# Properties

 Label 98.4.c.e.67.1 Level $98$ Weight $4$ Character 98.67 Analytic conductor $5.782$ Analytic rank $0$ Dimension $2$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$98 = 2 \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 98.c (of order $$3$$, degree $$2$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$5.78218718056$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(\zeta_{6})$$ Defining polynomial: $$x^{2} - x + 1$$ x^2 - x + 1 Coefficient ring: $$\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 14) Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 67.1 Root $$0.500000 + 0.866025i$$ of defining polynomial Character $$\chi$$ $$=$$ 98.67 Dual form 98.4.c.e.79.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(1.00000 + 1.73205i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-2.00000 + 3.46410i) q^{4} +(3.50000 + 6.06218i) q^{5} -2.00000 q^{6} -8.00000 q^{8} +(13.0000 + 22.5167i) q^{9} +O(q^{10})$$ $$q+(1.00000 + 1.73205i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-2.00000 + 3.46410i) q^{4} +(3.50000 + 6.06218i) q^{5} -2.00000 q^{6} -8.00000 q^{8} +(13.0000 + 22.5167i) q^{9} +(-7.00000 + 12.1244i) q^{10} +(-17.5000 + 30.3109i) q^{11} +(-2.00000 - 3.46410i) q^{12} -66.0000 q^{13} -7.00000 q^{15} +(-8.00000 - 13.8564i) q^{16} +(29.5000 - 51.0955i) q^{17} +(-26.0000 + 45.0333i) q^{18} +(68.5000 + 118.645i) q^{19} -28.0000 q^{20} -70.0000 q^{22} +(3.50000 + 6.06218i) q^{23} +(4.00000 - 6.92820i) q^{24} +(38.0000 - 65.8179i) q^{25} +(-66.0000 - 114.315i) q^{26} -53.0000 q^{27} +106.000 q^{29} +(-7.00000 - 12.1244i) q^{30} +(37.5000 - 64.9519i) q^{31} +(16.0000 - 27.7128i) q^{32} +(-17.5000 - 30.3109i) q^{33} +118.000 q^{34} -104.000 q^{36} +(-5.50000 - 9.52628i) q^{37} +(-137.000 + 237.291i) q^{38} +(33.0000 - 57.1577i) q^{39} +(-28.0000 - 48.4974i) q^{40} +498.000 q^{41} +260.000 q^{43} +(-70.0000 - 121.244i) q^{44} +(-91.0000 + 157.617i) q^{45} +(-7.00000 + 12.1244i) q^{46} +(-85.5000 - 148.090i) q^{47} +16.0000 q^{48} +152.000 q^{50} +(29.5000 + 51.0955i) q^{51} +(132.000 - 228.631i) q^{52} +(208.500 - 361.133i) q^{53} +(-53.0000 - 91.7987i) q^{54} -245.000 q^{55} -137.000 q^{57} +(106.000 + 183.597i) q^{58} +(-8.50000 + 14.7224i) q^{59} +(14.0000 - 24.2487i) q^{60} +(25.5000 + 44.1673i) q^{61} +150.000 q^{62} +64.0000 q^{64} +(-231.000 - 400.104i) q^{65} +(35.0000 - 60.6218i) q^{66} +(-219.500 + 380.185i) q^{67} +(118.000 + 204.382i) q^{68} -7.00000 q^{69} -784.000 q^{71} +(-104.000 - 180.133i) q^{72} +(147.500 - 255.477i) q^{73} +(11.0000 - 19.0526i) q^{74} +(38.0000 + 65.8179i) q^{75} -548.000 q^{76} +132.000 q^{78} +(247.500 + 428.683i) q^{79} +(56.0000 - 96.9948i) q^{80} +(-324.500 + 562.050i) q^{81} +(498.000 + 862.561i) q^{82} -932.000 q^{83} +413.000 q^{85} +(260.000 + 450.333i) q^{86} +(-53.0000 + 91.7987i) q^{87} +(140.000 - 242.487i) q^{88} +(-436.500 - 756.040i) q^{89} -364.000 q^{90} -28.0000 q^{92} +(37.5000 + 64.9519i) q^{93} +(171.000 - 296.181i) q^{94} +(-479.500 + 830.518i) q^{95} +(16.0000 + 27.7128i) q^{96} +290.000 q^{97} -910.000 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q + 2 q^{2} - q^{3} - 4 q^{4} + 7 q^{5} - 4 q^{6} - 16 q^{8} + 26 q^{9}+O(q^{10})$$ 2 * q + 2 * q^2 - q^3 - 4 * q^4 + 7 * q^5 - 4 * q^6 - 16 * q^8 + 26 * q^9 $$2 q + 2 q^{2} - q^{3} - 4 q^{4} + 7 q^{5} - 4 q^{6} - 16 q^{8} + 26 q^{9} - 14 q^{10} - 35 q^{11} - 4 q^{12} - 132 q^{13} - 14 q^{15} - 16 q^{16} + 59 q^{17} - 52 q^{18} + 137 q^{19} - 56 q^{20} - 140 q^{22} + 7 q^{23} + 8 q^{24} + 76 q^{25} - 132 q^{26} - 106 q^{27} + 212 q^{29} - 14 q^{30} + 75 q^{31} + 32 q^{32} - 35 q^{33} + 236 q^{34} - 208 q^{36} - 11 q^{37} - 274 q^{38} + 66 q^{39} - 56 q^{40} + 996 q^{41} + 520 q^{43} - 140 q^{44} - 182 q^{45} - 14 q^{46} - 171 q^{47} + 32 q^{48} + 304 q^{50} + 59 q^{51} + 264 q^{52} + 417 q^{53} - 106 q^{54} - 490 q^{55} - 274 q^{57} + 212 q^{58} - 17 q^{59} + 28 q^{60} + 51 q^{61} + 300 q^{62} + 128 q^{64} - 462 q^{65} + 70 q^{66} - 439 q^{67} + 236 q^{68} - 14 q^{69} - 1568 q^{71} - 208 q^{72} + 295 q^{73} + 22 q^{74} + 76 q^{75} - 1096 q^{76} + 264 q^{78} + 495 q^{79} + 112 q^{80} - 649 q^{81} + 996 q^{82} - 1864 q^{83} + 826 q^{85} + 520 q^{86} - 106 q^{87} + 280 q^{88} - 873 q^{89} - 728 q^{90} - 56 q^{92} + 75 q^{93} + 342 q^{94} - 959 q^{95} + 32 q^{96} + 580 q^{97} - 1820 q^{99}+O(q^{100})$$ 2 * q + 2 * q^2 - q^3 - 4 * q^4 + 7 * q^5 - 4 * q^6 - 16 * q^8 + 26 * q^9 - 14 * q^10 - 35 * q^11 - 4 * q^12 - 132 * q^13 - 14 * q^15 - 16 * q^16 + 59 * q^17 - 52 * q^18 + 137 * q^19 - 56 * q^20 - 140 * q^22 + 7 * q^23 + 8 * q^24 + 76 * q^25 - 132 * q^26 - 106 * q^27 + 212 * q^29 - 14 * q^30 + 75 * q^31 + 32 * q^32 - 35 * q^33 + 236 * q^34 - 208 * q^36 - 11 * q^37 - 274 * q^38 + 66 * q^39 - 56 * q^40 + 996 * q^41 + 520 * q^43 - 140 * q^44 - 182 * q^45 - 14 * q^46 - 171 * q^47 + 32 * q^48 + 304 * q^50 + 59 * q^51 + 264 * q^52 + 417 * q^53 - 106 * q^54 - 490 * q^55 - 274 * q^57 + 212 * q^58 - 17 * q^59 + 28 * q^60 + 51 * q^61 + 300 * q^62 + 128 * q^64 - 462 * q^65 + 70 * q^66 - 439 * q^67 + 236 * q^68 - 14 * q^69 - 1568 * q^71 - 208 * q^72 + 295 * q^73 + 22 * q^74 + 76 * q^75 - 1096 * q^76 + 264 * q^78 + 495 * q^79 + 112 * q^80 - 649 * q^81 + 996 * q^82 - 1864 * q^83 + 826 * q^85 + 520 * q^86 - 106 * q^87 + 280 * q^88 - 873 * q^89 - 728 * q^90 - 56 * q^92 + 75 * q^93 + 342 * q^94 - 959 * q^95 + 32 * q^96 + 580 * q^97 - 1820 * q^99

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/98\mathbb{Z}\right)^\times$$.

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

## Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 1.00000 + 1.73205i 0.353553 + 0.612372i
$$3$$ −0.500000 + 0.866025i −0.0962250 + 0.166667i −0.910119 0.414346i $$-0.864010\pi$$
0.813894 + 0.581013i $$0.197344\pi$$
$$4$$ −2.00000 + 3.46410i −0.250000 + 0.433013i
$$5$$ 3.50000 + 6.06218i 0.313050 + 0.542218i 0.979021 0.203760i $$-0.0653161\pi$$
−0.665971 + 0.745977i $$0.731983\pi$$
$$6$$ −2.00000 −0.136083
$$7$$ 0 0
$$8$$ −8.00000 −0.353553
$$9$$ 13.0000 + 22.5167i 0.481481 + 0.833950i
$$10$$ −7.00000 + 12.1244i −0.221359 + 0.383406i
$$11$$ −17.5000 + 30.3109i −0.479677 + 0.830825i −0.999728 0.0233099i $$-0.992580\pi$$
0.520051 + 0.854135i $$0.325913\pi$$
$$12$$ −2.00000 3.46410i −0.0481125 0.0833333i
$$13$$ −66.0000 −1.40809 −0.704043 0.710158i $$-0.748624\pi$$
−0.704043 + 0.710158i $$0.748624\pi$$
$$14$$ 0 0
$$15$$ −7.00000 −0.120493
$$16$$ −8.00000 13.8564i −0.125000 0.216506i
$$17$$ 29.5000 51.0955i 0.420871 0.728969i −0.575154 0.818045i $$-0.695058\pi$$
0.996025 + 0.0890757i $$0.0283913\pi$$
$$18$$ −26.0000 + 45.0333i −0.340459 + 0.589692i
$$19$$ 68.5000 + 118.645i 0.827104 + 1.43259i 0.900301 + 0.435269i $$0.143347\pi$$
−0.0731965 + 0.997318i $$0.523320\pi$$
$$20$$ −28.0000 −0.313050
$$21$$ 0 0
$$22$$ −70.0000 −0.678366
$$23$$ 3.50000 + 6.06218i 0.0317305 + 0.0549588i 0.881455 0.472269i $$-0.156565\pi$$
−0.849724 + 0.527228i $$0.823232\pi$$
$$24$$ 4.00000 6.92820i 0.0340207 0.0589256i
$$25$$ 38.0000 65.8179i 0.304000 0.526543i
$$26$$ −66.0000 114.315i −0.497833 0.862273i
$$27$$ −53.0000 −0.377772
$$28$$ 0 0
$$29$$ 106.000 0.678748 0.339374 0.940651i $$-0.389785\pi$$
0.339374 + 0.940651i $$0.389785\pi$$
$$30$$ −7.00000 12.1244i −0.0426006 0.0737865i
$$31$$ 37.5000 64.9519i 0.217264 0.376313i −0.736706 0.676213i $$-0.763620\pi$$
0.953971 + 0.299900i $$0.0969533\pi$$
$$32$$ 16.0000 27.7128i 0.0883883 0.153093i
$$33$$ −17.5000 30.3109i −0.0923139 0.159892i
$$34$$ 118.000 0.595201
$$35$$ 0 0
$$36$$ −104.000 −0.481481
$$37$$ −5.50000 9.52628i −0.0244377 0.0423273i 0.853548 0.521014i $$-0.174446\pi$$
−0.877986 + 0.478687i $$0.841113\pi$$
$$38$$ −137.000 + 237.291i −0.584851 + 1.01299i
$$39$$ 33.0000 57.1577i 0.135493 0.234681i
$$40$$ −28.0000 48.4974i −0.110680 0.191703i
$$41$$ 498.000 1.89694 0.948470 0.316867i $$-0.102631\pi$$
0.948470 + 0.316867i $$0.102631\pi$$
$$42$$ 0 0
$$43$$ 260.000 0.922084 0.461042 0.887378i $$-0.347476\pi$$
0.461042 + 0.887378i $$0.347476\pi$$
$$44$$ −70.0000 121.244i −0.239839 0.415413i
$$45$$ −91.0000 + 157.617i −0.301455 + 0.522136i
$$46$$ −7.00000 + 12.1244i −0.0224368 + 0.0388617i
$$47$$ −85.5000 148.090i −0.265350 0.459600i 0.702305 0.711876i $$-0.252154\pi$$
−0.967655 + 0.252276i $$0.918821\pi$$
$$48$$ 16.0000 0.0481125
$$49$$ 0 0
$$50$$ 152.000 0.429921
$$51$$ 29.5000 + 51.0955i 0.0809966 + 0.140290i
$$52$$ 132.000 228.631i 0.352021 0.609719i
$$53$$ 208.500 361.133i 0.540371 0.935951i −0.458511 0.888689i $$-0.651617\pi$$
0.998883 0.0472619i $$-0.0150495\pi$$
$$54$$ −53.0000 91.7987i −0.133563 0.231337i
$$55$$ −245.000 −0.600651
$$56$$ 0 0
$$57$$ −137.000 −0.318353
$$58$$ 106.000 + 183.597i 0.239974 + 0.415647i
$$59$$ −8.50000 + 14.7224i −0.0187560 + 0.0324864i −0.875251 0.483669i $$-0.839304\pi$$
0.856495 + 0.516155i $$0.172637\pi$$
$$60$$ 14.0000 24.2487i 0.0301232 0.0521749i
$$61$$ 25.5000 + 44.1673i 0.0535236 + 0.0927056i 0.891546 0.452930i $$-0.149621\pi$$
−0.838022 + 0.545636i $$0.816288\pi$$
$$62$$ 150.000 0.307258
$$63$$ 0 0
$$64$$ 64.0000 0.125000
$$65$$ −231.000 400.104i −0.440800 0.763489i
$$66$$ 35.0000 60.6218i 0.0652758 0.113061i
$$67$$ −219.500 + 380.185i −0.400242 + 0.693239i −0.993755 0.111585i $$-0.964407\pi$$
0.593513 + 0.804824i $$0.297740\pi$$
$$68$$ 118.000 + 204.382i 0.210435 + 0.364485i
$$69$$ −7.00000 −0.0122131
$$70$$ 0 0
$$71$$ −784.000 −1.31047 −0.655237 0.755423i $$-0.727431\pi$$
−0.655237 + 0.755423i $$0.727431\pi$$
$$72$$ −104.000 180.133i −0.170229 0.294846i
$$73$$ 147.500 255.477i 0.236487 0.409608i −0.723217 0.690621i $$-0.757337\pi$$
0.959704 + 0.281013i $$0.0906705\pi$$
$$74$$ 11.0000 19.0526i 0.0172801 0.0299299i
$$75$$ 38.0000 + 65.8179i 0.0585048 + 0.101333i
$$76$$ −548.000 −0.827104
$$77$$ 0 0
$$78$$ 132.000 0.191616
$$79$$ 247.500 + 428.683i 0.352480 + 0.610513i 0.986683 0.162653i $$-0.0520051\pi$$
−0.634203 + 0.773166i $$0.718672\pi$$
$$80$$ 56.0000 96.9948i 0.0782624 0.135554i
$$81$$ −324.500 + 562.050i −0.445130 + 0.770988i
$$82$$ 498.000 + 862.561i 0.670670 + 1.16163i
$$83$$ −932.000 −1.23253 −0.616267 0.787537i $$-0.711356\pi$$
−0.616267 + 0.787537i $$0.711356\pi$$
$$84$$ 0 0
$$85$$ 413.000 0.527013
$$86$$ 260.000 + 450.333i 0.326006 + 0.564659i
$$87$$ −53.0000 + 91.7987i −0.0653126 + 0.113125i
$$88$$ 140.000 242.487i 0.169591 0.293741i
$$89$$ −436.500 756.040i −0.519875 0.900451i −0.999733 0.0231042i $$-0.992645\pi$$
0.479858 0.877346i $$-0.340688\pi$$
$$90$$ −364.000 −0.426322
$$91$$ 0 0
$$92$$ −28.0000 −0.0317305
$$93$$ 37.5000 + 64.9519i 0.0418126 + 0.0724215i
$$94$$ 171.000 296.181i 0.187631 0.324986i
$$95$$ −479.500 + 830.518i −0.517849 + 0.896941i
$$96$$ 16.0000 + 27.7128i 0.0170103 + 0.0294628i
$$97$$ 290.000 0.303557 0.151779 0.988415i $$-0.451500\pi$$
0.151779 + 0.988415i $$0.451500\pi$$
$$98$$ 0 0
$$99$$ −910.000 −0.923823
$$100$$ 152.000 + 263.272i 0.152000 + 0.263272i
$$101$$ −542.500 + 939.638i −0.534463 + 0.925717i 0.464726 + 0.885454i $$0.346153\pi$$
−0.999189 + 0.0402627i $$0.987181\pi$$
$$102$$ −59.0000 + 102.191i −0.0572732 + 0.0992002i
$$103$$ 776.500 + 1344.94i 0.742823 + 1.28661i 0.951205 + 0.308560i $$0.0998472\pi$$
−0.208381 + 0.978048i $$0.566819\pi$$
$$104$$ 528.000 0.497833
$$105$$ 0 0
$$106$$ 834.000 0.764200
$$107$$ −64.5000 111.717i −0.0582752 0.100936i 0.835416 0.549618i $$-0.185227\pi$$
−0.893691 + 0.448682i $$0.851893\pi$$
$$108$$ 106.000 183.597i 0.0944431 0.163580i
$$109$$ 482.500 835.715i 0.423992 0.734376i −0.572334 0.820021i $$-0.693962\pi$$
0.996326 + 0.0856452i $$0.0272952\pi$$
$$110$$ −245.000 424.352i −0.212362 0.367822i
$$111$$ 11.0000 0.00940607
$$112$$ 0 0
$$113$$ −50.0000 −0.0416248 −0.0208124 0.999783i $$-0.506625\pi$$
−0.0208124 + 0.999783i $$0.506625\pi$$
$$114$$ −137.000 237.291i −0.112555 0.194950i
$$115$$ −24.5000 + 42.4352i −0.0198664 + 0.0344096i
$$116$$ −212.000 + 367.195i −0.169687 + 0.293907i
$$117$$ −858.000 1486.10i −0.677967 1.17427i
$$118$$ −34.0000 −0.0265250
$$119$$ 0 0
$$120$$ 56.0000 0.0426006
$$121$$ 53.0000 + 91.7987i 0.0398197 + 0.0689697i
$$122$$ −51.0000 + 88.3346i −0.0378469 + 0.0655528i
$$123$$ −249.000 + 431.281i −0.182533 + 0.316157i
$$124$$ 150.000 + 259.808i 0.108632 + 0.188157i
$$125$$ 1407.00 1.00677
$$126$$ 0 0
$$127$$ 936.000 0.653989 0.326994 0.945026i $$-0.393964\pi$$
0.326994 + 0.945026i $$0.393964\pi$$
$$128$$ 64.0000 + 110.851i 0.0441942 + 0.0765466i
$$129$$ −130.000 + 225.167i −0.0887276 + 0.153681i
$$130$$ 462.000 800.207i 0.311693 0.539868i
$$131$$ −377.500 653.849i −0.251773 0.436084i 0.712241 0.701935i $$-0.247680\pi$$
−0.964014 + 0.265851i $$0.914347\pi$$
$$132$$ 140.000 0.0923139
$$133$$ 0 0
$$134$$ −878.000 −0.566027
$$135$$ −185.500 321.295i −0.118261 0.204835i
$$136$$ −236.000 + 408.764i −0.148800 + 0.257730i
$$137$$ 1178.50 2041.22i 0.734935 1.27294i −0.219817 0.975541i $$-0.570546\pi$$
0.954752 0.297403i $$-0.0961205\pi$$
$$138$$ −7.00000 12.1244i −0.00431797 0.00747894i
$$139$$ −28.0000 −0.0170858 −0.00854291 0.999964i $$-0.502719\pi$$
−0.00854291 + 0.999964i $$0.502719\pi$$
$$140$$ 0 0
$$141$$ 171.000 0.102133
$$142$$ −784.000 1357.93i −0.463323 0.802498i
$$143$$ 1155.00 2000.52i 0.675426 1.16987i
$$144$$ 208.000 360.267i 0.120370 0.208488i
$$145$$ 371.000 + 642.591i 0.212482 + 0.368029i
$$146$$ 590.000 0.334443
$$147$$ 0 0
$$148$$ 44.0000 0.0244377
$$149$$ −1147.50 1987.53i −0.630919 1.09278i −0.987364 0.158467i $$-0.949345\pi$$
0.356446 0.934316i $$-0.383988\pi$$
$$150$$ −76.0000 + 131.636i −0.0413692 + 0.0716535i
$$151$$ 554.500 960.422i 0.298838 0.517603i −0.677032 0.735953i $$-0.736734\pi$$
0.975870 + 0.218350i $$0.0700676\pi$$
$$152$$ −548.000 949.164i −0.292425 0.506496i
$$153$$ 1534.00 0.810566
$$154$$ 0 0
$$155$$ 525.000 0.272058
$$156$$ 132.000 + 228.631i 0.0677465 + 0.117340i
$$157$$ 779.500 1350.13i 0.396248 0.686321i −0.597012 0.802232i $$-0.703646\pi$$
0.993260 + 0.115911i $$0.0369789\pi$$
$$158$$ −495.000 + 857.365i −0.249241 + 0.431698i
$$159$$ 208.500 + 361.133i 0.103995 + 0.180124i
$$160$$ 224.000 0.110680
$$161$$ 0 0
$$162$$ −1298.00 −0.629509
$$163$$ 1125.50 + 1949.42i 0.540834 + 0.936752i 0.998856 + 0.0478115i $$0.0152247\pi$$
−0.458022 + 0.888941i $$0.651442\pi$$
$$164$$ −996.000 + 1725.12i −0.474235 + 0.821399i
$$165$$ 122.500 212.176i 0.0577976 0.100108i
$$166$$ −932.000 1614.27i −0.435766 0.754770i
$$167$$ −2788.00 −1.29187 −0.645934 0.763393i $$-0.723532\pi$$
−0.645934 + 0.763393i $$0.723532\pi$$
$$168$$ 0 0
$$169$$ 2159.00 0.982704
$$170$$ 413.000 + 715.337i 0.186327 + 0.322728i
$$171$$ −1781.00 + 3084.78i −0.796471 + 1.37953i
$$172$$ −520.000 + 900.666i −0.230521 + 0.399274i
$$173$$ 789.500 + 1367.45i 0.346963 + 0.600957i 0.985708 0.168461i $$-0.0538797\pi$$
−0.638746 + 0.769418i $$0.720546\pi$$
$$174$$ −212.000 −0.0923660
$$175$$ 0 0
$$176$$ 560.000 0.239839
$$177$$ −8.50000 14.7224i −0.00360960 0.00625201i
$$178$$ 873.000 1512.08i 0.367607 0.636715i
$$179$$ −1225.50 + 2122.63i −0.511722 + 0.886328i 0.488186 + 0.872740i $$0.337659\pi$$
−0.999908 + 0.0135883i $$0.995675\pi$$
$$180$$ −364.000 630.466i −0.150728 0.261068i
$$181$$ 1170.00 0.480472 0.240236 0.970715i $$-0.422775\pi$$
0.240236 + 0.970715i $$0.422775\pi$$
$$182$$ 0 0
$$183$$ −51.0000 −0.0206012
$$184$$ −28.0000 48.4974i −0.0112184 0.0194309i
$$185$$ 38.5000 66.6840i 0.0153004 0.0265011i
$$186$$ −75.0000 + 129.904i −0.0295660 + 0.0512097i
$$187$$ 1032.50 + 1788.34i 0.403764 + 0.699340i
$$188$$ 684.000 0.265350
$$189$$ 0 0
$$190$$ −1918.00 −0.732349
$$191$$ 637.500 + 1104.18i 0.241507 + 0.418303i 0.961144 0.276048i $$-0.0890249\pi$$
−0.719637 + 0.694351i $$0.755692\pi$$
$$192$$ −32.0000 + 55.4256i −0.0120281 + 0.0208333i
$$193$$ −17.5000 + 30.3109i −0.00652683 + 0.0113048i −0.869270 0.494337i $$-0.835411\pi$$
0.862744 + 0.505642i $$0.168744\pi$$
$$194$$ 290.000 + 502.295i 0.107324 + 0.185890i
$$195$$ 462.000 0.169664
$$196$$ 0 0
$$197$$ −2734.00 −0.988779 −0.494389 0.869241i $$-0.664608\pi$$
−0.494389 + 0.869241i $$0.664608\pi$$
$$198$$ −910.000 1576.17i −0.326621 0.565724i
$$199$$ 1121.50 1942.49i 0.399503 0.691959i −0.594162 0.804345i $$-0.702516\pi$$
0.993665 + 0.112387i $$0.0358495\pi$$
$$200$$ −304.000 + 526.543i −0.107480 + 0.186161i
$$201$$ −219.500 380.185i −0.0770265 0.133414i
$$202$$ −2170.00 −0.755845
$$203$$ 0 0
$$204$$ −236.000 −0.0809966
$$205$$ 1743.00 + 3018.96i 0.593836 + 1.02855i
$$206$$ −1553.00 + 2689.87i −0.525256 + 0.909769i
$$207$$ −91.0000 + 157.617i −0.0305553 + 0.0529232i
$$208$$ 528.000 + 914.523i 0.176011 + 0.304859i
$$209$$ −4795.00 −1.58697
$$210$$ 0 0
$$211$$ 1172.00 0.382388 0.191194 0.981552i $$-0.438764\pi$$
0.191194 + 0.981552i $$0.438764\pi$$
$$212$$ 834.000 + 1444.53i 0.270186 + 0.467975i
$$213$$ 392.000 678.964i 0.126100 0.218412i
$$214$$ 129.000 223.435i 0.0412068 0.0713723i
$$215$$ 910.000 + 1576.17i 0.288658 + 0.499970i
$$216$$ 424.000 0.133563
$$217$$ 0 0
$$218$$ 1930.00 0.599615
$$219$$ 147.500 + 255.477i 0.0455120 + 0.0788291i
$$220$$ 490.000 848.705i 0.150163 0.260089i
$$221$$ −1947.00 + 3372.30i −0.592622 + 1.02645i
$$222$$ 11.0000 + 19.0526i 0.00332555 + 0.00576002i
$$223$$ −2024.00 −0.607790 −0.303895 0.952706i $$-0.598287\pi$$
−0.303895 + 0.952706i $$0.598287\pi$$
$$224$$ 0 0
$$225$$ 1976.00 0.585481
$$226$$ −50.0000 86.6025i −0.0147166 0.0254899i
$$227$$ 1285.50 2226.55i 0.375866 0.651019i −0.614590 0.788847i $$-0.710679\pi$$
0.990456 + 0.137827i $$0.0440119\pi$$
$$228$$ 274.000 474.582i 0.0795881 0.137851i
$$229$$ 447.500 + 775.093i 0.129134 + 0.223666i 0.923341 0.383980i $$-0.125447\pi$$
−0.794207 + 0.607647i $$0.792114\pi$$
$$230$$ −98.0000 −0.0280953
$$231$$ 0 0
$$232$$ −848.000 −0.239974
$$233$$ −893.500 1547.59i −0.251224 0.435132i 0.712639 0.701531i $$-0.247500\pi$$
−0.963863 + 0.266398i $$0.914166\pi$$
$$234$$ 1716.00 2972.20i 0.479395 0.830336i
$$235$$ 598.500 1036.63i 0.166135 0.287755i
$$236$$ −34.0000 58.8897i −0.00937801 0.0162432i
$$237$$ −495.000 −0.135670
$$238$$ 0 0
$$239$$ −5100.00 −1.38030 −0.690150 0.723667i $$-0.742455\pi$$
−0.690150 + 0.723667i $$0.742455\pi$$
$$240$$ 56.0000 + 96.9948i 0.0150616 + 0.0260875i
$$241$$ −2088.50 + 3617.39i −0.558225 + 0.966873i 0.439420 + 0.898282i $$0.355184\pi$$
−0.997645 + 0.0685917i $$0.978149\pi$$
$$242$$ −106.000 + 183.597i −0.0281568 + 0.0487690i
$$243$$ −1040.00 1801.33i −0.274552 0.475537i
$$244$$ −204.000 −0.0535236
$$245$$ 0 0
$$246$$ −996.000 −0.258141
$$247$$ −4521.00 7830.60i −1.16463 2.01720i
$$248$$ −300.000 + 519.615i −0.0768146 + 0.133047i
$$249$$ 466.000 807.136i 0.118601 0.205422i
$$250$$ 1407.00 + 2437.00i 0.355946 + 0.616517i
$$251$$ 4680.00 1.17689 0.588444 0.808538i $$-0.299741\pi$$
0.588444 + 0.808538i $$0.299741\pi$$
$$252$$ 0 0
$$253$$ −245.000 −0.0608815
$$254$$ 936.000 + 1621.20i 0.231220 + 0.400485i
$$255$$ −206.500 + 357.668i −0.0507119 + 0.0878356i
$$256$$ −128.000 + 221.703i −0.0312500 + 0.0541266i
$$257$$ −874.500 1514.68i −0.212256 0.367638i 0.740164 0.672426i $$-0.234748\pi$$
−0.952420 + 0.304788i $$0.901414\pi$$
$$258$$ −520.000 −0.125480
$$259$$ 0 0
$$260$$ 1848.00 0.440800
$$261$$ 1378.00 + 2386.77i 0.326805 + 0.566043i
$$262$$ 755.000 1307.70i 0.178031 0.308358i
$$263$$ 2236.50 3873.73i 0.524367 0.908230i −0.475231 0.879861i $$-0.657635\pi$$
0.999598 0.0283689i $$-0.00903130\pi$$
$$264$$ 140.000 + 242.487i 0.0326379 + 0.0565305i
$$265$$ 2919.00 0.676652
$$266$$ 0 0
$$267$$ 873.000 0.200100
$$268$$ −878.000 1520.74i −0.200121 0.346619i
$$269$$ 987.500 1710.40i 0.223825 0.387676i −0.732141 0.681153i $$-0.761479\pi$$
0.955966 + 0.293476i $$0.0948122\pi$$
$$270$$ 371.000 642.591i 0.0836235 0.144840i
$$271$$ −4219.50 7308.39i −0.945817 1.63820i −0.754107 0.656751i $$-0.771930\pi$$
−0.191710 0.981452i $$-0.561403\pi$$
$$272$$ −944.000 −0.210435
$$273$$ 0 0
$$274$$ 4714.00 1.03935
$$275$$ 1330.00 + 2303.63i 0.291644 + 0.505142i
$$276$$ 14.0000 24.2487i 0.00305326 0.00528841i
$$277$$ −263.500 + 456.395i −0.0571559 + 0.0989969i −0.893188 0.449684i $$-0.851537\pi$$
0.836032 + 0.548681i $$0.184870\pi$$
$$278$$ −28.0000 48.4974i −0.00604075 0.0104629i
$$279$$ 1950.00 0.418435
$$280$$ 0 0
$$281$$ −202.000 −0.0428837 −0.0214418 0.999770i $$-0.506826\pi$$
−0.0214418 + 0.999770i $$0.506826\pi$$
$$282$$ 171.000 + 296.181i 0.0361096 + 0.0625436i
$$283$$ −3974.50 + 6884.04i −0.834839 + 1.44598i 0.0593220 + 0.998239i $$0.481106\pi$$
−0.894161 + 0.447745i $$0.852227\pi$$
$$284$$ 1568.00 2715.86i 0.327619 0.567452i
$$285$$ −479.500 830.518i −0.0996601 0.172616i
$$286$$ 4620.00 0.955197
$$287$$ 0 0
$$288$$ 832.000 0.170229
$$289$$ 716.000 + 1240.15i 0.145736 + 0.252422i
$$290$$ −742.000 + 1285.18i −0.150247 + 0.260236i
$$291$$ −145.000 + 251.147i −0.0292098 + 0.0505929i
$$292$$ 590.000 + 1021.91i 0.118244 + 0.204804i
$$293$$ −318.000 −0.0634053 −0.0317027 0.999497i $$-0.510093\pi$$
−0.0317027 + 0.999497i $$0.510093\pi$$
$$294$$ 0 0
$$295$$ −119.000 −0.0234863
$$296$$ 44.0000 + 76.2102i 0.00864003 + 0.0149650i
$$297$$ 927.500 1606.48i 0.181209 0.313863i
$$298$$ 2295.00 3975.06i 0.446127 0.772714i
$$299$$ −231.000 400.104i −0.0446792 0.0773866i
$$300$$ −304.000 −0.0585048
$$301$$ 0 0
$$302$$ 2218.00 0.422621
$$303$$ −542.500 939.638i −0.102857 0.178154i
$$304$$ 1096.00 1898.33i 0.206776 0.358147i
$$305$$ −178.500 + 309.171i −0.0335111 + 0.0580429i
$$306$$ 1534.00 + 2656.97i 0.286578 + 0.496368i
$$307$$ 8132.00 1.51178 0.755892 0.654696i $$-0.227203\pi$$
0.755892 + 0.654696i $$0.227203\pi$$
$$308$$ 0 0
$$309$$ −1553.00 −0.285913
$$310$$ 525.000 + 909.327i 0.0961871 + 0.166601i
$$311$$ −464.500 + 804.538i −0.0846925 + 0.146692i −0.905260 0.424858i $$-0.860324\pi$$
0.820568 + 0.571549i $$0.193657\pi$$
$$312$$ −264.000 + 457.261i −0.0479040 + 0.0829722i
$$313$$ −104.500 180.999i −0.0188712 0.0326859i 0.856436 0.516254i $$-0.172674\pi$$
−0.875307 + 0.483568i $$0.839341\pi$$
$$314$$ 3118.00 0.560379
$$315$$ 0 0
$$316$$ −1980.00 −0.352480
$$317$$ −3565.50 6175.63i −0.631730 1.09419i −0.987198 0.159500i $$-0.949012\pi$$
0.355468 0.934689i $$-0.384322\pi$$
$$318$$ −417.000 + 722.265i −0.0735352 + 0.127367i
$$319$$ −1855.00 + 3212.95i −0.325580 + 0.563921i
$$320$$ 224.000 + 387.979i 0.0391312 + 0.0677772i
$$321$$ 129.000 0.0224301
$$322$$ 0 0
$$323$$ 8083.00 1.39242
$$324$$ −1298.00 2248.20i −0.222565 0.385494i
$$325$$ −2508.00 + 4343.98i −0.428058 + 0.741418i
$$326$$ −2251.00 + 3898.85i −0.382427 + 0.662384i
$$327$$ 482.500 + 835.715i 0.0815973 + 0.141331i
$$328$$ −3984.00 −0.670670
$$329$$ 0 0
$$330$$ 490.000 0.0817382
$$331$$ 3285.50 + 5690.65i 0.545581 + 0.944975i 0.998570 + 0.0534583i $$0.0170244\pi$$
−0.452989 + 0.891516i $$0.649642\pi$$
$$332$$ 1864.00 3228.54i 0.308133 0.533703i
$$333$$ 143.000 247.683i 0.0235326 0.0407596i
$$334$$ −2788.00 4828.96i −0.456744 0.791104i
$$335$$ −3073.00 −0.501182
$$336$$ 0 0
$$337$$ −11466.0 −1.85339 −0.926696 0.375813i $$-0.877364\pi$$
−0.926696 + 0.375813i $$0.877364\pi$$
$$338$$ 2159.00 + 3739.50i 0.347438 + 0.601781i
$$339$$ 25.0000 43.3013i 0.00400535 0.00693747i
$$340$$ −826.000 + 1430.67i −0.131753 + 0.228203i
$$341$$ 1312.50 + 2273.32i 0.208434 + 0.361018i
$$342$$ −7124.00 −1.12638
$$343$$ 0 0
$$344$$ −2080.00 −0.326006
$$345$$ −24.5000 42.4352i −0.00382329 0.00662214i
$$346$$ −1579.00 + 2734.91i −0.245340 + 0.424941i
$$347$$ 4888.50 8467.13i 0.756278 1.30991i −0.188459 0.982081i $$-0.560349\pi$$
0.944737 0.327831i $$-0.106318\pi$$
$$348$$ −212.000 367.195i −0.0326563 0.0565624i
$$349$$ −11914.0 −1.82734 −0.913670 0.406456i $$-0.866764\pi$$
−0.913670 + 0.406456i $$0.866764\pi$$
$$350$$ 0 0
$$351$$ 3498.00 0.531936
$$352$$ 560.000 + 969.948i 0.0847957 + 0.146871i
$$353$$ 4561.50 7900.75i 0.687774 1.19126i −0.284783 0.958592i $$-0.591921\pi$$
0.972556 0.232667i $$-0.0747452\pi$$
$$354$$ 17.0000 29.4449i 0.00255237 0.00442084i
$$355$$ −2744.00 4752.75i −0.410243 0.710562i
$$356$$ 3492.00 0.519875
$$357$$ 0 0
$$358$$ −4902.00 −0.723684
$$359$$ −4074.50 7057.24i −0.599008 1.03751i −0.992968 0.118385i $$-0.962228\pi$$
0.393960 0.919128i $$-0.371105\pi$$
$$360$$ 728.000 1260.93i 0.106580 0.184603i
$$361$$ −5955.00 + 10314.4i −0.868202 + 1.50377i
$$362$$ 1170.00 + 2026.50i 0.169872 + 0.294228i
$$363$$ −106.000 −0.0153266
$$364$$ 0 0
$$365$$ 2065.00 0.296129
$$366$$ −51.0000 88.3346i −0.00728364 0.0126156i
$$367$$ 4835.50 8375.33i 0.687769 1.19125i −0.284790 0.958590i $$-0.591924\pi$$
0.972558 0.232660i $$-0.0747429\pi$$
$$368$$ 56.0000 96.9948i 0.00793261 0.0137397i
$$369$$ 6474.00 + 11213.3i 0.913341 + 1.58195i
$$370$$ 154.000 0.0216381
$$371$$ 0 0
$$372$$ −300.000 −0.0418126
$$373$$ 2054.50 + 3558.50i 0.285196 + 0.493973i 0.972657 0.232248i $$-0.0746081\pi$$
−0.687461 + 0.726221i $$0.741275\pi$$
$$374$$ −2065.00 + 3576.68i −0.285504 + 0.494508i
$$375$$ −703.500 + 1218.50i −0.0968762 + 0.167795i
$$376$$ 684.000 + 1184.72i 0.0938154 + 0.162493i
$$377$$ −6996.00 −0.955736
$$378$$ 0 0
$$379$$ −3488.00 −0.472735 −0.236367 0.971664i $$-0.575957\pi$$
−0.236367 + 0.971664i $$0.575957\pi$$
$$380$$ −1918.00 3322.07i −0.258925 0.448470i
$$381$$ −468.000 + 810.600i −0.0629301 + 0.108998i
$$382$$ −1275.00 + 2208.36i −0.170771 + 0.295785i
$$383$$ 4358.50 + 7549.14i 0.581485 + 1.00716i 0.995304 + 0.0968028i $$0.0308616\pi$$
−0.413818 + 0.910360i $$0.635805\pi$$
$$384$$ −128.000 −0.0170103
$$385$$ 0 0
$$386$$ −70.0000 −0.00923033
$$387$$ 3380.00 + 5854.33i 0.443967 + 0.768973i
$$388$$ −580.000 + 1004.59i −0.0758893 + 0.131444i
$$389$$ −81.5000 + 141.162i −0.0106227 + 0.0183990i −0.871288 0.490772i $$-0.836715\pi$$
0.860665 + 0.509171i $$0.170048\pi$$
$$390$$ 462.000 + 800.207i 0.0599853 + 0.103898i
$$391$$ 413.000 0.0534177
$$392$$ 0 0
$$393$$ 755.000 0.0969077
$$394$$ −2734.00 4735.43i −0.349586 0.605501i
$$395$$ −1732.50 + 3000.78i −0.220687 + 0.382242i
$$396$$ 1820.00 3152.33i 0.230956 0.400027i
$$397$$ 499.500 + 865.159i 0.0631466 + 0.109373i 0.895870 0.444316i $$-0.146553\pi$$
−0.832724 + 0.553689i $$0.813220\pi$$
$$398$$ 4486.00 0.564982
$$399$$ 0 0
$$400$$ −1216.00 −0.152000
$$401$$ 7378.50 + 12779.9i 0.918865 + 1.59152i 0.801143 + 0.598474i $$0.204226\pi$$
0.117722 + 0.993047i $$0.462441\pi$$
$$402$$ 439.000 760.370i 0.0544660 0.0943379i
$$403$$ −2475.00 + 4286.83i −0.305927 + 0.529881i
$$404$$ −2170.00 3758.55i −0.267232 0.462859i
$$405$$ −4543.00 −0.557391
$$406$$ 0 0
$$407$$ 385.000 0.0468888
$$408$$ −236.000 408.764i −0.0286366 0.0496001i
$$409$$ −66.5000 + 115.181i −0.00803964 + 0.0139251i −0.870017 0.493021i $$-0.835892\pi$$
0.861978 + 0.506946i $$0.169226\pi$$
$$410$$ −3486.00 + 6037.93i −0.419906 + 0.727298i
$$411$$ 1178.50 + 2041.22i 0.141438 + 0.244978i
$$412$$ −6212.00 −0.742823
$$413$$ 0 0
$$414$$ −364.000 −0.0432117
$$415$$ −3262.00 5649.95i −0.385844 0.668302i
$$416$$ −1056.00 + 1829.05i −0.124458 + 0.215568i
$$417$$ 14.0000 24.2487i 0.00164408 0.00284764i
$$418$$ −4795.00 8305.18i −0.561079 0.971818i
$$419$$ 6420.00 0.748538 0.374269 0.927320i $$-0.377894\pi$$
0.374269 + 0.927320i $$0.377894\pi$$
$$420$$ 0 0
$$421$$ 10266.0 1.18844 0.594221 0.804302i $$-0.297460\pi$$
0.594221 + 0.804302i $$0.297460\pi$$
$$422$$ 1172.00 + 2029.96i 0.135194 + 0.234164i
$$423$$ 2223.00 3850.35i 0.255522 0.442578i
$$424$$ −1668.00 + 2889.06i −0.191050 + 0.330908i
$$425$$ −2242.00 3883.26i −0.255889 0.443213i
$$426$$ 1568.00 0.178333
$$427$$ 0 0
$$428$$ 516.000 0.0582752
$$429$$ 1155.00 + 2000.52i 0.129986 + 0.225142i
$$430$$ −1820.00 + 3152.33i −0.204112 + 0.353532i
$$431$$ 7606.50 13174.8i 0.850098 1.47241i −0.0310213 0.999519i $$-0.509876\pi$$
0.881119 0.472894i $$-0.156791\pi$$
$$432$$ 424.000 + 734.390i 0.0472215 + 0.0817901i
$$433$$ 1378.00 0.152939 0.0764693 0.997072i $$-0.475635\pi$$
0.0764693 + 0.997072i $$0.475635\pi$$
$$434$$ 0 0
$$435$$ −742.000 −0.0817843
$$436$$ 1930.00 + 3342.86i 0.211996 + 0.367188i
$$437$$ −479.500 + 830.518i −0.0524888 + 0.0909132i
$$438$$ −295.000 + 510.955i −0.0321818 + 0.0557406i
$$439$$ −1381.50 2392.83i −0.150195 0.260145i 0.781104 0.624401i $$-0.214657\pi$$
−0.931299 + 0.364256i $$0.881323\pi$$
$$440$$ 1960.00 0.212362
$$441$$ 0 0
$$442$$ −7788.00 −0.838094
$$443$$ −2924.50 5065.38i −0.313651 0.543259i 0.665499 0.746399i $$-0.268219\pi$$
−0.979150 + 0.203140i $$0.934885\pi$$
$$444$$ −22.0000 + 38.1051i −0.00235152 + 0.00407295i
$$445$$ 3055.50 5292.28i 0.325493 0.563771i
$$446$$ −2024.00 3505.67i −0.214886 0.372194i
$$447$$ 2295.00 0.242841
$$448$$ 0 0
$$449$$ 4582.00 0.481599 0.240799 0.970575i $$-0.422590\pi$$
0.240799 + 0.970575i $$0.422590\pi$$
$$450$$ 1976.00 + 3422.53i 0.206999 + 0.358533i
$$451$$ −8715.00 + 15094.8i −0.909919 + 1.57603i
$$452$$ 100.000 173.205i 0.0104062 0.0180241i
$$453$$ 554.500 + 960.422i 0.0575114 + 0.0996127i
$$454$$ 5142.00 0.531555
$$455$$ 0 0
$$456$$ 1096.00 0.112555
$$457$$ −5775.50 10003.5i −0.591174 1.02394i −0.994075 0.108700i $$-0.965331\pi$$
0.402901 0.915244i $$-0.368002\pi$$
$$458$$ −895.000 + 1550.19i −0.0913114 + 0.158156i
$$459$$ −1563.50 + 2708.06i −0.158993 + 0.275384i
$$460$$ −98.0000 169.741i −0.00993320 0.0172048i
$$461$$ 9494.00 0.959175 0.479587 0.877494i $$-0.340786\pi$$
0.479587 + 0.877494i $$0.340786\pi$$
$$462$$ 0 0
$$463$$ −10160.0 −1.01982 −0.509908 0.860229i $$-0.670321\pi$$
−0.509908 + 0.860229i $$0.670321\pi$$
$$464$$ −848.000 1468.78i −0.0848436 0.146953i
$$465$$ −262.500 + 454.663i −0.0261788 + 0.0453430i
$$466$$ 1787.00 3095.17i 0.177642 0.307685i
$$467$$ −653.500 1131.90i −0.0647545 0.112158i 0.831831 0.555030i $$-0.187293\pi$$
−0.896585 + 0.442872i $$0.853960\pi$$
$$468$$ 6864.00 0.677967
$$469$$ 0 0
$$470$$ 2394.00 0.234951
$$471$$ 779.500 + 1350.13i 0.0762579 + 0.132083i
$$472$$ 68.0000 117.779i 0.00663126 0.0114857i
$$473$$ −4550.00 + 7880.83i −0.442303 + 0.766091i
$$474$$ −495.000 857.365i −0.0479665 0.0830803i
$$475$$ 10412.0 1.00576
$$476$$ 0 0
$$477$$ 10842.0 1.04072
$$478$$ −5100.00 8833.46i −0.488010 0.845257i
$$479$$ 9143.50 15837.0i 0.872186 1.51067i 0.0124559 0.999922i $$-0.496035\pi$$
0.859730 0.510748i $$-0.170632\pi$$
$$480$$ −112.000 + 193.990i −0.0106502 + 0.0184466i
$$481$$ 363.000 + 628.734i 0.0344103 + 0.0596005i
$$482$$ −8354.00 −0.789449
$$483$$ 0 0
$$484$$ −424.000 −0.0398197
$$485$$ 1015.00 + 1758.03i 0.0950284 + 0.164594i
$$486$$ 2080.00 3602.67i 0.194137 0.336256i
$$487$$ 7476.50 12949.7i 0.695673 1.20494i −0.274281 0.961650i $$-0.588440\pi$$
0.969953 0.243291i $$-0.0782269\pi$$
$$488$$ −204.000 353.338i −0.0189235 0.0327764i
$$489$$ −2251.00 −0.208167
$$490$$ 0 0
$$491$$ 14352.0 1.31914 0.659569 0.751644i $$-0.270739\pi$$
0.659569 + 0.751644i $$0.270739\pi$$
$$492$$ −996.000 1725.12i −0.0912666 0.158078i
$$493$$ 3127.00 5416.12i 0.285665 0.494787i
$$494$$ 9042.00 15661.2i 0.823520 1.42638i
$$495$$ −3185.00 5516.58i −0.289202 0.500913i
$$496$$ −1200.00 −0.108632
$$497$$ 0 0
$$498$$ 1864.00 0.167727
$$499$$ 2765.50 + 4789.99i 0.248098 + 0.429718i 0.962998 0.269509i $$-0.0868612\pi$$
−0.714900 + 0.699226i $$0.753528\pi$$
$$500$$ −2814.00 + 4873.99i −0.251692 + 0.435943i
$$501$$ 1394.00 2414.48i 0.124310 0.215311i
$$502$$ 4680.00 + 8106.00i 0.416093 + 0.720694i
$$503$$ −8400.00 −0.744607 −0.372304 0.928111i $$-0.621432\pi$$
−0.372304 + 0.928111i $$0.621432\pi$$
$$504$$ 0 0
$$505$$ −7595.00 −0.669254
$$506$$ −245.000 424.352i −0.0215249 0.0372821i
$$507$$ −1079.50 + 1869.75i −0.0945607 + 0.163784i
$$508$$ −1872.00 + 3242.40i −0.163497 + 0.283185i
$$509$$ −1192.50 2065.47i −0.103844 0.179863i 0.809421 0.587228i $$-0.199781\pi$$
−0.913265 + 0.407365i $$0.866448\pi$$
$$510$$ −826.000 −0.0717174
$$511$$ 0 0
$$512$$ −512.000 −0.0441942
$$513$$ −3630.50 6288.21i −0.312457 0.541192i
$$514$$ 1749.00 3029.36i 0.150088 0.259960i
$$515$$ −5435.50 + 9414.56i −0.465081 + 0.805544i
$$516$$ −520.000 900.666i −0.0443638 0.0768404i
$$517$$ 5985.00 0.509130
$$518$$ 0 0
$$519$$ −1579.00 −0.133546
$$520$$ 1848.00 + 3200.83i 0.155846 + 0.269934i
$$521$$ −4576.50 + 7926.73i −0.384837 + 0.666557i −0.991747 0.128214i $$-0.959076\pi$$
0.606910 + 0.794771i $$0.292409\pi$$
$$522$$ −2756.00 + 4773.53i −0.231086 + 0.400253i
$$523$$ −6903.50 11957.2i −0.577187 0.999718i −0.995800 0.0915530i $$-0.970817\pi$$
0.418613 0.908165i $$-0.362516\pi$$
$$524$$ 3020.00 0.251773
$$525$$ 0 0
$$526$$ 8946.00 0.741567
$$527$$ −2212.50 3832.16i −0.182880 0.316758i
$$528$$ −280.000 + 484.974i −0.0230785 + 0.0399731i
$$529$$ 6059.00 10494.5i 0.497986 0.862538i
$$530$$ 2919.00 + 5055.86i 0.239233 + 0.414363i
$$531$$ −442.000 −0.0361227
$$532$$ 0 0
$$533$$ −32868.0 −2.67105
$$534$$ 873.000 + 1512.08i 0.0707461 + 0.122536i
$$535$$ 451.500 782.021i 0.0364861 0.0631957i
$$536$$ 1756.00 3041.48i 0.141507 0.245097i
$$537$$ −1225.50 2122.63i −0.0984809 0.170574i
$$538$$ 3950.00 0.316536
$$539$$ 0 0
$$540$$ 1484.00 0.118261
$$541$$ −4087.50 7079.76i −0.324834 0.562629i 0.656645 0.754200i $$-0.271975\pi$$
−0.981479 + 0.191571i $$0.938642\pi$$
$$542$$ 8439.00 14616.8i 0.668794 1.15838i
$$543$$ −585.000 + 1013.25i −0.0462334 + 0.0800787i
$$544$$ −944.000 1635.06i −0.0744001 0.128865i
$$545$$ 6755.00 0.530922
$$546$$ 0 0
$$547$$ 4656.00 0.363942 0.181971 0.983304i $$-0.441752\pi$$
0.181971 + 0.983304i $$0.441752\pi$$
$$548$$ 4714.00 + 8164.89i 0.367467 + 0.636472i
$$549$$ −663.000 + 1148.35i −0.0515413 + 0.0892721i
$$550$$ −2660.00 + 4607.26i −0.206223 + 0.357189i
$$551$$ 7261.00 + 12576.4i 0.561396 + 0.972366i
$$552$$ 56.0000 0.00431797
$$553$$ 0 0
$$554$$ −1054.00 −0.0808306
$$555$$ 38.5000 + 66.6840i 0.00294457 + 0.00510014i
$$556$$ 56.0000 96.9948i 0.00427146 0.00739838i
$$557$$ −3501.50 + 6064.78i −0.266361 + 0.461352i −0.967919 0.251261i $$-0.919155\pi$$
0.701558 + 0.712612i $$0.252488\pi$$
$$558$$ 1950.00 + 3377.50i 0.147939 + 0.256238i
$$559$$ −17160.0 −1.29837
$$560$$ 0 0
$$561$$ −2065.00 −0.155409
$$562$$ −202.000 349.874i −0.0151617 0.0262608i
$$563$$ −9876.50 + 17106.6i −0.739334 + 1.28056i 0.213462 + 0.976951i $$0.431526\pi$$
−0.952796 + 0.303612i $$0.901807\pi$$
$$564$$ −342.000 + 592.361i −0.0255333 + 0.0442250i
$$565$$ −175.000 303.109i −0.0130306 0.0225697i
$$566$$ −15898.0 −1.18064
$$567$$ 0 0
$$568$$ 6272.00 0.463323
$$569$$ 3448.50 + 5972.98i 0.254075 + 0.440071i 0.964644 0.263557i $$-0.0848957\pi$$
−0.710569 + 0.703628i $$0.751562\pi$$
$$570$$ 959.000 1661.04i 0.0704703 0.122058i
$$571$$ −12457.5 + 21577.0i −0.913013 + 1.58138i −0.103227 + 0.994658i $$0.532917\pi$$
−0.809785 + 0.586726i $$0.800416\pi$$
$$572$$ 4620.00 + 8002.07i 0.337713 + 0.584936i
$$573$$ −1275.00 −0.0929562
$$574$$ 0 0
$$575$$ 532.000 0.0385842
$$576$$ 832.000 + 1441.07i 0.0601852 + 0.104244i
$$577$$ 63.5000 109.985i 0.00458152 0.00793543i −0.863726 0.503962i $$-0.831875\pi$$
0.868307 + 0.496027i $$0.165208\pi$$
$$578$$ −1432.00 + 2480.30i −0.103051 + 0.178489i
$$579$$ −17.5000 30.3109i −0.00125609 0.00217561i
$$580$$ −2968.00 −0.212482
$$581$$ 0 0
$$582$$ −580.000 −0.0413089
$$583$$ 7297.50 + 12639.6i 0.518407 + 0.897908i
$$584$$ −1180.00 + 2043.82i −0.0836109 + 0.144818i
$$585$$ 6006.00 10402.7i 0.424474 0.735211i
$$586$$ −318.000 550.792i −0.0224172 0.0388277i
$$587$$ −9044.00 −0.635921 −0.317961 0.948104i $$-0.602998\pi$$
−0.317961 + 0.948104i $$0.602998\pi$$
$$588$$ 0 0
$$589$$ 10275.0 0.718801
$$590$$ −119.000 206.114i −0.00830365 0.0143823i
$$591$$ 1367.00 2367.71i 0.0951453 0.164796i
$$592$$ −88.0000 + 152.420i −0.00610942 + 0.0105818i
$$593$$ −5350.50 9267.34i −0.370521 0.641760i 0.619125 0.785292i $$-0.287487\pi$$
−0.989646 + 0.143532i $$0.954154\pi$$
$$594$$ 3710.00 0.256268
$$595$$ 0 0
$$596$$ 9180.00 0.630919
$$597$$ 1121.50 + 1942.49i 0.0768843 + 0.133168i
$$598$$ 462.000 800.207i 0.0315930 0.0547206i
$$599$$ −10399.5 + 18012.5i −0.709369 + 1.22866i 0.255722 + 0.966750i $$0.417687\pi$$
−0.965091 + 0.261913i $$0.915647\pi$$
$$600$$ −304.000 526.543i −0.0206846 0.0358267i
$$601$$ 1402.00 0.0951560 0.0475780 0.998868i $$-0.484850\pi$$
0.0475780 + 0.998868i $$0.484850\pi$$
$$602$$ 0 0
$$603$$ −11414.0 −0.770836
$$604$$ 2218.00 + 3841.69i 0.149419 + 0.258801i
$$605$$ −371.000 + 642.591i −0.0249311 + 0.0431819i
$$606$$ 1085.00 1879.28i 0.0727312 0.125974i
$$607$$ 3262.50 + 5650.82i 0.218156 + 0.377858i 0.954244 0.299028i $$-0.0966625\pi$$
−0.736088 + 0.676886i $$0.763329\pi$$
$$608$$ 4384.00 0.292425
$$609$$ 0 0
$$610$$ −714.000 −0.0473918
$$611$$ 5643.00 + 9773.96i 0.373636 + 0.647156i
$$612$$ −3068.00 + 5313.93i −0.202641 + 0.350985i
$$613$$ −7525.50 + 13034.5i −0.495844 + 0.858826i −0.999989 0.00479285i $$-0.998474\pi$$
0.504145 + 0.863619i $$0.331808\pi$$
$$614$$ 8132.00 + 14085.0i 0.534496 + 0.925775i
$$615$$ −3486.00 −0.228568
$$616$$ 0 0
$$617$$ 11150.0 0.727524 0.363762 0.931492i $$-0.381492\pi$$
0.363762 + 0.931492i $$0.381492\pi$$
$$618$$ −1553.00 2689.87i −0.101085 0.175085i
$$619$$ 1707.50 2957.48i 0.110873 0.192037i −0.805250 0.592936i $$-0.797969\pi$$
0.916122 + 0.400899i $$0.131302\pi$$
$$620$$ −1050.00 + 1818.65i −0.0680145 + 0.117805i
$$621$$ −185.500 321.295i −0.0119869 0.0207619i
$$622$$ −1858.00 −0.119773
$$623$$ 0 0
$$624$$ −1056.00 −0.0677465
$$625$$ 174.500 + 302.243i 0.0111680 + 0.0193435i
$$626$$ 209.000 361.999i 0.0133440 0.0231124i
$$627$$ 2397.50 4152.59i 0.152706 0.264495i
$$628$$ 3118.00 + 5400.53i 0.198124 + 0.343160i
$$629$$ −649.000 −0.0411404
$$630$$ 0 0
$$631$$ −21184.0 −1.33648 −0.668242 0.743944i $$-0.732953\pi$$
−0.668242 + 0.743944i $$0.732953\pi$$
$$632$$ −1980.00 3429.46i −0.124621 0.215849i
$$633$$ −586.000 + 1014.98i −0.0367953 + 0.0637313i
$$634$$ 7131.00 12351.3i 0.446701 0.773708i
$$635$$ 3276.00 + 5674.20i 0.204731 + 0.354604i
$$636$$ −1668.00 −0.103995
$$637$$ 0 0
$$638$$ −7420.00 −0.460440
$$639$$ −10192.0 17653.1i −0.630969 1.09287i
$$640$$ −448.000 + 775.959i −0.0276699 + 0.0479257i
$$641$$ 5352.50 9270.80i 0.329814 0.571255i −0.652660 0.757651i $$-0.726347\pi$$
0.982475 + 0.186395i $$0.0596805\pi$$
$$642$$ 129.000 + 223.435i 0.00793026 + 0.0137356i
$$643$$ −6860.00 −0.420734 −0.210367 0.977622i $$-0.567466\pi$$
−0.210367 + 0.977622i $$0.567466\pi$$
$$644$$ 0 0
$$645$$ −1820.00 −0.111105
$$646$$ 8083.00 + 14000.2i 0.492293 + 0.852677i
$$647$$ 7231.50 12525.3i 0.439412 0.761084i −0.558232 0.829685i $$-0.688520\pi$$
0.997644 + 0.0686008i $$0.0218535\pi$$
$$648$$ 2596.00 4496.40i 0.157377 0.272586i
$$649$$ −297.500 515.285i −0.0179937 0.0311660i
$$650$$ −10032.0 −0.605365
$$651$$ 0 0
$$652$$ −9004.00 −0.540834
$$653$$ −2989.50 5177.97i −0.179155 0.310305i 0.762436 0.647063i $$-0.224003\pi$$
−0.941591 + 0.336758i $$0.890670\pi$$
$$654$$ −965.000 + 1671.43i −0.0576980 + 0.0999359i
$$655$$ 2642.50 4576.94i 0.157635 0.273032i
$$656$$ −3984.00 6900.49i −0.237117 0.410700i
$$657$$ 7670.00 0.455457
$$658$$ 0 0
$$659$$ −6940.00 −0.410234 −0.205117 0.978737i $$-0.565757\pi$$
−0.205117 + 0.978737i $$0.565757\pi$$
$$660$$ 490.000 + 848.705i 0.0288988 + 0.0500542i
$$661$$ 6699.50 11603.9i 0.394221 0.682812i −0.598780 0.800914i $$-0.704348\pi$$
0.993001 + 0.118102i $$0.0376810\pi$$
$$662$$ −6571.00 + 11381.3i −0.385784 + 0.668198i
$$663$$ −1947.00 3372.30i −0.114050 0.197541i
$$664$$ 7456.00 0.435766
$$665$$ 0 0
$$666$$ 572.000 0.0332801
$$667$$ 371.000 + 642.591i 0.0215370 + 0.0373032i
$$668$$ 5576.00 9657.92i 0.322967 0.559395i
$$669$$ 1012.00 1752.84i 0.0584846 0.101298i
$$670$$ −3073.00 5322.59i −0.177195 0.306910i
$$671$$ −1785.00 −0.102696
$$672$$ 0 0
$$673$$ 29510.0 1.69023 0.845117 0.534582i $$-0.179531\pi$$
0.845117 + 0.534582i $$0.179531\pi$$
$$674$$ −11466.0 19859.7i −0.655273 1.13497i
$$675$$ −2014.00 + 3488.35i −0.114843 + 0.198914i
$$676$$ −4318.00 + 7479.00i −0.245676 + 0.425523i
$$677$$ −13000.5 22517.5i −0.738035 1.27831i −0.953379 0.301776i $$-0.902421\pi$$
0.215344 0.976538i $$-0.430913\pi$$
$$678$$ 100.000 0.00566442
$$679$$ 0 0
$$680$$ −3304.00 −0.186327
$$681$$ 1285.50 + 2226.55i 0.0723355 + 0.125289i
$$682$$ −2625.00 + 4546.63i −0.147385 + 0.255278i
$$683$$ 4402.50 7625.35i 0.246643 0.427198i −0.715949 0.698152i $$-0.754006\pi$$
0.962592 + 0.270954i $$0.0873393\pi$$
$$684$$ −7124.00 12339.1i −0.398235 0.689764i
$$685$$ 16499.0 0.920284
$$686$$ 0 0
$$687$$ −895.000 −0.0497036
$$688$$ −2080.00 3602.67i −0.115261 0.199637i
$$689$$ −13761.0 + 23834.8i −0.760889 + 1.31790i
$$690$$ 49.0000 84.8705i 0.00270348 0.00468256i
$$691$$ 14342.5 + 24841.9i 0.789601 + 1.36763i 0.926211 + 0.377004i $$0.123046\pi$$
−0.136610 + 0.990625i $$0.543621\pi$$
$$692$$ −6316.00 −0.346963
$$693$$ 0 0
$$694$$ 19554.0 1.06954
$$695$$ −98.0000 169.741i −0.00534871 0.00926423i
$$696$$ 424.000 734.390i 0.0230915 0.0399956i
$$697$$ 14691.0 25445.6i 0.798366 1.38281i
$$698$$ −11914.0 20635.7i −0.646062 1.11901i
$$699$$ 1787.00 0.0966961
$$700$$ 0 0
$$701$$ −3146.00 −0.169505 −0.0847523 0.996402i $$-0.527010\pi$$
−0.0847523 + 0.996402i $$0.527010\pi$$
$$702$$ 3498.00 + 6058.71i 0.188068 + 0.325743i
$$703$$ 753.500 1305.10i 0.0404250 0.0700182i
$$704$$ −1120.00 + 1939.90i −0.0599596 + 0.103853i
$$705$$ 598.500 + 1036.63i 0.0319728 + 0.0553785i
$$706$$ 18246.0 0.972659
$$707$$ 0 0
$$708$$ 68.0000 0.00360960
$$709$$ −629.500 1090.33i −0.0333447 0.0577547i 0.848871 0.528599i $$-0.177283\pi$$
−0.882216 + 0.470845i $$0.843949\pi$$
$$710$$ 5488.00 9505.49i 0.290086 0.502443i
$$711$$ −6435.00 + 11145.7i −0.339425 + 0.587902i
$$712$$ 3492.00 + 6048.32i 0.183804 + 0.318357i
$$713$$ 525.000 0.0275756
$$714$$ 0 0
$$715$$ 16170.0 0.845767
$$716$$ −4902.00 8490.51i −0.255861 0.443164i
$$717$$ 2550.00 4416.73i 0.132819 0.230050i
$$718$$ 8149.00 14114.5i 0.423563 0.733632i
$$719$$ 8212.50 + 14224.5i 0.425973 + 0.737807i 0.996511 0.0834645i $$-0.0265985\pi$$
−0.570538 + 0.821271i $$0.693265\pi$$
$$720$$ 2912.00 0.150728
$$721$$ 0 0
$$722$$ −23820.0 −1.22782
$$723$$ −2088.50 3617.39i −0.107430 0.186075i
$$724$$ −2340.00 + 4053.00i −0.120118 + 0.208050i
$$725$$ 4028.00 6976.70i 0.206340 0.357391i
$$726$$ −106.000 183.597i −0.00541877 0.00938559i
$$727$$ 6032.00 0.307723 0.153861 0.988092i $$-0.450829\pi$$
0.153861 + 0.988092i $$0.450829\pi$$
$$728$$ 0 0
$$729$$ −15443.0 −0.784586
$$730$$ 2065.00 + 3576.68i 0.104697 + 0.181341i
$$731$$ 7670.00 13284.8i 0.388078 0.672171i
$$732$$ 102.000 176.669i 0.00515031 0.00892060i
$$733$$ 7621.50 + 13200.8i 0.384047 + 0.665189i 0.991636 0.129062i $$-0.0411967\pi$$
−0.607589 + 0.794251i $$0.707863\pi$$
$$734$$ 19342.0 0.972652
$$735$$ 0 0
$$736$$ 224.000 0.0112184
$$737$$ −7682.50 13306.5i −0.383974 0.665062i
$$738$$ −12948.0 + 22426.6i −0.645830 + 1.11861i
$$739$$ 5026.50 8706.15i 0.250207 0.433371i −0.713376 0.700782i $$-0.752835\pi$$
0.963583 + 0.267411i $$0.0861681\pi$$
$$740$$ 154.000 + 266.736i 0.00765021 + 0.0132505i
$$741$$ 9042.00 0.448267
$$742$$ 0 0
$$743$$ 24384.0 1.20399 0.601993 0.798501i $$-0.294373\pi$$
0.601993 + 0.798501i $$0.294373\pi$$
$$744$$ −300.000 519.615i −0.0147830 0.0256049i
$$745$$ 8032.50 13912.7i 0.395017 0.684190i
$$746$$ −4109.00 + 7117.00i −0.201664 + 0.349292i
$$747$$ −12116.0 20985.5i −0.593442 1.02787i
$$748$$ −8260.00 −0.403764
$$749$$ 0 0
$$750$$ −2814.00 −0.137004
$$751$$ −5794.50 10036.4i −0.281550 0.487660i 0.690216 0.723603i $$-0.257515\pi$$
−0.971767 + 0.235943i $$0.924182\pi$$
$$752$$ −1368.00 + 2369.45i −0.0663375 + 0.114900i
$$753$$ −2340.00 + 4053.00i −0.113246 + 0.196148i
$$754$$ −6996.00 12117.4i −0.337904 0.585266i
$$755$$ 7763.00 0.374205
$$756$$ 0 0
$$757$$ 14562.0 0.699161 0.349581 0.936906i $$-0.386324\pi$$
0.349581 + 0.936906i $$0.386324\pi$$
$$758$$ −3488.00 6041.39i −0.167137 0.289490i
$$759$$ 122.500 212.176i 0.00585832 0.0101469i
$$760$$ 3836.00 6644.15i 0.183087 0.317116i
$$761$$ −11382.5 19715.1i −0.542201 0.939120i −0.998777 0.0494360i $$-0.984258\pi$$
0.456576 0.889684i $$-0.349076\pi$$
$$762$$ −1872.00 −0.0889966
$$763$$ 0 0
$$764$$ −5100.00 −0.241507
$$765$$ 5369.00 + 9299.38i 0.253747 + 0.439503i
$$766$$ −8717.00 + 15098.3i −0.411172 + 0.712171i
$$767$$ 561.000 971.681i 0.0264101 0.0457436i
$$768$$ −128.000 221.703i −0.00601407 0.0104167i
$$769$$ −3766.00 −0.176600 −0.0883000 0.996094i $$-0.528143\pi$$
−0.0883000 + 0.996094i $$0.528143\pi$$
$$770$$ 0 0
$$771$$ 1749.00 0.0816974
$$772$$ −70.0000 121.244i −0.00326341 0.00565240i
$$773$$ −13430.5 + 23262.3i −0.624918 + 1.08239i 0.363639 + 0.931540i $$0.381534\pi$$
−0.988557 + 0.150849i $$0.951799\pi$$
$$774$$ −6760.00 + 11708.7i −0.313932 + 0.543746i
$$775$$ −2850.00 4936.34i −0.132097 0.228798i
$$776$$ −2320.00 −0.107324
$$777$$