# Properties

 Label 490.2.c.e.99.1 Level $490$ Weight $2$ Character 490.99 Analytic conductor $3.913$ Analytic rank $0$ Dimension $4$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$490 = 2 \cdot 5 \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 490.c (of order $$2$$, degree $$1$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$3.91266969904$$ Analytic rank: $$0$$ Dimension: $$4$$ Coefficient field: $$\Q(i, \sqrt{6})$$ Defining polynomial: $$x^{4} + 9$$ x^4 + 9 Coefficient ring: $$\Z[a_1, \ldots, a_{5}]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 70) Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

## Embedding invariants

 Embedding label 99.1 Root $$1.22474 - 1.22474i$$ of defining polynomial Character $$\chi$$ $$=$$ 490.99 Dual form 490.2.c.e.99.4

## $q$-expansion

 $$f(q)$$ $$=$$ $$q-1.00000i q^{2} -2.44949i q^{3} -1.00000 q^{4} +(-2.22474 + 0.224745i) q^{5} -2.44949 q^{6} +1.00000i q^{8} -3.00000 q^{9} +O(q^{10})$$ $$q-1.00000i q^{2} -2.44949i q^{3} -1.00000 q^{4} +(-2.22474 + 0.224745i) q^{5} -2.44949 q^{6} +1.00000i q^{8} -3.00000 q^{9} +(0.224745 + 2.22474i) q^{10} -4.89898 q^{11} +2.44949i q^{12} +4.44949i q^{13} +(0.550510 + 5.44949i) q^{15} +1.00000 q^{16} -2.00000i q^{17} +3.00000i q^{18} +1.55051 q^{19} +(2.22474 - 0.224745i) q^{20} +4.89898i q^{22} -2.89898i q^{23} +2.44949 q^{24} +(4.89898 - 1.00000i) q^{25} +4.44949 q^{26} -6.89898 q^{29} +(5.44949 - 0.550510i) q^{30} -8.89898 q^{31} -1.00000i q^{32} +12.0000i q^{33} -2.00000 q^{34} +3.00000 q^{36} +2.00000i q^{37} -1.55051i q^{38} +10.8990 q^{39} +(-0.224745 - 2.22474i) q^{40} +1.10102 q^{41} +0.898979i q^{43} +4.89898 q^{44} +(6.67423 - 0.674235i) q^{45} -2.89898 q^{46} -8.89898i q^{47} -2.44949i q^{48} +(-1.00000 - 4.89898i) q^{50} -4.89898 q^{51} -4.44949i q^{52} +10.8990i q^{53} +(10.8990 - 1.10102i) q^{55} -3.79796i q^{57} +6.89898i q^{58} -1.55051 q^{59} +(-0.550510 - 5.44949i) q^{60} -3.55051 q^{61} +8.89898i q^{62} -1.00000 q^{64} +(-1.00000 - 9.89898i) q^{65} +12.0000 q^{66} -8.00000i q^{67} +2.00000i q^{68} -7.10102 q^{69} -1.10102 q^{71} -3.00000i q^{72} +2.89898i q^{73} +2.00000 q^{74} +(-2.44949 - 12.0000i) q^{75} -1.55051 q^{76} -10.8990i q^{78} -6.89898 q^{79} +(-2.22474 + 0.224745i) q^{80} -9.00000 q^{81} -1.10102i q^{82} -2.44949i q^{83} +(0.449490 + 4.44949i) q^{85} +0.898979 q^{86} +16.8990i q^{87} -4.89898i q^{88} -10.0000 q^{89} +(-0.674235 - 6.67423i) q^{90} +2.89898i q^{92} +21.7980i q^{93} -8.89898 q^{94} +(-3.44949 + 0.348469i) q^{95} -2.44949 q^{96} -15.7980i q^{97} +14.6969 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4 q - 4 q^{4} - 4 q^{5} - 12 q^{9}+O(q^{10})$$ 4 * q - 4 * q^4 - 4 * q^5 - 12 * q^9 $$4 q - 4 q^{4} - 4 q^{5} - 12 q^{9} - 4 q^{10} + 12 q^{15} + 4 q^{16} + 16 q^{19} + 4 q^{20} + 8 q^{26} - 8 q^{29} + 12 q^{30} - 16 q^{31} - 8 q^{34} + 12 q^{36} + 24 q^{39} + 4 q^{40} + 24 q^{41} + 12 q^{45} + 8 q^{46} - 4 q^{50} + 24 q^{55} - 16 q^{59} - 12 q^{60} - 24 q^{61} - 4 q^{64} - 4 q^{65} + 48 q^{66} - 48 q^{69} - 24 q^{71} + 8 q^{74} - 16 q^{76} - 8 q^{79} - 4 q^{80} - 36 q^{81} - 8 q^{85} - 16 q^{86} - 40 q^{89} + 12 q^{90} - 16 q^{94} - 4 q^{95}+O(q^{100})$$ 4 * q - 4 * q^4 - 4 * q^5 - 12 * q^9 - 4 * q^10 + 12 * q^15 + 4 * q^16 + 16 * q^19 + 4 * q^20 + 8 * q^26 - 8 * q^29 + 12 * q^30 - 16 * q^31 - 8 * q^34 + 12 * q^36 + 24 * q^39 + 4 * q^40 + 24 * q^41 + 12 * q^45 + 8 * q^46 - 4 * q^50 + 24 * q^55 - 16 * q^59 - 12 * q^60 - 24 * q^61 - 4 * q^64 - 4 * q^65 + 48 * q^66 - 48 * q^69 - 24 * q^71 + 8 * q^74 - 16 * q^76 - 8 * q^79 - 4 * q^80 - 36 * q^81 - 8 * q^85 - 16 * q^86 - 40 * q^89 + 12 * q^90 - 16 * q^94 - 4 * q^95

## Character values

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

 $$n$$ $$101$$ $$197$$ $$\chi(n)$$ $$1$$ $$-1$$

## Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 1.00000i 0.707107i
$$3$$ 2.44949i 1.41421i −0.707107 0.707107i $$-0.750000\pi$$
0.707107 0.707107i $$-0.250000\pi$$
$$4$$ −1.00000 −0.500000
$$5$$ −2.22474 + 0.224745i −0.994936 + 0.100509i
$$6$$ −2.44949 −1.00000
$$7$$ 0 0
$$8$$ 1.00000i 0.353553i
$$9$$ −3.00000 −1.00000
$$10$$ 0.224745 + 2.22474i 0.0710706 + 0.703526i
$$11$$ −4.89898 −1.47710 −0.738549 0.674200i $$-0.764489\pi$$
−0.738549 + 0.674200i $$0.764489\pi$$
$$12$$ 2.44949i 0.707107i
$$13$$ 4.44949i 1.23407i 0.786937 + 0.617033i $$0.211666\pi$$
−0.786937 + 0.617033i $$0.788334\pi$$
$$14$$ 0 0
$$15$$ 0.550510 + 5.44949i 0.142141 + 1.40705i
$$16$$ 1.00000 0.250000
$$17$$ 2.00000i 0.485071i −0.970143 0.242536i $$-0.922021\pi$$
0.970143 0.242536i $$-0.0779791\pi$$
$$18$$ 3.00000i 0.707107i
$$19$$ 1.55051 0.355711 0.177856 0.984057i $$-0.443084\pi$$
0.177856 + 0.984057i $$0.443084\pi$$
$$20$$ 2.22474 0.224745i 0.497468 0.0502545i
$$21$$ 0 0
$$22$$ 4.89898i 1.04447i
$$23$$ 2.89898i 0.604479i −0.953232 0.302240i $$-0.902266\pi$$
0.953232 0.302240i $$-0.0977342\pi$$
$$24$$ 2.44949 0.500000
$$25$$ 4.89898 1.00000i 0.979796 0.200000i
$$26$$ 4.44949 0.872617
$$27$$ 0 0
$$28$$ 0 0
$$29$$ −6.89898 −1.28111 −0.640554 0.767913i $$-0.721295\pi$$
−0.640554 + 0.767913i $$0.721295\pi$$
$$30$$ 5.44949 0.550510i 0.994936 0.100509i
$$31$$ −8.89898 −1.59830 −0.799152 0.601129i $$-0.794718\pi$$
−0.799152 + 0.601129i $$0.794718\pi$$
$$32$$ 1.00000i 0.176777i
$$33$$ 12.0000i 2.08893i
$$34$$ −2.00000 −0.342997
$$35$$ 0 0
$$36$$ 3.00000 0.500000
$$37$$ 2.00000i 0.328798i 0.986394 + 0.164399i $$0.0525685\pi$$
−0.986394 + 0.164399i $$0.947432\pi$$
$$38$$ 1.55051i 0.251526i
$$39$$ 10.8990 1.74523
$$40$$ −0.224745 2.22474i −0.0355353 0.351763i
$$41$$ 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 $$0.0218362\pi$$
−0.997648 + 0.0685465i $$0.978164\pi$$
$$44$$ 4.89898 0.738549
$$45$$ 6.67423 0.674235i 0.994936 0.100509i
$$46$$ −2.89898 −0.427431
$$47$$ 8.89898i 1.29805i −0.760767 0.649025i $$-0.775177\pi$$
0.760767 0.649025i $$-0.224823\pi$$
$$48$$ 2.44949i 0.353553i
$$49$$ 0 0
$$50$$ −1.00000 4.89898i −0.141421 0.692820i
$$51$$ −4.89898 −0.685994
$$52$$ 4.44949i 0.617033i
$$53$$ 10.8990i 1.49709i 0.663084 + 0.748545i $$0.269247\pi$$
−0.663084 + 0.748545i $$0.730753\pi$$
$$54$$ 0 0
$$55$$ 10.8990 1.10102i 1.46962 0.148462i
$$56$$ 0 0
$$57$$ 3.79796i 0.503052i
$$58$$ 6.89898i 0.905880i
$$59$$ −1.55051 −0.201859 −0.100930 0.994894i $$-0.532182\pi$$
−0.100930 + 0.994894i $$0.532182\pi$$
$$60$$ −0.550510 5.44949i −0.0710706 0.703526i
$$61$$ −3.55051 −0.454596 −0.227298 0.973825i $$-0.572989\pi$$
−0.227298 + 0.973825i $$0.572989\pi$$
$$62$$ 8.89898i 1.13017i
$$63$$ 0 0
$$64$$ −1.00000 −0.125000
$$65$$ −1.00000 9.89898i −0.124035 1.22782i
$$66$$ 12.0000 1.47710
$$67$$ 8.00000i 0.977356i −0.872464 0.488678i $$-0.837479\pi$$
0.872464 0.488678i $$-0.162521\pi$$
$$68$$ 2.00000i 0.242536i
$$69$$ −7.10102 −0.854862
$$70$$ 0 0
$$71$$ −1.10102 −0.130667 −0.0653335 0.997863i $$-0.520811\pi$$
−0.0653335 + 0.997863i $$0.520811\pi$$
$$72$$ 3.00000i 0.353553i
$$73$$ 2.89898i 0.339300i 0.985504 + 0.169650i $$0.0542637\pi$$
−0.985504 + 0.169650i $$0.945736\pi$$
$$74$$ 2.00000 0.232495
$$75$$ −2.44949 12.0000i −0.282843 1.38564i
$$76$$ −1.55051 −0.177856
$$77$$ 0 0
$$78$$ 10.8990i 1.23407i
$$79$$ −6.89898 −0.776196 −0.388098 0.921618i $$-0.626868\pi$$
−0.388098 + 0.921618i $$0.626868\pi$$
$$80$$ −2.22474 + 0.224745i −0.248734 + 0.0251272i
$$81$$ −9.00000 −1.00000
$$82$$ 1.10102i 0.121587i
$$83$$ 2.44949i 0.268866i −0.990923 0.134433i $$-0.957079\pi$$
0.990923 0.134433i $$-0.0429214\pi$$
$$84$$ 0 0
$$85$$ 0.449490 + 4.44949i 0.0487540 + 0.482615i
$$86$$ 0.898979 0.0969395
$$87$$ 16.8990i 1.81176i
$$88$$ 4.89898i 0.522233i
$$89$$ −10.0000 −1.06000 −0.529999 0.847998i $$-0.677808\pi$$
−0.529999 + 0.847998i $$0.677808\pi$$
$$90$$ −0.674235 6.67423i −0.0710706 0.703526i
$$91$$ 0 0
$$92$$ 2.89898i 0.302240i
$$93$$ 21.7980i 2.26034i
$$94$$ −8.89898 −0.917860
$$95$$ −3.44949 + 0.348469i −0.353910 + 0.0357522i
$$96$$ −2.44949 −0.250000
$$97$$ 15.7980i 1.60404i −0.597297 0.802020i $$-0.703759\pi$$
0.597297 0.802020i $$-0.296241\pi$$
$$98$$ 0 0
$$99$$ 14.6969 1.47710
$$100$$ −4.89898 + 1.00000i −0.489898 + 0.100000i
$$101$$ −3.55051 −0.353289 −0.176644 0.984275i $$-0.556524\pi$$
−0.176644 + 0.984275i $$0.556524\pi$$
$$102$$ 4.89898i 0.485071i
$$103$$ 12.8990i 1.27097i 0.772111 + 0.635487i $$0.219201\pi$$
−0.772111 + 0.635487i $$0.780799\pi$$
$$104$$ −4.44949 −0.436308
$$105$$ 0 0
$$106$$ 10.8990 1.05860
$$107$$ 8.00000i 0.773389i −0.922208 0.386695i $$-0.873617\pi$$
0.922208 0.386695i $$-0.126383\pi$$
$$108$$ 0 0
$$109$$ −6.89898 −0.660802 −0.330401 0.943841i $$-0.607184\pi$$
−0.330401 + 0.943841i $$0.607184\pi$$
$$110$$ −1.10102 10.8990i −0.104978 1.03918i
$$111$$ 4.89898 0.464991
$$112$$ 0 0
$$113$$ 19.7980i 1.86244i −0.364464 0.931218i $$-0.618748\pi$$
0.364464 0.931218i $$-0.381252\pi$$
$$114$$ −3.79796 −0.355711
$$115$$ 0.651531 + 6.44949i 0.0607556 + 0.601418i
$$116$$ 6.89898 0.640554
$$117$$ 13.3485i 1.23407i
$$118$$ 1.55051i 0.142736i
$$119$$ 0 0
$$120$$ −5.44949 + 0.550510i −0.497468 + 0.0502545i
$$121$$ 13.0000 1.18182
$$122$$ 3.55051i 0.321448i
$$123$$ 2.69694i 0.243175i
$$124$$ 8.89898 0.799152
$$125$$ −10.6742 + 3.32577i −0.954733 + 0.297465i
$$126$$ 0 0
$$127$$ 14.8990i 1.32207i −0.750355 0.661035i $$-0.770117\pi$$
0.750355 0.661035i $$-0.229883\pi$$
$$128$$ 1.00000i 0.0883883i
$$129$$ 2.20204 0.193879
$$130$$ −9.89898 + 1.00000i −0.868198 + 0.0877058i
$$131$$ 6.44949 0.563495 0.281747 0.959489i $$-0.409086\pi$$
0.281747 + 0.959489i $$0.409086\pi$$
$$132$$ 12.0000i 1.04447i
$$133$$ 0 0
$$134$$ −8.00000 −0.691095
$$135$$ 0 0
$$136$$ 2.00000 0.171499
$$137$$ 1.79796i 0.153610i −0.997046 0.0768050i $$-0.975528\pi$$
0.997046 0.0768050i $$-0.0244719\pi$$
$$138$$ 7.10102i 0.604479i
$$139$$ 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
$$142$$ 1.10102i 0.0923956i
$$143$$ 21.7980i 1.82284i
$$144$$ −3.00000 −0.250000
$$145$$ 15.3485 1.55051i 1.27462 0.128763i
$$146$$ 2.89898 0.239921
$$147$$ 0 0
$$148$$ 2.00000i 0.164399i
$$149$$ 3.79796 0.311141 0.155570 0.987825i $$-0.450278\pi$$
0.155570 + 0.987825i $$0.450278\pi$$
$$150$$ −12.0000 + 2.44949i −0.979796 + 0.200000i
$$151$$ 19.5959 1.59469 0.797347 0.603522i $$-0.206236\pi$$
0.797347 + 0.603522i $$0.206236\pi$$
$$152$$ 1.55051i 0.125763i
$$153$$ 6.00000i 0.485071i
$$154$$ 0 0
$$155$$ 19.7980 2.00000i 1.59021 0.160644i
$$156$$ −10.8990 −0.872617
$$157$$ 3.55051i 0.283362i −0.989912 0.141681i $$-0.954749\pi$$
0.989912 0.141681i $$-0.0452507\pi$$
$$158$$ 6.89898i 0.548853i
$$159$$ 26.6969 2.11720
$$160$$ 0.224745 + 2.22474i 0.0177676 + 0.175882i
$$161$$ 0 0
$$162$$ 9.00000i 0.707107i
$$163$$ 7.10102i 0.556195i 0.960553 + 0.278097i $$0.0897038\pi$$
−0.960553 + 0.278097i $$0.910296\pi$$
$$164$$ −1.10102 −0.0859753
$$165$$ −2.69694 26.6969i −0.209956 2.07835i
$$166$$ −2.44949 −0.190117
$$167$$ 4.89898i 0.379094i 0.981872 + 0.189547i $$0.0607020\pi$$
−0.981872 + 0.189547i $$0.939298\pi$$
$$168$$ 0 0
$$169$$ −6.79796 −0.522920
$$170$$ 4.44949 0.449490i 0.341260 0.0344743i
$$171$$ −4.65153 −0.355711
$$172$$ 0.898979i 0.0685465i
$$173$$ 6.24745i 0.474985i −0.971389 0.237492i $$-0.923675\pi$$
0.971389 0.237492i $$-0.0763255\pi$$
$$174$$ 16.8990 1.28111
$$175$$ 0 0
$$176$$ −4.89898 −0.369274
$$177$$ 3.79796i 0.285472i
$$178$$ 10.0000i 0.749532i
$$179$$ −13.7980 −1.03131 −0.515654 0.856797i $$-0.672451\pi$$
−0.515654 + 0.856797i $$0.672451\pi$$
$$180$$ −6.67423 + 0.674235i −0.497468 + 0.0502545i
$$181$$ 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
$$184$$ 2.89898 0.213716
$$185$$ −0.449490 4.44949i −0.0330471 0.327133i
$$186$$ 21.7980 1.59830
$$187$$ 9.79796i 0.716498i
$$188$$ 8.89898i 0.649025i
$$189$$ 0 0
$$190$$ 0.348469 + 3.44949i 0.0252806 + 0.250252i
$$191$$ 12.6969 0.918718 0.459359 0.888251i $$-0.348079\pi$$
0.459359 + 0.888251i $$0.348079\pi$$
$$192$$ 2.44949i 0.176777i
$$193$$ 21.5959i 1.55451i 0.629187 + 0.777254i $$0.283388\pi$$
−0.629187 + 0.777254i $$0.716612\pi$$
$$194$$ −15.7980 −1.13423
$$195$$ −24.2474 + 2.44949i −1.73640 + 0.175412i
$$196$$ 0 0
$$197$$ 18.8990i 1.34650i 0.739417 + 0.673248i $$0.235101\pi$$
−0.739417 + 0.673248i $$0.764899\pi$$
$$198$$ 14.6969i 1.04447i
$$199$$ 16.8990 1.19794 0.598968 0.800773i $$-0.295577\pi$$
0.598968 + 0.800773i $$0.295577\pi$$
$$200$$ 1.00000 + 4.89898i 0.0707107 + 0.346410i
$$201$$ −19.5959 −1.38219
$$202$$ 3.55051i 0.249813i
$$203$$ 0 0
$$204$$ 4.89898 0.342997
$$205$$ −2.44949 + 0.247449i −0.171080 + 0.0172826i
$$206$$ 12.8990 0.898714
$$207$$ 8.69694i 0.604479i
$$208$$ 4.44949i 0.308517i
$$209$$ −7.59592 −0.525421
$$210$$ 0 0
$$211$$ 12.0000 0.826114 0.413057 0.910705i $$-0.364461\pi$$
0.413057 + 0.910705i $$0.364461\pi$$
$$212$$ 10.8990i 0.748545i
$$213$$ 2.69694i 0.184791i
$$214$$ −8.00000 −0.546869
$$215$$ −0.202041 2.00000i −0.0137791 0.136399i
$$216$$ 0 0
$$217$$ 0 0
$$218$$ 6.89898i 0.467258i
$$219$$ 7.10102 0.479842
$$220$$ −10.8990 + 1.10102i −0.734809 + 0.0742308i
$$221$$ 8.89898 0.598610
$$222$$ 4.89898i 0.328798i
$$223$$ 4.00000i 0.267860i −0.990991 0.133930i $$-0.957240\pi$$
0.990991 0.133930i $$-0.0427597\pi$$
$$224$$ 0 0
$$225$$ −14.6969 + 3.00000i −0.979796 + 0.200000i
$$226$$ −19.7980 −1.31694
$$227$$ 7.34847i 0.487735i −0.969809 0.243868i $$-0.921584\pi$$
0.969809 0.243868i $$-0.0784162\pi$$
$$228$$ 3.79796i 0.251526i
$$229$$ −19.1464 −1.26523 −0.632616 0.774466i $$-0.718019\pi$$
−0.632616 + 0.774466i $$0.718019\pi$$
$$230$$ 6.44949 0.651531i 0.425267 0.0429607i
$$231$$ 0 0
$$232$$ 6.89898i 0.452940i
$$233$$ 29.7980i 1.95213i −0.217481 0.976065i $$-0.569784\pi$$
0.217481 0.976065i $$-0.430216\pi$$
$$234$$ −13.3485 −0.872617
$$235$$ 2.00000 + 19.7980i 0.130466 + 1.29148i
$$236$$ 1.55051 0.100930
$$237$$ 16.8990i 1.09771i
$$238$$ 0 0
$$239$$ 6.20204 0.401177 0.200588 0.979676i $$-0.435715\pi$$
0.200588 + 0.979676i $$0.435715\pi$$
$$240$$ 0.550510 + 5.44949i 0.0355353 + 0.351763i
$$241$$ 8.69694 0.560219 0.280110 0.959968i $$-0.409629\pi$$
0.280110 + 0.959968i $$0.409629\pi$$
$$242$$ 13.0000i 0.835672i
$$243$$ 22.0454i 1.41421i
$$244$$ 3.55051 0.227298
$$245$$ 0 0
$$246$$ −2.69694 −0.171951
$$247$$ 6.89898i 0.438972i
$$248$$ 8.89898i 0.565086i
$$249$$ −6.00000 −0.380235
$$250$$ 3.32577 + 10.6742i 0.210340 + 0.675098i
$$251$$ 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
$$254$$ −14.8990 −0.934845
$$255$$ 10.8990 1.10102i 0.682521 0.0689486i
$$256$$ 1.00000 0.0625000
$$257$$ 8.69694i 0.542500i 0.962509 + 0.271250i $$0.0874370\pi$$
−0.962509 + 0.271250i $$0.912563\pi$$
$$258$$ 2.20204i 0.137093i
$$259$$ 0 0
$$260$$ 1.00000 + 9.89898i 0.0620174 + 0.613909i
$$261$$ 20.6969 1.28111
$$262$$ 6.44949i 0.398451i
$$263$$ 9.79796i 0.604168i −0.953281 0.302084i $$-0.902318\pi$$
0.953281 0.302084i $$-0.0976823\pi$$
$$264$$ −12.0000 −0.738549
$$265$$ −2.44949 24.2474i −0.150471 1.48951i
$$266$$ 0 0
$$267$$ 24.4949i 1.49906i
$$268$$ 8.00000i 0.488678i
$$269$$ 19.1464 1.16738 0.583689 0.811977i $$-0.301609\pi$$
0.583689 + 0.811977i $$0.301609\pi$$
$$270$$ 0 0
$$271$$ −12.0000 −0.728948 −0.364474 0.931214i $$-0.618751\pi$$
−0.364474 + 0.931214i $$0.618751\pi$$
$$272$$ 2.00000i 0.121268i
$$273$$ 0 0
$$274$$ −1.79796 −0.108619
$$275$$ −24.0000 + 4.89898i −1.44725 + 0.295420i
$$276$$ 7.10102 0.427431
$$277$$ 14.8990i 0.895193i −0.894236 0.447596i $$-0.852280\pi$$
0.894236 0.447596i $$-0.147720\pi$$
$$278$$ 1.55051i 0.0929934i
$$279$$ 26.6969 1.59830
$$280$$ 0 0
$$281$$ −18.0000 −1.07379 −0.536895 0.843649i $$-0.680403\pi$$
−0.536895 + 0.843649i $$0.680403\pi$$
$$282$$ 21.7980i 1.29805i
$$283$$ 3.75255i 0.223066i 0.993761 + 0.111533i $$0.0355761\pi$$
−0.993761 + 0.111533i $$0.964424\pi$$
$$284$$ 1.10102 0.0653335
$$285$$ 0.853572 + 8.44949i 0.0505612 + 0.500505i
$$286$$ −21.7980 −1.28894
$$287$$ 0 0
$$288$$ 3.00000i 0.176777i
$$289$$ 13.0000 0.764706
$$290$$ −1.55051 15.3485i −0.0910491 0.901293i
$$291$$ −38.6969 −2.26845
$$292$$ 2.89898i 0.169650i
$$293$$ 18.2474i 1.06603i 0.846107 + 0.533014i $$0.178941\pi$$
−0.846107 + 0.533014i $$0.821059\pi$$
$$294$$ 0 0
$$295$$ 3.44949 0.348469i 0.200837 0.0202887i
$$296$$ −2.00000 −0.116248
$$297$$ 0 0
$$298$$ 3.79796i 0.220010i
$$299$$ 12.8990 0.745967
$$300$$ 2.44949 + 12.0000i 0.141421 + 0.692820i
$$301$$ 0 0
$$302$$ 19.5959i 1.12762i
$$303$$ 8.69694i 0.499626i
$$304$$ 1.55051 0.0889279
$$305$$ 7.89898 0.797959i 0.452294 0.0456910i
$$306$$ 6.00000 0.342997
$$307$$ 20.2474i 1.15558i 0.816184 + 0.577791i $$0.196085\pi$$
−0.816184 + 0.577791i $$0.803915\pi$$
$$308$$ 0 0
$$309$$ 31.5959 1.79743
$$310$$ −2.00000 19.7980i −0.113592 1.12445i
$$311$$ −12.0000 −0.680458 −0.340229 0.940343i $$-0.610505\pi$$
−0.340229 + 0.940343i $$0.610505\pi$$
$$312$$ 10.8990i 0.617033i
$$313$$ 21.5959i 1.22067i −0.792142 0.610337i $$-0.791034\pi$$
0.792142 0.610337i $$-0.208966\pi$$
$$314$$ −3.55051 −0.200367
$$315$$ 0 0
$$316$$ 6.89898 0.388098
$$317$$ 22.4949i 1.26344i −0.775197 0.631720i $$-0.782349\pi$$
0.775197 0.631720i $$-0.217651\pi$$
$$318$$ 26.6969i 1.49709i
$$319$$ 33.7980 1.89232
$$320$$ 2.22474 0.224745i 0.124367 0.0125636i
$$321$$ −19.5959 −1.09374
$$322$$ 0 0
$$323$$ 3.10102i 0.172545i
$$324$$ 9.00000 0.500000
$$325$$ 4.44949 + 21.7980i 0.246813 + 1.20913i
$$326$$ 7.10102 0.393289
$$327$$ 16.8990i 0.934516i
$$328$$ 1.10102i 0.0607937i
$$329$$ 0 0
$$330$$ −26.6969 + 2.69694i −1.46962 + 0.148462i
$$331$$ −18.6969 −1.02768 −0.513838 0.857887i $$-0.671777\pi$$
−0.513838 + 0.857887i $$0.671777\pi$$
$$332$$ 2.44949i 0.134433i
$$333$$ 6.00000i 0.328798i
$$334$$ 4.89898 0.268060
$$335$$ 1.79796 + 17.7980i 0.0982330 + 0.972406i
$$336$$ 0 0
$$337$$ 9.59592i 0.522723i 0.965241 + 0.261361i $$0.0841715\pi$$
−0.965241 + 0.261361i $$0.915829\pi$$
$$338$$ 6.79796i 0.369760i
$$339$$ −48.4949 −2.63388
$$340$$ −0.449490 4.44949i −0.0243770 0.241307i
$$341$$ 43.5959 2.36085
$$342$$ 4.65153i 0.251526i
$$343$$ 0 0
$$344$$ −0.898979 −0.0484697
$$345$$ 15.7980 1.59592i 0.850534 0.0859213i
$$346$$ −6.24745 −0.335865
$$347$$ 28.8990i 1.55138i 0.631115 + 0.775689i $$0.282598\pi$$
−0.631115 + 0.775689i $$0.717402\pi$$
$$348$$ 16.8990i 0.905880i
$$349$$ −8.44949 −0.452291 −0.226145 0.974094i $$-0.572612\pi$$
−0.226145 + 0.974094i $$0.572612\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 4.89898i 0.261116i
$$353$$ 22.8990i 1.21879i 0.792867 + 0.609395i $$0.208588\pi$$
−0.792867 + 0.609395i $$0.791412\pi$$
$$354$$ 3.79796 0.201859
$$355$$ 2.44949 0.247449i 0.130005 0.0131332i
$$356$$ 10.0000 0.529999
$$357$$ 0 0
$$358$$ 13.7980i 0.729245i
$$359$$ 27.5959 1.45646 0.728228 0.685334i $$-0.240344\pi$$
0.728228 + 0.685334i $$0.240344\pi$$
$$360$$ 0.674235 + 6.67423i 0.0355353 + 0.351763i
$$361$$ −16.5959 −0.873469
$$362$$ 10.2474i 0.538594i
$$363$$ 31.8434i 1.67134i
$$364$$ 0 0
$$365$$ −0.651531 6.44949i −0.0341027 0.337582i
$$366$$ 8.69694 0.454596
$$367$$ 32.0000i 1.67039i −0.549957 0.835193i $$-0.685356\pi$$
0.549957 0.835193i $$-0.314644\pi$$
$$368$$ 2.89898i 0.151120i
$$369$$ −3.30306 −0.171951
$$370$$ −4.44949 + 0.449490i −0.231318 + 0.0233679i
$$371$$ 0 0
$$372$$ 21.7980i 1.13017i
$$373$$ 4.69694i 0.243198i 0.992579 + 0.121599i $$0.0388022\pi$$
−0.992579 + 0.121599i $$0.961198\pi$$
$$374$$ 9.79796 0.506640
$$375$$ 8.14643 + 26.1464i 0.420680 + 1.35020i
$$376$$ 8.89898 0.458930
$$377$$ 30.6969i 1.58097i
$$378$$ 0 0
$$379$$ −30.6969 −1.57680 −0.788398 0.615166i $$-0.789089\pi$$
−0.788398 + 0.615166i $$0.789089\pi$$
$$380$$ 3.44949 0.348469i 0.176955 0.0178761i
$$381$$ −36.4949 −1.86969
$$382$$ 12.6969i 0.649632i
$$383$$ 7.10102i 0.362845i −0.983405 0.181423i $$-0.941930\pi$$
0.983405 0.181423i $$-0.0580702\pi$$
$$384$$ 2.44949 0.125000
$$385$$ 0 0
$$386$$ 21.5959 1.09920
$$387$$ 2.69694i 0.137093i
$$388$$ 15.7980i 0.802020i
$$389$$ −13.1010 −0.664248 −0.332124 0.943236i $$-0.607765\pi$$
−0.332124 + 0.943236i $$0.607765\pi$$
$$390$$ 2.44949 + 24.2474i 0.124035 + 1.22782i
$$391$$ −5.79796 −0.293215
$$392$$ 0 0
$$393$$ 15.7980i 0.796902i
$$394$$ 18.8990 0.952117
$$395$$ 15.3485 1.55051i 0.772265 0.0780146i
$$396$$ −14.6969 −0.738549
$$397$$ 2.65153i 0.133077i 0.997784 + 0.0665383i $$0.0211954\pi$$
−0.997784 + 0.0665383i $$0.978805\pi$$
$$398$$ 16.8990i 0.847069i
$$399$$ 0 0
$$400$$ 4.89898 1.00000i 0.244949 0.0500000i
$$401$$ −29.3939 −1.46786 −0.733930 0.679225i $$-0.762316\pi$$
−0.733930 + 0.679225i $$0.762316\pi$$
$$402$$ 19.5959i 0.977356i
$$403$$ 39.5959i 1.97241i
$$404$$ 3.55051 0.176644
$$405$$ 20.0227 2.02270i 0.994936 0.100509i
$$406$$ 0 0
$$407$$ 9.79796i 0.485667i
$$408$$ 4.89898i 0.242536i
$$409$$ 34.4949 1.70566 0.852831 0.522186i $$-0.174883\pi$$
0.852831 + 0.522186i $$0.174883\pi$$
$$410$$ 0.247449 + 2.44949i 0.0122206 + 0.120972i
$$411$$ −4.40408 −0.217237
$$412$$ 12.8990i 0.635487i
$$413$$ 0 0
$$414$$ 8.69694 0.427431
$$415$$ 0.550510 + 5.44949i 0.0270235 + 0.267505i
$$416$$ 4.44949 0.218154
$$417$$ 3.79796i 0.185987i
$$418$$ 7.59592i 0.371528i
$$419$$ −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 $$0.532651\pi$$
$$422$$ 12.0000i 0.584151i
$$423$$ 26.6969i 1.29805i
$$424$$ −10.8990 −0.529301
$$425$$ −2.00000 9.79796i −0.0970143 0.475271i
$$426$$ 2.69694 0.130667
$$427$$ 0 0
$$428$$ 8.00000i 0.386695i
$$429$$ −53.3939 −2.57788
$$430$$ −2.00000 + 0.202041i −0.0964486 + 0.00974328i
$$431$$ −1.79796 −0.0866046 −0.0433023 0.999062i $$-0.513788\pi$$
−0.0433023 + 0.999062i $$0.513788\pi$$
$$432$$ 0 0
$$433$$ 0.202041i 0.00970947i −0.999988 0.00485474i $$-0.998455\pi$$
0.999988 0.00485474i $$-0.00154532\pi$$
$$434$$ 0 0
$$435$$ −3.79796 37.5959i −0.182098 1.80259i
$$436$$ 6.89898 0.330401
$$437$$ 4.49490i 0.215020i
$$438$$ 7.10102i 0.339300i
$$439$$ −21.3939 −1.02107 −0.510537 0.859856i $$-0.670553\pi$$
−0.510537 + 0.859856i $$0.670553\pi$$
$$440$$ 1.10102 + 10.8990i 0.0524891 + 0.519588i
$$441$$ 0 0
$$442$$ 8.89898i 0.423281i
$$443$$ 9.79796i 0.465515i −0.972535 0.232758i $$-0.925225\pi$$
0.972535 0.232758i $$-0.0747749\pi$$
$$444$$ −4.89898 −0.232495
$$445$$ 22.2474 2.24745i 1.05463 0.106539i
$$446$$ −4.00000 −0.189405
$$447$$ 9.30306i 0.440020i
$$448$$ 0 0
$$449$$ 10.0000 0.471929 0.235965 0.971762i $$-0.424175\pi$$
0.235965 + 0.971762i $$0.424175\pi$$
$$450$$ 3.00000 + 14.6969i 0.141421 + 0.692820i
$$451$$ −5.39388 −0.253988
$$452$$ 19.7980i 0.931218i
$$453$$ 48.0000i 2.25524i
$$454$$ −7.34847 −0.344881
$$455$$ 0 0
$$456$$ 3.79796 0.177856
$$457$$ 29.5959i 1.38444i 0.721687 + 0.692219i $$0.243367\pi$$
−0.721687 + 0.692219i $$0.756633\pi$$
$$458$$ 19.1464i 0.894654i
$$459$$ 0 0
$$460$$ −0.651531 6.44949i −0.0303778 0.300709i
$$461$$ −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 $$-0.973372\pi$$
0.996503 0.0835582i $$-0.0266285\pi$$
$$464$$ −6.89898 −0.320277
$$465$$ −4.89898 48.4949i −0.227185 2.24890i
$$466$$ −29.7980 −1.38036
$$467$$ 10.4495i 0.483545i −0.970333 0.241772i $$-0.922271\pi$$
0.970333 0.241772i $$-0.0777287\pi$$
$$468$$ 13.3485i 0.617033i
$$469$$ 0 0
$$470$$ 19.7980 2.00000i 0.913212 0.0922531i
$$471$$ −8.69694 −0.400734
$$472$$ 1.55051i 0.0713680i
$$473$$ 4.40408i 0.202500i
$$474$$ 16.8990 0.776196
$$475$$ 7.59592 1.55051i 0.348525 0.0711423i
$$476$$ 0 0
$$477$$ 32.6969i 1.49709i
$$478$$ 6.20204i 0.283675i
$$479$$ 9.30306 0.425068 0.212534 0.977154i $$-0.431828\pi$$
0.212534 + 0.977154i $$0.431828\pi$$
$$480$$ 5.44949 0.550510i 0.248734 0.0251272i
$$481$$ −8.89898 −0.405759
$$482$$ 8.69694i 0.396135i
$$483$$ 0 0
$$484$$ −13.0000 −0.590909
$$485$$ 3.55051 + 35.1464i 0.161220 + 1.59592i
$$486$$ 22.0454 1.00000
$$487$$ 7.30306i 0.330933i −0.986215 0.165467i $$-0.947087\pi$$
0.986215 0.165467i $$-0.0529130\pi$$
$$488$$ 3.55051i 0.160724i
$$489$$ 17.3939 0.786578
$$490$$ 0 0
$$491$$ 19.5959 0.884351 0.442176 0.896928i $$-0.354207\pi$$
0.442176 + 0.896928i $$0.354207\pi$$
$$492$$ 2.69694i 0.121587i
$$493$$ 13.7980i 0.621429i
$$494$$ 6.89898 0.310400
$$495$$ −32.6969 + 3.30306i −1.46962 + 0.148462i
$$496$$ −8.89898 −0.399576
$$497$$ 0 0
$$498$$ 6.00000i 0.268866i
$$499$$ −6.20204 −0.277641 −0.138821 0.990318i $$-0.544331\pi$$
−0.138821 + 0.990318i $$0.544331\pi$$
$$500$$ 10.6742 3.32577i 0.477366 0.148733i
$$501$$ 12.0000 0.536120
$$502$$ 6.44949i 0.287855i
$$503$$ 4.00000i 0.178351i −0.996016 0.0891756i $$-0.971577\pi$$
0.996016 0.0891756i $$-0.0284232\pi$$
$$504$$ 0 0
$$505$$ 7.89898 0.797959i 0.351500 0.0355087i
$$506$$ 14.2020 0.631358
$$507$$ 16.6515i 0.739520i
$$508$$ 14.8990i 0.661035i
$$509$$ −31.5505 −1.39845 −0.699226 0.714901i $$-0.746472\pi$$
−0.699226 + 0.714901i $$0.746472\pi$$
$$510$$ −1.10102 10.8990i −0.0487540 0.482615i
$$511$$ 0 0
$$512$$ 1.00000i 0.0441942i
$$513$$ 0 0
$$514$$ 8.69694 0.383606
$$515$$ −2.89898 28.6969i −0.127744 1.26454i
$$516$$ −2.20204 −0.0969395
$$517$$ 43.5959i 1.91735i
$$518$$ 0 0
$$519$$ −15.3031 −0.671730
$$520$$ 9.89898 1.00000i 0.434099 0.0438529i
$$521$$ −32.6969 −1.43248 −0.716239 0.697855i $$-0.754138\pi$$
−0.716239 + 0.697855i $$0.754138\pi$$
$$522$$ 20.6969i 0.905880i
$$523$$ 33.1464i 1.44939i −0.689069 0.724696i $$-0.741980\pi$$
0.689069 0.724696i $$-0.258020\pi$$
$$524$$ −6.44949 −0.281747
$$525$$ 0 0
$$526$$ −9.79796 −0.427211
$$527$$ 17.7980i 0.775291i
$$528$$ 12.0000i 0.522233i
$$529$$ 14.5959 0.634605
$$530$$ −24.2474 + 2.44949i −1.05324 + 0.106399i
$$531$$ 4.65153 0.201859
$$532$$ 0 0
$$533$$ 4.89898i 0.212198i
$$534$$ 24.4949 1.06000
$$535$$ 1.79796 + 17.7980i 0.0777325 + 0.769473i
$$536$$ 8.00000 0.345547
$$537$$ 33.7980i 1.45849i
$$538$$ 19.1464i 0.825461i
$$539$$ 0 0
$$540$$ 0 0
$$541$$ 9.59592 0.412561 0.206280 0.978493i $$-0.433864\pi$$
0.206280 + 0.978493i $$0.433864\pi$$
$$542$$ 12.0000i 0.515444i
$$543$$ 25.1010i 1.07719i
$$544$$ −2.00000 −0.0857493
$$545$$ 15.3485 1.55051i 0.657456 0.0664166i
$$546$$ 0 0
$$547$$ 18.6969i 0.799423i −0.916641 0.399712i $$-0.869110\pi$$
0.916641 0.399712i $$-0.130890\pi$$
$$548$$ 1.79796i 0.0768050i
$$549$$ 10.6515 0.454596
$$550$$ 4.89898 + 24.0000i 0.208893 + 1.02336i
$$551$$ −10.6969 −0.455705
$$552$$ 7.10102i 0.302240i
$$553$$ 0 0
$$554$$ −14.8990 −0.632997
$$555$$ −10.8990 + 1.10102i −0.462636 + 0.0467357i
$$556$$ −1.55051 −0.0657563
$$557$$ 12.6969i 0.537987i 0.963142 + 0.268993i $$0.0866909\pi$$
−0.963142 + 0.268993i $$0.913309\pi$$
$$558$$ 26.6969i 1.13017i
$$559$$ −4.00000 −0.169182
$$560$$ 0 0
$$561$$ 24.0000 1.01328
$$562$$ 18.0000i 0.759284i
$$563$$ 30.0454i 1.26626i −0.774044 0.633131i $$-0.781769\pi$$
0.774044 0.633131i $$-0.218231\pi$$
$$564$$ 21.7980 0.917860
$$565$$ 4.44949 + 44.0454i 0.187191 + 1.85300i
$$566$$ 3.75255 0.157731
$$567$$ 0 0
$$568$$ 1.10102i 0.0461978i
$$569$$ −33.7980 −1.41688 −0.708442 0.705769i $$-0.750602\pi$$
−0.708442 + 0.705769i $$0.750602\pi$$
$$570$$ 8.44949 0.853572i 0.353910 0.0357522i
$$571$$ −11.1010 −0.464563 −0.232282 0.972649i $$-0.574619\pi$$
−0.232282 + 0.972649i $$0.574619\pi$$
$$572$$ 21.7980i 0.911418i
$$573$$ 31.1010i 1.29926i
$$574$$ 0 0
$$575$$ −2.89898 14.2020i −0.120896 0.592266i
$$576$$ 3.00000 0.125000
$$577$$ 2.49490i 0.103864i 0.998651 + 0.0519320i $$0.0165379\pi$$
−0.998651 + 0.0519320i $$0.983462\pi$$
$$578$$ 13.0000i 0.540729i
$$579$$ 52.8990 2.19841
$$580$$ −15.3485 + 1.55051i −0.637310 + 0.0643814i
$$581$$ 0 0
$$582$$ 38.6969i 1.60404i
$$583$$ 53.3939i 2.21135i
$$584$$ −2.89898 −0.119961
$$585$$ 3.00000 + 29.6969i 0.124035 + 1.22782i
$$586$$ 18.2474 0.753795
$$587$$ 1.14643i 0.0473182i −0.999720 0.0236591i $$-0.992468\pi$$
0.999720 0.0236591i $$-0.00753162\pi$$
$$588$$ 0 0
$$589$$ −13.7980 −0.568535
$$590$$ −0.348469 3.44949i −0.0143463 0.142013i
$$591$$ 46.2929 1.90423
$$592$$ 2.00000i 0.0821995i
$$593$$ 10.8990i 0.447567i −0.974639 0.223784i $$-0.928159\pi$$
0.974639 0.223784i $$-0.0718409\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ −3.79796 −0.155570
$$597$$ 41.3939i 1.69414i
$$598$$ 12.8990i 0.527478i
$$599$$ 13.1010 0.535293 0.267647 0.963517i $$-0.413754\pi$$
0.267647 + 0.963517i $$0.413754\pi$$
$$600$$ 12.0000 2.44949i 0.489898 0.100000i
$$601$$ 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
$$604$$ −19.5959 −0.797347
$$605$$ −28.9217 + 2.92168i −1.17583 + 0.118783i
$$606$$ 8.69694 0.353289
$$607$$ 33.3939i 1.35542i −0.735331 0.677708i $$-0.762973\pi$$
0.735331 0.677708i $$-0.237027\pi$$
$$608$$ 1.55051i 0.0628815i
$$609$$ 0 0
$$610$$ −0.797959 7.89898i −0.0323084 0.319820i
$$611$$ 39.5959 1.60188
$$612$$ 6.00000i 0.242536i
$$613$$ 27.7980i 1.12275i 0.827562 + 0.561374i $$0.189727\pi$$
−0.827562 + 0.561374i $$0.810273\pi$$
$$614$$ 20.2474 0.817121
$$615$$ 0.606123 + 6.00000i 0.0244412 + 0.241943i
$$616$$ 0 0
$$617$$ 29.5959i 1.19149i 0.803175 + 0.595743i $$0.203142\pi$$
−0.803175 + 0.595743i $$0.796858\pi$$
$$618$$ 31.5959i 1.27097i
$$619$$ −41.5505 −1.67006 −0.835028 0.550207i $$-0.814549\pi$$
−0.835028 + 0.550207i $$0.814549\pi$$
$$620$$ −19.7980 + 2.00000i −0.795105 + 0.0803219i
$$621$$ 0 0
$$622$$ 12.0000i 0.481156i
$$623$$ 0 0
$$624$$ 10.8990 0.436308
$$625$$ 23.0000 9.79796i 0.920000 0.391918i
$$626$$ −21.5959 −0.863146
$$627$$ 18.6061i 0.743057i
$$628$$ 3.55051i 0.141681i
$$629$$ 4.00000 0.159490
$$630$$ 0 0
$$631$$ −42.4949 −1.69170 −0.845848 0.533425i $$-0.820905\pi$$
−0.845848 + 0.533425i $$0.820905\pi$$
$$632$$ 6.89898i 0.274427i
$$633$$ 29.3939i 1.16830i
$$634$$ −22.4949 −0.893387
$$635$$ 3.34847 + 33.1464i 0.132880 + 1.31538i
$$636$$ −26.6969 −1.05860
$$637$$ 0 0
$$638$$ 33.7980i 1.33807i
$$639$$ 3.30306 0.130667
$$640$$ −0.224745 2.22474i −0.00888382 0.0879408i
$$641$$ 25.7980 1.01896 0.509479 0.860483i $$-0.329838\pi$$
0.509479 + 0.860483i $$0.329838\pi$$
$$642$$ 19.5959i 0.773389i
$$643$$ 25.1464i 0.991678i 0.868414 + 0.495839i $$0.165139\pi$$
−0.868414 + 0.495839i $$0.834861\pi$$
$$644$$ 0 0
$$645$$ −4.89898 + 0.494897i −0.192897 + 0.0194866i
$$646$$ −3.10102 −0.122008
$$647$$ 46.2929i 1.81996i 0.414652 + 0.909980i $$0.363903\pi$$
−0.414652 + 0.909980i $$0.636097\pi$$
$$648$$ 9.00000i 0.353553i
$$649$$ 7.59592 0.298166
$$650$$ 21.7980 4.44949i 0.854986 0.174523i
$$651$$ 0 0
$$652$$ 7.10102i 0.278097i
$$653$$ 20.2020i 0.790567i 0.918559 + 0.395283i $$0.129354\pi$$
−0.918559 + 0.395283i $$0.870646\pi$$
$$654$$ 16.8990 0.660802
$$655$$ −14.3485 + 1.44949i −0.560641 + 0.0566363i
$$656$$ 1.10102 0.0429876
$$657$$ 8.69694i 0.339300i
$$658$$ 0 0
$$659$$ −16.8990 −0.658291 −0.329145 0.944279i $$-0.606761\pi$$
−0.329145 + 0.944279i $$0.606761\pi$$
$$660$$ 2.69694 + 26.6969i 0.104978 + 1.03918i
$$661$$ 40.9444 1.59255 0.796276 0.604933i $$-0.206800\pi$$
0.796276 + 0.604933i $$0.206800\pi$$
$$662$$ 18.6969i 0.726677i
$$663$$ 21.7980i 0.846563i
$$664$$ 2.44949 0.0950586
$$665$$ 0 0
$$666$$ −6.00000 −0.232495
$$667$$ 20.0000i 0.774403i
$$668$$ 4.89898i 0.189547i
$$669$$ −9.79796 −0.378811
$$670$$ 17.7980 1.79796i 0.687595 0.0694612i
$$671$$ 17.3939 0.671483
$$672$$ 0 0
$$673$$ 17.7980i 0.686061i 0.939324 + 0.343030i $$0.111453\pi$$
−0.939324 + 0.343030i $$0.888547\pi$$
$$674$$ 9.59592 0.369621
$$675$$ 0 0
$$676$$ 6.79796 0.261460
$$677$$ 36.4495i 1.40087i 0.713717 + 0.700434i $$0.247010\pi$$
−0.713717 + 0.700434i $$0.752990\pi$$
$$678$$ 48.4949i 1.86244i
$$679$$ 0 0
$$680$$ −4.44949 + 0.449490i −0.170630 + 0.0172371i
$$681$$ −18.0000 −0.689761
$$682$$ 43.5959i 1.66937i
$$683$$ 3.59592i 0.137594i −0.997631 0.0687970i $$-0.978084\pi$$
0.997631 0.0687970i $$-0.0219161\pi$$
$$684$$ 4.65153 0.177856
$$685$$ 0.404082 + 4.00000i 0.0154392 + 0.152832i
$$686$$ 0 0
$$687$$ 46.8990i 1.78931i
$$688$$ 0.898979i 0.0342733i
$$689$$ −48.4949 −1.84751
$$690$$ −1.59592 15.7980i −0.0607556 0.601418i
$$691$$ −21.1464 −0.804448 −0.402224 0.915541i $$-0.631763\pi$$
−0.402224 + 0.915541i $$0.631763\pi$$
$$692$$ 6.24745i 0.237492i
$$693$$ 0 0
$$694$$ 28.8990 1.09699
$$695$$ −3.44949 + 0.348469i −0.130847 + 0.0132182i
$$696$$ −16.8990 −0.640554
$$697$$ 2.20204i 0.0834083i
$$698$$ 8.44949i 0.319818i
$$699$$ −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
$$703$$ 3.10102i 0.116957i
$$704$$ 4.89898 0.184637
$$705$$ 48.4949 4.89898i 1.82642 0.184506i
$$706$$ 22.8990 0.861814
$$707$$ 0 0
$$708$$ 3.79796i 0.142736i
$$709$$ 28.2929 1.06256 0.531280 0.847196i $$-0.321711\pi$$
0.531280 + 0.847196i $$0.321711\pi$$
$$710$$ −0.247449 2.44949i −0.00928658 0.0919277i
$$711$$ 20.6969 0.776196
$$712$$ 10.0000i 0.374766i
$$713$$ 25.7980i 0.966141i
$$714$$ 0 0
$$715$$ 4.89898 + 48.4949i 0.183211 + 1.81361i
$$716$$ 13.7980 0.515654
$$717$$ 15.1918i 0.567350i
$$718$$ 27.5959i 1.02987i
$$719$$ −4.49490 −0.167631 −0.0838157 0.996481i $$-0.526711\pi$$
−0.0838157 + 0.996481i $$0.526711\pi$$
$$720$$ 6.67423 0.674235i 0.248734 0.0251272i
$$721$$ 0 0
$$722$$ 16.5959i 0.617636i
$$723$$ 21.3031i 0.792269i
$$724$$ −10.2474 −0.380843
$$725$$ −33.7980 + 6.89898i −1.25522 + 0.256222i
$$726$$ −31.8434 −1.18182
$$727$$ 22.6969i 0.841783i −0.907111 0.420891i $$-0.861717\pi$$
0.907111 0.420891i $$-0.138283\pi$$
$$728$$ 0 0
$$729$$ 27.0000 1.00000
$$730$$ −6.44949 + 0.651531i −0.238706 + 0.0241142i
$$731$$ 1.79796 0.0664999
$$732$$ 8.69694i 0.321448i
$$733$$ 39.6413i 1.46419i 0.681205 + 0.732093i $$0.261456\pi$$
−0.681205 + 0.732093i $$0.738544\pi$$
$$734$$ −32.0000 −1.18114
$$735$$ 0 0
$$736$$ −2.89898 −0.106858
$$737$$ 39.1918i 1.44365i
$$738$$ 3.30306i 0.121587i
$$739$$ −4.49490 −0.165347 −0.0826737 0.996577i $$-0.526346\pi$$
−0.0826737 + 0.996577i $$0.526346\pi$$
$$740$$ 0.449490 + 4.44949i 0.0165236 + 0.163566i
$$741$$ 16.8990 0.620800
$$742$$ 0 0
$$743$$ 44.6969i 1.63977i 0.572527 + 0.819886i $$0.305963\pi$$
−0.572527 + 0.819886i $$0.694037\pi$$
$$744$$ −21.7980 −0.799152
$$745$$ −8.44949 + 0.853572i −0.309565 + 0.0312725i
$$746$$ 4.69694 0.171967
$$747$$ 7.34847i 0.268866i
$$748$$ 9.79796i 0.358249i
$$749$$ 0 0
$$750$$ 26.1464 8.14643i 0.954733 0.297465i
$$751$$ −41.7980 −1.52523 −0.762615 0.646853i $$-0.776085\pi$$
−0.762615 + 0.646853i $$0.776085\pi$$
$$752$$ 8.89898i 0.324512i
$$753$$ 15.7980i 0.575710i
$$754$$ −30.6969 −1.11792
$$755$$ −43.5959 + 4.40408i −1.58662 + 0.160281i
$$756$$ 0 0
$$757$$ 51.7980i 1.88263i −0.337531 0.941314i $$-0.609592\pi$$
0.337531 0.941314i $$-0.390408\pi$$
$$758$$ 30.6969i 1.11496i
$$759$$ 34.7878 1.26272
$$760$$ −0.348469 3.44949i −0.0126403 0.125126i
$$761$$ 21.1010 0.764911 0.382456 0.923974i $$-0.375078\pi$$
0.382456 + 0.923974i $$0.375078\pi$$
$$762$$ 36.4949i 1.32207i
$$763$$ 0 0
$$764$$ −12.6969 −0.459359
$$765$$ −1.34847 13.3485i −0.0487540 0.482615i
$$766$$ −7.10102 −0.256570
$$767$$ 6.89898i 0.249108i
$$768$$ 2.44949i 0.0883883i
$$769$$ −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
$$772$$ 21.5959i 0.777254i
$$773$$ 1.34847i 0.0485011i 0.999706 + 0.0242505i $$0.00771994\pi$$
−0.999706 + 0.0242505i $$0.992280\pi$$
$$774$$ −2.69694 −0.0969395
$$775$$ −43.5959 + 8.89898i −1.56601 + 0.319661i
$$776$$ 15.7980 0.567114
$$777$$ 0 0
$$778$$ 13.1010i 0.469694i
$$779$$ 1.70714 0.0611648
$$780$$ 24.2474 2.44949i 0.868198 0.0877058i
$$781$$ 5.39388 0.193008
$$782$$ 5.79796i 0.207335i
$$783$$ 0 0
$$784$$ 0 0
$$785$$ 0.797959 + 7.89898i 0.0284804 + 0.281927i
$$786$$ −15.7980 −0.563495
$$787$$ 50.4495i 1.79833i −0.437610 0.899165i $$-0.644175\pi$$
0.437610 0.899165i $$-0.355825\pi$$
$$788$$ 18.8990i 0.673248i
$$789$$ −24.0000 −0.854423
$$790$$ −1.55051 15.3485i −0.0551647