# Properties

 Label 169.4.e.b.147.1 Level $169$ Weight $4$ Character 169.147 Analytic conductor $9.971$ Analytic rank $0$ Dimension $2$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$169 = 13^{2}$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 169.e (of order $$6$$, degree $$2$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$9.97132279097$$ 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 13) Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

## Embedding invariants

 Embedding label 147.1 Root $$0.500000 + 0.866025i$$ of defining polynomial Character $$\chi$$ $$=$$ 169.147 Dual form 169.4.e.b.23.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(3.00000 + 1.73205i) q^{2} +(3.50000 - 6.06218i) q^{3} +(2.00000 + 3.46410i) q^{4} -13.8564i q^{5} +(21.0000 - 12.1244i) q^{6} +(-19.5000 + 11.2583i) q^{7} -13.8564i q^{8} +(-11.0000 - 19.0526i) q^{9} +O(q^{10})$$ $$q+(3.00000 + 1.73205i) q^{2} +(3.50000 - 6.06218i) q^{3} +(2.00000 + 3.46410i) q^{4} -13.8564i q^{5} +(21.0000 - 12.1244i) q^{6} +(-19.5000 + 11.2583i) q^{7} -13.8564i q^{8} +(-11.0000 - 19.0526i) q^{9} +(24.0000 - 41.5692i) q^{10} +(19.5000 + 11.2583i) q^{11} +28.0000 q^{12} -78.0000 q^{14} +(-84.0000 - 48.4974i) q^{15} +(40.0000 - 69.2820i) q^{16} +(-13.5000 - 23.3827i) q^{17} -76.2102i q^{18} +(76.5000 - 44.1673i) q^{19} +(48.0000 - 27.7128i) q^{20} +157.617i q^{21} +(39.0000 + 67.5500i) q^{22} +(-28.5000 + 49.3634i) q^{23} +(-84.0000 - 48.4974i) q^{24} -67.0000 q^{25} +35.0000 q^{27} +(-78.0000 - 45.0333i) q^{28} +(34.5000 - 59.7558i) q^{29} +(-168.000 - 290.985i) q^{30} +72.7461i q^{31} +(144.000 - 83.1384i) q^{32} +(136.500 - 78.8083i) q^{33} -93.5307i q^{34} +(156.000 + 270.200i) q^{35} +(44.0000 - 76.2102i) q^{36} +(34.5000 + 19.9186i) q^{37} +306.000 q^{38} -192.000 q^{40} +(340.500 + 196.588i) q^{41} +(-273.000 + 472.850i) q^{42} +(42.5000 + 73.6122i) q^{43} +90.0666i q^{44} +(-264.000 + 152.420i) q^{45} +(-171.000 + 98.7269i) q^{46} +342.946i q^{47} +(-280.000 - 484.974i) q^{48} +(82.0000 - 142.028i) q^{49} +(-201.000 - 116.047i) q^{50} -189.000 q^{51} +426.000 q^{53} +(105.000 + 60.6218i) q^{54} +(156.000 - 270.200i) q^{55} +(156.000 + 270.200i) q^{56} -618.342i q^{57} +(207.000 - 119.512i) q^{58} +(16.5000 - 9.52628i) q^{59} -387.979i q^{60} +(8.50000 + 14.7224i) q^{61} +(-126.000 + 218.238i) q^{62} +(429.000 + 247.683i) q^{63} -64.0000 q^{64} +546.000 q^{66} +(-142.500 - 82.2724i) q^{67} +(54.0000 - 93.5307i) q^{68} +(199.500 + 345.544i) q^{69} +1080.80i q^{70} +(-505.500 + 291.851i) q^{71} +(-264.000 + 152.420i) q^{72} -1004.59i q^{73} +(69.0000 + 119.512i) q^{74} +(-234.500 + 406.166i) q^{75} +(306.000 + 176.669i) q^{76} -507.000 q^{77} -1244.00 q^{79} +(-960.000 - 554.256i) q^{80} +(419.500 - 726.595i) q^{81} +(681.000 + 1179.53i) q^{82} +426.084i q^{83} +(-546.000 + 315.233i) q^{84} +(-324.000 + 187.061i) q^{85} +294.449i q^{86} +(-241.500 - 418.290i) q^{87} +(156.000 - 270.200i) q^{88} +(-265.500 - 153.286i) q^{89} -1056.00 q^{90} -228.000 q^{92} +(441.000 + 254.611i) q^{93} +(-594.000 + 1028.84i) q^{94} +(-612.000 - 1060.02i) q^{95} -1163.94i q^{96} +(-1069.50 + 617.476i) q^{97} +(492.000 - 284.056i) q^{98} -495.367i q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q + 6 q^{2} + 7 q^{3} + 4 q^{4} + 42 q^{6} - 39 q^{7} - 22 q^{9}+O(q^{10})$$ 2 * q + 6 * q^2 + 7 * q^3 + 4 * q^4 + 42 * q^6 - 39 * q^7 - 22 * q^9 $$2 q + 6 q^{2} + 7 q^{3} + 4 q^{4} + 42 q^{6} - 39 q^{7} - 22 q^{9} + 48 q^{10} + 39 q^{11} + 56 q^{12} - 156 q^{14} - 168 q^{15} + 80 q^{16} - 27 q^{17} + 153 q^{19} + 96 q^{20} + 78 q^{22} - 57 q^{23} - 168 q^{24} - 134 q^{25} + 70 q^{27} - 156 q^{28} + 69 q^{29} - 336 q^{30} + 288 q^{32} + 273 q^{33} + 312 q^{35} + 88 q^{36} + 69 q^{37} + 612 q^{38} - 384 q^{40} + 681 q^{41} - 546 q^{42} + 85 q^{43} - 528 q^{45} - 342 q^{46} - 560 q^{48} + 164 q^{49} - 402 q^{50} - 378 q^{51} + 852 q^{53} + 210 q^{54} + 312 q^{55} + 312 q^{56} + 414 q^{58} + 33 q^{59} + 17 q^{61} - 252 q^{62} + 858 q^{63} - 128 q^{64} + 1092 q^{66} - 285 q^{67} + 108 q^{68} + 399 q^{69} - 1011 q^{71} - 528 q^{72} + 138 q^{74} - 469 q^{75} + 612 q^{76} - 1014 q^{77} - 2488 q^{79} - 1920 q^{80} + 839 q^{81} + 1362 q^{82} - 1092 q^{84} - 648 q^{85} - 483 q^{87} + 312 q^{88} - 531 q^{89} - 2112 q^{90} - 456 q^{92} + 882 q^{93} - 1188 q^{94} - 1224 q^{95} - 2139 q^{97} + 984 q^{98}+O(q^{100})$$ 2 * q + 6 * q^2 + 7 * q^3 + 4 * q^4 + 42 * q^6 - 39 * q^7 - 22 * q^9 + 48 * q^10 + 39 * q^11 + 56 * q^12 - 156 * q^14 - 168 * q^15 + 80 * q^16 - 27 * q^17 + 153 * q^19 + 96 * q^20 + 78 * q^22 - 57 * q^23 - 168 * q^24 - 134 * q^25 + 70 * q^27 - 156 * q^28 + 69 * q^29 - 336 * q^30 + 288 * q^32 + 273 * q^33 + 312 * q^35 + 88 * q^36 + 69 * q^37 + 612 * q^38 - 384 * q^40 + 681 * q^41 - 546 * q^42 + 85 * q^43 - 528 * q^45 - 342 * q^46 - 560 * q^48 + 164 * q^49 - 402 * q^50 - 378 * q^51 + 852 * q^53 + 210 * q^54 + 312 * q^55 + 312 * q^56 + 414 * q^58 + 33 * q^59 + 17 * q^61 - 252 * q^62 + 858 * q^63 - 128 * q^64 + 1092 * q^66 - 285 * q^67 + 108 * q^68 + 399 * q^69 - 1011 * q^71 - 528 * q^72 + 138 * q^74 - 469 * q^75 + 612 * q^76 - 1014 * q^77 - 2488 * q^79 - 1920 * q^80 + 839 * q^81 + 1362 * q^82 - 1092 * q^84 - 648 * q^85 - 483 * q^87 + 312 * q^88 - 531 * q^89 - 2112 * q^90 - 456 * q^92 + 882 * q^93 - 1188 * q^94 - 1224 * q^95 - 2139 * q^97 + 984 * q^98

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/169\mathbb{Z}\right)^\times$$.

 $$n$$ $$2$$ $$\chi(n)$$ $$e\left(\frac{1}{6}\right)$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 3.00000 + 1.73205i 1.06066 + 0.612372i 0.925615 0.378467i $$-0.123549\pi$$
0.135045 + 0.990839i $$0.456882\pi$$
$$3$$ 3.50000 6.06218i 0.673575 1.16667i −0.303308 0.952893i $$-0.598091\pi$$
0.976883 0.213774i $$-0.0685756\pi$$
$$4$$ 2.00000 + 3.46410i 0.250000 + 0.433013i
$$5$$ 13.8564i 1.23935i −0.784857 0.619677i $$-0.787263\pi$$
0.784857 0.619677i $$-0.212737\pi$$
$$6$$ 21.0000 12.1244i 1.42887 0.824958i
$$7$$ −19.5000 + 11.2583i −1.05290 + 0.607893i −0.923460 0.383694i $$-0.874652\pi$$
−0.129441 + 0.991587i $$0.541318\pi$$
$$8$$ 13.8564i 0.612372i
$$9$$ −11.0000 19.0526i −0.407407 0.705650i
$$10$$ 24.0000 41.5692i 0.758947 1.31453i
$$11$$ 19.5000 + 11.2583i 0.534497 + 0.308592i 0.742846 0.669462i $$-0.233475\pi$$
−0.208349 + 0.978055i $$0.566809\pi$$
$$12$$ 28.0000 0.673575
$$13$$ 0 0
$$14$$ −78.0000 −1.48903
$$15$$ −84.0000 48.4974i −1.44591 0.834799i
$$16$$ 40.0000 69.2820i 0.625000 1.08253i
$$17$$ −13.5000 23.3827i −0.192602 0.333596i 0.753510 0.657437i $$-0.228359\pi$$
−0.946112 + 0.323840i $$0.895026\pi$$
$$18$$ 76.2102i 0.997940i
$$19$$ 76.5000 44.1673i 0.923700 0.533299i 0.0388865 0.999244i $$-0.487619\pi$$
0.884814 + 0.465945i $$0.154286\pi$$
$$20$$ 48.0000 27.7128i 0.536656 0.309839i
$$21$$ 157.617i 1.63785i
$$22$$ 39.0000 + 67.5500i 0.377947 + 0.654623i
$$23$$ −28.5000 + 49.3634i −0.258377 + 0.447521i −0.965807 0.259261i $$-0.916521\pi$$
0.707431 + 0.706783i $$0.249854\pi$$
$$24$$ −84.0000 48.4974i −0.714435 0.412479i
$$25$$ −67.0000 −0.536000
$$26$$ 0 0
$$27$$ 35.0000 0.249472
$$28$$ −78.0000 45.0333i −0.526451 0.303946i
$$29$$ 34.5000 59.7558i 0.220913 0.382633i −0.734172 0.678963i $$-0.762430\pi$$
0.955086 + 0.296330i $$0.0957628\pi$$
$$30$$ −168.000 290.985i −1.02242 1.77088i
$$31$$ 72.7461i 0.421471i 0.977543 + 0.210735i $$0.0675858\pi$$
−0.977543 + 0.210735i $$0.932414\pi$$
$$32$$ 144.000 83.1384i 0.795495 0.459279i
$$33$$ 136.500 78.8083i 0.720048 0.415720i
$$34$$ 93.5307i 0.471776i
$$35$$ 156.000 + 270.200i 0.753395 + 1.30492i
$$36$$ 44.0000 76.2102i 0.203704 0.352825i
$$37$$ 34.5000 + 19.9186i 0.153291 + 0.0885026i 0.574683 0.818376i $$-0.305125\pi$$
−0.421393 + 0.906878i $$0.638459\pi$$
$$38$$ 306.000 1.30631
$$39$$ 0 0
$$40$$ −192.000 −0.758947
$$41$$ 340.500 + 196.588i 1.29700 + 0.748826i 0.979886 0.199560i $$-0.0639514\pi$$
0.317118 + 0.948386i $$0.397285\pi$$
$$42$$ −273.000 + 472.850i −1.00297 + 1.73720i
$$43$$ 42.5000 + 73.6122i 0.150725 + 0.261064i 0.931494 0.363756i $$-0.118506\pi$$
−0.780769 + 0.624820i $$0.785172\pi$$
$$44$$ 90.0666i 0.308592i
$$45$$ −264.000 + 152.420i −0.874551 + 0.504922i
$$46$$ −171.000 + 98.7269i −0.548099 + 0.316445i
$$47$$ 342.946i 1.06434i 0.846639 + 0.532168i $$0.178623\pi$$
−0.846639 + 0.532168i $$0.821377\pi$$
$$48$$ −280.000 484.974i −0.841969 1.45833i
$$49$$ 82.0000 142.028i 0.239067 0.414076i
$$50$$ −201.000 116.047i −0.568514 0.328232i
$$51$$ −189.000 −0.518927
$$52$$ 0 0
$$53$$ 426.000 1.10407 0.552034 0.833822i $$-0.313852\pi$$
0.552034 + 0.833822i $$0.313852\pi$$
$$54$$ 105.000 + 60.6218i 0.264605 + 0.152770i
$$55$$ 156.000 270.200i 0.382455 0.662432i
$$56$$ 156.000 + 270.200i 0.372257 + 0.644768i
$$57$$ 618.342i 1.43687i
$$58$$ 207.000 119.512i 0.468628 0.270563i
$$59$$ 16.5000 9.52628i 0.0364088 0.0210206i −0.481685 0.876344i $$-0.659975\pi$$
0.518094 + 0.855324i $$0.326642\pi$$
$$60$$ 387.979i 0.834799i
$$61$$ 8.50000 + 14.7224i 0.0178412 + 0.0309019i 0.874808 0.484469i $$-0.160987\pi$$
−0.856967 + 0.515371i $$0.827654\pi$$
$$62$$ −126.000 + 218.238i −0.258097 + 0.447037i
$$63$$ 429.000 + 247.683i 0.857919 + 0.495320i
$$64$$ −64.0000 −0.125000
$$65$$ 0 0
$$66$$ 546.000 1.01830
$$67$$ −142.500 82.2724i −0.259838 0.150018i 0.364423 0.931234i $$-0.381266\pi$$
−0.624261 + 0.781216i $$0.714600\pi$$
$$68$$ 54.0000 93.5307i 0.0963009 0.166798i
$$69$$ 199.500 + 345.544i 0.348072 + 0.602879i
$$70$$ 1080.80i 1.84543i
$$71$$ −505.500 + 291.851i −0.844955 + 0.487835i −0.858945 0.512067i $$-0.828880\pi$$
0.0139904 + 0.999902i $$0.495547\pi$$
$$72$$ −264.000 + 152.420i −0.432121 + 0.249485i
$$73$$ 1004.59i 1.61066i −0.592826 0.805331i $$-0.701988\pi$$
0.592826 0.805331i $$-0.298012\pi$$
$$74$$ 69.0000 + 119.512i 0.108393 + 0.187742i
$$75$$ −234.500 + 406.166i −0.361036 + 0.625333i
$$76$$ 306.000 + 176.669i 0.461850 + 0.266649i
$$77$$ −507.000 −0.750364
$$78$$ 0 0
$$79$$ −1244.00 −1.77166 −0.885829 0.464012i $$-0.846409\pi$$
−0.885829 + 0.464012i $$0.846409\pi$$
$$80$$ −960.000 554.256i −1.34164 0.774597i
$$81$$ 419.500 726.595i 0.575446 0.996701i
$$82$$ 681.000 + 1179.53i 0.917120 + 1.58850i
$$83$$ 426.084i 0.563480i 0.959491 + 0.281740i $$0.0909116\pi$$
−0.959491 + 0.281740i $$0.909088\pi$$
$$84$$ −546.000 + 315.233i −0.709208 + 0.409462i
$$85$$ −324.000 + 187.061i −0.413444 + 0.238702i
$$86$$ 294.449i 0.369200i
$$87$$ −241.500 418.290i −0.297604 0.515465i
$$88$$ 156.000 270.200i 0.188973 0.327311i
$$89$$ −265.500 153.286i −0.316213 0.182566i 0.333490 0.942753i $$-0.391774\pi$$
−0.649703 + 0.760188i $$0.725107\pi$$
$$90$$ −1056.00 −1.23680
$$91$$ 0 0
$$92$$ −228.000 −0.258377
$$93$$ 441.000 + 254.611i 0.491716 + 0.283892i
$$94$$ −594.000 + 1028.84i −0.651770 + 1.12890i
$$95$$ −612.000 1060.02i −0.660946 1.14479i
$$96$$ 1163.94i 1.23744i
$$97$$ −1069.50 + 617.476i −1.11950 + 0.646342i −0.941273 0.337647i $$-0.890369\pi$$
−0.178225 + 0.983990i $$0.557035\pi$$
$$98$$ 492.000 284.056i 0.507138 0.292796i
$$99$$ 495.367i 0.502891i
$$100$$ −134.000 232.095i −0.134000 0.232095i
$$101$$ −979.500 + 1696.54i −0.964989 + 1.67141i −0.255345 + 0.966850i $$0.582189\pi$$
−0.709645 + 0.704560i $$0.751144\pi$$
$$102$$ −567.000 327.358i −0.550406 0.317777i
$$103$$ 1856.00 1.77551 0.887753 0.460320i $$-0.152265\pi$$
0.887753 + 0.460320i $$0.152265\pi$$
$$104$$ 0 0
$$105$$ 2184.00 2.02987
$$106$$ 1278.00 + 737.854i 1.17104 + 0.676101i
$$107$$ 127.500 220.836i 0.115195 0.199524i −0.802663 0.596433i $$-0.796584\pi$$
0.917858 + 0.396909i $$0.129917\pi$$
$$108$$ 70.0000 + 121.244i 0.0623681 + 0.108025i
$$109$$ 609.682i 0.535752i 0.963453 + 0.267876i $$0.0863217\pi$$
−0.963453 + 0.267876i $$0.913678\pi$$
$$110$$ 936.000 540.400i 0.811310 0.468410i
$$111$$ 241.500 139.430i 0.206506 0.119226i
$$112$$ 1801.33i 1.51973i
$$113$$ −205.500 355.936i −0.171078 0.296316i 0.767719 0.640787i $$-0.221392\pi$$
−0.938797 + 0.344471i $$0.888058\pi$$
$$114$$ 1071.00 1855.03i 0.879898 1.52403i
$$115$$ 684.000 + 394.908i 0.554638 + 0.320220i
$$116$$ 276.000 0.220913
$$117$$ 0 0
$$118$$ 66.0000 0.0514898
$$119$$ 526.500 + 303.975i 0.405581 + 0.234162i
$$120$$ −672.000 + 1163.94i −0.511208 + 0.885438i
$$121$$ −412.000 713.605i −0.309542 0.536142i
$$122$$ 58.8897i 0.0437018i
$$123$$ 2383.50 1376.11i 1.74726 1.00878i
$$124$$ −252.000 + 145.492i −0.182502 + 0.105368i
$$125$$ 803.672i 0.575061i
$$126$$ 858.000 + 1486.10i 0.606641 + 1.05073i
$$127$$ 1121.50 1942.49i 0.783599 1.35723i −0.146234 0.989250i $$-0.546715\pi$$
0.929833 0.367983i $$-0.119951\pi$$
$$128$$ −1344.00 775.959i −0.928078 0.535826i
$$129$$ 595.000 0.406099
$$130$$ 0 0
$$131$$ −372.000 −0.248105 −0.124053 0.992276i $$-0.539589\pi$$
−0.124053 + 0.992276i $$0.539589\pi$$
$$132$$ 546.000 + 315.233i 0.360024 + 0.207860i
$$133$$ −994.500 + 1722.52i −0.648377 + 1.12302i
$$134$$ −285.000 493.634i −0.183733 0.318235i
$$135$$ 484.974i 0.309185i
$$136$$ −324.000 + 187.061i −0.204285 + 0.117944i
$$137$$ 1030.50 594.959i 0.642639 0.371028i −0.142991 0.989724i $$-0.545672\pi$$
0.785630 + 0.618696i $$0.212339\pi$$
$$138$$ 1382.18i 0.852599i
$$139$$ 1272.50 + 2204.03i 0.776490 + 1.34492i 0.933953 + 0.357395i $$0.116335\pi$$
−0.157464 + 0.987525i $$0.550332\pi$$
$$140$$ −624.000 + 1080.80i −0.376697 + 0.652459i
$$141$$ 2079.00 + 1200.31i 1.24173 + 0.716911i
$$142$$ −2022.00 −1.19495
$$143$$ 0 0
$$144$$ −1760.00 −1.01852
$$145$$ −828.000 478.046i −0.474218 0.273790i
$$146$$ 1740.00 3013.77i 0.986325 1.70836i
$$147$$ −574.000 994.197i −0.322059 0.557823i
$$148$$ 159.349i 0.0885026i
$$149$$ −1129.50 + 652.117i −0.621022 + 0.358547i −0.777267 0.629171i $$-0.783394\pi$$
0.156245 + 0.987718i $$0.450061\pi$$
$$150$$ −1407.00 + 812.332i −0.765874 + 0.442177i
$$151$$ 86.6025i 0.0466729i 0.999728 + 0.0233365i $$0.00742890\pi$$
−0.999728 + 0.0233365i $$0.992571\pi$$
$$152$$ −612.000 1060.02i −0.326577 0.565649i
$$153$$ −297.000 + 514.419i −0.156935 + 0.271819i
$$154$$ −1521.00 878.150i −0.795881 0.459502i
$$155$$ 1008.00 0.522352
$$156$$ 0 0
$$157$$ −1534.00 −0.779787 −0.389893 0.920860i $$-0.627488\pi$$
−0.389893 + 0.920860i $$0.627488\pi$$
$$158$$ −3732.00 2154.67i −1.87913 1.08491i
$$159$$ 1491.00 2582.49i 0.743673 1.28808i
$$160$$ −1152.00 1995.32i −0.569210 0.985901i
$$161$$ 1283.45i 0.628261i
$$162$$ 2517.00 1453.19i 1.22070 0.704774i
$$163$$ 1414.50 816.662i 0.679707 0.392429i −0.120038 0.992769i $$-0.538302\pi$$
0.799745 + 0.600340i $$0.204968\pi$$
$$164$$ 1572.70i 0.748826i
$$165$$ −1092.00 1891.40i −0.515225 0.892395i
$$166$$ −738.000 + 1278.25i −0.345060 + 0.597661i
$$167$$ −1408.50 813.198i −0.652653 0.376809i 0.136819 0.990596i $$-0.456312\pi$$
−0.789472 + 0.613787i $$0.789645\pi$$
$$168$$ 2184.00 1.00297
$$169$$ 0 0
$$170$$ −1296.00 −0.584698
$$171$$ −1683.00 971.681i −0.752645 0.434540i
$$172$$ −170.000 + 294.449i −0.0753627 + 0.130532i
$$173$$ 436.500 + 756.040i 0.191829 + 0.332258i 0.945857 0.324585i $$-0.105225\pi$$
−0.754027 + 0.656843i $$0.771891\pi$$
$$174$$ 1673.16i 0.728977i
$$175$$ 1306.50 754.308i 0.564355 0.325830i
$$176$$ 1560.00 900.666i 0.668122 0.385740i
$$177$$ 133.368i 0.0566359i
$$178$$ −531.000 919.719i −0.223596 0.387280i
$$179$$ 643.500 1114.57i 0.268701 0.465403i −0.699826 0.714314i $$-0.746739\pi$$
0.968527 + 0.248910i $$0.0800724\pi$$
$$180$$ −1056.00 609.682i −0.437276 0.252461i
$$181$$ 2.00000 0.000821319 0.000410660 1.00000i $$-0.499869\pi$$
0.000410660 1.00000i $$0.499869\pi$$
$$182$$ 0 0
$$183$$ 119.000 0.0480696
$$184$$ 684.000 + 394.908i 0.274050 + 0.158223i
$$185$$ 276.000 478.046i 0.109686 0.189982i
$$186$$ 882.000 + 1527.67i 0.347696 + 0.602226i
$$187$$ 607.950i 0.237742i
$$188$$ −1188.00 + 685.892i −0.460871 + 0.266084i
$$189$$ −682.500 + 394.042i −0.262670 + 0.151652i
$$190$$ 4240.06i 1.61898i
$$191$$ 1420.50 + 2460.38i 0.538135 + 0.932077i 0.999005 + 0.0446092i $$0.0142043\pi$$
−0.460870 + 0.887468i $$0.652462\pi$$
$$192$$ −224.000 + 387.979i −0.0841969 + 0.145833i
$$193$$ 3676.50 + 2122.63i 1.37119 + 0.791659i 0.991078 0.133281i $$-0.0425512\pi$$
0.380115 + 0.924939i $$0.375885\pi$$
$$194$$ −4278.00 −1.58321
$$195$$ 0 0
$$196$$ 656.000 0.239067
$$197$$ −2383.50 1376.11i −0.862017 0.497686i 0.00267023 0.999996i $$-0.499150\pi$$
−0.864687 + 0.502311i $$0.832483\pi$$
$$198$$ 858.000 1486.10i 0.307957 0.533396i
$$199$$ 842.500 + 1459.25i 0.300117 + 0.519818i 0.976162 0.217042i $$-0.0696410\pi$$
−0.676045 + 0.736860i $$0.736308\pi$$
$$200$$ 928.379i 0.328232i
$$201$$ −997.500 + 575.907i −0.350041 + 0.202096i
$$202$$ −5877.00 + 3393.09i −2.04705 + 1.18187i
$$203$$ 1553.65i 0.537167i
$$204$$ −378.000 654.715i −0.129732 0.224702i
$$205$$ 2724.00 4718.11i 0.928061 1.60745i
$$206$$ 5568.00 + 3214.69i 1.88321 + 1.08727i
$$207$$ 1254.00 0.421058
$$208$$ 0 0
$$209$$ 1989.00 0.658287
$$210$$ 6552.00 + 3782.80i 2.15300 + 1.24304i
$$211$$ −840.500 + 1455.79i −0.274229 + 0.474979i −0.969940 0.243343i $$-0.921756\pi$$
0.695711 + 0.718322i $$0.255089\pi$$
$$212$$ 852.000 + 1475.71i 0.276017 + 0.478075i
$$213$$ 4085.91i 1.31437i
$$214$$ 765.000 441.673i 0.244366 0.141085i
$$215$$ 1020.00 588.897i 0.323551 0.186802i
$$216$$ 484.974i 0.152770i
$$217$$ −819.000 1418.55i −0.256209 0.443767i
$$218$$ −1056.00 + 1829.05i −0.328080 + 0.568250i
$$219$$ −6090.00 3516.06i −1.87911 1.08490i
$$220$$ 1248.00 0.382455
$$221$$ 0 0
$$222$$ 966.000 0.292044
$$223$$ 3547.50 + 2048.15i 1.06528 + 0.615042i 0.926889 0.375336i $$-0.122473\pi$$
0.138394 + 0.990377i $$0.455806\pi$$
$$224$$ −1872.00 + 3242.40i −0.558385 + 0.967151i
$$225$$ 737.000 + 1276.52i 0.218370 + 0.378229i
$$226$$ 1423.75i 0.419054i
$$227$$ −379.500 + 219.104i −0.110962 + 0.0640638i −0.554454 0.832215i $$-0.687073\pi$$
0.443492 + 0.896278i $$0.353739\pi$$
$$228$$ 2142.00 1236.68i 0.622182 0.359217i
$$229$$ 180.133i 0.0519805i −0.999662 0.0259903i $$-0.991726\pi$$
0.999662 0.0259903i $$-0.00827389\pi$$
$$230$$ 1368.00 + 2369.45i 0.392188 + 0.679290i
$$231$$ −1774.50 + 3073.52i −0.505427 + 0.875424i
$$232$$ −828.000 478.046i −0.234314 0.135281i
$$233$$ −5778.00 −1.62459 −0.812295 0.583247i $$-0.801782\pi$$
−0.812295 + 0.583247i $$0.801782\pi$$
$$234$$ 0 0
$$235$$ 4752.00 1.31909
$$236$$ 66.0000 + 38.1051i 0.0182044 + 0.0105103i
$$237$$ −4354.00 + 7541.35i −1.19334 + 2.06693i
$$238$$ 1053.00 + 1823.85i 0.286789 + 0.496734i
$$239$$ 1860.22i 0.503464i 0.967797 + 0.251732i $$0.0810001\pi$$
−0.967797 + 0.251732i $$0.919000\pi$$
$$240$$ −6720.00 + 3879.79i −1.80739 + 1.04350i
$$241$$ −1783.50 + 1029.70i −0.476703 + 0.275224i −0.719041 0.694967i $$-0.755419\pi$$
0.242339 + 0.970192i $$0.422085\pi$$
$$242$$ 2854.42i 0.758219i
$$243$$ −2464.00 4267.77i −0.650476 1.12666i
$$244$$ −34.0000 + 58.8897i −0.00892060 + 0.0154509i
$$245$$ −1968.00 1136.23i −0.513187 0.296289i
$$246$$ 9534.00 2.47100
$$247$$ 0 0
$$248$$ 1008.00 0.258097
$$249$$ 2583.00 + 1491.30i 0.657393 + 0.379546i
$$250$$ 1392.00 2411.01i 0.352151 0.609944i
$$251$$ −2245.50 3889.32i −0.564680 0.978055i −0.997079 0.0763724i $$-0.975666\pi$$
0.432399 0.901682i $$-0.357667\pi$$
$$252$$ 1981.47i 0.495320i
$$253$$ −1111.50 + 641.725i −0.276203 + 0.159466i
$$254$$ 6729.00 3884.99i 1.66226 0.959708i
$$255$$ 2618.86i 0.643135i
$$256$$ −2432.00 4212.35i −0.593750 1.02841i
$$257$$ −2725.50 + 4720.70i −0.661525 + 1.14580i 0.318690 + 0.947859i $$0.396757\pi$$
−0.980215 + 0.197936i $$0.936576\pi$$
$$258$$ 1785.00 + 1030.57i 0.430734 + 0.248684i
$$259$$ −897.000 −0.215200
$$260$$ 0 0
$$261$$ −1518.00 −0.360007
$$262$$ −1116.00 644.323i −0.263155 0.151933i
$$263$$ 391.500 678.098i 0.0917906 0.158986i −0.816474 0.577382i $$-0.804074\pi$$
0.908265 + 0.418396i $$0.137408\pi$$
$$264$$ −1092.00 1891.40i −0.254576 0.440938i
$$265$$ 5902.83i 1.36833i
$$266$$ −5967.00 + 3445.05i −1.37541 + 0.794096i
$$267$$ −1858.50 + 1073.01i −0.425986 + 0.245943i
$$268$$ 658.179i 0.150018i
$$269$$ 2542.50 + 4403.74i 0.576279 + 0.998144i 0.995901 + 0.0904453i $$0.0288290\pi$$
−0.419623 + 0.907699i $$0.637838\pi$$
$$270$$ 840.000 1454.92i 0.189336 0.327940i
$$271$$ 1147.50 + 662.509i 0.257216 + 0.148504i 0.623064 0.782171i $$-0.285888\pi$$
−0.365848 + 0.930675i $$0.619221\pi$$
$$272$$ −2160.00 −0.481505
$$273$$ 0 0
$$274$$ 4122.00 0.908829
$$275$$ −1306.50 754.308i −0.286491 0.165405i
$$276$$ −798.000 + 1382.18i −0.174036 + 0.301439i
$$277$$ 1710.50 + 2962.67i 0.371025 + 0.642635i 0.989724 0.142994i $$-0.0456730\pi$$
−0.618698 + 0.785629i $$0.712340\pi$$
$$278$$ 8816.14i 1.90200i
$$279$$ 1386.00 800.207i 0.297411 0.171710i
$$280$$ 3744.00 2161.60i 0.799096 0.461358i
$$281$$ 810.600i 0.172087i −0.996291 0.0860433i $$-0.972578\pi$$
0.996291 0.0860433i $$-0.0274223\pi$$
$$282$$ 4158.00 + 7201.87i 0.878033 + 1.52080i
$$283$$ −3588.50 + 6215.46i −0.753760 + 1.30555i 0.192228 + 0.981350i $$0.438429\pi$$
−0.945988 + 0.324201i $$0.894905\pi$$
$$284$$ −2022.00 1167.40i −0.422478 0.243918i
$$285$$ −8568.00 −1.78079
$$286$$ 0 0
$$287$$ −8853.00 −1.82082
$$288$$ −3168.00 1829.05i −0.648181 0.374228i
$$289$$ 2092.00 3623.45i 0.425809 0.737523i
$$290$$ −1656.00 2868.28i −0.335323 0.580796i
$$291$$ 8644.67i 1.74144i
$$292$$ 3480.00 2009.18i 0.697437 0.402665i
$$293$$ −8065.50 + 4656.62i −1.60816 + 0.928473i −0.618381 + 0.785878i $$0.712211\pi$$
−0.989781 + 0.142595i $$0.954456\pi$$
$$294$$ 3976.79i 0.788881i
$$295$$ −132.000 228.631i −0.0260520 0.0451234i
$$296$$ 276.000 478.046i 0.0541965 0.0938712i
$$297$$ 682.500 + 394.042i 0.133342 + 0.0769852i
$$298$$ −4518.00 −0.878257
$$299$$ 0 0
$$300$$ −1876.00 −0.361036
$$301$$ −1657.50 956.958i −0.317398 0.183250i
$$302$$ −150.000 + 259.808i −0.0285812 + 0.0495041i
$$303$$ 6856.50 + 11875.8i 1.29999 + 2.25164i
$$304$$ 7066.77i 1.33325i
$$305$$ 204.000 117.779i 0.0382984 0.0221116i
$$306$$ −1782.00 + 1028.84i −0.332909 + 0.192205i
$$307$$ 4777.00i 0.888070i 0.896009 + 0.444035i $$0.146453\pi$$
−0.896009 + 0.444035i $$0.853547\pi$$
$$308$$ −1014.00 1756.30i −0.187591 0.324917i
$$309$$ 6496.00 11251.4i 1.19594 2.07142i
$$310$$ 3024.00 + 1745.91i 0.554038 + 0.319874i
$$311$$ 6192.00 1.12899 0.564495 0.825436i $$-0.309071\pi$$
0.564495 + 0.825436i $$0.309071\pi$$
$$312$$ 0 0
$$313$$ −770.000 −0.139051 −0.0695255 0.997580i $$-0.522149\pi$$
−0.0695255 + 0.997580i $$0.522149\pi$$
$$314$$ −4602.00 2656.97i −0.827089 0.477520i
$$315$$ 3432.00 5944.40i 0.613877 1.06327i
$$316$$ −2488.00 4309.34i −0.442914 0.767150i
$$317$$ 8057.50i 1.42762i −0.700341 0.713808i $$-0.746969\pi$$
0.700341 0.713808i $$-0.253031\pi$$
$$318$$ 8946.00 5164.98i 1.57757 0.910810i
$$319$$ 1345.50 776.825i 0.236155 0.136344i
$$320$$ 886.810i 0.154919i
$$321$$ −892.500 1545.86i −0.155185 0.268789i
$$322$$ 2223.00 3850.35i 0.384730 0.666371i
$$323$$ −2065.50 1192.52i −0.355813 0.205429i
$$324$$ 3356.00 0.575446
$$325$$ 0 0
$$326$$ 5658.00 0.961250
$$327$$ 3696.00 + 2133.89i 0.625044 + 0.360869i
$$328$$ 2724.00 4718.11i 0.458560 0.794250i
$$329$$ −3861.00 6687.45i −0.647002 1.12064i
$$330$$ 7565.60i 1.26204i
$$331$$ 4570.50 2638.78i 0.758965 0.438189i −0.0699590 0.997550i $$-0.522287\pi$$
0.828924 + 0.559361i $$0.188954\pi$$
$$332$$ −1476.00 + 852.169i −0.243994 + 0.140870i
$$333$$ 876.418i 0.144226i
$$334$$ −2817.00 4879.19i −0.461495 0.799333i
$$335$$ −1140.00 + 1974.54i −0.185925 + 0.322031i
$$336$$ 10920.0 + 6304.66i 1.77302 + 1.02365i
$$337$$ 8278.00 1.33808 0.669038 0.743228i $$-0.266706\pi$$
0.669038 + 0.743228i $$0.266706\pi$$
$$338$$ 0 0
$$339$$ −2877.00 −0.460936
$$340$$ −1296.00 748.246i −0.206722 0.119351i
$$341$$ −819.000 + 1418.55i −0.130063 + 0.225275i
$$342$$ −3366.00 5830.08i −0.532200 0.921798i
$$343$$ 4030.48i 0.634477i
$$344$$ 1020.00 588.897i 0.159868 0.0923000i
$$345$$ 4788.00 2764.35i 0.747180 0.431385i
$$346$$ 3024.16i 0.469884i
$$347$$ −3433.50 5947.00i −0.531181 0.920033i −0.999338 0.0363875i $$-0.988415\pi$$
0.468156 0.883646i $$-0.344918\pi$$
$$348$$ 966.000 1673.16i 0.148802 0.257732i
$$349$$ −10525.5 6076.90i −1.61438 0.932060i −0.988340 0.152266i $$-0.951343\pi$$
−0.626036 0.779794i $$-0.715324\pi$$
$$350$$ 5226.00 0.798118
$$351$$ 0 0
$$352$$ 3744.00 0.566920
$$353$$ −5029.50 2903.78i −0.758338 0.437827i 0.0703608 0.997522i $$-0.477585\pi$$
−0.828699 + 0.559695i $$0.810918\pi$$
$$354$$ 231.000 400.104i 0.0346822 0.0600714i
$$355$$ 4044.00 + 7004.41i 0.604601 + 1.04720i
$$356$$ 1226.29i 0.182566i
$$357$$ 3685.50 2127.82i 0.546379 0.315452i
$$358$$ 3861.00 2229.15i 0.570001 0.329090i
$$359$$ 1340.61i 0.197088i −0.995133 0.0985439i $$-0.968581\pi$$
0.995133 0.0985439i $$-0.0314185\pi$$
$$360$$ 2112.00 + 3658.09i 0.309200 + 0.535551i
$$361$$ 472.000 817.528i 0.0688147 0.119191i
$$362$$ 6.00000 + 3.46410i 0.000871141 + 0.000502953i
$$363$$ −5768.00 −0.833999
$$364$$ 0 0
$$365$$ −13920.0 −1.99618
$$366$$ 357.000 + 206.114i 0.0509855 + 0.0294365i
$$367$$ −1832.50 + 3173.98i −0.260642 + 0.451446i −0.966413 0.256995i $$-0.917268\pi$$
0.705770 + 0.708441i $$0.250601\pi$$
$$368$$ 2280.00 + 3949.08i 0.322971 + 0.559402i
$$369$$ 8649.86i 1.22031i
$$370$$ 1656.00 956.092i 0.232679 0.134337i
$$371$$ −8307.00 + 4796.05i −1.16247 + 0.671155i
$$372$$ 2036.89i 0.283892i
$$373$$ −2685.50 4651.42i −0.372788 0.645688i 0.617205 0.786802i $$-0.288265\pi$$
−0.989993 + 0.141114i $$0.954931\pi$$
$$374$$ 1053.00 1823.85i 0.145586 0.252163i
$$375$$ −4872.00 2812.85i −0.670904 0.387347i
$$376$$ 4752.00 0.651770
$$377$$ 0 0
$$378$$ −2730.00 −0.371471
$$379$$ 9967.50 + 5754.74i 1.35091 + 0.779950i 0.988377 0.152020i $$-0.0485778\pi$$
0.362536 + 0.931970i $$0.381911\pi$$
$$380$$ 2448.00 4240.06i 0.330473 0.572396i
$$381$$ −7850.50 13597.5i −1.05563 1.82840i
$$382$$ 9841.51i 1.31816i
$$383$$ −2095.50 + 1209.84i −0.279569 + 0.161409i −0.633228 0.773965i $$-0.718271\pi$$
0.353659 + 0.935374i $$0.384937\pi$$
$$384$$ −9408.00 + 5431.71i −1.25026 + 0.721838i
$$385$$ 7025.20i 0.929967i
$$386$$ 7353.00 + 12735.8i 0.969580 + 1.67936i
$$387$$ 935.000 1619.47i 0.122813 0.212719i
$$388$$ −4278.00 2469.90i −0.559749 0.323171i
$$389$$ −9858.00 −1.28489 −0.642443 0.766334i $$-0.722079\pi$$
−0.642443 + 0.766334i $$0.722079\pi$$
$$390$$ 0 0
$$391$$ 1539.00 0.199055
$$392$$ −1968.00 1136.23i −0.253569 0.146398i
$$393$$ −1302.00 + 2255.13i −0.167118 + 0.289456i
$$394$$ −4767.00 8256.69i −0.609538 1.05575i
$$395$$ 17237.4i 2.19571i
$$396$$ 1716.00 990.733i 0.217758 0.125723i
$$397$$ 7552.50 4360.44i 0.954784 0.551245i 0.0602200 0.998185i $$-0.480820\pi$$
0.894564 + 0.446941i $$0.147486\pi$$
$$398$$ 5837.01i 0.735133i
$$399$$ 6961.50 + 12057.7i 0.873461 + 1.51288i
$$400$$ −2680.00 + 4641.90i −0.335000 + 0.580237i
$$401$$ 6568.50 + 3792.33i 0.817993 + 0.472269i 0.849724 0.527228i $$-0.176769\pi$$
−0.0317308 + 0.999496i $$0.510102\pi$$
$$402$$ −3990.00 −0.495033
$$403$$ 0 0
$$404$$ −7836.00 −0.964989
$$405$$ −10068.0 5812.76i −1.23527 0.713181i
$$406$$ −2691.00 + 4660.95i −0.328946 + 0.569751i
$$407$$ 448.500 + 776.825i 0.0546224 + 0.0946088i
$$408$$ 2618.86i 0.317777i
$$409$$ −3727.50 + 2152.07i −0.450643 + 0.260179i −0.708102 0.706110i $$-0.750448\pi$$
0.257459 + 0.966289i $$0.417115\pi$$
$$410$$ 16344.0 9436.21i 1.96871 1.13664i
$$411$$ 8329.43i 0.999661i
$$412$$ 3712.00 + 6429.37i 0.443876 + 0.768817i
$$413$$ −214.500 + 371.525i −0.0255565 + 0.0442652i
$$414$$ 3762.00 + 2171.99i 0.446600 + 0.257844i
$$415$$ 5904.00 0.698352
$$416$$ 0 0
$$417$$ 17815.0 2.09210
$$418$$ 5967.00 + 3445.05i 0.698219 + 0.403117i
$$419$$ −2698.50 + 4673.94i −0.314631 + 0.544957i −0.979359 0.202129i $$-0.935214\pi$$
0.664728 + 0.747085i $$0.268547\pi$$
$$420$$ 4368.00 + 7565.60i 0.507468 + 0.878960i
$$421$$ 7260.76i 0.840541i −0.907399 0.420270i $$-0.861935\pi$$
0.907399 0.420270i $$-0.138065\pi$$
$$422$$ −5043.00 + 2911.58i −0.581728 + 0.335861i
$$423$$ 6534.00 3772.41i 0.751050 0.433619i
$$424$$ 5902.83i 0.676101i
$$425$$ 904.500 + 1566.64i 0.103235 + 0.178808i
$$426$$ −7077.00 + 12257.7i −0.804887 + 1.39410i
$$427$$ −331.500 191.392i −0.0375700 0.0216911i
$$428$$ 1020.00 0.115195
$$429$$ 0 0
$$430$$ 4080.00 0.457570
$$431$$ 421.500 + 243.353i 0.0471066 + 0.0271970i 0.523368 0.852107i $$-0.324675\pi$$
−0.476262 + 0.879304i $$0.658009\pi$$
$$432$$ 1400.00 2424.87i 0.155920 0.270062i
$$433$$ −6069.50 10512.7i −0.673629 1.16676i −0.976867 0.213846i $$-0.931401\pi$$
0.303238 0.952915i $$-0.401932\pi$$
$$434$$ 5674.20i 0.627581i
$$435$$ −5796.00 + 3346.32i −0.638844 + 0.368836i
$$436$$ −2112.00 + 1219.36i −0.231987 + 0.133938i
$$437$$ 5035.07i 0.551167i
$$438$$ −12180.0 21096.4i −1.32873 2.30142i
$$439$$ −230.500 + 399.238i −0.0250596 + 0.0434045i −0.878283 0.478141i $$-0.841311\pi$$
0.853224 + 0.521545i $$0.174644\pi$$
$$440$$ −3744.00 2161.60i −0.405655 0.234205i
$$441$$ −3608.00 −0.389591
$$442$$ 0 0
$$443$$ 12156.0 1.30372 0.651861 0.758338i $$-0.273988\pi$$
0.651861 + 0.758338i $$0.273988\pi$$
$$444$$ 966.000 + 557.720i 0.103253 + 0.0596131i
$$445$$ −2124.00 + 3678.88i −0.226263 + 0.391900i
$$446$$ 7095.00 + 12288.9i 0.753269 + 1.30470i
$$447$$ 9129.64i 0.966034i
$$448$$ 1248.00 720.533i 0.131613 0.0759866i
$$449$$ 256.500 148.090i 0.0269599 0.0155653i −0.486459 0.873703i $$-0.661712\pi$$
0.513419 + 0.858138i $$0.328379\pi$$
$$450$$ 5106.09i 0.534896i
$$451$$ 4426.50 + 7666.92i 0.462164 + 0.800491i
$$452$$ 822.000 1423.75i 0.0855390 0.148158i
$$453$$ 525.000 + 303.109i 0.0544518 + 0.0314377i
$$454$$ −1518.00 −0.156924
$$455$$ 0 0
$$456$$ −8568.00 −0.879898
$$457$$ −529.500 305.707i −0.0541990 0.0312918i 0.472656 0.881247i $$-0.343295\pi$$
−0.526855 + 0.849955i $$0.676629\pi$$
$$458$$ 312.000 540.400i 0.0318314 0.0551337i
$$459$$ −472.500 818.394i −0.0480488 0.0832230i
$$460$$ 3159.26i 0.320220i
$$461$$ 11368.5 6563.61i 1.14855 0.663119i 0.200020 0.979792i $$-0.435899\pi$$
0.948535 + 0.316673i $$0.102566\pi$$
$$462$$ −10647.0 + 6147.05i −1.07217 + 0.619019i
$$463$$ 834.848i 0.0837985i 0.999122 + 0.0418992i $$0.0133408\pi$$
−0.999122 + 0.0418992i $$0.986659\pi$$
$$464$$ −2760.00 4780.46i −0.276142 0.478292i
$$465$$ 3528.00 6110.68i 0.351843 0.609410i
$$466$$ −17334.0 10007.8i −1.72314 0.994854i
$$467$$ 14496.0 1.43639 0.718196 0.695841i $$-0.244968\pi$$
0.718196 + 0.695841i $$0.244968\pi$$
$$468$$ 0 0
$$469$$ 3705.00 0.364778
$$470$$ 14256.0 + 8230.71i 1.39911 + 0.807775i
$$471$$ −5369.00 + 9299.38i −0.525245 + 0.909751i
$$472$$ −132.000 228.631i −0.0128724 0.0222957i
$$473$$ 1913.92i 0.186051i
$$474$$ −26124.0 + 15082.7i −2.53147 + 1.46154i
$$475$$ −5125.50 + 2959.21i −0.495103 + 0.285848i
$$476$$ 2431.80i 0.234162i
$$477$$ −4686.00 8116.39i −0.449805 0.779086i
$$478$$ −3222.00 + 5580.67i −0.308307 + 0.534004i
$$479$$ 7705.50 + 4448.77i 0.735017 + 0.424362i 0.820255 0.571998i $$-0.193832\pi$$
−0.0852376 + 0.996361i $$0.527165\pi$$
$$480$$ −16128.0 −1.53362
$$481$$ 0 0
$$482$$ −7134.00 −0.674159
$$483$$ −7780.50 4492.07i −0.732971 0.423181i
$$484$$ 1648.00 2854.42i 0.154771 0.268071i
$$485$$ 8556.00 + 14819.4i 0.801047 + 1.38745i
$$486$$ 17071.1i 1.59333i
$$487$$ −4117.50 + 2377.24i −0.383125 + 0.221197i −0.679177 0.733975i $$-0.737663\pi$$
0.296052 + 0.955172i $$0.404330\pi$$
$$488$$ 204.000 117.779i 0.0189235 0.0109255i
$$489$$ 11433.3i 1.05732i
$$490$$ −3936.00 6817.35i −0.362878 0.628524i
$$491$$ 817.500 1415.95i 0.0751390 0.130145i −0.826008 0.563659i $$-0.809393\pi$$
0.901147 + 0.433514i $$0.142727\pi$$
$$492$$ 9534.00 + 5504.46i 0.873630 + 0.504390i
$$493$$ −1863.00 −0.170193
$$494$$ 0 0
$$495$$ −6864.00 −0.623260
$$496$$ 5040.00 + 2909.85i 0.456255 + 0.263419i
$$497$$ 6571.50 11382.2i 0.593103 1.02728i
$$498$$ 5166.00 + 8947.77i 0.464847 + 0.805139i
$$499$$ 14434.9i 1.29498i 0.762074 + 0.647490i $$0.224181\pi$$
−0.762074 + 0.647490i $$0.775819\pi$$
$$500$$ 2784.00 1607.34i 0.249009 0.143765i
$$501$$ −9859.50 + 5692.38i −0.879222 + 0.507619i
$$502$$ 15557.3i 1.38318i
$$503$$ −6343.50 10987.3i −0.562312 0.973952i −0.997294 0.0735133i $$-0.976579\pi$$
0.434983 0.900439i $$-0.356754\pi$$
$$504$$ 3432.00 5944.40i 0.303320 0.525366i
$$505$$ 23508.0 + 13572.4i 2.07147 + 1.19596i
$$506$$ −4446.00 −0.390610
$$507$$ 0 0
$$508$$ 8972.00 0.783599
$$509$$ 4978.50 + 2874.34i 0.433533 + 0.250300i 0.700850 0.713308i $$-0.252804\pi$$
−0.267318 + 0.963608i $$0.586137\pi$$
$$510$$ −4536.00 + 7856.58i −0.393838 + 0.682148i
$$511$$ 11310.0 + 19589.5i 0.979109 + 1.69587i
$$512$$ 4434.05i 0.382733i
$$513$$ 2677.50 1545.86i 0.230438 0.133043i
$$514$$ −16353.0 + 9441.41i −1.40331 + 0.810200i
$$515$$ 25717.5i 2.20048i
$$516$$ 1190.00 + 2061.14i 0.101525 + 0.175846i
$$517$$ −3861.00 + 6687.45i −0.328446 + 0.568885i
$$518$$ −2691.00 1553.65i −0.228254 0.131783i
$$519$$ 6111.00 0.516846
$$520$$ 0 0
$$521$$ 6054.00 0.509080 0.254540 0.967062i $$-0.418076\pi$$
0.254540 + 0.967062i $$0.418076\pi$$
$$522$$ −4554.00 2629.25i −0.381845 0.220458i
$$523$$ 7401.50 12819.8i 0.618824 1.07183i −0.370877 0.928682i $$-0.620943\pi$$
0.989701 0.143153i $$-0.0457240\pi$$
$$524$$ −744.000 1288.65i −0.0620263 0.107433i
$$525$$ 10560.3i 0.877885i
$$526$$ 2349.00 1356.20i 0.194717 0.112420i
$$527$$ 1701.00 982.073i 0.140601 0.0811760i
$$528$$ 12609.3i 1.03930i
$$529$$ 4459.00 + 7723.21i 0.366483 + 0.634767i
$$530$$ 10224.0 17708.5i 0.837929 1.45133i
$$531$$ −363.000 209.578i −0.0296664 0.0171279i
$$532$$ −7956.00 −0.648377
$$533$$ 0 0
$$534$$ −7434.00 −0.602436
$$535$$ −3060.00 1766.69i −0.247281 0.142768i
$$536$$ −1140.00 + 1974.54i −0.0918666 + 0.159118i
$$537$$ −4504.50 7802.02i −0.361980 0.626969i
$$538$$ 17615.0i 1.41159i
$$539$$ 3198.00 1846.37i 0.255561 0.147548i
$$540$$ 1680.00 969.948i 0.133881 0.0772962i
$$541$$ 21470.5i 1.70626i 0.521695 + 0.853132i $$0.325300\pi$$
−0.521695 + 0.853132i $$0.674700\pi$$
$$542$$ 2295.00 + 3975.06i 0.181880 + 0.315025i
$$543$$ 7.00000 12.1244i 0.000553221 0.000958206i
$$544$$ −3888.00 2244.74i −0.306428 0.176916i
$$545$$ 8448.00 0.663986
$$546$$ 0 0
$$547$$ −13516.0 −1.05649 −0.528247 0.849091i $$-0.677151\pi$$
−0.528247 + 0.849091i $$0.677151\pi$$
$$548$$ 4122.00 + 2379.84i 0.321320 + 0.185514i
$$549$$ 187.000 323.894i 0.0145373 0.0251793i
$$550$$ −2613.00 4525.85i −0.202579 0.350878i
$$551$$ 6095.09i 0.471251i
$$552$$ 4788.00 2764.35i 0.369186 0.213150i
$$553$$ 24258.0 14005.4i 1.86538 1.07698i
$$554$$ 11850.7i 0.908822i
$$555$$ −1932.00 3346.32i −0.147764 0.255934i
$$556$$ −5090.00 + 8816.14i −0.388245 + 0.672460i
$$557$$ −2503.50 1445.40i −0.190443 0.109952i 0.401747 0.915751i $$-0.368403\pi$$
−0.592190 + 0.805798i $$0.701736\pi$$
$$558$$ 5544.00 0.420603
$$559$$ 0 0
$$560$$ 24960.0 1.88349
$$561$$ −3685.50 2127.82i −0.277365 0.160137i
$$562$$ 1404.00 2431.80i 0.105381 0.182525i
$$563$$ −5791.50 10031.2i −0.433539 0.750912i 0.563636 0.826023i $$-0.309402\pi$$
−0.997175 + 0.0751113i $$0.976069\pi$$
$$564$$ 9602.49i 0.716911i
$$565$$ −4932.00 + 2847.49i −0.367240 + 0.212026i
$$566$$ −21531.0 + 12430.9i −1.59897 + 0.923164i
$$567$$ 18891.5i 1.39924i
$$568$$ 4044.00 + 7004.41i 0.298737 + 0.517427i
$$569$$ −6439.50 + 11153.5i −0.474443 + 0.821759i −0.999572 0.0292638i $$-0.990684\pi$$
0.525129 + 0.851023i $$0.324017\pi$$
$$570$$ −25704.0 14840.2i −1.88881 1.09051i
$$571$$ −11636.0 −0.852805 −0.426402 0.904534i $$-0.640219\pi$$
−0.426402 + 0.904534i $$0.640219\pi$$
$$572$$ 0 0
$$573$$ 19887.0 1.44990
$$574$$ −26559.0 15333.8i −1.93127 1.11502i
$$575$$ 1909.50 3307.35i 0.138490 0.239871i
$$576$$ 704.000 + 1219.36i 0.0509259 + 0.0882063i
$$577$$ 12311.4i 0.888269i −0.895960 0.444134i $$-0.853511\pi$$
0.895960 0.444134i $$-0.146489\pi$$
$$578$$ 12552.0 7246.90i 0.903277 0.521507i
$$579$$ 25735.5 14858.4i 1.84720 1.06648i
$$580$$ 3824.37i 0.273790i
$$581$$ −4797.00 8308.65i −0.342535 0.593289i
$$582$$ −14973.0 + 25934.0i −1.06641 + 1.84708i
$$583$$ 8307.00 + 4796.05i 0.590121 + 0.340707i
$$584$$ −13920.0 −0.986325
$$585$$ 0 0
$$586$$ −32262.0 −2.27428
$$587$$ 13549.5 + 7822.81i 0.952722 + 0.550054i 0.893925 0.448216i $$-0.147940\pi$$
0.0587964 + 0.998270i $$0.481274\pi$$
$$588$$ 2296.00 3976.79i 0.161030 0.278912i
$$589$$ 3213.00 + 5565.08i 0.224770 + 0.389313i
$$590$$ 914.523i 0.0638141i
$$591$$ −16684.5 + 9632.80i −1.16127 + 0.670458i
$$592$$ 2760.00 1593.49i 0.191614 0.110628i
$$593$$ 25821.4i 1.78813i −0.447942 0.894063i $$-0.647843\pi$$
0.447942 0.894063i $$-0.352157\pi$$
$$594$$ 1365.00 + 2364.25i 0.0942873 + 0.163310i
$$595$$ 4212.00 7295.40i 0.290210 0.502659i
$$596$$ −4518.00 2608.47i −0.310511 0.179274i
$$597$$ 11795.0 0.808605
$$598$$ 0 0
$$599$$ 1668.00 0.113777 0.0568887 0.998381i $$-0.481882\pi$$
0.0568887 + 0.998381i $$0.481882\pi$$
$$600$$ 5628.00 + 3249.33i 0.382937 + 0.221089i
$$601$$ −6849.50 + 11863.7i −0.464887 + 0.805207i −0.999196 0.0400813i $$-0.987238\pi$$
0.534310 + 0.845289i $$0.320572\pi$$
$$602$$ −3315.00 5741.75i −0.224434 0.388731i
$$603$$ 3619.99i 0.244473i
$$604$$ −300.000 + 173.205i −0.0202100 + 0.0116682i
$$605$$ −9888.00 + 5708.84i −0.664470 + 0.383632i
$$606$$ 47503.2i 3.18430i
$$607$$ 11586.5 + 20068.4i 0.774764 + 1.34193i 0.934927 + 0.354839i $$0.115464\pi$$
−0.160164 + 0.987090i $$0.551202\pi$$
$$608$$ 7344.00 12720.2i 0.489866 0.848473i
$$609$$ 9418.50 + 5437.77i 0.626694 + 0.361822i
$$610$$ 816.000 0.0541621
$$611$$ 0 0
$$612$$ −2376.00 −0.156935
$$613$$ −14389.5 8307.78i −0.948102 0.547387i −0.0556111 0.998453i $$-0.517711\pi$$
−0.892491 + 0.451066i $$0.851044\pi$$
$$614$$ −8274.00 + 14331.0i −0.543830 + 0.941941i
$$615$$ −19068.0 33026.7i −1.25024 2.16547i
$$616$$ 7025.20i 0.459502i
$$617$$ −24589.5 + 14196.8i −1.60443 + 0.926321i −0.613849 + 0.789423i $$0.710380\pi$$
−0.990585 + 0.136897i $$0.956287\pi$$
$$618$$ 38976.0 22502.8i 2.53697 1.46472i
$$619$$ 6245.78i 0.405556i 0.979225 + 0.202778i $$0.0649969\pi$$
−0.979225 + 0.202778i $$0.935003\pi$$
$$620$$ 2016.00 + 3491.81i 0.130588 + 0.226185i
$$621$$ −997.500 + 1727.72i −0.0644578 + 0.111644i
$$622$$ 18576.0 + 10724.9i 1.19748 + 0.691363i
$$623$$ 6903.00 0.443921
$$624$$ 0 0
$$625$$ −19511.0 −1.24870
$$626$$ −2310.00 1333.68i −0.147486 0.0851510i
$$627$$ 6961.50 12057.7i 0.443406 0.768002i
$$628$$ −3068.00 5313.93i −0.194947 0.337658i
$$629$$ 1075.60i 0.0681830i
$$630$$ 20592.0 11888.8i 1.30223 0.751843i
$$631$$ −19381.5 + 11189.9i −1.22277 + 0.705964i −0.965507 0.260378i $$-0.916153\pi$$
−0.257259 + 0.966342i $$0.582819\pi$$
$$632$$ 17237.4i 1.08491i
$$633$$ 5883.50 + 10190.5i 0.369428 + 0.639869i
$$634$$ 13956.0 24172.5i 0.874233 1.51422i
$$635$$ −26916.0 15540.0i −1.68209 0.971157i
$$636$$ 11928.0 0.743673
$$637$$ 0 0
$$638$$ 5382.00 0.333974
$$639$$ 11121.0 + 6420.71i 0.688482 + 0.397495i
$$640$$ −10752.0 + 18623.0i −0.664078 + 1.15022i
$$641$$ −9913.50 17170.7i −0.610858 1.05804i −0.991096 0.133148i $$-0.957491\pi$$
0.380239 0.924888i $$-0.375842\pi$$
$$642$$ 6183.42i 0.380125i
$$643$$ 7318.50 4225.34i 0.448855 0.259146i −0.258492 0.966013i $$-0.583225\pi$$
0.707346 + 0.706867i $$0.249892\pi$$
$$644$$ 4446.00 2566.90i 0.272045 0.157065i
$$645$$ 8244.56i 0.503301i
$$646$$ −4131.00 7155.10i −0.251598 0.435780i
$$647$$ −1474.50 + 2553.91i −0.0895959 + 0.155185i −0.907340 0.420397i $$-0.861891\pi$$
0.817744 + 0.575581i $$0.195224\pi$$
$$648$$ −10068.0 5812.76i −0.610352 0.352387i
$$649$$ 429.000 0.0259472
$$650$$ 0 0
$$651$$ −11466.0 −0.690304
$$652$$ 5658.00 + 3266.65i 0.339853 + 0.196214i
$$653$$ −6019.50 + 10426.1i −0.360737 + 0.624815i −0.988082 0.153926i $$-0.950808\pi$$
0.627345 + 0.778741i $$0.284141\pi$$
$$654$$ 7392.00 + 12803.3i 0.441973 + 0.765519i
$$655$$ 5154.58i 0.307490i
$$656$$ 27240.0 15727.0i 1.62126 0.936032i
$$657$$ −19140.0 + 11050.5i −1.13656 + 0.656196i
$$658$$ 26749.8i 1.58483i
$$659$$ −1681.50 2912.44i −0.0993960 0.172159i 0.812039 0.583603i $$-0.198358\pi$$
−0.911435 + 0.411445i $$0.865024\pi$$
$$660$$ 4368.00 7565.60i 0.257612 0.446198i
$$661$$ −8797.50 5079.24i −0.517675 0.298880i 0.218308 0.975880i $$-0.429946\pi$$
−0.735983 + 0.677000i $$0.763280\pi$$
$$662$$ 18282.0 1.07334
$$663$$ 0 0
$$664$$ 5904.00 0.345060
$$665$$ 23868.0 + 13780.2i 1.39182 + 0.803569i
$$666$$ 1518.00 2629.25i 0.0883203 0.152975i
$$667$$ 1966.50 + 3406.08i 0.114158 + 0.197727i
$$668$$ 6505.58i 0.376809i
$$669$$ 24832.5 14337.1i 1.43510 0.828554i
$$670$$ −6840.00 + 3949.08i −0.394406 + 0.227711i
$$671$$ 382.783i 0.0220226i
$$672$$ 13104.0 + 22696.8i 0.752229 + 1.30290i
$$673$$ 9084.50 15734.8i 0.520329 0.901237i −0.479391 0.877601i $$-0.659142\pi$$
0.999721 0.0236358i $$-0.00752419\pi$$
$$674$$ 24834.0 + 14337.9i 1.41924 + 0.819400i
$$675$$ −2345.00 −0.133717
$$676$$ 0 0
$$677$$ 9042.00 0.513312 0.256656 0.966503i $$-0.417379\pi$$
0.256656 + 0.966503i $$0.417379\pi$$
$$678$$ −8631.00 4983.11i −0.488896 0.282264i
$$679$$ 13903.5 24081.6i 0.785813 1.36107i
$$680$$ 2592.00 + 4489.48i 0.146175 + 0.253182i
$$681$$ 3067.46i 0.172607i
$$682$$ −4914.00 + 2837.10i −0.275904 + 0.159293i
$$683$$ 10792.5 6231.05i 0.604632 0.349084i −0.166230 0.986087i $$-0.553159\pi$$
0.770862 + 0.637003i $$0.219826\pi$$
$$684$$ 7773.44i 0.434540i
$$685$$ −8244.00 14279.0i −0.459835 0.796458i
$$686$$ 6981.00 12091.4i 0.388536 0.672964i
$$687$$ −1092.00 630.466i −0.0606440 0.0350128i
$$688$$ 6800.00 0.376813
$$689$$ 0 0
$$690$$ 19152.0 1.05667
$$691$$ 3739.50 + 2159.00i 0.205872 + 0.118860i 0.599391 0.800456i $$-0.295409\pi$$
−0.393520 + 0.919316i $$0.628743\pi$$
$$692$$ −1746.00 + 3024.16i −0.0959147 + 0.166129i
$$693$$ 5577.00 + 9659.65i 0.305704 + 0.529494i
$$694$$ 23788.0i 1.30112i
$$695$$ 30540.0 17632.3i 1.66683 0.962346i
$$696$$ −5796.00 + 3346.32i −0.315656 + 0.182244i
$$697$$ 10615.7i 0.576901i
$$698$$ −21051.0 36461.4i −1.14154 1.97720i
$$699$$ −20223.0 + 35027.3i −1.09428 + 1.89535i
$$700$$ 5226.00 + 3017.23i 0.282177 + 0.162915i
$$701$$ −18270.0 −0.984377 −0.492189 0.870489i $$-0.663803\pi$$
−0.492189 + 0.870489i $$0.663803\pi$$
$$702$$ 0 0
$$703$$ 3519.00 0.188793
$$704$$ −1248.00 720.533i −0.0668122 0.0385740i
$$705$$ 16632.0 28807.5i 0.888507 1.53894i
$$706$$ −10059.0 17422.7i −0.536226 0.928770i
$$707$$ 44110.1i 2.34644i
$$708$$ 462.000 266.736i 0.0245240 0.0141590i
$$709$$ −1411.50 + 814.930i −0.0747673 + 0.0431669i −0.536918 0.843635i $$-0.680411\pi$$
0.462150 + 0.886802i $$0.347078\pi$$
$$710$$ 28017.7i 1.48096i
$$711$$ 13684.0 + 23701.4i 0.721786 + 1.25017i
$$712$$ −2124.00 + 3678.88i −0.111798 + 0.193640i
$$713$$ −3591.00 2073.26i −0.188617 0.108898i
$$714$$ 14742.0 0.772697
$$715$$ 0 0
$$716$$ 5148.00 0.268701
$$717$$ 11277.0 + 6510.78i 0.587374 + 0.339121i
$$718$$ 2322.00 4021.82i 0.120691 0.209043i
$$719$$ −4915.50 8513.90i −0.254961 0.441606i 0.709924 0.704279i $$-0.248729\pi$$
−0.964885 + 0.262673i $$0.915396\pi$$
$$720$$ 24387.3i 1.26231i
$$721$$ −36192.0 + 20895.5i −1.86943 + 1.07932i
$$722$$ 2832.00 1635.06i 0.145978 0.0842804i
$$723$$ 14415.9i 0.741537i
$$724$$ 4.00000 + 6.92820i 0.000205330 + 0.000355642i
$$725$$ −2311.50 + 4003.64i −0.118410 + 0.205091i
$$726$$ −17304.0 9990.47i −0.884589 0.510718i
$$727$$ −15464.0 −0.788897 −0.394448 0.918918i $$-0.629064\pi$$
−0.394448 + 0.918918i $$0.629064\pi$$
$$728$$ 0 0
$$729$$ −11843.0 −0.601687
$$730$$ −41760.0 24110.1i −2.11727 1.22241i
$$731$$ 1147.50 1987.53i 0.0580599 0.100563i
$$732$$ 238.000 + 412.228i 0.0120174 + 0.0208147i
$$733$$ 12616.3i 0.635733i 0.948136 + 0.317866i $$0.102966\pi$$
−0.948136 + 0.317866i $$0.897034\pi$$
$$734$$ −10995.0 + 6347.97i −0.552906 + 0.319220i
$$735$$ −13776.0 + 7953.58i −0.691341 + 0.399146i
$$736$$ 9477.78i 0.474668i
$$737$$ −1852.50 3208.62i −0.0925885 0.160368i
$$738$$ 14982.0 25949.6i 0.747283 1.29433i
$$739$$ 14101.5 + 8141.50i 0.701938 + 0.405264i 0.808069 0.589088i $$-0.200513\pi$$
−0.106131 + 0.994352i $$0.533846\pi$$
$$740$$ 2208.00 0.109686
$$741$$ 0 0
$$742$$ −33228.0 −1.64399
$$743$$ −9358.50 5403.13i −0.462086 0.266786i 0.250835 0.968030i $$-0.419295\pi$$
−0.712921 + 0.701244i $$0.752628\pi$$
$$744$$ 3528.00 6110.68i 0.173848 0.301113i
$$745$$ 9036.00 + 15650.8i 0.444367 + 0.769666i
$$746$$ 18605.7i 0.913140i
$$747$$ 8118.00 4686.93i 0.397620 0.229566i
$$748$$ 2106.00 1215.90i 0.102945 0.0594354i
$$749$$ 5741.75i 0.280105i
$$750$$ −9744.00 16877.1i −0.474401 0.821686i
$$751$$ 6807.50 11790.9i 0.330771 0.572913i −0.651892 0.758312i $$-0.726024\pi$$
0.982663 + 0.185399i $$0.0593578\pi$$
$$752$$ 23760.0 + 13717.8i 1.15218 + 0.665210i
$$753$$ −31437.0 −1.52142
$$754$$ 0 0
$$755$$ 1200.00 0.0578443
$$756$$ −2730.00 1576.17i −0.131335 0.0758262i
$$757$$ −2775.50 + 4807.31i −0.133259 + 0.230812i −0.924931 0.380135i $$-0.875878\pi$$
0.791672 + 0.610947i $$0.209211\pi$$
$$758$$ 19935.0 + 34528.4i 0.955240 + 1.65452i
$$759$$ 8984.15i 0.429649i
$$760$$ −14688.0 + 8480.12i −0.701039 + 0.404745i
$$761$$ −8731.50 + 5041.13i −0.415922 + 0.240133i −0.693331 0.720619i $$-0.743858\pi$$
0.277409 + 0.960752i $$0.410524\pi$$
$$762$$ 54389.9i 2.58574i
$$763$$ −6864.00 11888.8i −0.325680 0.564093i
$$764$$ −5682.00 + 9841.51i −0.269067 + 0.466039i
$$765$$ 7128.00 + 4115.35i 0.336880 + 0.194498i
$$766$$ −8382.00 −0.395371
$$767$$ 0 0
$$768$$ −34048.0 −1.59974
$$769$$ −25771.5 14879.2i −1.20851 0.697733i −0.246076 0.969250i $$-0.579141\pi$$
−0.962434 + 0.271517i $$0.912475\pi$$
$$770$$ −12168.0 + 21075.6i −0.569486 + 0.986379i
$$771$$ 19078.5 + 33044.9i 0.891174 + 1.54356i
$$772$$ 16981.0i 0.791659i