# Properties

 Label 350.2.e.j.151.1 Level $350$ Weight $2$ Character 350.151 Analytic conductor $2.795$ Analytic rank $0$ Dimension $2$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$350 = 2 \cdot 5^{2} \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 350.e (of order $$3$$, degree $$2$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$2.79476407074$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(\zeta_{6})$$ Defining polynomial: $$x^{2} - x + 1$$ x^2 - x + 1 Coefficient ring: $$\Z[a_1, a_2]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 70) Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 151.1 Root $$0.500000 + 0.866025i$$ of defining polynomial Character $$\chi$$ $$=$$ 350.151 Dual form 350.2.e.j.51.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(2.00000 - 1.73205i) q^{7} -1.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})$$ $$q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(2.00000 - 1.73205i) q^{7} -1.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +(-1.50000 + 2.59808i) q^{11} +5.00000 q^{13} +(2.50000 + 0.866025i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-1.00000 + 1.73205i) q^{17} +(-1.50000 + 2.59808i) q^{18} +(2.50000 + 4.33013i) q^{19} -3.00000 q^{22} +(-3.50000 - 6.06218i) q^{23} +(2.50000 + 4.33013i) q^{26} +(0.500000 + 2.59808i) q^{28} -4.00000 q^{29} +(1.00000 - 1.73205i) q^{31} +(0.500000 - 0.866025i) q^{32} -2.00000 q^{34} -3.00000 q^{36} +(0.500000 + 0.866025i) q^{37} +(-2.50000 + 4.33013i) q^{38} +3.00000 q^{41} -2.00000 q^{43} +(-1.50000 - 2.59808i) q^{44} +(3.50000 - 6.06218i) q^{46} +(-3.50000 - 6.06218i) q^{47} +(1.00000 - 6.92820i) q^{49} +(-2.50000 + 4.33013i) q^{52} +(4.50000 - 7.79423i) q^{53} +(-2.00000 + 1.73205i) q^{56} +(-2.00000 - 3.46410i) q^{58} +(2.00000 - 3.46410i) q^{59} +(-3.00000 - 5.19615i) q^{61} +2.00000 q^{62} +(7.50000 + 2.59808i) q^{63} +1.00000 q^{64} +(1.00000 - 1.73205i) q^{67} +(-1.00000 - 1.73205i) q^{68} -6.00000 q^{71} +(-1.50000 - 2.59808i) q^{72} +(-8.00000 + 13.8564i) q^{73} +(-0.500000 + 0.866025i) q^{74} -5.00000 q^{76} +(1.50000 + 7.79423i) q^{77} +(-7.00000 - 12.1244i) q^{79} +(-4.50000 + 7.79423i) q^{81} +(1.50000 + 2.59808i) q^{82} +6.00000 q^{83} +(-1.00000 - 1.73205i) q^{86} +(1.50000 - 2.59808i) q^{88} +(-1.00000 - 1.73205i) q^{89} +(10.0000 - 8.66025i) q^{91} +7.00000 q^{92} +(3.50000 - 6.06218i) q^{94} +12.0000 q^{97} +(6.50000 - 2.59808i) q^{98} -9.00000 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q + q^{2} - q^{4} + 4 q^{7} - 2 q^{8} + 3 q^{9}+O(q^{10})$$ 2 * q + q^2 - q^4 + 4 * q^7 - 2 * q^8 + 3 * q^9 $$2 q + q^{2} - q^{4} + 4 q^{7} - 2 q^{8} + 3 q^{9} - 3 q^{11} + 10 q^{13} + 5 q^{14} - q^{16} - 2 q^{17} - 3 q^{18} + 5 q^{19} - 6 q^{22} - 7 q^{23} + 5 q^{26} + q^{28} - 8 q^{29} + 2 q^{31} + q^{32} - 4 q^{34} - 6 q^{36} + q^{37} - 5 q^{38} + 6 q^{41} - 4 q^{43} - 3 q^{44} + 7 q^{46} - 7 q^{47} + 2 q^{49} - 5 q^{52} + 9 q^{53} - 4 q^{56} - 4 q^{58} + 4 q^{59} - 6 q^{61} + 4 q^{62} + 15 q^{63} + 2 q^{64} + 2 q^{67} - 2 q^{68} - 12 q^{71} - 3 q^{72} - 16 q^{73} - q^{74} - 10 q^{76} + 3 q^{77} - 14 q^{79} - 9 q^{81} + 3 q^{82} + 12 q^{83} - 2 q^{86} + 3 q^{88} - 2 q^{89} + 20 q^{91} + 14 q^{92} + 7 q^{94} + 24 q^{97} + 13 q^{98} - 18 q^{99}+O(q^{100})$$ 2 * q + q^2 - q^4 + 4 * q^7 - 2 * q^8 + 3 * q^9 - 3 * q^11 + 10 * q^13 + 5 * q^14 - q^16 - 2 * q^17 - 3 * q^18 + 5 * q^19 - 6 * q^22 - 7 * q^23 + 5 * q^26 + q^28 - 8 * q^29 + 2 * q^31 + q^32 - 4 * q^34 - 6 * q^36 + q^37 - 5 * q^38 + 6 * q^41 - 4 * q^43 - 3 * q^44 + 7 * q^46 - 7 * q^47 + 2 * q^49 - 5 * q^52 + 9 * q^53 - 4 * q^56 - 4 * q^58 + 4 * q^59 - 6 * q^61 + 4 * q^62 + 15 * q^63 + 2 * q^64 + 2 * q^67 - 2 * q^68 - 12 * q^71 - 3 * q^72 - 16 * q^73 - q^74 - 10 * q^76 + 3 * q^77 - 14 * q^79 - 9 * q^81 + 3 * q^82 + 12 * q^83 - 2 * q^86 + 3 * q^88 - 2 * q^89 + 20 * q^91 + 14 * q^92 + 7 * q^94 + 24 * q^97 + 13 * q^98 - 18 * q^99

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/350\mathbb{Z}\right)^\times$$.

 $$n$$ $$101$$ $$127$$ $$\chi(n)$$ $$e\left(\frac{2}{3}\right)$$ $$1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0.500000 + 0.866025i 0.353553 + 0.612372i
$$3$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$4$$ −0.500000 + 0.866025i −0.250000 + 0.433013i
$$5$$ 0 0
$$6$$ 0 0
$$7$$ 2.00000 1.73205i 0.755929 0.654654i
$$8$$ −1.00000 −0.353553
$$9$$ 1.50000 + 2.59808i 0.500000 + 0.866025i
$$10$$ 0 0
$$11$$ −1.50000 + 2.59808i −0.452267 + 0.783349i −0.998526 0.0542666i $$-0.982718\pi$$
0.546259 + 0.837616i $$0.316051\pi$$
$$12$$ 0 0
$$13$$ 5.00000 1.38675 0.693375 0.720577i $$-0.256123\pi$$
0.693375 + 0.720577i $$0.256123\pi$$
$$14$$ 2.50000 + 0.866025i 0.668153 + 0.231455i
$$15$$ 0 0
$$16$$ −0.500000 0.866025i −0.125000 0.216506i
$$17$$ −1.00000 + 1.73205i −0.242536 + 0.420084i −0.961436 0.275029i $$-0.911312\pi$$
0.718900 + 0.695113i $$0.244646\pi$$
$$18$$ −1.50000 + 2.59808i −0.353553 + 0.612372i
$$19$$ 2.50000 + 4.33013i 0.573539 + 0.993399i 0.996199 + 0.0871106i $$0.0277634\pi$$
−0.422659 + 0.906289i $$0.638903\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ −3.00000 −0.639602
$$23$$ −3.50000 6.06218i −0.729800 1.26405i −0.956967 0.290196i $$-0.906280\pi$$
0.227167 0.973856i $$-0.427054\pi$$
$$24$$ 0 0
$$25$$ 0 0
$$26$$ 2.50000 + 4.33013i 0.490290 + 0.849208i
$$27$$ 0 0
$$28$$ 0.500000 + 2.59808i 0.0944911 + 0.490990i
$$29$$ −4.00000 −0.742781 −0.371391 0.928477i $$-0.621119\pi$$
−0.371391 + 0.928477i $$0.621119\pi$$
$$30$$ 0 0
$$31$$ 1.00000 1.73205i 0.179605 0.311086i −0.762140 0.647412i $$-0.775851\pi$$
0.941745 + 0.336327i $$0.109185\pi$$
$$32$$ 0.500000 0.866025i 0.0883883 0.153093i
$$33$$ 0 0
$$34$$ −2.00000 −0.342997
$$35$$ 0 0
$$36$$ −3.00000 −0.500000
$$37$$ 0.500000 + 0.866025i 0.0821995 + 0.142374i 0.904194 0.427121i $$-0.140472\pi$$
−0.821995 + 0.569495i $$0.807139\pi$$
$$38$$ −2.50000 + 4.33013i −0.405554 + 0.702439i
$$39$$ 0 0
$$40$$ 0 0
$$41$$ 3.00000 0.468521 0.234261 0.972174i $$-0.424733\pi$$
0.234261 + 0.972174i $$0.424733\pi$$
$$42$$ 0 0
$$43$$ −2.00000 −0.304997 −0.152499 0.988304i $$-0.548732\pi$$
−0.152499 + 0.988304i $$0.548732\pi$$
$$44$$ −1.50000 2.59808i −0.226134 0.391675i
$$45$$ 0 0
$$46$$ 3.50000 6.06218i 0.516047 0.893819i
$$47$$ −3.50000 6.06218i −0.510527 0.884260i −0.999926 0.0121990i $$-0.996117\pi$$
0.489398 0.872060i $$-0.337217\pi$$
$$48$$ 0 0
$$49$$ 1.00000 6.92820i 0.142857 0.989743i
$$50$$ 0 0
$$51$$ 0 0
$$52$$ −2.50000 + 4.33013i −0.346688 + 0.600481i
$$53$$ 4.50000 7.79423i 0.618123 1.07062i −0.371706 0.928351i $$-0.621227\pi$$
0.989828 0.142269i $$-0.0454398\pi$$
$$54$$ 0 0
$$55$$ 0 0
$$56$$ −2.00000 + 1.73205i −0.267261 + 0.231455i
$$57$$ 0 0
$$58$$ −2.00000 3.46410i −0.262613 0.454859i
$$59$$ 2.00000 3.46410i 0.260378 0.450988i −0.705965 0.708247i $$-0.749486\pi$$
0.966342 + 0.257260i $$0.0828195\pi$$
$$60$$ 0 0
$$61$$ −3.00000 5.19615i −0.384111 0.665299i 0.607535 0.794293i $$-0.292159\pi$$
−0.991645 + 0.128994i $$0.958825\pi$$
$$62$$ 2.00000 0.254000
$$63$$ 7.50000 + 2.59808i 0.944911 + 0.327327i
$$64$$ 1.00000 0.125000
$$65$$ 0 0
$$66$$ 0 0
$$67$$ 1.00000 1.73205i 0.122169 0.211604i −0.798454 0.602056i $$-0.794348\pi$$
0.920623 + 0.390453i $$0.127682\pi$$
$$68$$ −1.00000 1.73205i −0.121268 0.210042i
$$69$$ 0 0
$$70$$ 0 0
$$71$$ −6.00000 −0.712069 −0.356034 0.934473i $$-0.615871\pi$$
−0.356034 + 0.934473i $$0.615871\pi$$
$$72$$ −1.50000 2.59808i −0.176777 0.306186i
$$73$$ −8.00000 + 13.8564i −0.936329 + 1.62177i −0.164083 + 0.986447i $$0.552466\pi$$
−0.772246 + 0.635323i $$0.780867\pi$$
$$74$$ −0.500000 + 0.866025i −0.0581238 + 0.100673i
$$75$$ 0 0
$$76$$ −5.00000 −0.573539
$$77$$ 1.50000 + 7.79423i 0.170941 + 0.888235i
$$78$$ 0 0
$$79$$ −7.00000 12.1244i −0.787562 1.36410i −0.927457 0.373930i $$-0.878010\pi$$
0.139895 0.990166i $$-0.455323\pi$$
$$80$$ 0 0
$$81$$ −4.50000 + 7.79423i −0.500000 + 0.866025i
$$82$$ 1.50000 + 2.59808i 0.165647 + 0.286910i
$$83$$ 6.00000 0.658586 0.329293 0.944228i $$-0.393190\pi$$
0.329293 + 0.944228i $$0.393190\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ −1.00000 1.73205i −0.107833 0.186772i
$$87$$ 0 0
$$88$$ 1.50000 2.59808i 0.159901 0.276956i
$$89$$ −1.00000 1.73205i −0.106000 0.183597i 0.808146 0.588982i $$-0.200471\pi$$
−0.914146 + 0.405385i $$0.867138\pi$$
$$90$$ 0 0
$$91$$ 10.0000 8.66025i 1.04828 0.907841i
$$92$$ 7.00000 0.729800
$$93$$ 0 0
$$94$$ 3.50000 6.06218i 0.360997 0.625266i
$$95$$ 0 0
$$96$$ 0 0
$$97$$ 12.0000 1.21842 0.609208 0.793011i $$-0.291488\pi$$
0.609208 + 0.793011i $$0.291488\pi$$
$$98$$ 6.50000 2.59808i 0.656599 0.262445i
$$99$$ −9.00000 −0.904534
$$100$$ 0 0
$$101$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$102$$ 0 0
$$103$$ −4.00000 6.92820i −0.394132 0.682656i 0.598858 0.800855i $$-0.295621\pi$$
−0.992990 + 0.118199i $$0.962288\pi$$
$$104$$ −5.00000 −0.490290
$$105$$ 0 0
$$106$$ 9.00000 0.874157
$$107$$ −8.00000 13.8564i −0.773389 1.33955i −0.935695 0.352809i $$-0.885227\pi$$
0.162306 0.986740i $$-0.448107\pi$$
$$108$$ 0 0
$$109$$ −1.00000 + 1.73205i −0.0957826 + 0.165900i −0.909935 0.414751i $$-0.863869\pi$$
0.814152 + 0.580651i $$0.197202\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ −2.50000 0.866025i −0.236228 0.0818317i
$$113$$ −14.0000 −1.31701 −0.658505 0.752577i $$-0.728811\pi$$
−0.658505 + 0.752577i $$0.728811\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ 2.00000 3.46410i 0.185695 0.321634i
$$117$$ 7.50000 + 12.9904i 0.693375 + 1.20096i
$$118$$ 4.00000 0.368230
$$119$$ 1.00000 + 5.19615i 0.0916698 + 0.476331i
$$120$$ 0 0
$$121$$ 1.00000 + 1.73205i 0.0909091 + 0.157459i
$$122$$ 3.00000 5.19615i 0.271607 0.470438i
$$123$$ 0 0
$$124$$ 1.00000 + 1.73205i 0.0898027 + 0.155543i
$$125$$ 0 0
$$126$$ 1.50000 + 7.79423i 0.133631 + 0.694365i
$$127$$ −7.00000 −0.621150 −0.310575 0.950549i $$-0.600522\pi$$
−0.310575 + 0.950549i $$0.600522\pi$$
$$128$$ 0.500000 + 0.866025i 0.0441942 + 0.0765466i
$$129$$ 0 0
$$130$$ 0 0
$$131$$ 0.500000 + 0.866025i 0.0436852 + 0.0756650i 0.887041 0.461690i $$-0.152757\pi$$
−0.843356 + 0.537355i $$0.819423\pi$$
$$132$$ 0 0
$$133$$ 12.5000 + 4.33013i 1.08389 + 0.375470i
$$134$$ 2.00000 0.172774
$$135$$ 0 0
$$136$$ 1.00000 1.73205i 0.0857493 0.148522i
$$137$$ −4.00000 + 6.92820i −0.341743 + 0.591916i −0.984757 0.173939i $$-0.944351\pi$$
0.643013 + 0.765855i $$0.277684\pi$$
$$138$$ 0 0
$$139$$ 16.0000 1.35710 0.678551 0.734553i $$-0.262608\pi$$
0.678551 + 0.734553i $$0.262608\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ −3.00000 5.19615i −0.251754 0.436051i
$$143$$ −7.50000 + 12.9904i −0.627182 + 1.08631i
$$144$$ 1.50000 2.59808i 0.125000 0.216506i
$$145$$ 0 0
$$146$$ −16.0000 −1.32417
$$147$$ 0 0
$$148$$ −1.00000 −0.0821995
$$149$$ 9.00000 + 15.5885i 0.737309 + 1.27706i 0.953703 + 0.300750i $$0.0972370\pi$$
−0.216394 + 0.976306i $$0.569430\pi$$
$$150$$ 0 0
$$151$$ 3.00000 5.19615i 0.244137 0.422857i −0.717752 0.696299i $$-0.754829\pi$$
0.961888 + 0.273442i $$0.0881622\pi$$
$$152$$ −2.50000 4.33013i −0.202777 0.351220i
$$153$$ −6.00000 −0.485071
$$154$$ −6.00000 + 5.19615i −0.483494 + 0.418718i
$$155$$ 0 0
$$156$$ 0 0
$$157$$ −4.50000 + 7.79423i −0.359139 + 0.622047i −0.987817 0.155618i $$-0.950263\pi$$
0.628678 + 0.777666i $$0.283596\pi$$
$$158$$ 7.00000 12.1244i 0.556890 0.964562i
$$159$$ 0 0
$$160$$ 0 0
$$161$$ −17.5000 6.06218i −1.37919 0.477767i
$$162$$ −9.00000 −0.707107
$$163$$ −6.00000 10.3923i −0.469956 0.813988i 0.529454 0.848339i $$-0.322397\pi$$
−0.999410 + 0.0343508i $$0.989064\pi$$
$$164$$ −1.50000 + 2.59808i −0.117130 + 0.202876i
$$165$$ 0 0
$$166$$ 3.00000 + 5.19615i 0.232845 + 0.403300i
$$167$$ −15.0000 −1.16073 −0.580367 0.814355i $$-0.697091\pi$$
−0.580367 + 0.814355i $$0.697091\pi$$
$$168$$ 0 0
$$169$$ 12.0000 0.923077
$$170$$ 0 0
$$171$$ −7.50000 + 12.9904i −0.573539 + 0.993399i
$$172$$ 1.00000 1.73205i 0.0762493 0.132068i
$$173$$ 4.50000 + 7.79423i 0.342129 + 0.592584i 0.984828 0.173534i $$-0.0555188\pi$$
−0.642699 + 0.766119i $$0.722185\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 3.00000 0.226134
$$177$$ 0 0
$$178$$ 1.00000 1.73205i 0.0749532 0.129823i
$$179$$ −6.50000 + 11.2583i −0.485833 + 0.841487i −0.999867 0.0162823i $$-0.994817\pi$$
0.514035 + 0.857769i $$0.328150\pi$$
$$180$$ 0 0
$$181$$ 26.0000 1.93256 0.966282 0.257485i $$-0.0828937\pi$$
0.966282 + 0.257485i $$0.0828937\pi$$
$$182$$ 12.5000 + 4.33013i 0.926562 + 0.320970i
$$183$$ 0 0
$$184$$ 3.50000 + 6.06218i 0.258023 + 0.446910i
$$185$$ 0 0
$$186$$ 0 0
$$187$$ −3.00000 5.19615i −0.219382 0.379980i
$$188$$ 7.00000 0.510527
$$189$$ 0 0
$$190$$ 0 0
$$191$$ 10.0000 + 17.3205i 0.723575 + 1.25327i 0.959558 + 0.281511i $$0.0908356\pi$$
−0.235983 + 0.971757i $$0.575831\pi$$
$$192$$ 0 0
$$193$$ −5.00000 + 8.66025i −0.359908 + 0.623379i −0.987945 0.154805i $$-0.950525\pi$$
0.628037 + 0.778183i $$0.283859\pi$$
$$194$$ 6.00000 + 10.3923i 0.430775 + 0.746124i
$$195$$ 0 0
$$196$$ 5.50000 + 4.33013i 0.392857 + 0.309295i
$$197$$ 5.00000 0.356235 0.178118 0.984009i $$-0.442999\pi$$
0.178118 + 0.984009i $$0.442999\pi$$
$$198$$ −4.50000 7.79423i −0.319801 0.553912i
$$199$$ −9.00000 + 15.5885i −0.637993 + 1.10504i 0.347879 + 0.937539i $$0.386902\pi$$
−0.985873 + 0.167497i $$0.946431\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ 0 0
$$203$$ −8.00000 + 6.92820i −0.561490 + 0.486265i
$$204$$ 0 0
$$205$$ 0 0
$$206$$ 4.00000 6.92820i 0.278693 0.482711i
$$207$$ 10.5000 18.1865i 0.729800 1.26405i
$$208$$ −2.50000 4.33013i −0.173344 0.300240i
$$209$$ −15.0000 −1.03757
$$210$$ 0 0
$$211$$ −9.00000 −0.619586 −0.309793 0.950804i $$-0.600260\pi$$
−0.309793 + 0.950804i $$0.600260\pi$$
$$212$$ 4.50000 + 7.79423i 0.309061 + 0.535310i
$$213$$ 0 0
$$214$$ 8.00000 13.8564i 0.546869 0.947204i
$$215$$ 0 0
$$216$$ 0 0
$$217$$ −1.00000 5.19615i −0.0678844 0.352738i
$$218$$ −2.00000 −0.135457
$$219$$ 0 0
$$220$$ 0 0
$$221$$ −5.00000 + 8.66025i −0.336336 + 0.582552i
$$222$$ 0 0
$$223$$ 8.00000 0.535720 0.267860 0.963458i $$-0.413684\pi$$
0.267860 + 0.963458i $$0.413684\pi$$
$$224$$ −0.500000 2.59808i −0.0334077 0.173591i
$$225$$ 0 0
$$226$$ −7.00000 12.1244i −0.465633 0.806500i
$$227$$ −3.00000 + 5.19615i −0.199117 + 0.344881i −0.948242 0.317547i $$-0.897141\pi$$
0.749125 + 0.662428i $$0.230474\pi$$
$$228$$ 0 0
$$229$$ −8.00000 13.8564i −0.528655 0.915657i −0.999442 0.0334101i $$-0.989363\pi$$
0.470787 0.882247i $$-0.343970\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 4.00000 0.262613
$$233$$ −4.00000 6.92820i −0.262049 0.453882i 0.704737 0.709468i $$-0.251065\pi$$
−0.966786 + 0.255586i $$0.917731\pi$$
$$234$$ −7.50000 + 12.9904i −0.490290 + 0.849208i
$$235$$ 0 0
$$236$$ 2.00000 + 3.46410i 0.130189 + 0.225494i
$$237$$ 0 0
$$238$$ −4.00000 + 3.46410i −0.259281 + 0.224544i
$$239$$ 20.0000 1.29369 0.646846 0.762620i $$-0.276088\pi$$
0.646846 + 0.762620i $$0.276088\pi$$
$$240$$ 0 0
$$241$$ 4.50000 7.79423i 0.289870 0.502070i −0.683908 0.729568i $$-0.739721\pi$$
0.973779 + 0.227498i $$0.0730544\pi$$
$$242$$ −1.00000 + 1.73205i −0.0642824 + 0.111340i
$$243$$ 0 0
$$244$$ 6.00000 0.384111
$$245$$ 0 0
$$246$$ 0 0
$$247$$ 12.5000 + 21.6506i 0.795356 + 1.37760i
$$248$$ −1.00000 + 1.73205i −0.0635001 + 0.109985i
$$249$$ 0 0
$$250$$ 0 0
$$251$$ 5.00000 0.315597 0.157799 0.987471i $$-0.449560\pi$$
0.157799 + 0.987471i $$0.449560\pi$$
$$252$$ −6.00000 + 5.19615i −0.377964 + 0.327327i
$$253$$ 21.0000 1.32026
$$254$$ −3.50000 6.06218i −0.219610 0.380375i
$$255$$ 0 0
$$256$$ −0.500000 + 0.866025i −0.0312500 + 0.0541266i
$$257$$ −3.00000 5.19615i −0.187135 0.324127i 0.757159 0.653231i $$-0.226587\pi$$
−0.944294 + 0.329104i $$0.893253\pi$$
$$258$$ 0 0
$$259$$ 2.50000 + 0.866025i 0.155342 + 0.0538122i
$$260$$ 0 0
$$261$$ −6.00000 10.3923i −0.371391 0.643268i
$$262$$ −0.500000 + 0.866025i −0.0308901 + 0.0535032i
$$263$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$264$$ 0 0
$$265$$ 0 0
$$266$$ 2.50000 + 12.9904i 0.153285 + 0.796491i
$$267$$ 0 0
$$268$$ 1.00000 + 1.73205i 0.0610847 + 0.105802i
$$269$$ 5.00000 8.66025i 0.304855 0.528025i −0.672374 0.740212i $$-0.734725\pi$$
0.977229 + 0.212187i $$0.0680585\pi$$
$$270$$ 0 0
$$271$$ −12.0000 20.7846i −0.728948 1.26258i −0.957328 0.289003i $$-0.906676\pi$$
0.228380 0.973572i $$-0.426657\pi$$
$$272$$ 2.00000 0.121268
$$273$$ 0 0
$$274$$ −8.00000 −0.483298
$$275$$ 0 0
$$276$$ 0 0
$$277$$ −1.00000 + 1.73205i −0.0600842 + 0.104069i −0.894503 0.447062i $$-0.852470\pi$$
0.834419 + 0.551131i $$0.185804\pi$$
$$278$$ 8.00000 + 13.8564i 0.479808 + 0.831052i
$$279$$ 6.00000 0.359211
$$280$$ 0 0
$$281$$ 9.00000 0.536895 0.268447 0.963294i $$-0.413489\pi$$
0.268447 + 0.963294i $$0.413489\pi$$
$$282$$ 0 0
$$283$$ 7.00000 12.1244i 0.416107 0.720718i −0.579437 0.815017i $$-0.696728\pi$$
0.995544 + 0.0942988i $$0.0300609\pi$$
$$284$$ 3.00000 5.19615i 0.178017 0.308335i
$$285$$ 0 0
$$286$$ −15.0000 −0.886969
$$287$$ 6.00000 5.19615i 0.354169 0.306719i
$$288$$ 3.00000 0.176777
$$289$$ 6.50000 + 11.2583i 0.382353 + 0.662255i
$$290$$ 0 0
$$291$$ 0 0
$$292$$ −8.00000 13.8564i −0.468165 0.810885i
$$293$$ 9.00000 0.525786 0.262893 0.964825i $$-0.415323\pi$$
0.262893 + 0.964825i $$0.415323\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ −0.500000 0.866025i −0.0290619 0.0503367i
$$297$$ 0 0
$$298$$ −9.00000 + 15.5885i −0.521356 + 0.903015i
$$299$$ −17.5000 30.3109i −1.01205 1.75292i
$$300$$ 0 0
$$301$$ −4.00000 + 3.46410i −0.230556 + 0.199667i
$$302$$ 6.00000 0.345261
$$303$$ 0 0
$$304$$ 2.50000 4.33013i 0.143385 0.248350i
$$305$$ 0 0
$$306$$ −3.00000 5.19615i −0.171499 0.297044i
$$307$$ 22.0000 1.25561 0.627803 0.778372i $$-0.283954\pi$$
0.627803 + 0.778372i $$0.283954\pi$$
$$308$$ −7.50000 2.59808i −0.427352 0.148039i
$$309$$ 0 0
$$310$$ 0 0
$$311$$ −3.00000 + 5.19615i −0.170114 + 0.294647i −0.938460 0.345389i $$-0.887747\pi$$
0.768345 + 0.640036i $$0.221080\pi$$
$$312$$ 0 0
$$313$$ −11.0000 19.0526i −0.621757 1.07691i −0.989158 0.146852i $$-0.953086\pi$$
0.367402 0.930062i $$-0.380247\pi$$
$$314$$ −9.00000 −0.507899
$$315$$ 0 0
$$316$$ 14.0000 0.787562
$$317$$ −1.00000 1.73205i −0.0561656 0.0972817i 0.836576 0.547852i $$-0.184554\pi$$
−0.892741 + 0.450570i $$0.851221\pi$$
$$318$$ 0 0
$$319$$ 6.00000 10.3923i 0.335936 0.581857i
$$320$$ 0 0
$$321$$ 0 0
$$322$$ −3.50000 18.1865i −0.195047 1.01350i
$$323$$ −10.0000 −0.556415
$$324$$ −4.50000 7.79423i −0.250000 0.433013i
$$325$$ 0 0
$$326$$ 6.00000 10.3923i 0.332309 0.575577i
$$327$$ 0 0
$$328$$ −3.00000 −0.165647
$$329$$ −17.5000 6.06218i −0.964806 0.334219i
$$330$$ 0 0
$$331$$ −2.50000 4.33013i −0.137412 0.238005i 0.789104 0.614260i $$-0.210545\pi$$
−0.926516 + 0.376254i $$0.877212\pi$$
$$332$$ −3.00000 + 5.19615i −0.164646 + 0.285176i
$$333$$ −1.50000 + 2.59808i −0.0821995 + 0.142374i
$$334$$ −7.50000 12.9904i −0.410382 0.710802i
$$335$$ 0 0
$$336$$ 0 0
$$337$$ −10.0000 −0.544735 −0.272367 0.962193i $$-0.587807\pi$$
−0.272367 + 0.962193i $$0.587807\pi$$
$$338$$ 6.00000 + 10.3923i 0.326357 + 0.565267i
$$339$$ 0 0
$$340$$ 0 0
$$341$$ 3.00000 + 5.19615i 0.162459 + 0.281387i
$$342$$ −15.0000 −0.811107
$$343$$ −10.0000 15.5885i −0.539949 0.841698i
$$344$$ 2.00000 0.107833
$$345$$ 0 0
$$346$$ −4.50000 + 7.79423i −0.241921 + 0.419020i
$$347$$ −6.00000 + 10.3923i −0.322097 + 0.557888i −0.980921 0.194409i $$-0.937721\pi$$
0.658824 + 0.752297i $$0.271054\pi$$
$$348$$ 0 0
$$349$$ −12.0000 −0.642345 −0.321173 0.947021i $$-0.604077\pi$$
−0.321173 + 0.947021i $$0.604077\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 1.50000 + 2.59808i 0.0799503 + 0.138478i
$$353$$ 12.0000 20.7846i 0.638696 1.10625i −0.347024 0.937856i $$-0.612808\pi$$
0.985719 0.168397i $$-0.0538590\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ 2.00000 0.106000
$$357$$ 0 0
$$358$$ −13.0000 −0.687071
$$359$$ −8.00000 13.8564i −0.422224 0.731313i 0.573933 0.818902i $$-0.305417\pi$$
−0.996157 + 0.0875892i $$0.972084\pi$$
$$360$$ 0 0
$$361$$ −3.00000 + 5.19615i −0.157895 + 0.273482i
$$362$$ 13.0000 + 22.5167i 0.683265 + 1.18345i
$$363$$ 0 0
$$364$$ 2.50000 + 12.9904i 0.131036 + 0.680881i
$$365$$ 0 0
$$366$$ 0 0
$$367$$ 6.50000 11.2583i 0.339297 0.587680i −0.645003 0.764180i $$-0.723144\pi$$
0.984301 + 0.176500i $$0.0564774\pi$$
$$368$$ −3.50000 + 6.06218i −0.182450 + 0.316013i
$$369$$ 4.50000 + 7.79423i 0.234261 + 0.405751i
$$370$$ 0 0
$$371$$ −4.50000 23.3827i −0.233628 1.21397i
$$372$$ 0 0
$$373$$ 13.0000 + 22.5167i 0.673114 + 1.16587i 0.977016 + 0.213165i $$0.0683772\pi$$
−0.303902 + 0.952703i $$0.598289\pi$$
$$374$$ 3.00000 5.19615i 0.155126 0.268687i
$$375$$ 0 0
$$376$$ 3.50000 + 6.06218i 0.180499 + 0.312633i
$$377$$ −20.0000 −1.03005
$$378$$ 0 0
$$379$$ −29.0000 −1.48963 −0.744815 0.667271i $$-0.767462\pi$$
−0.744815 + 0.667271i $$0.767462\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ −10.0000 + 17.3205i −0.511645 + 0.886194i
$$383$$ 10.5000 + 18.1865i 0.536525 + 0.929288i 0.999088 + 0.0427020i $$0.0135966\pi$$
−0.462563 + 0.886586i $$0.653070\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ −10.0000 −0.508987
$$387$$ −3.00000 5.19615i −0.152499 0.264135i
$$388$$ −6.00000 + 10.3923i −0.304604 + 0.527589i
$$389$$ 3.00000 5.19615i 0.152106 0.263455i −0.779895 0.625910i $$-0.784728\pi$$
0.932002 + 0.362454i $$0.118061\pi$$
$$390$$ 0 0
$$391$$ 14.0000 0.708010
$$392$$ −1.00000 + 6.92820i −0.0505076 + 0.349927i
$$393$$ 0 0
$$394$$ 2.50000 + 4.33013i 0.125948 + 0.218149i
$$395$$ 0 0
$$396$$ 4.50000 7.79423i 0.226134 0.391675i
$$397$$ −7.00000 12.1244i −0.351320 0.608504i 0.635161 0.772380i $$-0.280934\pi$$
−0.986481 + 0.163876i $$0.947600\pi$$
$$398$$ −18.0000 −0.902258
$$399$$ 0 0
$$400$$ 0 0
$$401$$ 7.50000 + 12.9904i 0.374532 + 0.648709i 0.990257 0.139253i $$-0.0444700\pi$$
−0.615725 + 0.787961i $$0.711137\pi$$
$$402$$ 0 0
$$403$$ 5.00000 8.66025i 0.249068 0.431398i
$$404$$ 0 0
$$405$$ 0 0
$$406$$ −10.0000 3.46410i −0.496292 0.171920i
$$407$$ −3.00000 −0.148704
$$408$$ 0 0
$$409$$ 7.00000 12.1244i 0.346128 0.599511i −0.639430 0.768849i $$-0.720830\pi$$
0.985558 + 0.169338i $$0.0541630\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 8.00000 0.394132
$$413$$ −2.00000 10.3923i −0.0984136 0.511372i
$$414$$ 21.0000 1.03209
$$415$$ 0 0
$$416$$ 2.50000 4.33013i 0.122573 0.212302i
$$417$$ 0 0
$$418$$ −7.50000 12.9904i −0.366837 0.635380i
$$419$$ 35.0000 1.70986 0.854931 0.518742i $$-0.173599\pi$$
0.854931 + 0.518742i $$0.173599\pi$$
$$420$$ 0 0
$$421$$ −20.0000 −0.974740 −0.487370 0.873195i $$-0.662044\pi$$
−0.487370 + 0.873195i $$0.662044\pi$$
$$422$$ −4.50000 7.79423i −0.219057 0.379417i
$$423$$ 10.5000 18.1865i 0.510527 0.884260i
$$424$$ −4.50000 + 7.79423i −0.218539 + 0.378521i
$$425$$ 0 0
$$426$$ 0 0
$$427$$ −15.0000 5.19615i −0.725901 0.251459i
$$428$$ 16.0000 0.773389
$$429$$ 0 0
$$430$$ 0 0
$$431$$ −1.00000 + 1.73205i −0.0481683 + 0.0834300i −0.889104 0.457705i $$-0.848672\pi$$
0.840936 + 0.541135i $$0.182005\pi$$
$$432$$ 0 0
$$433$$ −28.0000 −1.34559 −0.672797 0.739827i $$-0.734907\pi$$
−0.672797 + 0.739827i $$0.734907\pi$$
$$434$$ 4.00000 3.46410i 0.192006 0.166282i
$$435$$ 0 0
$$436$$ −1.00000 1.73205i −0.0478913 0.0829502i
$$437$$ 17.5000 30.3109i 0.837139 1.44997i
$$438$$ 0 0
$$439$$ 14.0000 + 24.2487i 0.668184 + 1.15733i 0.978412 + 0.206666i $$0.0662612\pi$$
−0.310228 + 0.950662i $$0.600405\pi$$
$$440$$ 0 0
$$441$$ 19.5000 7.79423i 0.928571 0.371154i
$$442$$ −10.0000 −0.475651
$$443$$ 15.0000 + 25.9808i 0.712672 + 1.23438i 0.963851 + 0.266443i $$0.0858483\pi$$
−0.251179 + 0.967941i $$0.580818\pi$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ 4.00000 + 6.92820i 0.189405 + 0.328060i
$$447$$ 0 0
$$448$$ 2.00000 1.73205i 0.0944911 0.0818317i
$$449$$ 5.00000 0.235965 0.117982 0.993016i $$-0.462357\pi$$
0.117982 + 0.993016i $$0.462357\pi$$
$$450$$ 0 0
$$451$$ −4.50000 + 7.79423i −0.211897 + 0.367016i
$$452$$ 7.00000 12.1244i 0.329252 0.570282i
$$453$$ 0 0
$$454$$ −6.00000 −0.281594
$$455$$ 0 0
$$456$$ 0 0
$$457$$ −5.00000 8.66025i −0.233890 0.405110i 0.725059 0.688686i $$-0.241812\pi$$
−0.958950 + 0.283577i $$0.908479\pi$$
$$458$$ 8.00000 13.8564i 0.373815 0.647467i
$$459$$ 0 0
$$460$$ 0 0
$$461$$ −32.0000 −1.49039 −0.745194 0.666847i $$-0.767643\pi$$
−0.745194 + 0.666847i $$0.767643\pi$$
$$462$$ 0 0
$$463$$ 17.0000 0.790057 0.395029 0.918669i $$-0.370735\pi$$
0.395029 + 0.918669i $$0.370735\pi$$
$$464$$ 2.00000 + 3.46410i 0.0928477 + 0.160817i
$$465$$ 0 0
$$466$$ 4.00000 6.92820i 0.185296 0.320943i
$$467$$ 17.0000 + 29.4449i 0.786666 + 1.36255i 0.927999 + 0.372584i $$0.121528\pi$$
−0.141332 + 0.989962i $$0.545139\pi$$
$$468$$ −15.0000 −0.693375
$$469$$ −1.00000 5.19615i −0.0461757 0.239936i
$$470$$ 0 0
$$471$$ 0 0
$$472$$ −2.00000 + 3.46410i −0.0920575 + 0.159448i
$$473$$ 3.00000 5.19615i 0.137940 0.238919i
$$474$$ 0 0
$$475$$ 0 0
$$476$$ −5.00000 1.73205i −0.229175 0.0793884i
$$477$$ 27.0000 1.23625
$$478$$ 10.0000 + 17.3205i 0.457389 + 0.792222i
$$479$$ −18.0000 + 31.1769i −0.822441 + 1.42451i 0.0814184 + 0.996680i $$0.474055\pi$$
−0.903859 + 0.427830i $$0.859278\pi$$
$$480$$ 0 0
$$481$$ 2.50000 + 4.33013i 0.113990 + 0.197437i
$$482$$ 9.00000 0.409939
$$483$$ 0 0
$$484$$ −2.00000 −0.0909091
$$485$$ 0 0
$$486$$ 0 0
$$487$$ −16.0000 + 27.7128i −0.725029 + 1.25579i 0.233933 + 0.972253i $$0.424840\pi$$
−0.958962 + 0.283535i $$0.908493\pi$$
$$488$$ 3.00000 + 5.19615i 0.135804 + 0.235219i
$$489$$ 0 0
$$490$$ 0 0
$$491$$ 24.0000 1.08310 0.541552 0.840667i $$-0.317837\pi$$
0.541552 + 0.840667i $$0.317837\pi$$
$$492$$ 0 0
$$493$$ 4.00000 6.92820i 0.180151 0.312031i
$$494$$ −12.5000 + 21.6506i −0.562402 + 0.974108i
$$495$$ 0 0
$$496$$ −2.00000 −0.0898027
$$497$$ −12.0000 + 10.3923i −0.538274 + 0.466159i
$$498$$ 0 0
$$499$$ −2.00000 3.46410i −0.0895323 0.155074i 0.817781 0.575529i $$-0.195204\pi$$
−0.907314 + 0.420455i $$0.861871\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 2.50000 + 4.33013i 0.111580 + 0.193263i
$$503$$ −40.0000 −1.78351 −0.891756 0.452517i $$-0.850526\pi$$
−0.891756 + 0.452517i $$0.850526\pi$$
$$504$$ −7.50000 2.59808i −0.334077 0.115728i
$$505$$ 0 0
$$506$$ 10.5000 + 18.1865i 0.466782 + 0.808490i
$$507$$ 0 0
$$508$$ 3.50000 6.06218i 0.155287 0.268966i
$$509$$ 17.0000 + 29.4449i 0.753512 + 1.30512i 0.946111 + 0.323843i $$0.104975\pi$$
−0.192599 + 0.981278i $$0.561692\pi$$
$$510$$ 0 0
$$511$$ 8.00000 + 41.5692i 0.353899 + 1.83891i
$$512$$ −1.00000 −0.0441942
$$513$$ 0 0
$$514$$ 3.00000 5.19615i 0.132324 0.229192i
$$515$$ 0 0
$$516$$ 0 0
$$517$$ 21.0000 0.923579
$$518$$ 0.500000 + 2.59808i 0.0219687 + 0.114153i
$$519$$ 0 0
$$520$$ 0 0
$$521$$ 13.5000 23.3827i 0.591446 1.02441i −0.402592 0.915379i $$-0.631891\pi$$
0.994038 0.109035i $$-0.0347759\pi$$
$$522$$ 6.00000 10.3923i 0.262613 0.454859i
$$523$$ 8.00000 + 13.8564i 0.349816 + 0.605898i 0.986216 0.165460i $$-0.0529109\pi$$
−0.636401 + 0.771358i $$0.719578\pi$$
$$524$$ −1.00000 −0.0436852
$$525$$ 0 0
$$526$$ 0 0
$$527$$ 2.00000 + 3.46410i 0.0871214 + 0.150899i
$$528$$ 0 0
$$529$$ −13.0000 + 22.5167i −0.565217 + 0.978985i
$$530$$ 0 0
$$531$$ 12.0000 0.520756
$$532$$ −10.0000 + 8.66025i −0.433555 + 0.375470i
$$533$$ 15.0000 0.649722
$$534$$ 0 0
$$535$$ 0 0
$$536$$ −1.00000 + 1.73205i −0.0431934 + 0.0748132i
$$537$$ 0 0
$$538$$ 10.0000 0.431131
$$539$$ 16.5000 + 12.9904i 0.710705 + 0.559535i
$$540$$ 0 0
$$541$$ 8.00000 + 13.8564i 0.343947 + 0.595733i 0.985162 0.171628i $$-0.0549027\pi$$
−0.641215 + 0.767361i $$0.721569\pi$$
$$542$$ 12.0000 20.7846i 0.515444 0.892775i
$$543$$ 0 0
$$544$$ 1.00000 + 1.73205i 0.0428746 + 0.0742611i
$$545$$ 0 0
$$546$$ 0 0
$$547$$ 26.0000 1.11168 0.555840 0.831289i $$-0.312397\pi$$
0.555840 + 0.831289i $$0.312397\pi$$
$$548$$ −4.00000 6.92820i −0.170872 0.295958i
$$549$$ 9.00000 15.5885i 0.384111 0.665299i
$$550$$ 0 0
$$551$$ −10.0000 17.3205i −0.426014 0.737878i
$$552$$ 0 0
$$553$$ −35.0000 12.1244i −1.48835 0.515580i
$$554$$ −2.00000 −0.0849719
$$555$$ 0 0
$$556$$ −8.00000 + 13.8564i −0.339276 + 0.587643i
$$557$$ 11.5000 19.9186i 0.487271 0.843978i −0.512622 0.858614i $$-0.671326\pi$$
0.999893 + 0.0146368i $$0.00465919\pi$$
$$558$$ 3.00000 + 5.19615i 0.127000 + 0.219971i
$$559$$ −10.0000 −0.422955
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 4.50000 + 7.79423i 0.189821 + 0.328780i
$$563$$ 1.00000 1.73205i 0.0421450 0.0729972i −0.844183 0.536054i $$-0.819914\pi$$
0.886328 + 0.463057i $$0.153248\pi$$
$$564$$ 0 0
$$565$$ 0 0
$$566$$ 14.0000 0.588464
$$567$$ 4.50000 + 23.3827i 0.188982 + 0.981981i
$$568$$ 6.00000 0.251754
$$569$$ 7.50000 + 12.9904i 0.314416 + 0.544585i 0.979313 0.202350i $$-0.0648579\pi$$
−0.664897 + 0.746935i $$0.731525\pi$$
$$570$$ 0 0
$$571$$ −16.0000 + 27.7128i −0.669579 + 1.15975i 0.308443 + 0.951243i $$0.400192\pi$$
−0.978022 + 0.208502i $$0.933141\pi$$
$$572$$ −7.50000 12.9904i −0.313591 0.543155i
$$573$$ 0 0
$$574$$ 7.50000 + 2.59808i 0.313044 + 0.108442i
$$575$$ 0 0
$$576$$ 1.50000 + 2.59808i 0.0625000 + 0.108253i
$$577$$ −2.00000 + 3.46410i −0.0832611 + 0.144212i −0.904649 0.426158i $$-0.859867\pi$$
0.821388 + 0.570370i $$0.193200\pi$$
$$578$$ −6.50000 + 11.2583i −0.270364 + 0.468285i
$$579$$ 0 0
$$580$$ 0 0
$$581$$ 12.0000 10.3923i 0.497844 0.431145i
$$582$$ 0 0
$$583$$ 13.5000 + 23.3827i 0.559113 + 0.968412i
$$584$$ 8.00000 13.8564i 0.331042 0.573382i
$$585$$ 0 0
$$586$$ 4.50000 + 7.79423i 0.185893 + 0.321977i
$$587$$ −34.0000 −1.40333 −0.701665 0.712507i $$-0.747560\pi$$
−0.701665 + 0.712507i $$0.747560\pi$$
$$588$$ 0 0
$$589$$ 10.0000 0.412043
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 0.500000 0.866025i 0.0205499 0.0355934i
$$593$$ −3.00000 5.19615i −0.123195 0.213380i 0.797831 0.602881i $$-0.205981\pi$$
−0.921026 + 0.389501i $$0.872647\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ −18.0000 −0.737309
$$597$$ 0 0
$$598$$ 17.5000 30.3109i 0.715628 1.23950i
$$599$$ 6.00000 10.3923i 0.245153 0.424618i −0.717021 0.697051i $$-0.754495\pi$$
0.962175 + 0.272433i $$0.0878284\pi$$
$$600$$ 0 0
$$601$$ −22.0000 −0.897399 −0.448699 0.893683i $$-0.648113\pi$$
−0.448699 + 0.893683i $$0.648113\pi$$
$$602$$ −5.00000 1.73205i −0.203785 0.0705931i
$$603$$ 6.00000 0.244339
$$604$$ 3.00000 + 5.19615i 0.122068 + 0.211428i
$$605$$ 0 0
$$606$$ 0 0
$$607$$ −6.50000 11.2583i −0.263827 0.456962i 0.703429 0.710766i $$-0.251651\pi$$
−0.967256 + 0.253804i $$0.918318\pi$$
$$608$$ 5.00000 0.202777
$$609$$ 0 0
$$610$$ 0 0
$$611$$ −17.5000 30.3109i −0.707974 1.22625i
$$612$$ 3.00000 5.19615i 0.121268 0.210042i
$$613$$ −7.50000 + 12.9904i −0.302922 + 0.524677i −0.976797 0.214169i $$-0.931296\pi$$
0.673874 + 0.738846i $$0.264629\pi$$
$$614$$ 11.0000 + 19.0526i 0.443924 + 0.768899i
$$615$$ 0 0
$$616$$ −1.50000 7.79423i −0.0604367 0.314038i
$$617$$ −14.0000 −0.563619 −0.281809 0.959470i $$-0.590935\pi$$
−0.281809 + 0.959470i $$0.590935\pi$$
$$618$$ 0 0
$$619$$ −9.50000 + 16.4545i −0.381837 + 0.661361i −0.991325 0.131434i $$-0.958042\pi$$
0.609488 + 0.792796i $$0.291375\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ −6.00000 −0.240578
$$623$$ −5.00000 1.73205i −0.200321 0.0693932i
$$624$$ 0 0
$$625$$ 0 0
$$626$$ 11.0000 19.0526i 0.439648 0.761493i
$$627$$ 0 0
$$628$$ −4.50000 7.79423i −0.179570 0.311024i
$$629$$ −2.00000 −0.0797452
$$630$$ 0 0
$$631$$ −18.0000 −0.716569 −0.358284 0.933613i $$-0.616638\pi$$
−0.358284 + 0.933613i $$0.616638\pi$$
$$632$$ 7.00000 + 12.1244i 0.278445 + 0.482281i
$$633$$ 0 0
$$634$$ 1.00000 1.73205i 0.0397151 0.0687885i
$$635$$ 0 0
$$636$$ 0 0
$$637$$ 5.00000 34.6410i 0.198107 1.37253i
$$638$$ 12.0000 0.475085
$$639$$ −9.00000 15.5885i −0.356034 0.616670i
$$640$$ 0 0
$$641$$ 2.50000 4.33013i 0.0987441 0.171030i −0.812421 0.583071i $$-0.801851\pi$$
0.911165 + 0.412042i $$0.135184\pi$$
$$642$$ 0 0
$$643$$ 14.0000 0.552106 0.276053 0.961142i $$-0.410973\pi$$
0.276053 + 0.961142i $$0.410973\pi$$
$$644$$ 14.0000 12.1244i 0.551677 0.477767i
$$645$$ 0 0
$$646$$ −5.00000 8.66025i −0.196722 0.340733i
$$647$$ −13.5000 + 23.3827i −0.530740 + 0.919268i 0.468617 + 0.883402i $$0.344753\pi$$
−0.999357 + 0.0358667i $$0.988581\pi$$
$$648$$ 4.50000 7.79423i 0.176777 0.306186i
$$649$$ 6.00000 + 10.3923i 0.235521 + 0.407934i
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 12.0000 0.469956
$$653$$ 1.50000 + 2.59808i 0.0586995 + 0.101671i 0.893882 0.448303i $$-0.147971\pi$$
−0.835182 + 0.549973i $$0.814638\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ −1.50000 2.59808i −0.0585652 0.101438i
$$657$$ −48.0000 −1.87266
$$658$$ −3.50000 18.1865i −0.136444 0.708985i
$$659$$ −36.0000 −1.40236 −0.701180 0.712984i $$-0.747343\pi$$
−0.701180 + 0.712984i $$0.747343\pi$$
$$660$$ 0 0
$$661$$ −8.00000 + 13.8564i −0.311164 + 0.538952i −0.978615 0.205702i $$-0.934052\pi$$
0.667451 + 0.744654i $$0.267385\pi$$
$$662$$ 2.50000 4.33013i 0.0971653 0.168295i
$$663$$ 0 0
$$664$$ −6.00000 −0.232845
$$665$$ 0 0
$$666$$ −3.00000 −0.116248
$$667$$ 14.0000 + 24.2487i 0.542082 + 0.938914i
$$668$$ 7.50000 12.9904i 0.290184 0.502613i
$$669$$ 0 0
$$670$$ 0 0
$$671$$ 18.0000 0.694882
$$672$$ 0 0
$$673$$ −32.0000 −1.23351 −0.616755 0.787155i $$-0.711553\pi$$
−0.616755 + 0.787155i $$0.711553\pi$$
$$674$$ −5.00000 8.66025i −0.192593 0.333581i
$$675$$ 0 0
$$676$$ −6.00000 + 10.3923i −0.230769 + 0.399704i
$$677$$ −8.50000 14.7224i −0.326682 0.565829i 0.655170 0.755482i $$-0.272597\pi$$
−0.981851 + 0.189653i $$0.939264\pi$$
$$678$$ 0 0
$$679$$ 24.0000 20.7846i 0.921035 0.797640i
$$680$$ 0 0
$$681$$ 0 0
$$682$$ −3.00000 + 5.19615i −0.114876 + 0.198971i
$$683$$ −22.0000 + 38.1051i −0.841807 + 1.45805i 0.0465592 + 0.998916i $$0.485174\pi$$
−0.888366 + 0.459136i $$0.848159\pi$$
$$684$$ −7.50000 12.9904i −0.286770 0.496700i
$$685$$ 0 0
$$686$$ 8.50000 16.4545i 0.324532 0.628235i
$$687$$ 0 0
$$688$$ 1.00000 + 1.73205i 0.0381246 + 0.0660338i
$$689$$ 22.5000 38.9711i 0.857182 1.48468i
$$690$$ 0 0
$$691$$ 22.0000 + 38.1051i 0.836919 + 1.44959i 0.892458 + 0.451130i $$0.148979\pi$$
−0.0555386 + 0.998457i $$0.517688\pi$$
$$692$$ −9.00000 −0.342129
$$693$$ −18.0000 + 15.5885i −0.683763 + 0.592157i
$$694$$ −12.0000 −0.455514
$$695$$ 0 0
$$696$$ 0 0
$$697$$ −3.00000 + 5.19615i −0.113633 + 0.196818i
$$698$$ −6.00000 10.3923i −0.227103 0.393355i
$$699$$ 0 0
$$700$$ 0 0
$$701$$ 26.0000 0.982006 0.491003 0.871158i $$-0.336630\pi$$
0.491003 + 0.871158i $$0.336630\pi$$
$$702$$ 0 0
$$703$$ −2.50000 + 4.33013i −0.0942893 + 0.163314i
$$704$$ −1.50000 + 2.59808i −0.0565334 + 0.0979187i
$$705$$ 0 0
$$706$$ 24.0000 0.903252
$$707$$ 0 0
$$708$$ 0 0
$$709$$ −6.00000 10.3923i −0.225335 0.390291i 0.731085 0.682286i $$-0.239014\pi$$
−0.956420 + 0.291995i $$0.905681\pi$$
$$710$$ 0 0
$$711$$ 21.0000 36.3731i 0.787562 1.36410i
$$712$$ 1.00000 + 1.73205i 0.0374766 + 0.0649113i
$$713$$ −14.0000 −0.524304
$$714$$ 0 0
$$715$$ 0 0
$$716$$ −6.50000 11.2583i −0.242916 0.420744i
$$717$$ 0 0
$$718$$ 8.00000 13.8564i 0.298557 0.517116i
$$719$$ −13.0000 22.5167i −0.484818 0.839730i 0.515030 0.857172i $$-0.327781\pi$$
−0.999848 + 0.0174426i $$0.994448\pi$$
$$720$$ 0 0
$$721$$ −20.0000 6.92820i −0.744839 0.258020i
$$722$$ −6.00000 −0.223297
$$723$$ 0 0
$$724$$ −13.0000 + 22.5167i −0.483141 + 0.836825i
$$725$$ 0 0
$$726$$ 0 0
$$727$$ 29.0000 1.07555 0.537775 0.843088i $$-0.319265\pi$$
0.537775 + 0.843088i $$0.319265\pi$$
$$728$$ −10.0000 + 8.66025i −0.370625 + 0.320970i
$$729$$ −27.0000 −1.00000
$$730$$ 0 0
$$731$$ 2.00000 3.46410i 0.0739727 0.128124i
$$732$$ 0 0
$$733$$ 20.5000 + 35.5070i 0.757185 + 1.31148i 0.944281 + 0.329141i $$0.106759\pi$$
−0.187096 + 0.982342i $$0.559908\pi$$
$$734$$ 13.0000 0.479839
$$735$$ 0 0
$$736$$ −7.00000 −0.258023
$$737$$ 3.00000 + 5.19615i 0.110506 + 0.191403i
$$738$$ −4.50000 + 7.79423i −0.165647 + 0.286910i
$$739$$ 14.5000 25.1147i 0.533391 0.923861i −0.465848 0.884865i $$-0.654251\pi$$
0.999239 0.0389959i $$-0.0124159\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 18.0000 15.5885i 0.660801 0.572270i
$$743$$ 21.0000 0.770415 0.385208 0.922830i $$-0.374130\pi$$
0.385208 + 0.922830i $$0.374130\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ −13.0000 + 22.5167i −0.475964 + 0.824394i
$$747$$ 9.00000 + 15.5885i 0.329293 + 0.570352i
$$748$$ 6.00000 0.219382
$$749$$ −40.0000 13.8564i −1.46157 0.506302i
$$750$$ 0 0
$$751$$ −14.0000 24.2487i −0.510867 0.884848i −0.999921 0.0125942i $$-0.995991\pi$$
0.489053 0.872254i $$-0.337342\pi$$
$$752$$ −3.50000 + 6.06218i −0.127632 + 0.221065i
$$753$$ 0 0
$$754$$ −10.0000 17.3205i −0.364179 0.630776i
$$755$$ 0 0
$$756$$ 0 0
$$757$$ −42.0000 −1.52652 −0.763258 0.646094i $$-0.776401\pi$$
−0.763258 + 0.646094i $$0.776401\pi$$
$$758$$ −14.5000 25.1147i −0.526664 0.912208i
$$759$$ 0 0
$$760$$ 0 0
$$761$$ −0.500000 0.866025i −0.0181250 0.0313934i 0.856821 0.515615i $$-0.172436\pi$$
−0.874946 + 0.484221i $$0.839103\pi$$
$$762$$ 0 0
$$763$$ 1.00000 + 5.19615i 0.0362024 + 0.188113i
$$764$$ −20.0000 −0.723575
$$765$$ 0 0
$$766$$ −10.5000 + 18.1865i −0.379380 + 0.657106i
$$767$$ 10.0000 17.3205i 0.361079 0.625407i
$$768$$ 0 0
$$769$$ −29.0000 −1.04577 −0.522883 0.852404i $$-0.675144\pi$$
−0.522883 + 0.852404i $$0.675144\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ −5.00000 8.66025i −0.179954 0.311689i
$$773$$ 22.5000 38.9711i 0.809269 1.40169i −0.104102 0.994567i $$-0.533197\pi$$
0.913371 0.407128i $$-0.133470\pi$$
$$774$$ 3.00000 5.19615i 0.107833 0.186772i
$$775$$ 0 0
$$776$$ −12.0000 −0.430775
$$777$$ 0 0
$$778$$ 6.00000 0.215110
$$779$$ 7.50000 + 12.9904i 0.268715 + 0.465429i
$$780$$ 0 0
$$781$$ 9.00000 15.5885i 0.322045 0.557799i
$$782$$ 7.00000 + 12.1244i 0.250319 + 0.433566i
$$783$$ 0 0
$$784$$ −6.50000 + 2.59808i −0.232143 + 0.0927884i
$$785$$ 0 0
$$786$$ 0 0
$$787$$ 9.00000 15.5885i 0.320815 0.555668i −0.659841 0.751405i $$-0.729376\pi$$
0.980656 + 0.195737i $$0.0627098\pi$$
$$788$$ −2.50000 + 4.33013i −0.0890588 + 0.154254i
$$789$$ 0 0
$$790$$ 0