# Properties

 Label 490.2.i.f.459.3 Level $490$ Weight $2$ Character 490.459 Analytic conductor $3.913$ Analytic rank $0$ Dimension $8$ CM no Inner twists $4$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$490 = 2 \cdot 5 \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 490.i (of order $$6$$, degree $$2$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$3.91266969904$$ Analytic rank: $$0$$ Dimension: $$8$$ Relative dimension: $$4$$ over $$\Q(\zeta_{6})$$ Coefficient field: $$\Q(\zeta_{24})$$ Defining polynomial: $$x^{8} - x^{4} + 1$$ x^8 - x^4 + 1 Coefficient ring: $$\Z[a_1, \ldots, a_{5}]$$ Coefficient ring index: $$3^{2}$$ Twist minimal: no (minimal twist has level 70) Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

## Embedding invariants

 Embedding label 459.3 Root $$-0.258819 + 0.965926i$$ of defining polynomial Character $$\chi$$ $$=$$ 490.459 Dual form 490.2.i.f.79.3

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(0.866025 - 0.500000i) q^{2} +(-2.12132 - 1.22474i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.917738 + 2.03906i) q^{5} -2.44949 q^{6} -1.00000i q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})$$ $$q+(0.866025 - 0.500000i) q^{2} +(-2.12132 - 1.22474i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.917738 + 2.03906i) q^{5} -2.44949 q^{6} -1.00000i q^{8} +(1.50000 + 2.59808i) q^{9} +(1.81431 + 1.30701i) q^{10} +(2.44949 - 4.24264i) q^{11} +(-2.12132 + 1.22474i) q^{12} -4.44949i q^{13} +(0.550510 - 5.44949i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.73205 - 1.00000i) q^{17} +(2.59808 + 1.50000i) q^{18} +(-0.775255 - 1.34278i) q^{19} +(2.22474 + 0.224745i) q^{20} -4.89898i q^{22} +(2.51059 - 1.44949i) q^{23} +(-1.22474 + 2.12132i) q^{24} +(-3.31552 + 3.74264i) q^{25} +(-2.22474 - 3.85337i) q^{26} -6.89898 q^{29} +(-2.24799 - 4.99465i) q^{30} +(4.44949 - 7.70674i) q^{31} +(-0.866025 - 0.500000i) q^{32} +(-10.3923 + 6.00000i) q^{33} -2.00000 q^{34} +3.00000 q^{36} +(-1.73205 + 1.00000i) q^{37} +(-1.34278 - 0.775255i) q^{38} +(-5.44949 + 9.43879i) q^{39} +(2.03906 - 0.917738i) q^{40} +1.10102 q^{41} -0.898979i q^{43} +(-2.44949 - 4.24264i) q^{44} +(-3.92102 + 5.44294i) q^{45} +(1.44949 - 2.51059i) q^{46} +(7.70674 - 4.44949i) q^{47} +2.44949i q^{48} +(-1.00000 + 4.89898i) q^{50} +(2.44949 + 4.24264i) q^{51} +(-3.85337 - 2.22474i) q^{52} +(9.43879 + 5.44949i) q^{53} +(10.8990 + 1.10102i) q^{55} +3.79796i q^{57} +(-5.97469 + 3.44949i) q^{58} +(0.775255 - 1.34278i) q^{59} +(-4.44414 - 3.20150i) q^{60} +(1.77526 + 3.07483i) q^{61} -8.89898i q^{62} -1.00000 q^{64} +(9.07277 - 4.08346i) q^{65} +(-6.00000 + 10.3923i) q^{66} +(-6.92820 - 4.00000i) q^{67} +(-1.73205 + 1.00000i) q^{68} -7.10102 q^{69} -1.10102 q^{71} +(2.59808 - 1.50000i) q^{72} +(2.51059 + 1.44949i) q^{73} +(-1.00000 + 1.73205i) q^{74} +(11.6170 - 3.87868i) q^{75} -1.55051 q^{76} +10.8990i q^{78} +(3.44949 + 5.97469i) q^{79} +(1.30701 - 1.81431i) q^{80} +(4.50000 - 7.79423i) q^{81} +(0.953512 - 0.550510i) q^{82} +2.44949i q^{83} +(0.449490 - 4.44949i) q^{85} +(-0.449490 - 0.778539i) q^{86} +(14.6349 + 8.44949i) q^{87} +(-4.24264 - 2.44949i) q^{88} +(5.00000 + 8.66025i) q^{89} +(-0.674235 + 6.67423i) q^{90} -2.89898i q^{92} +(-18.8776 + 10.8990i) q^{93} +(4.44949 - 7.70674i) q^{94} +(2.02653 - 2.81311i) q^{95} +(1.22474 + 2.12132i) q^{96} +15.7980i q^{97} +14.6969 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$8 q + 4 q^{4} + 4 q^{5} + 12 q^{9}+O(q^{10})$$ 8 * q + 4 * q^4 + 4 * q^5 + 12 * q^9 $$8 q + 4 q^{4} + 4 q^{5} + 12 q^{9} + 4 q^{10} + 24 q^{15} - 4 q^{16} - 16 q^{19} + 8 q^{20} - 8 q^{26} - 16 q^{29} - 12 q^{30} + 16 q^{31} - 16 q^{34} + 24 q^{36} - 24 q^{39} - 4 q^{40} + 48 q^{41} - 12 q^{45} - 8 q^{46} - 8 q^{50} + 48 q^{55} + 16 q^{59} + 12 q^{60} + 24 q^{61} - 8 q^{64} + 4 q^{65} - 48 q^{66} - 96 q^{69} - 48 q^{71} - 8 q^{74} - 32 q^{76} + 8 q^{79} + 4 q^{80} + 36 q^{81} - 16 q^{85} + 16 q^{86} + 40 q^{89} + 24 q^{90} + 16 q^{94} + 4 q^{95}+O(q^{100})$$ 8 * q + 4 * q^4 + 4 * q^5 + 12 * q^9 + 4 * q^10 + 24 * q^15 - 4 * q^16 - 16 * q^19 + 8 * q^20 - 8 * q^26 - 16 * q^29 - 12 * q^30 + 16 * q^31 - 16 * q^34 + 24 * q^36 - 24 * q^39 - 4 * q^40 + 48 * q^41 - 12 * q^45 - 8 * q^46 - 8 * q^50 + 48 * q^55 + 16 * q^59 + 12 * q^60 + 24 * q^61 - 8 * q^64 + 4 * q^65 - 48 * q^66 - 96 * q^69 - 48 * q^71 - 8 * q^74 - 32 * q^76 + 8 * q^79 + 4 * q^80 + 36 * q^81 - 16 * q^85 + 16 * q^86 + 40 * q^89 + 24 * q^90 + 16 * q^94 + 4 * q^95

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/490\mathbb{Z}\right)^\times$$.

 $$n$$ $$101$$ $$197$$ $$\chi(n)$$ $$e\left(\frac{2}{3}\right)$$ $$-1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0.866025 0.500000i 0.612372 0.353553i
$$3$$ −2.12132 1.22474i −1.22474 0.707107i −0.258819 0.965926i $$-0.583333\pi$$
−0.965926 + 0.258819i $$0.916667\pi$$
$$4$$ 0.500000 0.866025i 0.250000 0.433013i
$$5$$ 0.917738 + 2.03906i 0.410425 + 0.911894i
$$6$$ −2.44949 −1.00000
$$7$$ 0 0
$$8$$ 1.00000i 0.353553i
$$9$$ 1.50000 + 2.59808i 0.500000 + 0.866025i
$$10$$ 1.81431 + 1.30701i 0.573736 + 0.413312i
$$11$$ 2.44949 4.24264i 0.738549 1.27920i −0.214600 0.976702i $$-0.568845\pi$$
0.953149 0.302502i $$-0.0978220\pi$$
$$12$$ −2.12132 + 1.22474i −0.612372 + 0.353553i
$$13$$ 4.44949i 1.23407i −0.786937 0.617033i $$-0.788334\pi$$
0.786937 0.617033i $$-0.211666\pi$$
$$14$$ 0 0
$$15$$ 0.550510 5.44949i 0.142141 1.40705i
$$16$$ −0.500000 0.866025i −0.125000 0.216506i
$$17$$ −1.73205 1.00000i −0.420084 0.242536i 0.275029 0.961436i $$-0.411312\pi$$
−0.695113 + 0.718900i $$0.744646\pi$$
$$18$$ 2.59808 + 1.50000i 0.612372 + 0.353553i
$$19$$ −0.775255 1.34278i −0.177856 0.308055i 0.763290 0.646056i $$-0.223583\pi$$
−0.941146 + 0.338001i $$0.890249\pi$$
$$20$$ 2.22474 + 0.224745i 0.497468 + 0.0502545i
$$21$$ 0 0
$$22$$ 4.89898i 1.04447i
$$23$$ 2.51059 1.44949i 0.523494 0.302240i −0.214869 0.976643i $$-0.568932\pi$$
0.738363 + 0.674403i $$0.235599\pi$$
$$24$$ −1.22474 + 2.12132i −0.250000 + 0.433013i
$$25$$ −3.31552 + 3.74264i −0.663103 + 0.748528i
$$26$$ −2.22474 3.85337i −0.436308 0.755708i
$$27$$ 0 0
$$28$$ 0 0
$$29$$ −6.89898 −1.28111 −0.640554 0.767913i $$-0.721295\pi$$
−0.640554 + 0.767913i $$0.721295\pi$$
$$30$$ −2.24799 4.99465i −0.410425 0.911894i
$$31$$ 4.44949 7.70674i 0.799152 1.38417i −0.121017 0.992650i $$-0.538616\pi$$
0.920169 0.391521i $$-0.128051\pi$$
$$32$$ −0.866025 0.500000i −0.153093 0.0883883i
$$33$$ −10.3923 + 6.00000i −1.80907 + 1.04447i
$$34$$ −2.00000 −0.342997
$$35$$ 0 0
$$36$$ 3.00000 0.500000
$$37$$ −1.73205 + 1.00000i −0.284747 + 0.164399i −0.635571 0.772043i $$-0.719235\pi$$
0.350823 + 0.936442i $$0.385902\pi$$
$$38$$ −1.34278 0.775255i −0.217828 0.125763i
$$39$$ −5.44949 + 9.43879i −0.872617 + 1.51142i
$$40$$ 2.03906 0.917738i 0.322403 0.145107i
$$41$$ 1.10102 0.171951 0.0859753 0.996297i $$-0.472599\pi$$
0.0859753 + 0.996297i $$0.472599\pi$$
$$42$$ 0 0
$$43$$ 0.898979i 0.137093i −0.997648 0.0685465i $$-0.978164\pi$$
0.997648 0.0685465i $$-0.0218362\pi$$
$$44$$ −2.44949 4.24264i −0.369274 0.639602i
$$45$$ −3.92102 + 5.44294i −0.584511 + 0.811386i
$$46$$ 1.44949 2.51059i 0.213716 0.370166i
$$47$$ 7.70674 4.44949i 1.12414 0.649025i 0.181688 0.983356i $$-0.441844\pi$$
0.942456 + 0.334331i $$0.108510\pi$$
$$48$$ 2.44949i 0.353553i
$$49$$ 0 0
$$50$$ −1.00000 + 4.89898i −0.141421 + 0.692820i
$$51$$ 2.44949 + 4.24264i 0.342997 + 0.594089i
$$52$$ −3.85337 2.22474i −0.534366 0.308517i
$$53$$ 9.43879 + 5.44949i 1.29652 + 0.748545i 0.979801 0.199975i $$-0.0640861\pi$$
0.316717 + 0.948520i $$0.397419\pi$$
$$54$$ 0 0
$$55$$ 10.8990 + 1.10102i 1.46962 + 0.148462i
$$56$$ 0 0
$$57$$ 3.79796i 0.503052i
$$58$$ −5.97469 + 3.44949i −0.784515 + 0.452940i
$$59$$ 0.775255 1.34278i 0.100930 0.174815i −0.811138 0.584854i $$-0.801152\pi$$
0.912068 + 0.410039i $$0.134485\pi$$
$$60$$ −4.44414 3.20150i −0.573736 0.413312i
$$61$$ 1.77526 + 3.07483i 0.227298 + 0.393692i 0.957006 0.290067i $$-0.0936775\pi$$
−0.729708 + 0.683759i $$0.760344\pi$$
$$62$$ 8.89898i 1.13017i
$$63$$ 0 0
$$64$$ −1.00000 −0.125000
$$65$$ 9.07277 4.08346i 1.12534 0.506491i
$$66$$ −6.00000 + 10.3923i −0.738549 + 1.27920i
$$67$$ −6.92820 4.00000i −0.846415 0.488678i 0.0130248 0.999915i $$-0.495854\pi$$
−0.859440 + 0.511237i $$0.829187\pi$$
$$68$$ −1.73205 + 1.00000i −0.210042 + 0.121268i
$$69$$ −7.10102 −0.854862
$$70$$ 0 0
$$71$$ −1.10102 −0.130667 −0.0653335 0.997863i $$-0.520811\pi$$
−0.0653335 + 0.997863i $$0.520811\pi$$
$$72$$ 2.59808 1.50000i 0.306186 0.176777i
$$73$$ 2.51059 + 1.44949i 0.293842 + 0.169650i 0.639673 0.768647i $$-0.279070\pi$$
−0.345831 + 0.938297i $$0.612403\pi$$
$$74$$ −1.00000 + 1.73205i −0.116248 + 0.201347i
$$75$$ 11.6170 3.87868i 1.34142 0.447871i
$$76$$ −1.55051 −0.177856
$$77$$ 0 0
$$78$$ 10.8990i 1.23407i
$$79$$ 3.44949 + 5.97469i 0.388098 + 0.672205i 0.992194 0.124706i $$-0.0397989\pi$$
−0.604096 + 0.796912i $$0.706466\pi$$
$$80$$ 1.30701 1.81431i 0.146128 0.202846i
$$81$$ 4.50000 7.79423i 0.500000 0.866025i
$$82$$ 0.953512 0.550510i 0.105298 0.0607937i
$$83$$ 2.44949i 0.268866i 0.990923 + 0.134433i $$0.0429214\pi$$
−0.990923 + 0.134433i $$0.957079\pi$$
$$84$$ 0 0
$$85$$ 0.449490 4.44949i 0.0487540 0.482615i
$$86$$ −0.449490 0.778539i −0.0484697 0.0839520i
$$87$$ 14.6349 + 8.44949i 1.56903 + 0.905880i
$$88$$ −4.24264 2.44949i −0.452267 0.261116i
$$89$$ 5.00000 + 8.66025i 0.529999 + 0.917985i 0.999388 + 0.0349934i $$0.0111410\pi$$
−0.469389 + 0.882992i $$0.655526\pi$$
$$90$$ −0.674235 + 6.67423i −0.0710706 + 0.703526i
$$91$$ 0 0
$$92$$ 2.89898i 0.302240i
$$93$$ −18.8776 + 10.8990i −1.95751 + 1.13017i
$$94$$ 4.44949 7.70674i 0.458930 0.794890i
$$95$$ 2.02653 2.81311i 0.207917 0.288619i
$$96$$ 1.22474 + 2.12132i 0.125000 + 0.216506i
$$97$$ 15.7980i 1.60404i 0.597297 + 0.802020i $$0.296241\pi$$
−0.597297 + 0.802020i $$0.703759\pi$$
$$98$$ 0 0
$$99$$ 14.6969 1.47710
$$100$$ 1.58346 + 4.74264i 0.158346 + 0.474264i
$$101$$ 1.77526 3.07483i 0.176644 0.305957i −0.764085 0.645116i $$-0.776809\pi$$
0.940729 + 0.339159i $$0.110142\pi$$
$$102$$ 4.24264 + 2.44949i 0.420084 + 0.242536i
$$103$$ −11.1708 + 6.44949i −1.10070 + 0.635487i −0.936404 0.350925i $$-0.885867\pi$$
−0.164292 + 0.986412i $$0.552534\pi$$
$$104$$ −4.44949 −0.436308
$$105$$ 0 0
$$106$$ 10.8990 1.05860
$$107$$ 6.92820 4.00000i 0.669775 0.386695i −0.126217 0.992003i $$-0.540283\pi$$
0.795991 + 0.605308i $$0.206950\pi$$
$$108$$ 0 0
$$109$$ 3.44949 5.97469i 0.330401 0.572272i −0.652189 0.758056i $$-0.726149\pi$$
0.982591 + 0.185784i $$0.0594826\pi$$
$$110$$ 9.98930 4.49598i 0.952443 0.428675i
$$111$$ 4.89898 0.464991
$$112$$ 0 0
$$113$$ 19.7980i 1.86244i 0.364464 + 0.931218i $$0.381252\pi$$
−0.364464 + 0.931218i $$0.618748\pi$$
$$114$$ 1.89898 + 3.28913i 0.177856 + 0.308055i
$$115$$ 5.25966 + 3.78899i 0.490466 + 0.353325i
$$116$$ −3.44949 + 5.97469i −0.320277 + 0.554736i
$$117$$ 11.5601 6.67423i 1.06873 0.617033i
$$118$$ 1.55051i 0.142736i
$$119$$ 0 0
$$120$$ −5.44949 0.550510i −0.497468 0.0502545i
$$121$$ −6.50000 11.2583i −0.590909 1.02348i
$$122$$ 3.07483 + 1.77526i 0.278382 + 0.160724i
$$123$$ −2.33562 1.34847i −0.210596 0.121587i
$$124$$ −4.44949 7.70674i −0.399576 0.692086i
$$125$$ −10.6742 3.32577i −0.954733 0.297465i
$$126$$ 0 0
$$127$$ 14.8990i 1.32207i 0.750355 + 0.661035i $$0.229883\pi$$
−0.750355 + 0.661035i $$0.770117\pi$$
$$128$$ −0.866025 + 0.500000i −0.0765466 + 0.0441942i
$$129$$ −1.10102 + 1.90702i −0.0969395 + 0.167904i
$$130$$ 5.81552 8.07277i 0.510054 0.708029i
$$131$$ −3.22474 5.58542i −0.281747 0.488001i 0.690068 0.723745i $$-0.257581\pi$$
−0.971815 + 0.235744i $$0.924247\pi$$
$$132$$ 12.0000i 1.04447i
$$133$$ 0 0
$$134$$ −8.00000 −0.691095
$$135$$ 0 0
$$136$$ −1.00000 + 1.73205i −0.0857493 + 0.148522i
$$137$$ −1.55708 0.898979i −0.133030 0.0768050i 0.432008 0.901870i $$-0.357805\pi$$
−0.565038 + 0.825065i $$0.691139\pi$$
$$138$$ −6.14966 + 3.55051i −0.523494 + 0.302240i
$$139$$ 1.55051 0.131513 0.0657563 0.997836i $$-0.479054\pi$$
0.0657563 + 0.997836i $$0.479054\pi$$
$$140$$ 0 0
$$141$$ −21.7980 −1.83572
$$142$$ −0.953512 + 0.550510i −0.0800169 + 0.0461978i
$$143$$ −18.8776 10.8990i −1.57862 0.911418i
$$144$$ 1.50000 2.59808i 0.125000 0.216506i
$$145$$ −6.33145 14.0674i −0.525799 1.16824i
$$146$$ 2.89898 0.239921
$$147$$ 0 0
$$148$$ 2.00000i 0.164399i
$$149$$ −1.89898 3.28913i −0.155570 0.269456i 0.777696 0.628640i $$-0.216388\pi$$
−0.933267 + 0.359184i $$0.883055\pi$$
$$150$$ 8.12132 9.16756i 0.663103 0.748528i
$$151$$ −9.79796 + 16.9706i −0.797347 + 1.38104i 0.123992 + 0.992283i $$0.460430\pi$$
−0.921338 + 0.388762i $$0.872903\pi$$
$$152$$ −1.34278 + 0.775255i −0.108914 + 0.0628815i
$$153$$ 6.00000i 0.485071i
$$154$$ 0 0
$$155$$ 19.7980 + 2.00000i 1.59021 + 0.160644i
$$156$$ 5.44949 + 9.43879i 0.436308 + 0.755708i
$$157$$ −3.07483 1.77526i −0.245398 0.141681i 0.372257 0.928130i $$-0.378584\pi$$
−0.617655 + 0.786449i $$0.711917\pi$$
$$158$$ 5.97469 + 3.44949i 0.475321 + 0.274427i
$$159$$ −13.3485 23.1202i −1.05860 1.83355i
$$160$$ 0.224745 2.22474i 0.0177676 0.175882i
$$161$$ 0 0
$$162$$ 9.00000i 0.707107i
$$163$$ −6.14966 + 3.55051i −0.481679 + 0.278097i −0.721116 0.692814i $$-0.756370\pi$$
0.239437 + 0.970912i $$0.423037\pi$$
$$164$$ 0.550510 0.953512i 0.0429876 0.0744568i
$$165$$ −21.7718 15.6841i −1.69493 1.22100i
$$166$$ 1.22474 + 2.12132i 0.0950586 + 0.164646i
$$167$$ 4.89898i 0.379094i −0.981872 0.189547i $$-0.939298\pi$$
0.981872 0.189547i $$-0.0607020\pi$$
$$168$$ 0 0
$$169$$ −6.79796 −0.522920
$$170$$ −1.83548 4.07812i −0.140775 0.312777i
$$171$$ 2.32577 4.02834i 0.177856 0.308055i
$$172$$ −0.778539 0.449490i −0.0593630 0.0342733i
$$173$$ 5.41045 3.12372i 0.411349 0.237492i −0.280020 0.959994i $$-0.590341\pi$$
0.691369 + 0.722502i $$0.257008\pi$$
$$174$$ 16.8990 1.28111
$$175$$ 0 0
$$176$$ −4.89898 −0.369274
$$177$$ −3.28913 + 1.89898i −0.247226 + 0.142736i
$$178$$ 8.66025 + 5.00000i 0.649113 + 0.374766i
$$179$$ 6.89898 11.9494i 0.515654 0.893139i −0.484181 0.874968i $$-0.660882\pi$$
0.999835 0.0181709i $$-0.00578431\pi$$
$$180$$ 2.75321 + 6.11717i 0.205212 + 0.455947i
$$181$$ 10.2474 0.761687 0.380843 0.924640i $$-0.375634\pi$$
0.380843 + 0.924640i $$0.375634\pi$$
$$182$$ 0 0
$$183$$ 8.69694i 0.642896i
$$184$$ −1.44949 2.51059i −0.106858 0.185083i
$$185$$ −3.62863 2.61401i −0.266782 0.192186i
$$186$$ −10.8990 + 18.8776i −0.799152 + 1.38417i
$$187$$ −8.48528 + 4.89898i −0.620505 + 0.358249i
$$188$$ 8.89898i 0.649025i
$$189$$ 0 0
$$190$$ 0.348469 3.44949i 0.0252806 0.250252i
$$191$$ −6.34847 10.9959i −0.459359 0.795633i 0.539568 0.841942i $$-0.318588\pi$$
−0.998927 + 0.0463087i $$0.985254\pi$$
$$192$$ 2.12132 + 1.22474i 0.153093 + 0.0883883i
$$193$$ 18.7026 + 10.7980i 1.34624 + 0.777254i 0.987715 0.156265i $$-0.0499453\pi$$
0.358528 + 0.933519i $$0.383279\pi$$
$$194$$ 7.89898 + 13.6814i 0.567114 + 0.982270i
$$195$$ −24.2474 2.44949i −1.73640 0.175412i
$$196$$ 0 0
$$197$$ 18.8990i 1.34650i −0.739417 0.673248i $$-0.764899\pi$$
0.739417 0.673248i $$-0.235101\pi$$
$$198$$ 12.7279 7.34847i 0.904534 0.522233i
$$199$$ −8.44949 + 14.6349i −0.598968 + 1.03744i 0.394005 + 0.919108i $$0.371089\pi$$
−0.992974 + 0.118336i $$0.962244\pi$$
$$200$$ 3.74264 + 3.31552i 0.264645 + 0.234442i
$$201$$ 9.79796 + 16.9706i 0.691095 + 1.19701i
$$202$$ 3.55051i 0.249813i
$$203$$ 0 0
$$204$$ 4.89898 0.342997
$$205$$ 1.01045 + 2.24504i 0.0705727 + 0.156801i
$$206$$ −6.44949 + 11.1708i −0.449357 + 0.778310i
$$207$$ 7.53177 + 4.34847i 0.523494 + 0.302240i
$$208$$ −3.85337 + 2.22474i −0.267183 + 0.154258i
$$209$$ −7.59592 −0.525421
$$210$$ 0 0
$$211$$ 12.0000 0.826114 0.413057 0.910705i $$-0.364461\pi$$
0.413057 + 0.910705i $$0.364461\pi$$
$$212$$ 9.43879 5.44949i 0.648259 0.374272i
$$213$$ 2.33562 + 1.34847i 0.160034 + 0.0923956i
$$214$$ 4.00000 6.92820i 0.273434 0.473602i
$$215$$ 1.83307 0.825027i 0.125014 0.0562664i
$$216$$ 0 0
$$217$$ 0 0
$$218$$ 6.89898i 0.467258i
$$219$$ −3.55051 6.14966i −0.239921 0.415556i
$$220$$ 6.40300 8.88828i 0.431690 0.599248i
$$221$$ −4.44949 + 7.70674i −0.299305 + 0.518412i
$$222$$ 4.24264 2.44949i 0.284747 0.164399i
$$223$$ 4.00000i 0.267860i 0.990991 + 0.133930i $$0.0427597\pi$$
−0.990991 + 0.133930i $$0.957240\pi$$
$$224$$ 0 0
$$225$$ −14.6969 3.00000i −0.979796 0.200000i
$$226$$ 9.89898 + 17.1455i 0.658470 + 1.14050i
$$227$$ −6.36396 3.67423i −0.422391 0.243868i 0.273709 0.961813i $$-0.411750\pi$$
−0.696100 + 0.717945i $$0.745083\pi$$
$$228$$ 3.28913 + 1.89898i 0.217828 + 0.125763i
$$229$$ 9.57321 + 16.5813i 0.632616 + 1.09572i 0.987015 + 0.160628i $$0.0513521\pi$$
−0.354399 + 0.935094i $$0.615315\pi$$
$$230$$ 6.44949 + 0.651531i 0.425267 + 0.0429607i
$$231$$ 0 0
$$232$$ 6.89898i 0.452940i
$$233$$ 25.8058 14.8990i 1.69059 0.976065i 0.736556 0.676376i $$-0.236451\pi$$
0.954037 0.299688i $$-0.0968827\pi$$
$$234$$ 6.67423 11.5601i 0.436308 0.755708i
$$235$$ 16.1455 + 11.6310i 1.05322 + 0.758725i
$$236$$ −0.775255 1.34278i −0.0504648 0.0874076i
$$237$$ 16.8990i 1.09771i
$$238$$ 0 0
$$239$$ 6.20204 0.401177 0.200588 0.979676i $$-0.435715\pi$$
0.200588 + 0.979676i $$0.435715\pi$$
$$240$$ −4.99465 + 2.24799i −0.322403 + 0.145107i
$$241$$ −4.34847 + 7.53177i −0.280110 + 0.485164i −0.971411 0.237402i $$-0.923704\pi$$
0.691302 + 0.722566i $$0.257037\pi$$
$$242$$ −11.2583 6.50000i −0.723713 0.417836i
$$243$$ −19.0919 + 11.0227i −1.22474 + 0.707107i
$$244$$ 3.55051 0.227298
$$245$$ 0 0
$$246$$ −2.69694 −0.171951
$$247$$ −5.97469 + 3.44949i −0.380161 + 0.219486i
$$248$$ −7.70674 4.44949i −0.489379 0.282543i
$$249$$ 3.00000 5.19615i 0.190117 0.329293i
$$250$$ −10.9070 + 2.45692i −0.689822 + 0.155389i
$$251$$ 6.44949 0.407088 0.203544 0.979066i $$-0.434754\pi$$
0.203544 + 0.979066i $$0.434754\pi$$
$$252$$ 0 0
$$253$$ 14.2020i 0.892875i
$$254$$ 7.44949 + 12.9029i 0.467423 + 0.809600i
$$255$$ −6.40300 + 8.88828i −0.400972 + 0.556606i
$$256$$ −0.500000 + 0.866025i −0.0312500 + 0.0541266i
$$257$$ −7.53177 + 4.34847i −0.469819 + 0.271250i −0.716164 0.697932i $$-0.754104\pi$$
0.246345 + 0.969182i $$0.420770\pi$$
$$258$$ 2.20204i 0.137093i
$$259$$ 0 0
$$260$$ 1.00000 9.89898i 0.0620174 0.613909i
$$261$$ −10.3485 17.9241i −0.640554 1.10947i
$$262$$ −5.58542 3.22474i −0.345069 0.199225i
$$263$$ −8.48528 4.89898i −0.523225 0.302084i 0.215028 0.976608i $$-0.431016\pi$$
−0.738253 + 0.674524i $$0.764349\pi$$
$$264$$ 6.00000 + 10.3923i 0.369274 + 0.639602i
$$265$$ −2.44949 + 24.2474i −0.150471 + 1.48951i
$$266$$ 0 0
$$267$$ 24.4949i 1.49906i
$$268$$ −6.92820 + 4.00000i −0.423207 + 0.244339i
$$269$$ −9.57321 + 16.5813i −0.583689 + 1.01098i 0.411348 + 0.911478i $$0.365058\pi$$
−0.995037 + 0.0995010i $$0.968275\pi$$
$$270$$ 0 0
$$271$$ 6.00000 + 10.3923i 0.364474 + 0.631288i 0.988692 0.149963i $$-0.0479155\pi$$
−0.624218 + 0.781251i $$0.714582\pi$$
$$272$$ 2.00000i 0.121268i
$$273$$ 0 0
$$274$$ −1.79796 −0.108619
$$275$$ 7.75736 + 23.2341i 0.467786 + 1.40107i
$$276$$ −3.55051 + 6.14966i −0.213716 + 0.370166i
$$277$$ −12.9029 7.44949i −0.775260 0.447596i 0.0594879 0.998229i $$-0.481053\pi$$
−0.834748 + 0.550633i $$0.814387\pi$$
$$278$$ 1.34278 0.775255i 0.0805347 0.0464967i
$$279$$ 26.6969 1.59830
$$280$$ 0 0
$$281$$ −18.0000 −1.07379 −0.536895 0.843649i $$-0.680403\pi$$
−0.536895 + 0.843649i $$0.680403\pi$$
$$282$$ −18.8776 + 10.8990i −1.12414 + 0.649025i
$$283$$ 3.24980 + 1.87628i 0.193181 + 0.111533i 0.593471 0.804856i $$-0.297757\pi$$
−0.400290 + 0.916389i $$0.631091\pi$$
$$284$$ −0.550510 + 0.953512i −0.0326668 + 0.0565805i
$$285$$ −7.74426 + 3.48553i −0.458730 + 0.206465i
$$286$$ −21.7980 −1.28894
$$287$$ 0 0
$$288$$ 3.00000i 0.176777i
$$289$$ −6.50000 11.2583i −0.382353 0.662255i
$$290$$ −12.5169 9.01702i −0.735018 0.529497i
$$291$$ 19.3485 33.5125i 1.13423 1.96454i
$$292$$ 2.51059 1.44949i 0.146921 0.0848250i
$$293$$ 18.2474i 1.06603i −0.846107 0.533014i $$-0.821059\pi$$
0.846107 0.533014i $$-0.178941\pi$$
$$294$$ 0 0
$$295$$ 3.44949 + 0.348469i 0.200837 + 0.0202887i
$$296$$ 1.00000 + 1.73205i 0.0581238 + 0.100673i
$$297$$ 0 0
$$298$$ −3.28913 1.89898i −0.190534 0.110005i
$$299$$ −6.44949 11.1708i −0.372984 0.646027i
$$300$$ 2.44949 12.0000i 0.141421 0.692820i
$$301$$ 0 0
$$302$$ 19.5959i 1.12762i
$$303$$ −7.53177 + 4.34847i −0.432689 + 0.249813i
$$304$$ −0.775255 + 1.34278i −0.0444639 + 0.0770138i
$$305$$ −4.64054 + 6.44174i −0.265717 + 0.368853i
$$306$$ −3.00000 5.19615i −0.171499 0.297044i
$$307$$ 20.2474i 1.15558i −0.816184 0.577791i $$-0.803915\pi$$
0.816184 0.577791i $$-0.196085\pi$$
$$308$$ 0 0
$$309$$ 31.5959 1.79743
$$310$$ 18.1455 8.16693i 1.03060 0.463850i
$$311$$ 6.00000 10.3923i 0.340229 0.589294i −0.644246 0.764818i $$-0.722829\pi$$
0.984475 + 0.175525i $$0.0561621\pi$$
$$312$$ 9.43879 + 5.44949i 0.534366 + 0.308517i
$$313$$ 18.7026 10.7980i 1.05713 0.610337i 0.132496 0.991184i $$-0.457701\pi$$
0.924638 + 0.380847i $$0.124367\pi$$
$$314$$ −3.55051 −0.200367
$$315$$ 0 0
$$316$$ 6.89898 0.388098
$$317$$ 19.4812 11.2474i 1.09417 0.631720i 0.159487 0.987200i $$-0.449016\pi$$
0.934684 + 0.355480i $$0.115683\pi$$
$$318$$ −23.1202 13.3485i −1.29652 0.748545i
$$319$$ −16.8990 + 29.2699i −0.946161 + 1.63880i
$$320$$ −0.917738 2.03906i −0.0513031 0.113987i
$$321$$ −19.5959 −1.09374
$$322$$ 0 0
$$323$$ 3.10102i 0.172545i
$$324$$ −4.50000 7.79423i −0.250000 0.433013i
$$325$$ 16.6528 + 14.7524i 0.923733 + 0.818313i
$$326$$ −3.55051 + 6.14966i −0.196645 + 0.340598i
$$327$$ −14.6349 + 8.44949i −0.809314 + 0.467258i
$$328$$ 1.10102i 0.0607937i
$$329$$ 0 0
$$330$$ −26.6969 2.69694i −1.46962 0.148462i
$$331$$ 9.34847 + 16.1920i 0.513838 + 0.889994i 0.999871 + 0.0160535i $$0.00511022\pi$$
−0.486033 + 0.873941i $$0.661556\pi$$
$$332$$ 2.12132 + 1.22474i 0.116423 + 0.0672166i
$$333$$ −5.19615 3.00000i −0.284747 0.164399i
$$334$$ −2.44949 4.24264i −0.134030 0.232147i
$$335$$ 1.79796 17.7980i 0.0982330 0.972406i
$$336$$ 0 0
$$337$$ 9.59592i 0.522723i −0.965241 0.261361i $$-0.915829\pi$$
0.965241 0.261361i $$-0.0841715\pi$$
$$338$$ −5.88721 + 3.39898i −0.320222 + 0.184880i
$$339$$ 24.2474 41.9978i 1.31694 2.28101i
$$340$$ −3.62863 2.61401i −0.196790 0.141765i
$$341$$ −21.7980 37.7552i −1.18043 2.04456i
$$342$$ 4.65153i 0.251526i
$$343$$ 0 0
$$344$$ −0.898979 −0.0484697
$$345$$ −6.51687 14.4794i −0.350857 0.779544i
$$346$$ 3.12372 5.41045i 0.167932 0.290868i
$$347$$ 25.0273 + 14.4495i 1.34353 + 0.775689i 0.987324 0.158717i $$-0.0507358\pi$$
0.356209 + 0.934406i $$0.384069\pi$$
$$348$$ 14.6349 8.44949i 0.784515 0.452940i
$$349$$ −8.44949 −0.452291 −0.226145 0.974094i $$-0.572612\pi$$
−0.226145 + 0.974094i $$0.572612\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ −4.24264 + 2.44949i −0.226134 + 0.130558i
$$353$$ 19.8311 + 11.4495i 1.05550 + 0.609395i 0.924185 0.381945i $$-0.124746\pi$$
0.131318 + 0.991340i $$0.458079\pi$$
$$354$$ −1.89898 + 3.28913i −0.100930 + 0.174815i
$$355$$ −1.01045 2.24504i −0.0536290 0.119155i
$$356$$ 10.0000 0.529999
$$357$$ 0 0
$$358$$ 13.7980i 0.729245i
$$359$$ −13.7980 23.8988i −0.728228 1.26133i −0.957631 0.287997i $$-0.907011\pi$$
0.229403 0.973332i $$-0.426323\pi$$
$$360$$ 5.44294 + 3.92102i 0.286868 + 0.206656i
$$361$$ 8.29796 14.3725i 0.436735 0.756447i
$$362$$ 8.87455 5.12372i 0.466436 0.269297i
$$363$$ 31.8434i 1.67134i
$$364$$ 0 0
$$365$$ −0.651531 + 6.44949i −0.0341027 + 0.337582i
$$366$$ −4.34847 7.53177i −0.227298 0.393692i
$$367$$ −27.7128 16.0000i −1.44660 0.835193i −0.448320 0.893873i $$-0.647978\pi$$
−0.998277 + 0.0586798i $$0.981311\pi$$
$$368$$ −2.51059 1.44949i −0.130874 0.0755599i
$$369$$ 1.65153 + 2.86054i 0.0859753 + 0.148914i
$$370$$ −4.44949 0.449490i −0.231318 0.0233679i
$$371$$ 0 0
$$372$$ 21.7980i 1.13017i
$$373$$ −4.06767 + 2.34847i −0.210616 + 0.121599i −0.601598 0.798799i $$-0.705469\pi$$
0.390982 + 0.920398i $$0.372136\pi$$
$$374$$ −4.89898 + 8.48528i −0.253320 + 0.438763i
$$375$$ 18.5703 + 20.1282i 0.958964 + 1.03942i
$$376$$ −4.44949 7.70674i −0.229465 0.397445i
$$377$$ 30.6969i 1.58097i
$$378$$ 0 0
$$379$$ −30.6969 −1.57680 −0.788398 0.615166i $$-0.789089\pi$$
−0.788398 + 0.615166i $$0.789089\pi$$
$$380$$ −1.42296 3.16158i −0.0729964 0.162186i
$$381$$ 18.2474 31.6055i 0.934845 1.61920i
$$382$$ −10.9959 6.34847i −0.562598 0.324816i
$$383$$ 6.14966 3.55051i 0.314233 0.181423i −0.334586 0.942365i $$-0.608596\pi$$
0.648819 + 0.760943i $$0.275263\pi$$
$$384$$ 2.44949 0.125000
$$385$$ 0 0
$$386$$ 21.5959 1.09920
$$387$$ 2.33562 1.34847i 0.118726 0.0685465i
$$388$$ 13.6814 + 7.89898i 0.694570 + 0.401010i
$$389$$ 6.55051 11.3458i 0.332124 0.575256i −0.650804 0.759246i $$-0.725568\pi$$
0.982928 + 0.183990i $$0.0589014\pi$$
$$390$$ −22.2237 + 10.0024i −1.12534 + 0.506491i
$$391$$ −5.79796 −0.293215
$$392$$ 0 0
$$393$$ 15.7980i 0.796902i
$$394$$ −9.44949 16.3670i −0.476058 0.824557i
$$395$$ −9.01702 + 12.5169i −0.453695 + 0.629794i
$$396$$ 7.34847 12.7279i 0.369274 0.639602i
$$397$$ −2.29629 + 1.32577i −0.115248 + 0.0665383i −0.556516 0.830837i $$-0.687862\pi$$
0.441268 + 0.897375i $$0.354529\pi$$
$$398$$ 16.8990i 0.847069i
$$399$$ 0 0
$$400$$ 4.89898 + 1.00000i 0.244949 + 0.0500000i
$$401$$ 14.6969 + 25.4558i 0.733930 + 1.27120i 0.955191 + 0.295990i $$0.0956494\pi$$
−0.221261 + 0.975215i $$0.571017\pi$$
$$402$$ 16.9706 + 9.79796i 0.846415 + 0.488678i
$$403$$ −34.2911 19.7980i −1.70816 0.986207i
$$404$$ −1.77526 3.07483i −0.0883222 0.152979i
$$405$$ 20.0227 + 2.02270i 0.994936 + 0.100509i
$$406$$ 0 0
$$407$$ 9.79796i 0.485667i
$$408$$ 4.24264 2.44949i 0.210042 0.121268i
$$409$$ −17.2474 + 29.8735i −0.852831 + 1.47715i 0.0258109 + 0.999667i $$0.491783\pi$$
−0.878642 + 0.477481i $$0.841550\pi$$
$$410$$ 1.99760 + 1.43904i 0.0986542 + 0.0710692i
$$411$$ 2.20204 + 3.81405i 0.108619 + 0.188133i
$$412$$ 12.8990i 0.635487i
$$413$$ 0 0
$$414$$ 8.69694 0.427431
$$415$$ −4.99465 + 2.24799i −0.245178 + 0.110349i
$$416$$ −2.22474 + 3.85337i −0.109077 + 0.188927i
$$417$$ −3.28913 1.89898i −0.161069 0.0929934i
$$418$$ −6.57826 + 3.79796i −0.321753 + 0.185764i
$$419$$ −1.55051 −0.0757474 −0.0378737 0.999283i $$-0.512058\pi$$
−0.0378737 + 0.999283i $$0.512058\pi$$
$$420$$ 0 0
$$421$$ −4.20204 −0.204795 −0.102397 0.994744i $$-0.532651\pi$$
−0.102397 + 0.994744i $$0.532651\pi$$
$$422$$ 10.3923 6.00000i 0.505889 0.292075i
$$423$$ 23.1202 + 13.3485i 1.12414 + 0.649025i
$$424$$ 5.44949 9.43879i 0.264651 0.458388i
$$425$$ 9.48528 3.16693i 0.460104 0.153619i
$$426$$ 2.69694 0.130667
$$427$$ 0 0
$$428$$ 8.00000i 0.386695i
$$429$$ 26.6969 + 46.2405i 1.28894 + 2.23251i
$$430$$ 1.17497 1.63103i 0.0566622 0.0786553i
$$431$$ 0.898979 1.55708i 0.0433023 0.0750018i −0.843562 0.537032i $$-0.819545\pi$$
0.886864 + 0.462030i $$0.152879\pi$$
$$432$$ 0 0
$$433$$ 0.202041i 0.00970947i 0.999988 + 0.00485474i $$0.00154532\pi$$
−0.999988 + 0.00485474i $$0.998455\pi$$
$$434$$ 0 0
$$435$$ −3.79796 + 37.5959i −0.182098 + 1.80259i
$$436$$ −3.44949 5.97469i −0.165201 0.286136i
$$437$$ −3.89270 2.24745i −0.186213 0.107510i
$$438$$ −6.14966 3.55051i −0.293842 0.169650i
$$439$$ 10.6969 + 18.5276i 0.510537 + 0.884276i 0.999925 + 0.0122101i $$0.00388670\pi$$
−0.489388 + 0.872066i $$0.662780\pi$$
$$440$$ 1.10102 10.8990i 0.0524891 0.519588i
$$441$$ 0 0
$$442$$ 8.89898i 0.423281i
$$443$$ 8.48528 4.89898i 0.403148 0.232758i −0.284693 0.958619i $$-0.591892\pi$$
0.687841 + 0.725861i $$0.258558\pi$$
$$444$$ 2.44949 4.24264i 0.116248 0.201347i
$$445$$ −13.0701 + 18.1431i −0.619581 + 0.860067i
$$446$$ 2.00000 + 3.46410i 0.0947027 + 0.164030i
$$447$$ 9.30306i 0.440020i
$$448$$ 0 0
$$449$$ 10.0000 0.471929 0.235965 0.971762i $$-0.424175\pi$$
0.235965 + 0.971762i $$0.424175\pi$$
$$450$$ −14.2279 + 4.75039i −0.670711 + 0.223936i
$$451$$ 2.69694 4.67123i 0.126994 0.219960i
$$452$$ 17.1455 + 9.89898i 0.806458 + 0.465609i
$$453$$ 41.5692 24.0000i 1.95309 1.12762i
$$454$$ −7.34847 −0.344881
$$455$$ 0 0
$$456$$ 3.79796 0.177856
$$457$$ −25.6308 + 14.7980i −1.19896 + 0.692219i −0.960323 0.278890i $$-0.910034\pi$$
−0.238636 + 0.971109i $$0.576700\pi$$
$$458$$ 16.5813 + 9.57321i 0.774793 + 0.447327i
$$459$$ 0 0
$$460$$ 5.91119 2.66050i 0.275611 0.124047i
$$461$$ −17.3485 −0.807999 −0.403999 0.914759i $$-0.632380\pi$$
−0.403999 + 0.914759i $$0.632380\pi$$
$$462$$ 0 0
$$463$$ 3.59592i 0.167116i 0.996503 + 0.0835582i $$0.0266285\pi$$
−0.996503 + 0.0835582i $$0.973372\pi$$
$$464$$ 3.44949 + 5.97469i 0.160139 + 0.277368i
$$465$$ −39.5483 28.4901i −1.83401 1.32120i
$$466$$ 14.8990 25.8058i 0.690182 1.19543i
$$467$$ 9.04952 5.22474i 0.418762 0.241772i −0.275785 0.961219i $$-0.588938\pi$$
0.694548 + 0.719447i $$0.255605\pi$$
$$468$$ 13.3485i 0.617033i
$$469$$ 0 0
$$470$$ 19.7980 + 2.00000i 0.913212 + 0.0922531i
$$471$$ 4.34847 + 7.53177i 0.200367 + 0.347046i
$$472$$ −1.34278 0.775255i −0.0618065 0.0356840i
$$473$$ −3.81405 2.20204i −0.175370 0.101250i
$$474$$ −8.44949 14.6349i −0.388098 0.672205i
$$475$$ 7.59592 + 1.55051i 0.348525 + 0.0711423i
$$476$$ 0 0
$$477$$ 32.6969i 1.49709i
$$478$$ 5.37113 3.10102i 0.245670 0.141837i
$$479$$ −4.65153 + 8.05669i −0.212534 + 0.368119i −0.952507 0.304517i $$-0.901505\pi$$
0.739973 + 0.672637i $$0.234838\pi$$
$$480$$ −3.20150 + 4.44414i −0.146128 + 0.202846i
$$481$$ 4.44949 + 7.70674i 0.202879 + 0.351397i
$$482$$ 8.69694i 0.396135i
$$483$$ 0 0
$$484$$ −13.0000 −0.590909
$$485$$ −32.2130 + 14.4984i −1.46271 + 0.658338i
$$486$$ −11.0227 + 19.0919i −0.500000 + 0.866025i
$$487$$ −6.32464 3.65153i −0.286597 0.165467i 0.349809 0.936821i $$-0.386246\pi$$
−0.636406 + 0.771354i $$0.719580\pi$$
$$488$$ 3.07483 1.77526i 0.139191 0.0803620i
$$489$$ 17.3939 0.786578
$$490$$ 0 0
$$491$$ 19.5959 0.884351 0.442176 0.896928i $$-0.354207\pi$$
0.442176 + 0.896928i $$0.354207\pi$$
$$492$$ −2.33562 + 1.34847i −0.105298 + 0.0607937i
$$493$$ 11.9494 + 6.89898i 0.538173 + 0.310714i
$$494$$ −3.44949 + 5.97469i −0.155200 + 0.268814i
$$495$$ 13.4879 + 29.9679i 0.606238 + 1.34696i
$$496$$ −8.89898 −0.399576
$$497$$ 0 0
$$498$$ 6.00000i 0.268866i
$$499$$ 3.10102 + 5.37113i 0.138821 + 0.240445i 0.927051 0.374936i $$-0.122335\pi$$
−0.788230 + 0.615381i $$0.789002\pi$$
$$500$$ −8.21731 + 7.58128i −0.367489 + 0.339045i
$$501$$ −6.00000 + 10.3923i −0.268060 + 0.464294i
$$502$$ 5.58542 3.22474i 0.249290 0.143927i
$$503$$ 4.00000i 0.178351i 0.996016 + 0.0891756i $$0.0284232\pi$$
−0.996016 + 0.0891756i $$0.971577\pi$$
$$504$$ 0 0
$$505$$ 7.89898 + 0.797959i 0.351500 + 0.0355087i
$$506$$ −7.10102 12.2993i −0.315679 0.546772i
$$507$$ 14.4206 + 8.32577i 0.640443 + 0.369760i
$$508$$ 12.9029 + 7.44949i 0.572473 + 0.330518i
$$509$$ 15.7753 + 27.3235i 0.699226 + 1.21109i 0.968735 + 0.248097i $$0.0798052\pi$$
−0.269509 + 0.962998i $$0.586861\pi$$
$$510$$ −1.10102 + 10.8990i −0.0487540 + 0.482615i
$$511$$ 0 0
$$512$$ 1.00000i 0.0441942i
$$513$$ 0 0
$$514$$ −4.34847 + 7.53177i −0.191803 + 0.332212i
$$515$$ −23.4028 16.8591i −1.03125 0.742899i
$$516$$ 1.10102 + 1.90702i 0.0484697 + 0.0839520i
$$517$$ 43.5959i 1.91735i
$$518$$ 0 0
$$519$$ −15.3031 −0.671730
$$520$$ −4.08346 9.07277i −0.179072 0.397867i
$$521$$ 16.3485 28.3164i 0.716239 1.24056i −0.246240 0.969209i $$-0.579195\pi$$
0.962480 0.271354i $$-0.0874715\pi$$
$$522$$ −17.9241 10.3485i −0.784515 0.452940i
$$523$$ 28.7056 16.5732i 1.25521 0.724696i 0.283071 0.959099i $$-0.408647\pi$$
0.972140 + 0.234403i $$0.0753135\pi$$
$$524$$ −6.44949 −0.281747
$$525$$ 0 0
$$526$$ −9.79796 −0.427211
$$527$$ −15.4135 + 8.89898i −0.671422 + 0.387646i
$$528$$ 10.3923 + 6.00000i 0.452267 + 0.261116i
$$529$$ −7.29796 + 12.6404i −0.317303 + 0.549584i
$$530$$ 10.0024 + 22.2237i 0.434477 + 0.965334i
$$531$$ 4.65153 0.201859
$$532$$ 0 0
$$533$$ 4.89898i 0.212198i
$$534$$ −12.2474 21.2132i −0.529999 0.917985i
$$535$$ 14.5145 + 10.4561i 0.627517 + 0.452055i
$$536$$ −4.00000 + 6.92820i −0.172774 + 0.299253i
$$537$$ −29.2699 + 16.8990i −1.26309 + 0.729245i
$$538$$ 19.1464i 0.825461i
$$539$$ 0 0
$$540$$ 0 0
$$541$$ −4.79796 8.31031i −0.206280 0.357288i 0.744260 0.667891i $$-0.232803\pi$$
−0.950540 + 0.310602i $$0.899469\pi$$
$$542$$ 10.3923 + 6.00000i 0.446388 + 0.257722i
$$543$$ −21.7381 12.5505i −0.932872 0.538594i
$$544$$ 1.00000 + 1.73205i 0.0428746 + 0.0742611i
$$545$$ 15.3485 + 1.55051i 0.657456 + 0.0664166i
$$546$$ 0 0
$$547$$ 18.6969i 0.799423i 0.916641 + 0.399712i $$0.130890\pi$$
−0.916641 + 0.399712i $$0.869110\pi$$
$$548$$ −1.55708 + 0.898979i −0.0665151 + 0.0384025i
$$549$$ −5.32577 + 9.22450i −0.227298 + 0.393692i
$$550$$ 18.3351 + 16.2426i 0.781812 + 0.692589i
$$551$$ 5.34847 + 9.26382i 0.227852 + 0.394652i
$$552$$ 7.10102i 0.302240i
$$553$$ 0 0
$$554$$ −14.8990 −0.632997
$$555$$ 4.49598 + 9.98930i 0.190844 + 0.424022i
$$556$$ 0.775255 1.34278i 0.0328781 0.0569466i
$$557$$ 10.9959 + 6.34847i 0.465910 + 0.268993i 0.714526 0.699609i $$-0.246642\pi$$
−0.248616 + 0.968602i $$0.579976\pi$$
$$558$$ 23.1202 13.3485i 0.978757 0.565086i
$$559$$ −4.00000 −0.169182
$$560$$ 0 0
$$561$$ 24.0000 1.01328
$$562$$ −15.5885 + 9.00000i −0.657559 + 0.379642i
$$563$$ −26.0201 15.0227i −1.09662 0.633131i −0.161286 0.986908i $$-0.551564\pi$$
−0.935330 + 0.353776i $$0.884897\pi$$
$$564$$ −10.8990 + 18.8776i −0.458930 + 0.794890i
$$565$$ −40.3692 + 18.1693i −1.69834 + 0.764390i
$$566$$ 3.75255 0.157731
$$567$$ 0 0
$$568$$ 1.10102i 0.0461978i
$$569$$ 16.8990 + 29.2699i 0.708442 + 1.22706i 0.965435 + 0.260644i $$0.0839350\pi$$
−0.256993 + 0.966413i $$0.582732\pi$$
$$570$$ −4.96396 + 6.89069i −0.207917 + 0.288619i
$$571$$ 5.55051 9.61377i 0.232282 0.402324i −0.726198 0.687486i $$-0.758714\pi$$
0.958479 + 0.285162i $$0.0920476\pi$$
$$572$$ −18.8776 + 10.8990i −0.789312 + 0.455709i
$$573$$ 31.1010i 1.29926i
$$574$$ 0 0
$$575$$ −2.89898 + 14.2020i −0.120896 + 0.592266i
$$576$$ −1.50000 2.59808i −0.0625000 0.108253i
$$577$$ 2.16064 + 1.24745i 0.0899488 + 0.0519320i 0.544300 0.838891i $$-0.316795\pi$$
−0.454351 + 0.890823i $$0.650129\pi$$
$$578$$ −11.2583 6.50000i −0.468285 0.270364i
$$579$$ −26.4495 45.8119i −1.09920 1.90388i
$$580$$ −15.3485 1.55051i −0.637310 0.0643814i
$$581$$ 0 0
$$582$$ 38.6969i 1.60404i
$$583$$ 46.2405 26.6969i 1.91508 1.10567i
$$584$$ 1.44949 2.51059i 0.0599803 0.103889i
$$585$$ 24.2183 + 17.4465i 1.00130 + 0.721326i
$$586$$ −9.12372 15.8028i −0.376898 0.652806i
$$587$$ 1.14643i 0.0473182i 0.999720 + 0.0236591i $$0.00753162\pi$$
−0.999720 + 0.0236591i $$0.992468\pi$$
$$588$$ 0 0
$$589$$ −13.7980 −0.568535
$$590$$ 3.16158 1.42296i 0.130160 0.0585824i
$$591$$ −23.1464 + 40.0908i −0.952117 + 1.64911i
$$592$$ 1.73205 + 1.00000i 0.0711868 + 0.0410997i
$$593$$ 9.43879 5.44949i 0.387605 0.223784i −0.293517 0.955954i $$-0.594826\pi$$
0.681122 + 0.732170i $$0.261492\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ −3.79796 −0.155570
$$597$$ 35.8481 20.6969i 1.46717 0.847069i
$$598$$ −11.1708 6.44949i −0.456810 0.263739i
$$599$$ −6.55051 + 11.3458i −0.267647 + 0.463577i −0.968254 0.249970i $$-0.919579\pi$$
0.700607 + 0.713547i $$0.252913\pi$$
$$600$$ −3.87868 11.6170i −0.158346 0.474264i
$$601$$ 39.3939 1.60691 0.803455 0.595366i $$-0.202993\pi$$
0.803455 + 0.595366i $$0.202993\pi$$
$$602$$ 0 0
$$603$$ 24.0000i 0.977356i
$$604$$ 9.79796 + 16.9706i 0.398673 + 0.690522i
$$605$$ 16.9911 23.5861i 0.690786 0.958910i
$$606$$ −4.34847 + 7.53177i −0.176644 + 0.305957i
$$607$$ 28.9199 16.6969i 1.17382 0.677708i 0.219247 0.975669i $$-0.429640\pi$$
0.954578 + 0.297962i $$0.0963068\pi$$
$$608$$ 1.55051i 0.0628815i
$$609$$ 0 0
$$610$$ −0.797959 + 7.89898i −0.0323084 + 0.319820i
$$611$$ −19.7980 34.2911i −0.800940 1.38727i
$$612$$ −5.19615 3.00000i −0.210042 0.121268i
$$613$$ 24.0737 + 13.8990i 0.972329 + 0.561374i 0.899946 0.436002i $$-0.143606\pi$$
0.0723836 + 0.997377i $$0.476939\pi$$
$$614$$ −10.1237 17.5348i −0.408560 0.707647i
$$615$$ 0.606123 6.00000i 0.0244412 0.241943i
$$616$$ 0 0
$$617$$ 29.5959i 1.19149i −0.803175 0.595743i $$-0.796858\pi$$
0.803175 0.595743i $$-0.203142\pi$$
$$618$$ 27.3629 15.7980i 1.10070 0.635487i
$$619$$ 20.7753 35.9838i 0.835028 1.44631i −0.0589796 0.998259i $$-0.518785\pi$$
0.894008 0.448052i $$-0.147882\pi$$
$$620$$ 11.6310 16.1455i 0.467113 0.648420i
$$621$$ 0 0
$$622$$ 12.0000i 0.481156i
$$623$$ 0 0
$$624$$ 10.8990 0.436308
$$625$$ −3.01472 24.8176i −0.120589 0.992703i
$$626$$ 10.7980 18.7026i 0.431573 0.747507i
$$627$$ 16.1134 + 9.30306i 0.643506 + 0.371528i
$$628$$ −3.07483 + 1.77526i −0.122699 + 0.0708404i
$$629$$ 4.00000 0.159490
$$630$$ 0 0
$$631$$ −42.4949 −1.69170 −0.845848 0.533425i $$-0.820905\pi$$
−0.845848 + 0.533425i $$0.820905\pi$$
$$632$$ 5.97469 3.44949i 0.237660 0.137213i
$$633$$ −25.4558 14.6969i −1.01178 0.584151i
$$634$$ 11.2474 19.4812i 0.446693 0.773695i
$$635$$ −30.3799 + 13.6734i −1.20559 + 0.542611i
$$636$$ −26.6969 −1.05860
$$637$$ 0 0
$$638$$ 33.7980i 1.33807i
$$639$$ −1.65153 2.86054i −0.0653335 0.113161i
$$640$$ −1.81431 1.30701i −0.0717170 0.0516640i
$$641$$ −12.8990 + 22.3417i −0.509479 + 0.882444i 0.490461 + 0.871463i $$0.336829\pi$$
−0.999940 + 0.0109803i $$0.996505\pi$$
$$642$$ −16.9706 + 9.79796i −0.669775 + 0.386695i
$$643$$ 25.1464i 0.991678i −0.868414 0.495839i $$-0.834861\pi$$
0.868414 0.495839i $$-0.165139\pi$$
$$644$$ 0 0
$$645$$ −4.89898 0.494897i −0.192897 0.0194866i
$$646$$ 1.55051 + 2.68556i 0.0610040 + 0.105662i
$$647$$ 40.0908 + 23.1464i 1.57613 + 0.909980i 0.995392 + 0.0958907i $$0.0305699\pi$$
0.580740 + 0.814089i $$0.302763\pi$$
$$648$$ −7.79423 4.50000i −0.306186 0.176777i
$$649$$ −3.79796 6.57826i −0.149083 0.258219i
$$650$$ 21.7980 + 4.44949i 0.854986 + 0.174523i
$$651$$ 0 0
$$652$$ 7.10102i 0.278097i
$$653$$ −17.4955 + 10.1010i −0.684651 + 0.395283i −0.801605 0.597854i $$-0.796020\pi$$
0.116954 + 0.993137i $$0.462687\pi$$
$$654$$ −8.44949 + 14.6349i −0.330401 + 0.572272i
$$655$$ 8.42953 11.7014i 0.329369 0.457211i
$$656$$ −0.550510 0.953512i −0.0214938 0.0372284i
$$657$$ 8.69694i 0.339300i
$$658$$ 0 0
$$659$$ −16.8990 −0.658291 −0.329145 0.944279i $$-0.606761\pi$$
−0.329145 + 0.944279i $$0.606761\pi$$
$$660$$ −24.4687 + 11.0129i −0.952443 + 0.428675i
$$661$$ −20.4722 + 35.4589i −0.796276 + 1.37919i 0.125750 + 0.992062i $$0.459866\pi$$
−0.922026 + 0.387129i $$0.873467\pi$$
$$662$$ 16.1920 + 9.34847i 0.629321 + 0.363339i
$$663$$ 18.8776 10.8990i 0.733145 0.423281i
$$664$$ 2.44949 0.0950586
$$665$$ 0 0
$$666$$ −6.00000 −0.232495
$$667$$ −17.3205 + 10.0000i −0.670653 + 0.387202i
$$668$$ −4.24264 2.44949i −0.164153 0.0947736i
$$669$$ 4.89898 8.48528i 0.189405 0.328060i
$$670$$ −7.34190 16.3125i −0.283642 0.630205i
$$671$$ 17.3939 0.671483
$$672$$ 0 0
$$673$$ 17.7980i 0.686061i −0.939324 0.343030i $$-0.888547\pi$$
0.939324 0.343030i $$-0.111453\pi$$
$$674$$ −4.79796 8.31031i −0.184810 0.320101i
$$675$$ 0 0
$$676$$ −3.39898 + 5.88721i −0.130730 + 0.226431i
$$677$$ −31.5662 + 18.2247i −1.21319 + 0.700434i −0.963452 0.267880i $$-0.913677\pi$$
−0.249735 + 0.968314i $$0.580343\pi$$
$$678$$ 48.4949i 1.86244i
$$679$$ 0 0
$$680$$ −4.44949 0.449490i −0.170630 0.0172371i
$$681$$ 9.00000 + 15.5885i 0.344881 + 0.597351i
$$682$$ −37.7552 21.7980i −1.44572 0.834687i
$$683$$ −3.11416 1.79796i −0.119160 0.0687970i 0.439235 0.898372i $$-0.355249\pi$$
−0.558395 + 0.829575i $$0.688583\pi$$
$$684$$ −2.32577 4.02834i −0.0889279 0.154028i
$$685$$ 0.404082 4.00000i 0.0154392 0.152832i
$$686$$ 0 0
$$687$$ 46.8990i 1.78931i
$$688$$ −0.778539 + 0.449490i −0.0296815 + 0.0171366i
$$689$$ 24.2474 41.9978i 0.923754 1.59999i
$$690$$ −12.8835 9.28108i −0.490466 0.353325i
$$691$$ 10.5732 + 18.3133i 0.402224 + 0.696672i 0.993994 0.109434i $$-0.0349040\pi$$
−0.591770 + 0.806107i $$0.701571\pi$$
$$692$$ 6.24745i 0.237492i
$$693$$ 0 0
$$694$$ 28.8990 1.09699
$$695$$ 1.42296 + 3.16158i 0.0539760 + 0.119926i
$$696$$ 8.44949 14.6349i 0.320277 0.554736i
$$697$$ −1.90702 1.10102i −0.0722337 0.0417041i
$$698$$ −7.31747 + 4.22474i −0.276970 + 0.159909i
$$699$$ −72.9898 −2.76073
$$700$$ 0 0
$$701$$ 11.3031 0.426911 0.213455 0.976953i $$-0.431528\pi$$
0.213455 + 0.976953i $$0.431528\pi$$
$$702$$ 0 0
$$703$$ 2.68556 + 1.55051i 0.101288 + 0.0584786i
$$704$$ −2.44949 + 4.24264i −0.0923186 + 0.159901i
$$705$$ −20.0048 44.4473i −0.753425 1.67398i
$$706$$ 22.8990 0.861814
$$707$$ 0 0
$$708$$ 3.79796i 0.142736i
$$709$$ −14.1464 24.5023i −0.531280 0.920204i −0.999334 0.0365041i $$-0.988378\pi$$
0.468053 0.883700i $$-0.344956\pi$$
$$710$$ −1.99760 1.43904i −0.0749684 0.0540063i
$$711$$ −10.3485 + 17.9241i −0.388098 + 0.672205i
$$712$$ 8.66025 5.00000i 0.324557 0.187383i
$$713$$ 25.7980i 0.966141i
$$714$$ 0 0
$$715$$ 4.89898 48.4949i 0.183211 1.81361i
$$716$$ −6.89898 11.9494i −0.257827 0.446569i
$$717$$ −13.1565 7.59592i −0.491339 0.283675i
$$718$$ −23.8988 13.7980i −0.891894 0.514935i
$$719$$ 2.24745 + 3.89270i 0.0838157 + 0.145173i 0.904886 0.425654i $$-0.139956\pi$$
−0.821070 + 0.570827i $$0.806623\pi$$
$$720$$ 6.67423 + 0.674235i 0.248734 + 0.0251272i
$$721$$ 0 0
$$722$$ 16.5959i 0.617636i
$$723$$ 18.4490 10.6515i 0.686125 0.396135i
$$724$$ 5.12372 8.87455i 0.190422 0.329820i
$$725$$ 22.8737 25.8204i 0.849507 0.958946i
$$726$$ 15.9217 + 27.5772i 0.590909 + 1.02348i
$$727$$ 22.6969i 0.841783i 0.907111 + 0.420891i $$0.138283\pi$$
−0.907111 + 0.420891i $$0.861717\pi$$
$$728$$ 0 0
$$729$$ 27.0000 1.00000
$$730$$ 2.66050 + 5.91119i 0.0984696 + 0.218783i
$$731$$ −0.898979 + 1.55708i −0.0332500 + 0.0575906i
$$732$$ −7.53177 4.34847i −0.278382 0.160724i
$$733$$ −34.3304 + 19.8207i −1.26802 + 0.732093i −0.974613 0.223894i $$-0.928123\pi$$
−0.293409 + 0.955987i $$0.594790\pi$$
$$734$$ −32.0000 −1.18114
$$735$$ 0 0
$$736$$ −2.89898 −0.106858
$$737$$ −33.9411 + 19.5959i −1.25024 + 0.721825i
$$738$$ 2.86054 + 1.65153i 0.105298 + 0.0607937i
$$739$$ 2.24745 3.89270i 0.0826737 0.143195i −0.821724 0.569886i $$-0.806987\pi$$
0.904398 + 0.426691i $$0.140321\pi$$
$$740$$ −4.07812 + 1.83548i −0.149915 + 0.0674734i
$$741$$ 16.8990 0.620800
$$742$$ 0 0
$$743$$ 44.6969i 1.63977i −0.572527 0.819886i $$-0.694037\pi$$
0.572527 0.819886i $$-0.305963\pi$$
$$744$$ 10.8990 + 18.8776i 0.399576 + 0.692086i
$$745$$ 4.96396 6.89069i 0.181865 0.252455i
$$746$$ −2.34847 + 4.06767i −0.0859836 + 0.148928i
$$747$$ −6.36396 + 3.67423i −0.232845 + 0.134433i
$$748$$ 9.79796i 0.358249i
$$749$$ 0 0
$$750$$ 26.1464 + 8.14643i 0.954733 + 0.297465i
$$751$$ 20.8990 + 36.1981i 0.762615 + 1.32089i 0.941499 + 0.337017i $$0.109418\pi$$
−0.178884 + 0.983870i $$0.557249\pi$$
$$752$$ −7.70674 4.44949i −0.281036 0.162256i
$$753$$ −13.6814 7.89898i −0.498579 0.287855i
$$754$$ 15.3485 + 26.5843i 0.558958 + 0.968144i
$$755$$ −43.5959 4.40408i −1.58662 0.160281i
$$756$$ 0 0
$$757$$ 51.7980i 1.88263i 0.337531 + 0.941314i $$0.390408\pi$$
−0.337531 + 0.941314i $$0.609592\pi$$
$$758$$ −26.5843 + 15.3485i −0.965586 + 0.557482i
$$759$$ −17.3939 + 30.1271i −0.631358 + 1.09354i
$$760$$ −2.81311 2.02653i −0.102042 0.0735099i
$$761$$ −10.5505 18.2740i −0.382456 0.662433i 0.608957 0.793203i $$-0.291588\pi$$
−0.991413 + 0.130771i $$0.958255\pi$$
$$762$$ 36.4949i 1.32207i
$$763$$ 0 0
$$764$$ −12.6969 −0.459359
$$765$$ 12.2343 5.50643i 0.442334 0.199085i
$$766$$ 3.55051 6.14966i 0.128285 0.222196i
$$767$$ −5.97469 3.44949i −0.215734 0.124554i
$$768$$ 2.12132 1.22474i 0.0765466 0.0441942i
$$769$$ −40.6969 −1.46757 −0.733785 0.679382i $$-0.762248\pi$$
−0.733785 + 0.679382i $$0.762248\pi$$
$$770$$ 0 0
$$771$$ 21.3031 0.767211
$$772$$ 18.7026 10.7980i 0.673122 0.388627i
$$773$$ 1.16781 + 0.674235i 0.0420032 + 0.0242505i 0.520855 0.853645i $$-0.325613\pi$$
−0.478851 + 0.877896i $$0.658947\pi$$
$$774$$ 1.34847 2.33562i 0.0484697 0.0839520i
$$775$$ 14.0912 + 42.2047i 0.506171 + 1.51604i
$$776$$ 15.7980 0.567114
$$777$$ 0 0
$$778$$ 13.1010i 0.469694i
$$779$$ −0.853572 1.47843i −0.0305824 0.0529702i
$$780$$ −14.2450 + 19.7742i