i 0.0383765 + 0.0664700i
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 10.0000 + 17.3205i 0.382920 + 0.663237i
$$683$$ 44.0000 1.68361 0.841807 0.539779i $$-0.181492\pi$$
0.841807 + 0.539779i $$0.181492\pi$$
$$684$$ 10.5000 7.79423i 0.401478 0.298020i
$$685$$ 0 0
$$686$$ 6.50000 + 11.2583i 0.248171 + 0.429845i
$$687$$ 0 0
$$688$$ 3.00000 5.19615i 0.114374 0.198101i
$$689$$ −5.00000 8.66025i −0.190485 0.329929i
$$690$$ 0 0
$$691$$ −15.0000 −0.570627 −0.285313 0.958434i $$-0.592098\pi$$
−0.285313 + 0.958434i $$0.592098\pi$$
$$692$$ −1.00000 −0.0380143
$$693$$ −7.50000 + 12.9904i −0.284901 + 0.493464i
$$694$$ −9.00000 + 15.5885i −0.341635 + 0.591730i
$$695$$ 0 0
$$696$$ 0 0
$$697$$ 0 0
$$698$$ −14.0000 24.2487i −0.529908 0.917827i
$$699$$ 0 0
$$700$$ 0 0
$$701$$ −3.00000 5.19615i −0.113308 0.196256i 0.803794 0.594908i $$-0.202811\pi$$
−0.917102 + 0.398652i $$0.869478\pi$$
$$702$$ 0 0
$$703$$ −5.50000 47.6314i −0.207436 1.79645i
$$704$$ 5.00000 0.188445
$$705$$ 0 0
$$706$$ −2.00000 3.46410i −0.0752710 0.130373i
$$707$$ 5.00000 8.66025i 0.188044 0.325702i
$$708$$ 0 0
$$709$$ −4.00000 + 6.92820i −0.150223 + 0.260194i −0.931309 0.364229i $$-0.881333\pi$$
0.781086 + 0.624423i $$0.214666\pi$$
$$710$$ 0 0
$$711$$ −30.0000 −1.12509
$$712$$ −3.50000 + 6.06218i −0.131168 + 0.227190i
$$713$$ 2.00000 3.46410i 0.0749006 0.129732i
$$714$$ 0 0
$$715$$ 0 0
$$716$$ −9.50000 + 16.4545i −0.355032 + 0.614933i
$$717$$ 0 0
$$718$$ 5.00000 8.66025i 0.186598 0.323198i
$$719$$ 24.0000 + 41.5692i 0.895049 + 1.55027i 0.833744 + 0.552151i $$0.186193\pi$$
0.0613050 + 0.998119i $$0.480474\pi$$
$$720$$ 0 0
$$721$$ 13.0000 0.484145
$$722$$ −13.0000 13.8564i −0.483810 0.515682i
$$723$$ 0 0
$$724$$ −1.00000 1.73205i −0.0371647 0.0643712i
$$725$$ 0 0
$$726$$ 0 0
$$727$$ −8.00000 13.8564i −0.296704 0.513906i 0.678676 0.734438i $$-0.262554\pi$$
−0.975380 + 0.220532i $$0.929221\pi$$
$$728$$ 1.00000 1.73205i 0.0370625 0.0641941i
$$729$$ −27.0000 −1.00000
$$730$$ 0 0
$$731$$ 0 0
$$732$$ 0 0
$$733$$ 15.0000 0.554038 0.277019 0.960864i $$-0.410654\pi$$
0.277019 + 0.960864i $$0.410654\pi$$
$$734$$ −4.00000 −0.147643
$$735$$ 0 0
$$736$$ −0.500000 0.866025i −0.0184302 0.0319221i
$$737$$ 30.0000 51.9615i 1.10506 1.91403i
$$738$$ 13.5000 + 23.3827i 0.496942 + 0.860729i
$$739$$ 15.5000 + 26.8468i 0.570177 + 0.987575i 0.996547 + 0.0830265i $$0.0264586\pi$$
−0.426371 + 0.904549i $$0.640208\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ −5.00000 −0.183556
$$743$$ −7.50000 12.9904i −0.275148 0.476571i 0.695024 0.718986i $$-0.255394\pi$$
−0.970173 + 0.242415i $$0.922060\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ −15.5000 26.8468i −0.567495 0.982931i
$$747$$ −21.0000 + 36.3731i −0.768350 + 1.33082i
$$748$$ 0 0
$$749$$ −4.00000 −0.146157
$$750$$ 0 0
$$751$$ 10.0000 17.3205i 0.364905 0.632034i −0.623856 0.781540i $$-0.714435\pi$$
0.988761 + 0.149505i $$0.0477681\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ −6.00000 + 10.3923i −0.218507 + 0.378465i
$$755$$ 0 0
$$756$$ 0 0
$$757$$ −7.50000 12.9904i −0.272592 0.472143i 0.696933 0.717137i $$-0.254548\pi$$
−0.969525 + 0.244993i $$0.921214\pi$$
$$758$$ −6.00000 10.3923i −0.217930 0.377466i
$$759$$ 0 0
$$760$$ 0 0
$$761$$ −43.0000 −1.55875 −0.779374 0.626559i $$-0.784463\pi$$
−0.779374 + 0.626559i $$0.784463\pi$$
$$762$$ 0 0
$$763$$ 2.00000 + 3.46410i 0.0724049 + 0.125409i
$$764$$ 9.00000 15.5885i 0.325609 0.563971i
$$765$$ 0 0
$$766$$ −4.00000 + 6.92820i −0.144526 + 0.250326i
$$767$$ 0 0
$$768$$ 0 0
$$769$$ 13.0000 22.5167i 0.468792 0.811972i −0.530572 0.847640i $$-0.678023\pi$$
0.999364 + 0.0356685i $$0.0113561\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ −4.00000 −0.143963
$$773$$ 22.5000 38.9711i 0.809269 1.40169i −0.104102 0.994567i $$-0.533197\pi$$
0.913371 0.407128i $$-0.133470\pi$$
$$774$$ 9.00000 + 15.5885i 0.323498 + 0.560316i
$$775$$ 0 0
$$776$$ 1.00000 + 1.73205i 0.0358979 + 0.0621770i
$$777$$ 0 0
$$778$$ −26.0000 −0.932145
$$779$$ 31.5000 23.3827i 1.12860 0.837772i
$$780$$ 0 0
$$781$$ −15.0000 25.9808i −0.536742 0.929665i
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 3.00000 + 5.19615i 0.107143 + 0.185577i
$$785$$ 0 0
$$786$$ 0 0
$$787$$ −18.0000 −0.641631 −0.320815 0.947142i $$-0.603957\pi$$
−0.320815 + 0.947142i $$0.603957\pi$$
$$788$$ 11.5000 19.9186i 0.409671 0.709570i
$$789$$ 0 0
$$790$$ 0 0
$$791$$ −12.0000 −0.426671
$$792$$ −7.50000 + 12.9904i −0.266501 + 0.461593i
$$793$$ 0 0
$$794$$ −14.5000 + 25.1147i −0.514586 + 0.891289i
$$795$$ 0