# Properties

 Label 225.4.e.f.76.6 Level $225$ Weight $4$ Character 225.76 Analytic conductor $13.275$ Analytic rank $0$ Dimension $24$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$225 = 3^{2} \cdot 5^{2}$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 225.e (of order $$3$$, degree $$2$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$13.2754297513$$ Analytic rank: $$0$$ Dimension: $$24$$ Relative dimension: $$12$$ over $$\Q(\zeta_{3})$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 76.6 Character $$\chi$$ $$=$$ 225.76 Dual form 225.4.e.f.151.6

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-0.238017 - 0.412258i) q^{2} +(3.09012 - 4.17746i) q^{3} +(3.88670 - 6.73195i) q^{4} +(-2.45769 - 0.279619i) q^{6} +(-6.34045 - 10.9820i) q^{7} -7.50869 q^{8} +(-7.90234 - 25.8177i) q^{9} +O(q^{10})$$ $$q+(-0.238017 - 0.412258i) q^{2} +(3.09012 - 4.17746i) q^{3} +(3.88670 - 6.73195i) q^{4} +(-2.45769 - 0.279619i) q^{6} +(-6.34045 - 10.9820i) q^{7} -7.50869 q^{8} +(-7.90234 - 25.8177i) q^{9} +(0.794994 + 1.37697i) q^{11} +(-16.1121 - 37.0390i) q^{12} +(-5.36718 + 9.29622i) q^{13} +(-3.01828 + 5.22781i) q^{14} +(-29.3064 - 50.7601i) q^{16} -69.7787 q^{17} +(-8.76266 + 9.40287i) q^{18} +98.5661 q^{19} +(-65.4695 - 7.44864i) q^{21} +(0.378445 - 0.655486i) q^{22} +(15.7777 - 27.3278i) q^{23} +(-23.2027 + 31.3672i) q^{24} +5.10993 q^{26} +(-132.272 - 46.7680i) q^{27} -98.5736 q^{28} +(150.627 + 260.893i) q^{29} +(58.6364 - 101.561i) q^{31} +(-43.9856 + 76.1853i) q^{32} +(8.20886 + 0.933944i) q^{33} +(16.6086 + 28.7669i) q^{34} +(-204.517 - 47.1473i) q^{36} -169.562 q^{37} +(-23.4605 - 40.6347i) q^{38} +(22.2494 + 51.1476i) q^{39} +(-70.9376 + 122.868i) q^{41} +(12.5121 + 28.7633i) q^{42} +(-150.121 - 260.018i) q^{43} +12.3596 q^{44} -15.0215 q^{46} +(-243.712 - 422.122i) q^{47} +(-302.608 - 34.4286i) q^{48} +(91.0974 - 157.785i) q^{49} +(-215.625 + 291.498i) q^{51} +(41.7212 + 72.2632i) q^{52} +459.166 q^{53} +(12.2024 + 65.6616i) q^{54} +(47.6084 + 82.4602i) q^{56} +(304.581 - 411.756i) q^{57} +(71.7037 - 124.194i) q^{58} +(250.099 - 433.185i) q^{59} +(-290.915 - 503.880i) q^{61} -55.8259 q^{62} +(-233.425 + 250.479i) q^{63} -427.024 q^{64} +(-1.56883 - 3.60647i) q^{66} +(-250.468 + 433.823i) q^{67} +(-271.209 + 469.747i) q^{68} +(-65.4059 - 150.357i) q^{69} +1066.69 q^{71} +(59.3362 + 193.857i) q^{72} +435.288 q^{73} +(40.3588 + 69.9034i) q^{74} +(383.096 - 663.542i) q^{76} +(10.0812 - 17.4612i) q^{77} +(15.7903 - 21.3465i) q^{78} +(-187.644 - 325.009i) q^{79} +(-604.106 + 408.040i) q^{81} +67.5375 q^{82} +(646.617 + 1119.97i) q^{83} +(-304.604 + 411.787i) q^{84} +(-71.4630 + 123.778i) q^{86} +(1555.33 + 176.954i) q^{87} +(-5.96936 - 10.3392i) q^{88} -403.296 q^{89} +136.121 q^{91} +(-122.646 - 212.430i) q^{92} +(-243.074 - 558.787i) q^{93} +(-116.016 + 200.945i) q^{94} +(182.340 + 419.170i) q^{96} +(790.735 + 1369.59i) q^{97} -86.7311 q^{98} +(29.2679 - 31.4062i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$24 q + 4 q^{2} + q^{3} - 48 q^{4} - 13 q^{6} - 6 q^{7} - 90 q^{8} - 61 q^{9}+O(q^{10})$$ 24 * q + 4 * q^2 + q^3 - 48 * q^4 - 13 * q^6 - 6 * q^7 - 90 * q^8 - 61 * q^9 $$24 q + 4 q^{2} + q^{3} - 48 q^{4} - 13 q^{6} - 6 q^{7} - 90 q^{8} - 61 q^{9} - 29 q^{11} + 77 q^{12} - 24 q^{13} + 69 q^{14} - 192 q^{16} - 158 q^{17} - 125 q^{18} - 150 q^{19} - 60 q^{21} + 18 q^{22} + 318 q^{23} + 342 q^{24} - 308 q^{26} + 394 q^{27} + 192 q^{28} - 106 q^{29} - 60 q^{31} + 914 q^{32} + 80 q^{33} + 108 q^{34} + 1303 q^{36} - 168 q^{37} + 640 q^{38} - 410 q^{39} + 353 q^{41} - 1521 q^{42} + 426 q^{43} + 1142 q^{44} + 540 q^{46} + 1210 q^{47} - 2680 q^{48} - 666 q^{49} - 1369 q^{51} + 75 q^{52} - 896 q^{53} - 2128 q^{54} + 570 q^{56} - 1544 q^{57} - 594 q^{58} - 482 q^{59} - 402 q^{61} - 5088 q^{62} + 1038 q^{63} + 1950 q^{64} + 2041 q^{66} + 201 q^{67} + 3437 q^{68} + 2856 q^{69} - 1888 q^{71} + 5493 q^{72} - 906 q^{73} - 10 q^{74} + 462 q^{76} + 2652 q^{77} + 4589 q^{78} - 258 q^{79} + 3071 q^{81} + 1746 q^{82} + 3012 q^{83} - 2703 q^{84} - 1952 q^{86} - 2708 q^{87} + 216 q^{88} - 1476 q^{89} - 1236 q^{91} + 5232 q^{92} - 3024 q^{93} - 63 q^{94} - 10424 q^{96} + 318 q^{97} - 15022 q^{98} - 1697 q^{99}+O(q^{100})$$ 24 * q + 4 * q^2 + q^3 - 48 * q^4 - 13 * q^6 - 6 * q^7 - 90 * q^8 - 61 * q^9 - 29 * q^11 + 77 * q^12 - 24 * q^13 + 69 * q^14 - 192 * q^16 - 158 * q^17 - 125 * q^18 - 150 * q^19 - 60 * q^21 + 18 * q^22 + 318 * q^23 + 342 * q^24 - 308 * q^26 + 394 * q^27 + 192 * q^28 - 106 * q^29 - 60 * q^31 + 914 * q^32 + 80 * q^33 + 108 * q^34 + 1303 * q^36 - 168 * q^37 + 640 * q^38 - 410 * q^39 + 353 * q^41 - 1521 * q^42 + 426 * q^43 + 1142 * q^44 + 540 * q^46 + 1210 * q^47 - 2680 * q^48 - 666 * q^49 - 1369 * q^51 + 75 * q^52 - 896 * q^53 - 2128 * q^54 + 570 * q^56 - 1544 * q^57 - 594 * q^58 - 482 * q^59 - 402 * q^61 - 5088 * q^62 + 1038 * q^63 + 1950 * q^64 + 2041 * q^66 + 201 * q^67 + 3437 * q^68 + 2856 * q^69 - 1888 * q^71 + 5493 * q^72 - 906 * q^73 - 10 * q^74 + 462 * q^76 + 2652 * q^77 + 4589 * q^78 - 258 * q^79 + 3071 * q^81 + 1746 * q^82 + 3012 * q^83 - 2703 * q^84 - 1952 * q^86 - 2708 * q^87 + 216 * q^88 - 1476 * q^89 - 1236 * q^91 + 5232 * q^92 - 3024 * q^93 - 63 * q^94 - 10424 * q^96 + 318 * q^97 - 15022 * q^98 - 1697 * q^99

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/225\mathbb{Z}\right)^\times$$.

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

## Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −0.238017 0.412258i −0.0841519 0.145755i 0.820878 0.571104i $$-0.193485\pi$$
−0.905030 + 0.425349i $$0.860151\pi$$
$$3$$ 3.09012 4.17746i 0.594694 0.803953i
$$4$$ 3.88670 6.73195i 0.485837 0.841494i
$$5$$ 0 0
$$6$$ −2.45769 0.279619i −0.167225 0.0190256i
$$7$$ −6.34045 10.9820i −0.342352 0.592971i 0.642517 0.766271i $$-0.277890\pi$$
−0.984869 + 0.173300i $$0.944557\pi$$
$$8$$ −7.50869 −0.331840
$$9$$ −7.90234 25.8177i −0.292679 0.956211i
$$10$$ 0 0
$$11$$ 0.794994 + 1.37697i 0.0217909 + 0.0377429i 0.876715 0.481010i $$-0.159730\pi$$
−0.854924 + 0.518753i $$0.826397\pi$$
$$12$$ −16.1121 37.0390i −0.387597 0.891021i
$$13$$ −5.36718 + 9.29622i −0.114507 + 0.198331i −0.917582 0.397546i $$-0.869862\pi$$
0.803076 + 0.595877i $$0.203195\pi$$
$$14$$ −3.01828 + 5.22781i −0.0576191 + 0.0997993i
$$15$$ 0 0
$$16$$ −29.3064 50.7601i −0.457912 0.793127i
$$17$$ −69.7787 −0.995519 −0.497760 0.867315i $$-0.665844\pi$$
−0.497760 + 0.867315i $$0.665844\pi$$
$$18$$ −8.76266 + 9.40287i −0.114743 + 0.123127i
$$19$$ 98.5661 1.19014 0.595069 0.803675i $$-0.297125\pi$$
0.595069 + 0.803675i $$0.297125\pi$$
$$20$$ 0 0
$$21$$ −65.4695 7.44864i −0.680315 0.0774013i
$$22$$ 0.378445 0.655486i 0.00366749 0.00635227i
$$23$$ 15.7777 27.3278i 0.143038 0.247750i −0.785601 0.618734i $$-0.787646\pi$$
0.928639 + 0.370984i $$0.120979\pi$$
$$24$$ −23.2027 + 31.3672i −0.197343 + 0.266784i
$$25$$ 0 0
$$26$$ 5.10993 0.0385438
$$27$$ −132.272 46.7680i −0.942802 0.333352i
$$28$$ −98.5736 −0.665309
$$29$$ 150.627 + 260.893i 0.964507 + 1.67058i 0.710933 + 0.703260i $$0.248273\pi$$
0.253574 + 0.967316i $$0.418394\pi$$
$$30$$ 0 0
$$31$$ 58.6364 101.561i 0.339723 0.588417i −0.644658 0.764471i $$-0.723000\pi$$
0.984380 + 0.176054i $$0.0563334\pi$$
$$32$$ −43.9856 + 76.1853i −0.242988 + 0.420868i
$$33$$ 8.20886 + 0.933944i 0.0433024 + 0.00492663i
$$34$$ 16.6086 + 28.7669i 0.0837748 + 0.145102i
$$35$$ 0 0
$$36$$ −204.517 47.1473i −0.946840 0.218275i
$$37$$ −169.562 −0.753402 −0.376701 0.926335i $$-0.622941\pi$$
−0.376701 + 0.926335i $$0.622941\pi$$
$$38$$ −23.4605 40.6347i −0.100152 0.173469i
$$39$$ 22.2494 + 51.1476i 0.0913526 + 0.210004i
$$40$$ 0 0
$$41$$ −70.9376 + 122.868i −0.270210 + 0.468017i −0.968915 0.247392i $$-0.920426\pi$$
0.698706 + 0.715409i $$0.253760\pi$$
$$42$$ 12.5121 + 28.7633i 0.0459682 + 0.105673i
$$43$$ −150.121 260.018i −0.532402 0.922147i −0.999284 0.0378277i $$-0.987956\pi$$
0.466882 0.884319i $$-0.345377\pi$$
$$44$$ 12.3596 0.0423472
$$45$$ 0 0
$$46$$ −15.0215 −0.0481478
$$47$$ −243.712 422.122i −0.756364 1.31006i −0.944694 0.327954i $$-0.893641\pi$$
0.188330 0.982106i $$-0.439693\pi$$
$$48$$ −302.608 34.4286i −0.909953 0.103528i
$$49$$ 91.0974 157.785i 0.265590 0.460016i
$$50$$ 0 0
$$51$$ −215.625 + 291.498i −0.592029 + 0.800350i
$$52$$ 41.7212 + 72.2632i 0.111263 + 0.192713i
$$53$$ 459.166 1.19002 0.595012 0.803717i $$-0.297147\pi$$
0.595012 + 0.803717i $$0.297147\pi$$
$$54$$ 12.2024 + 65.6616i 0.0307508 + 0.165471i
$$55$$ 0 0
$$56$$ 47.6084 + 82.4602i 0.113606 + 0.196772i
$$57$$ 304.581 411.756i 0.707767 0.956814i
$$58$$ 71.7037 124.194i 0.162330 0.281164i
$$59$$ 250.099 433.185i 0.551867 0.955862i −0.446273 0.894897i $$-0.647249\pi$$
0.998140 0.0609650i $$-0.0194178\pi$$
$$60$$ 0 0
$$61$$ −290.915 503.880i −0.610621 1.05763i −0.991136 0.132852i $$-0.957587\pi$$
0.380515 0.924775i $$-0.375747\pi$$
$$62$$ −55.8259 −0.114353
$$63$$ −233.425 + 250.479i −0.466806 + 0.500911i
$$64$$ −427.024 −0.834032
$$65$$ 0 0
$$66$$ −1.56883 3.60647i −0.00292589 0.00672614i
$$67$$ −250.468 + 433.823i −0.456709 + 0.791044i −0.998785 0.0492862i $$-0.984305\pi$$
0.542075 + 0.840330i $$0.317639\pi$$
$$68$$ −271.209 + 469.747i −0.483660 + 0.837724i
$$69$$ −65.4059 150.357i −0.114115 0.262331i
$$70$$ 0 0
$$71$$ 1066.69 1.78299 0.891495 0.453031i $$-0.149657\pi$$
0.891495 + 0.453031i $$0.149657\pi$$
$$72$$ 59.3362 + 193.857i 0.0971227 + 0.317309i
$$73$$ 435.288 0.697899 0.348950 0.937141i $$-0.386538\pi$$
0.348950 + 0.937141i $$0.386538\pi$$
$$74$$ 40.3588 + 69.9034i 0.0634002 + 0.109812i
$$75$$ 0 0
$$76$$ 383.096 663.542i 0.578213 1.00149i
$$77$$ 10.0812 17.4612i 0.0149203 0.0258427i
$$78$$ 15.7903 21.3465i 0.0229218 0.0309874i
$$79$$ −187.644 325.009i −0.267236 0.462866i 0.700911 0.713248i $$-0.252777\pi$$
−0.968147 + 0.250383i $$0.919444\pi$$
$$80$$ 0 0
$$81$$ −604.106 + 408.040i −0.828678 + 0.559726i
$$82$$ 67.5375 0.0909546
$$83$$ 646.617 + 1119.97i 0.855126 + 1.48112i 0.876528 + 0.481351i $$0.159854\pi$$
−0.0214014 + 0.999771i $$0.506813\pi$$
$$84$$ −304.604 + 411.787i −0.395655 + 0.534877i
$$85$$ 0 0
$$86$$ −71.4630 + 123.778i −0.0896053 + 0.155201i
$$87$$ 1555.33 + 176.954i 1.91665 + 0.218062i
$$88$$ −5.96936 10.3392i −0.00723109 0.0125246i
$$89$$ −403.296 −0.480330 −0.240165 0.970732i $$-0.577201\pi$$
−0.240165 + 0.970732i $$0.577201\pi$$
$$90$$ 0 0
$$91$$ 136.121 0.156806
$$92$$ −122.646 212.430i −0.138987 0.240732i
$$93$$ −243.074 558.787i −0.271028 0.623049i
$$94$$ −116.016 + 200.945i −0.127299 + 0.220488i
$$95$$ 0 0
$$96$$ 182.340 + 419.170i 0.193854 + 0.445639i
$$97$$ 790.735 + 1369.59i 0.827700 + 1.43362i 0.899838 + 0.436225i $$0.143685\pi$$
−0.0721373 + 0.997395i $$0.522982\pi$$
$$98$$ −86.7311 −0.0893996
$$99$$ 29.2679 31.4062i 0.0297124 0.0318832i
$$100$$ 0 0
$$101$$ 577.422 + 1000.12i 0.568867 + 0.985307i 0.996678 + 0.0814388i $$0.0259515\pi$$
−0.427811 + 0.903868i $$0.640715\pi$$
$$102$$ 171.495 + 19.5114i 0.166476 + 0.0189404i
$$103$$ 725.615 1256.80i 0.694145 1.20229i −0.276323 0.961065i $$-0.589116\pi$$
0.970468 0.241230i $$-0.0775507\pi$$
$$104$$ 40.3004 69.8024i 0.0379979 0.0658143i
$$105$$ 0 0
$$106$$ −109.290 189.295i −0.100143 0.173452i
$$107$$ 136.728 0.123533 0.0617664 0.998091i $$-0.480327\pi$$
0.0617664 + 0.998091i $$0.480327\pi$$
$$108$$ −828.939 + 708.673i −0.738562 + 0.631408i
$$109$$ 40.1176 0.0352529 0.0176265 0.999845i $$-0.494389\pi$$
0.0176265 + 0.999845i $$0.494389\pi$$
$$110$$ 0 0
$$111$$ −523.967 + 708.339i −0.448043 + 0.605699i
$$112$$ −371.631 + 643.684i −0.313534 + 0.543057i
$$113$$ 989.231 1713.40i 0.823531 1.42640i −0.0795054 0.996834i $$-0.525334\pi$$
0.903037 0.429564i $$-0.141333\pi$$
$$114$$ −242.245 27.5609i −0.199021 0.0226431i
$$115$$ 0 0
$$116$$ 2341.76 1.87437
$$117$$ 282.420 + 65.1062i 0.223160 + 0.0514450i
$$118$$ −238.112 −0.185763
$$119$$ 442.428 + 766.309i 0.340818 + 0.590314i
$$120$$ 0 0
$$121$$ 664.236 1150.49i 0.499050 0.864381i
$$122$$ −138.486 + 239.865i −0.102770 + 0.178003i
$$123$$ 294.069 + 676.014i 0.215571 + 0.495562i
$$124$$ −455.804 789.475i −0.330100 0.571750i
$$125$$ 0 0
$$126$$ 158.821 + 36.6130i 0.112293 + 0.0258869i
$$127$$ 1318.35 0.921142 0.460571 0.887623i $$-0.347645\pi$$
0.460571 + 0.887623i $$0.347645\pi$$
$$128$$ 453.524 + 785.527i 0.313174 + 0.542433i
$$129$$ −1550.11 176.360i −1.05798 0.120369i
$$130$$ 0 0
$$131$$ −792.463 + 1372.59i −0.528533 + 0.915446i 0.470913 + 0.882179i $$0.343924\pi$$
−0.999447 + 0.0332667i $$0.989409\pi$$
$$132$$ 38.1926 51.6317i 0.0251836 0.0340452i
$$133$$ −624.953 1082.45i −0.407446 0.705717i
$$134$$ 238.463 0.153732
$$135$$ 0 0
$$136$$ 523.947 0.330353
$$137$$ −190.760 330.406i −0.118961 0.206047i 0.800395 0.599473i $$-0.204623\pi$$
−0.919356 + 0.393426i $$0.871290\pi$$
$$138$$ −46.4182 + 62.7517i −0.0286332 + 0.0387086i
$$139$$ 1231.19 2132.49i 0.751283 1.30126i −0.195918 0.980620i $$-0.562769\pi$$
0.947201 0.320641i $$-0.103898\pi$$
$$140$$ 0 0
$$141$$ −2516.50 286.309i −1.50303 0.171004i
$$142$$ −253.890 439.750i −0.150042 0.259880i
$$143$$ −17.0675 −0.00998080
$$144$$ −1078.92 + 1157.75i −0.624375 + 0.669992i
$$145$$ 0 0
$$146$$ −103.606 179.451i −0.0587295 0.101723i
$$147$$ −377.640 868.131i −0.211886 0.487090i
$$148$$ −659.037 + 1141.48i −0.366030 + 0.633983i
$$149$$ −192.172 + 332.852i −0.105660 + 0.183008i −0.914008 0.405697i $$-0.867029\pi$$
0.808348 + 0.588705i $$0.200362\pi$$
$$150$$ 0 0
$$151$$ −398.550 690.308i −0.214792 0.372030i 0.738417 0.674345i $$-0.235574\pi$$
−0.953208 + 0.302315i $$0.902241\pi$$
$$152$$ −740.102 −0.394935
$$153$$ 551.415 + 1801.53i 0.291368 + 0.951926i
$$154$$ −9.59804 −0.00502229
$$155$$ 0 0
$$156$$ 430.800 + 49.0133i 0.221100 + 0.0251551i
$$157$$ 435.496 754.300i 0.221378 0.383438i −0.733849 0.679313i $$-0.762278\pi$$
0.955227 + 0.295875i $$0.0956112\pi$$
$$158$$ −89.3252 + 154.716i −0.0449768 + 0.0779021i
$$159$$ 1418.88 1918.15i 0.707700 0.956723i
$$160$$ 0 0
$$161$$ −400.152 −0.195878
$$162$$ 312.006 + 151.927i 0.151318 + 0.0736822i
$$163$$ −31.2604 −0.0150215 −0.00751074 0.999972i $$-0.502391\pi$$
−0.00751074 + 0.999972i $$0.502391\pi$$
$$164$$ 551.426 + 955.097i 0.262556 + 0.454759i
$$165$$ 0 0
$$166$$ 307.813 533.147i 0.143921 0.249278i
$$167$$ 18.6415 32.2881i 0.00863787 0.0149612i −0.861674 0.507462i $$-0.830584\pi$$
0.870312 + 0.492501i $$0.163917\pi$$
$$168$$ 491.590 + 55.9295i 0.225756 + 0.0256849i
$$169$$ 1040.89 + 1802.87i 0.473776 + 0.820605i
$$170$$ 0 0
$$171$$ −778.903 2544.75i −0.348329 1.13802i
$$172$$ −2333.90 −1.03464
$$173$$ 590.590 + 1022.93i 0.259548 + 0.449550i 0.966121 0.258090i $$-0.0830932\pi$$
−0.706573 + 0.707640i $$0.749760\pi$$
$$174$$ −297.244 683.315i −0.129506 0.297712i
$$175$$ 0 0
$$176$$ 46.5967 80.7079i 0.0199566 0.0345658i
$$177$$ −1036.78 2383.37i −0.440276 1.01212i
$$178$$ 95.9916 + 166.262i 0.0404206 + 0.0700106i
$$179$$ −429.484 −0.179336 −0.0896680 0.995972i $$-0.528581\pi$$
−0.0896680 + 0.995972i $$0.528581\pi$$
$$180$$ 0 0
$$181$$ −1787.97 −0.734246 −0.367123 0.930172i $$-0.619657\pi$$
−0.367123 + 0.930172i $$0.619657\pi$$
$$182$$ −32.3992 56.1171i −0.0131956 0.0228554i
$$183$$ −3003.90 341.762i −1.21341 0.138053i
$$184$$ −118.470 + 205.196i −0.0474659 + 0.0822134i
$$185$$ 0 0
$$186$$ −172.509 + 233.211i −0.0680051 + 0.0919346i
$$187$$ −55.4736 96.0832i −0.0216932 0.0375738i
$$188$$ −3788.94 −1.46988
$$189$$ 325.056 + 1749.13i 0.125102 + 0.673178i
$$190$$ 0 0
$$191$$ −392.583 679.974i −0.148724 0.257598i 0.782032 0.623238i $$-0.214183\pi$$
−0.930756 + 0.365640i $$0.880850\pi$$
$$192$$ −1319.56 + 1783.88i −0.495994 + 0.670522i
$$193$$ 238.539 413.162i 0.0889659 0.154093i −0.818108 0.575064i $$-0.804977\pi$$
0.907074 + 0.420971i $$0.138310\pi$$
$$194$$ 376.417 651.974i 0.139305 0.241284i
$$195$$ 0 0
$$196$$ −708.136 1226.53i −0.258067 0.446985i
$$197$$ −4628.37 −1.67390 −0.836949 0.547281i $$-0.815663\pi$$
−0.836949 + 0.547281i $$0.815663\pi$$
$$198$$ −19.9137 4.59070i −0.00714751 0.00164771i
$$199$$ 2533.85 0.902611 0.451305 0.892370i $$-0.350958\pi$$
0.451305 + 0.892370i $$0.350958\pi$$
$$200$$ 0 0
$$201$$ 1038.30 + 2386.88i 0.364359 + 0.837601i
$$202$$ 274.873 476.094i 0.0957425 0.165831i
$$203$$ 1910.08 3308.36i 0.660402 1.14385i
$$204$$ 1124.28 + 2584.54i 0.385861 + 0.887029i
$$205$$ 0 0
$$206$$ −690.836 −0.233654
$$207$$ −830.222 191.391i −0.278765 0.0642636i
$$208$$ 629.170 0.209736
$$209$$ 78.3594 + 135.722i 0.0259341 + 0.0449192i
$$210$$ 0 0
$$211$$ −1382.70 + 2394.90i −0.451131 + 0.781382i −0.998457 0.0555378i $$-0.982313\pi$$
0.547325 + 0.836920i $$0.315646\pi$$
$$212$$ 1784.64 3091.08i 0.578158 1.00140i
$$213$$ 3296.18 4456.03i 1.06033 1.43344i
$$214$$ −32.5437 56.3673i −0.0103955 0.0180056i
$$215$$ 0 0
$$216$$ 993.185 + 351.166i 0.312860 + 0.110620i
$$217$$ −1487.12 −0.465219
$$218$$ −9.54869 16.5388i −0.00296660 0.00513830i
$$219$$ 1345.09 1818.40i 0.415036 0.561078i
$$220$$ 0 0
$$221$$ 374.515 648.679i 0.113994 0.197443i
$$222$$ 416.732 + 47.4128i 0.125988 + 0.0143339i
$$223$$ −234.694 406.502i −0.0704767 0.122069i 0.828634 0.559791i $$-0.189119\pi$$
−0.899110 + 0.437722i $$0.855785\pi$$
$$224$$ 1115.55 0.332750
$$225$$ 0 0
$$226$$ −941.817 −0.277207
$$227$$ 2143.99 + 3713.50i 0.626879 + 1.08579i 0.988174 + 0.153335i $$0.0490015\pi$$
−0.361295 + 0.932452i $$0.617665\pi$$
$$228$$ −1588.11 3650.79i −0.461294 1.06044i
$$229$$ −2052.30 + 3554.69i −0.592227 + 1.02577i 0.401705 + 0.915769i $$0.368418\pi$$
−0.993932 + 0.109998i $$0.964916\pi$$
$$230$$ 0 0
$$231$$ −41.7913 96.0711i −0.0119033 0.0273637i
$$232$$ −1131.01 1958.97i −0.320062 0.554364i
$$233$$ −4272.57 −1.20131 −0.600656 0.799508i $$-0.705094\pi$$
−0.600656 + 0.799508i $$0.705094\pi$$
$$234$$ −40.3804 131.927i −0.0112810 0.0368560i
$$235$$ 0 0
$$236$$ −1944.12 3367.31i −0.536235 0.928786i
$$237$$ −1937.56 220.441i −0.531045 0.0604185i
$$238$$ 210.611 364.790i 0.0573610 0.0993521i
$$239$$ 780.619 1352.07i 0.211272 0.365934i −0.740841 0.671681i $$-0.765573\pi$$
0.952113 + 0.305747i $$0.0989061\pi$$
$$240$$ 0 0
$$241$$ 2410.77 + 4175.58i 0.644362 + 1.11607i 0.984448 + 0.175674i $$0.0562105\pi$$
−0.340086 + 0.940394i $$0.610456\pi$$
$$242$$ −632.399 −0.167984
$$243$$ −162.187 + 3784.52i −0.0428161 + 0.999083i
$$244$$ −4522.80 −1.18665
$$245$$ 0 0
$$246$$ 208.699 282.135i 0.0540901 0.0731232i
$$247$$ −529.021 + 916.292i −0.136279 + 0.236042i
$$248$$ −440.282 + 762.591i −0.112734 + 0.195260i
$$249$$ 6676.77 + 759.634i 1.69929 + 0.193333i
$$250$$ 0 0
$$251$$ −3487.72 −0.877063 −0.438532 0.898716i $$-0.644501\pi$$
−0.438532 + 0.898716i $$0.644501\pi$$
$$252$$ 778.962 + 2544.94i 0.194722 + 0.636176i
$$253$$ 50.1728 0.0124677
$$254$$ −313.791 543.503i −0.0775158 0.134261i
$$255$$ 0 0
$$256$$ −1492.20 + 2584.57i −0.364308 + 0.631000i
$$257$$ 2460.87 4262.35i 0.597295 1.03454i −0.395924 0.918283i $$-0.629576\pi$$
0.993219 0.116261i $$-0.0370910\pi$$
$$258$$ 296.247 + 681.021i 0.0714865 + 0.164335i
$$259$$ 1075.10 + 1862.13i 0.257929 + 0.446745i
$$260$$ 0 0
$$261$$ 5545.36 5950.51i 1.31513 1.41121i
$$262$$ 754.480 0.177908
$$263$$ 2758.58 + 4777.99i 0.646772 + 1.12024i 0.983889 + 0.178780i $$0.0572149\pi$$
−0.337117 + 0.941463i $$0.609452\pi$$
$$264$$ −61.6377 7.01269i −0.0143695 0.00163485i
$$265$$ 0 0
$$266$$ −297.500 + 515.284i −0.0685747 + 0.118775i
$$267$$ −1246.23 + 1684.75i −0.285649 + 0.386162i
$$268$$ 1946.98 + 3372.28i 0.443772 + 0.768636i
$$269$$ −7844.13 −1.77794 −0.888969 0.457968i $$-0.848577\pi$$
−0.888969 + 0.457968i $$0.848577\pi$$
$$270$$ 0 0
$$271$$ 4301.35 0.964164 0.482082 0.876126i $$-0.339881\pi$$
0.482082 + 0.876126i $$0.339881\pi$$
$$272$$ 2044.96 + 3541.98i 0.455860 + 0.789573i
$$273$$ 420.631 568.641i 0.0932517 0.126065i
$$274$$ −90.8083 + 157.285i −0.0200216 + 0.0346785i
$$275$$ 0 0
$$276$$ −1266.41 144.083i −0.276192 0.0314231i
$$277$$ −925.922 1603.74i −0.200842 0.347869i 0.747958 0.663746i $$-0.231034\pi$$
−0.948800 + 0.315877i $$0.897701\pi$$
$$278$$ −1172.18 −0.252888
$$279$$ −3085.44 711.285i −0.662081 0.152629i
$$280$$ 0 0
$$281$$ −3470.93 6011.82i −0.736862 1.27628i −0.953902 0.300119i $$-0.902974\pi$$
0.217040 0.976163i $$-0.430360\pi$$
$$282$$ 480.937 + 1105.59i 0.101558 + 0.233465i
$$283$$ −3216.21 + 5570.64i −0.675562 + 1.17011i 0.300743 + 0.953705i $$0.402765\pi$$
−0.976304 + 0.216402i $$0.930568\pi$$
$$284$$ 4145.88 7180.87i 0.866242 1.50038i
$$285$$ 0 0
$$286$$ 4.06236 + 7.03621i 0.000839903 + 0.00145476i
$$287$$ 1799.10 0.370027
$$288$$ 2314.52 + 533.564i 0.473556 + 0.109169i
$$289$$ −43.9287 −0.00894133
$$290$$ 0 0
$$291$$ 8164.88 + 928.941i 1.64479 + 0.187132i
$$292$$ 1691.83 2930.34i 0.339065 0.587278i
$$293$$ 3820.89 6617.98i 0.761840 1.31955i −0.180062 0.983655i $$-0.557630\pi$$
0.941901 0.335890i $$-0.109037\pi$$
$$294$$ −268.009 + 362.316i −0.0531654 + 0.0718731i
$$295$$ 0 0
$$296$$ 1273.19 0.250009
$$297$$ −40.7569 219.314i −0.00796281 0.0428481i
$$298$$ 182.961 0.0355660
$$299$$ 169.364 + 293.347i 0.0327577 + 0.0567380i
$$300$$ 0 0
$$301$$ −1903.67 + 3297.26i −0.364538 + 0.631398i
$$302$$ −189.724 + 328.611i −0.0361502 + 0.0626140i
$$303$$ 5962.28 + 678.344i 1.13044 + 0.128613i
$$304$$ −2888.61 5003.23i −0.544978 0.943930i
$$305$$ 0 0
$$306$$ 611.448 656.120i 0.114229 0.122575i
$$307$$ 4517.66 0.839857 0.419929 0.907557i $$-0.362055\pi$$
0.419929 + 0.907557i $$0.362055\pi$$
$$308$$ −78.3654 135.733i −0.0144977 0.0251107i
$$309$$ −3008.00 6914.89i −0.553784 1.27306i
$$310$$ 0 0
$$311$$ −1966.54 + 3406.15i −0.358560 + 0.621044i −0.987721 0.156231i $$-0.950066\pi$$
0.629160 + 0.777275i $$0.283399\pi$$
$$312$$ −167.064 384.051i −0.0303145 0.0696879i
$$313$$ 1583.09 + 2742.00i 0.285884 + 0.495165i 0.972823 0.231549i $$-0.0743795\pi$$
−0.686939 + 0.726715i $$0.741046\pi$$
$$314$$ −414.622 −0.0745175
$$315$$ 0 0
$$316$$ −2917.26 −0.519332
$$317$$ 3920.86 + 6791.13i 0.694692 + 1.20324i 0.970284 + 0.241967i $$0.0777927\pi$$
−0.275592 + 0.961275i $$0.588874\pi$$
$$318$$ −1128.49 128.391i −0.199002 0.0226410i
$$319$$ −239.495 + 414.817i −0.0420349 + 0.0728066i
$$320$$ 0 0
$$321$$ 422.506 571.176i 0.0734641 0.0993145i
$$322$$ 95.2431 + 164.966i 0.0164835 + 0.0285503i
$$323$$ −6877.82 −1.18480
$$324$$ 398.932 + 5652.74i 0.0684040 + 0.969263i
$$325$$ 0 0
$$326$$ 7.44051 + 12.8873i 0.00126409 + 0.00218946i
$$327$$ 123.968 167.590i 0.0209647 0.0283417i
$$328$$ 532.648 922.574i 0.0896664 0.155307i
$$329$$ −3090.49 + 5352.89i −0.517885 + 0.897004i
$$330$$ 0 0
$$331$$ 5426.53 + 9399.03i 0.901115 + 1.56078i 0.826049 + 0.563599i $$0.190584\pi$$
0.0750663 + 0.997179i $$0.476083\pi$$
$$332$$ 10052.8 1.66181
$$333$$ 1339.94 + 4377.70i 0.220505 + 0.720411i
$$334$$ −17.7480 −0.00290757
$$335$$ 0 0
$$336$$ 1540.58 + 3541.53i 0.250135 + 0.575019i
$$337$$ 3258.64 5644.13i 0.526735 0.912331i −0.472780 0.881180i $$-0.656749\pi$$
0.999515 0.0311507i $$-0.00991719\pi$$
$$338$$ 495.499 858.229i 0.0797384 0.138111i
$$339$$ −4100.81 9427.08i −0.657008 1.51035i
$$340$$ 0 0
$$341$$ 186.462 0.0296114
$$342$$ −863.701 + 926.804i −0.136560 + 0.146537i
$$343$$ −6659.94 −1.04841
$$344$$ 1127.21 + 1952.39i 0.176672 + 0.306005i
$$345$$ 0 0
$$346$$ 281.142 486.952i 0.0436829 0.0756609i
$$347$$ −2969.27 + 5142.93i −0.459363 + 0.795640i −0.998927 0.0463041i $$-0.985256\pi$$
0.539564 + 0.841944i $$0.318589\pi$$
$$348$$ 7236.33 9782.62i 1.11468 1.50691i
$$349$$ 3648.27 + 6318.99i 0.559563 + 0.969192i 0.997533 + 0.0702022i $$0.0223644\pi$$
−0.437970 + 0.898990i $$0.644302\pi$$
$$350$$ 0 0
$$351$$ 1144.69 978.613i 0.174071 0.148816i
$$352$$ −139.873 −0.0211797
$$353$$ −625.356 1083.15i −0.0942900 0.163315i 0.815022 0.579430i $$-0.196725\pi$$
−0.909312 + 0.416115i $$0.863391\pi$$
$$354$$ −735.795 + 994.704i −0.110472 + 0.149344i
$$355$$ 0 0
$$356$$ −1567.49 + 2714.97i −0.233362 + 0.404195i
$$357$$ 4568.38 + 519.757i 0.677267 + 0.0770545i
$$358$$ 102.225 + 177.058i 0.0150915 + 0.0261392i
$$359$$ −10928.3 −1.60661 −0.803303 0.595570i $$-0.796926\pi$$
−0.803303 + 0.595570i $$0.796926\pi$$
$$360$$ 0 0
$$361$$ 2856.27 0.416427
$$362$$ 425.567 + 737.104i 0.0617882 + 0.107020i
$$363$$ −2753.56 6329.97i −0.398139 0.915254i
$$364$$ 529.062 916.362i 0.0761823 0.131952i
$$365$$ 0 0
$$366$$ 574.087 + 1319.73i 0.0819891 + 0.188479i
$$367$$ 3215.66 + 5569.68i 0.457373 + 0.792194i 0.998821 0.0485405i $$-0.0154570\pi$$
−0.541448 + 0.840734i $$0.682124\pi$$
$$368$$ −1849.55 −0.261996
$$369$$ 3732.73 + 860.504i 0.526607 + 0.121398i
$$370$$ 0 0
$$371$$ −2911.32 5042.55i −0.407407 0.705650i
$$372$$ −4706.49 535.470i −0.655968 0.0746312i
$$373$$ −2455.85 + 4253.66i −0.340909 + 0.590472i −0.984602 0.174812i $$-0.944068\pi$$
0.643693 + 0.765284i $$0.277402\pi$$
$$374$$ −26.4074 + 45.7389i −0.00365105 + 0.00632381i
$$375$$ 0 0
$$376$$ 1829.96 + 3169.58i 0.250992 + 0.434731i
$$377$$ −3233.76 −0.441770
$$378$$ 643.726 550.331i 0.0875918 0.0748836i
$$379$$ 4805.81 0.651340 0.325670 0.945483i $$-0.394410\pi$$
0.325670 + 0.945483i $$0.394410\pi$$
$$380$$ 0 0
$$381$$ 4073.87 5507.37i 0.547797 0.740554i
$$382$$ −186.883 + 323.691i −0.0250308 + 0.0433547i
$$383$$ 2116.08 3665.15i 0.282314 0.488983i −0.689640 0.724152i $$-0.742231\pi$$
0.971954 + 0.235170i $$0.0755645\pi$$
$$384$$ 4682.95 + 532.792i 0.622333 + 0.0708045i
$$385$$ 0 0
$$386$$ −227.106 −0.0299466
$$387$$ −5526.75 + 5930.53i −0.725944 + 0.778982i
$$388$$ 12293.4 1.60851
$$389$$ 1758.54 + 3045.89i 0.229208 + 0.396999i 0.957573 0.288189i $$-0.0930532\pi$$
−0.728366 + 0.685188i $$0.759720\pi$$
$$390$$ 0 0
$$391$$ −1100.95 + 1906.90i −0.142398 + 0.246640i
$$392$$ −684.022 + 1184.76i −0.0881335 + 0.152652i
$$393$$ 3285.12 + 7551.94i 0.421660 + 0.969325i
$$394$$ 1101.63 + 1908.09i 0.140862 + 0.243980i
$$395$$ 0 0
$$396$$ −97.6697 319.096i −0.0123942 0.0404929i
$$397$$ 3925.05 0.496203 0.248101 0.968734i $$-0.420193\pi$$
0.248101 + 0.968734i $$0.420193\pi$$
$$398$$ −603.100 1044.60i −0.0759564 0.131560i
$$399$$ −6453.07 734.184i −0.809669 0.0921182i
$$400$$ 0 0
$$401$$ −403.676 + 699.188i −0.0502709 + 0.0870718i −0.890066 0.455832i $$-0.849342\pi$$
0.839795 + 0.542904i $$0.182675\pi$$
$$402$$ 736.879 996.169i 0.0914233 0.123593i
$$403$$ 629.424 + 1090.19i 0.0778011 + 0.134755i
$$404$$ 8977.05 1.10551
$$405$$ 0 0
$$406$$ −1818.53 −0.222296
$$407$$ −134.801 233.482i −0.0164173 0.0284356i
$$408$$ 1619.06 2188.77i 0.196459 0.265588i
$$409$$ −404.224 + 700.137i −0.0488694 + 0.0846444i −0.889425 0.457080i $$-0.848895\pi$$
0.840556 + 0.541725i $$0.182228\pi$$
$$410$$ 0 0
$$411$$ −1969.73 224.101i −0.236398 0.0268956i
$$412$$ −5640.49 9769.61i −0.674482 1.16824i
$$413$$ −6342.97 −0.755732
$$414$$ 118.705 + 387.821i 0.0140919 + 0.0460395i
$$415$$ 0 0
$$416$$ −472.157 817.800i −0.0556476 0.0963844i
$$417$$ −5103.85 11732.9i −0.599369 1.37785i
$$418$$ 37.3018 64.6086i 0.00436481 0.00756008i
$$419$$ −880.089 + 1524.36i −0.102614 + 0.177732i −0.912761 0.408495i $$-0.866054\pi$$
0.810147 + 0.586227i $$0.199387\pi$$
$$420$$ 0 0
$$421$$ −7287.86 12622.9i −0.843678 1.46129i −0.886765 0.462221i $$-0.847053\pi$$
0.0430868 0.999071i $$-0.486281\pi$$
$$422$$ 1316.42 0.151854
$$423$$ −8972.32 + 9627.84i −1.03132 + 1.10667i
$$424$$ −3447.73 −0.394898
$$425$$ 0 0
$$426$$ −2621.59 298.265i −0.298160 0.0339225i
$$427$$ −3689.07 + 6389.65i −0.418095 + 0.724161i
$$428$$ 531.421 920.447i 0.0600168 0.103952i
$$429$$ −52.7405 + 71.2987i −0.00593552 + 0.00802409i
$$430$$ 0 0
$$431$$ 5715.34 0.638743 0.319371 0.947630i $$-0.396528\pi$$
0.319371 + 0.947630i $$0.396528\pi$$
$$432$$ 1502.45 + 8084.72i 0.167330 + 0.900408i
$$433$$ −12751.4 −1.41523 −0.707614 0.706599i $$-0.750228\pi$$
−0.707614 + 0.706599i $$0.750228\pi$$
$$434$$ 353.962 + 613.079i 0.0391491 + 0.0678082i
$$435$$ 0 0
$$436$$ 155.925 270.070i 0.0171272 0.0296651i
$$437$$ 1555.15 2693.60i 0.170235 0.294856i
$$438$$ −1069.81 121.715i −0.116706 0.0132780i
$$439$$ −2420.51 4192.44i −0.263154 0.455796i 0.703924 0.710275i $$-0.251429\pi$$
−0.967078 + 0.254479i $$0.918096\pi$$
$$440$$ 0 0
$$441$$ −4793.54 1105.05i −0.517605 0.119323i
$$442$$ −356.564 −0.0383711
$$443$$ 4472.98 + 7747.43i 0.479724 + 0.830907i 0.999730 0.0232564i $$-0.00740339\pi$$
−0.520005 + 0.854163i $$0.674070\pi$$
$$444$$ 2732.01 + 6280.42i 0.292016 + 0.671297i
$$445$$ 0 0
$$446$$ −111.723 + 193.509i −0.0118615 + 0.0205447i
$$447$$ 796.640 + 1831.34i 0.0842948 + 0.193780i
$$448$$ 2707.53 + 4689.57i 0.285533 + 0.494557i
$$449$$ −2743.57 −0.288367 −0.144184 0.989551i $$-0.546056\pi$$
−0.144184 + 0.989551i $$0.546056\pi$$
$$450$$ 0 0
$$451$$ −225.580 −0.0235524
$$452$$ −7689.68 13318.9i −0.800204 1.38599i
$$453$$ −4115.30 468.209i −0.426829 0.0485615i
$$454$$ 1020.61 1767.76i 0.105506 0.182742i
$$455$$ 0 0
$$456$$ −2287.00 + 3091.75i −0.234865 + 0.317509i
$$457$$ −2806.35 4860.74i −0.287255 0.497540i 0.685899 0.727697i $$-0.259409\pi$$
−0.973153 + 0.230157i $$0.926076\pi$$
$$458$$ 1953.93 0.199348
$$459$$ 9229.74 + 3263.41i 0.938578 + 0.331858i
$$460$$ 0 0
$$461$$ −6273.50 10866.0i −0.633809 1.09779i −0.986766 0.162150i $$-0.948157\pi$$
0.352957 0.935640i $$-0.385176\pi$$
$$462$$ −29.6591 + 40.0954i −0.00298672 + 0.00403768i
$$463$$ 5361.12 9285.74i 0.538126 0.932062i −0.460879 0.887463i $$-0.652466\pi$$
0.999005 0.0445990i $$-0.0142010\pi$$
$$464$$ 8828.65 15291.7i 0.883319 1.52995i
$$465$$ 0 0
$$466$$ 1016.95 + 1761.40i 0.101093 + 0.175098i
$$467$$ −12798.4 −1.26818 −0.634089 0.773260i $$-0.718625\pi$$
−0.634089 + 0.773260i $$0.718625\pi$$
$$468$$ 1535.97 1648.19i 0.151710 0.162794i
$$469$$ 6352.31 0.625421
$$470$$ 0 0
$$471$$ −1805.33 4150.14i −0.176614 0.406005i
$$472$$ −1877.92 + 3252.65i −0.183132 + 0.317193i
$$473$$ 238.691 413.425i 0.0232030 0.0401888i
$$474$$ 370.293 + 851.242i 0.0358822 + 0.0824870i
$$475$$ 0 0
$$476$$ 6878.34 0.662328
$$477$$ −3628.49 11854.6i −0.348296 1.13791i
$$478$$ −743.203 −0.0711158
$$479$$ −1207.38 2091.25i −0.115171 0.199481i 0.802677 0.596413i $$-0.203408\pi$$
−0.917848 + 0.396932i $$0.870075\pi$$
$$480$$ 0 0
$$481$$ 910.070 1576.29i 0.0862695 0.149423i
$$482$$ 1147.61 1987.72i 0.108449 0.187839i
$$483$$ −1236.52 + 1671.62i −0.116487 + 0.157477i
$$484$$ −5163.37 8943.21i −0.484914 0.839896i
$$485$$ 0 0
$$486$$ 1598.80 833.919i 0.149225 0.0778340i
$$487$$ −16386.9 −1.52477 −0.762384 0.647125i $$-0.775971\pi$$
−0.762384 + 0.647125i $$0.775971\pi$$
$$488$$ 2184.39 + 3783.48i 0.202629 + 0.350963i
$$489$$ −96.5982 + 130.589i −0.00893317 + 0.0120766i
$$490$$ 0 0
$$491$$ −7935.54 + 13744.8i −0.729381 + 1.26332i 0.227764 + 0.973716i $$0.426858\pi$$
−0.957145 + 0.289609i $$0.906475\pi$$
$$492$$ 5693.85 + 647.805i 0.521745 + 0.0593604i
$$493$$ −10510.6 18204.8i −0.960186 1.66309i
$$494$$ 503.665 0.0458724
$$495$$ 0 0
$$496$$ −6873.68 −0.622252
$$497$$ −6763.26 11714.3i −0.610410 1.05726i
$$498$$ −1276.02 2933.36i −0.114819 0.263950i
$$499$$ −5730.39 + 9925.33i −0.514083 + 0.890419i 0.485783 + 0.874079i $$0.338534\pi$$
−0.999867 + 0.0163392i $$0.994799\pi$$
$$500$$ 0 0
$$501$$ −77.2776 177.648i −0.00689123 0.0158418i
$$502$$ 830.138 + 1437.84i 0.0738065 + 0.127837i
$$503$$ 1038.52 0.0920585 0.0460293 0.998940i $$-0.485343\pi$$
0.0460293 + 0.998940i $$0.485343\pi$$
$$504$$ 1752.71 1880.77i 0.154905 0.166222i
$$505$$ 0 0
$$506$$ −11.9420 20.6841i −0.00104918 0.00181724i
$$507$$ 10747.9 + 1222.81i 0.941479 + 0.107115i
$$508$$ 5124.04 8875.10i 0.447525 0.775135i
$$509$$ 2514.44 4355.14i 0.218960 0.379249i −0.735530 0.677492i $$-0.763067\pi$$
0.954490 + 0.298242i $$0.0964003\pi$$
$$510$$ 0 0
$$511$$ −2759.92 4780.33i −0.238927 0.413834i
$$512$$ 8677.07 0.748976
$$513$$ −13037.5 4609.74i −1.12206 0.396735i
$$514$$ −2342.92 −0.201054
$$515$$ 0 0
$$516$$ −7212.04 + 9749.79i −0.615295 + 0.831803i
$$517$$ 387.499 671.169i 0.0329636 0.0570947i
$$518$$ 511.785 886.438i 0.0434104 0.0751889i
$$519$$ 6098.25 + 693.815i 0.515768 + 0.0586803i
$$520$$ 0 0
$$521$$ 7057.78 0.593487 0.296744 0.954957i $$-0.404099\pi$$
0.296744 + 0.954957i $$0.404099\pi$$
$$522$$ −3773.04 869.797i −0.316363 0.0729310i
$$523$$ 14453.5 1.20843 0.604215 0.796821i $$-0.293487\pi$$
0.604215 + 0.796821i $$0.293487\pi$$
$$524$$ 6160.13 + 10669.7i 0.513562 + 0.889515i
$$525$$ 0 0
$$526$$ 1313.18 2274.49i 0.108854 0.188541i
$$527$$ −4091.57 + 7086.81i −0.338201 + 0.585781i
$$528$$ −193.165 444.053i −0.0159212 0.0366002i
$$529$$ 5585.63 + 9674.59i 0.459080 + 0.795150i
$$530$$ 0 0
$$531$$ −13160.2 3033.81i −1.07553 0.247940i
$$532$$ −9716.01 −0.791809
$$533$$ −761.469 1318.90i −0.0618816 0.107182i
$$534$$ 991.180 + 112.769i 0.0803231 + 0.00913858i
$$535$$ 0 0
$$536$$ 1880.68 3257.44i 0.151554 0.262500i
$$537$$ −1327.16 + 1794.15i −0.106650 + 0.144178i
$$538$$ 1867.04 + 3233.81i 0.149617 + 0.259144i
$$539$$ 289.687 0.0231498
$$540$$ 0 0
$$541$$ 4101.59 0.325954 0.162977 0.986630i $$-0.447890\pi$$
0.162977 + 0.986630i $$0.447890\pi$$
$$542$$ −1023.80 1773.27i −0.0811362 0.140532i
$$543$$ −5525.03 + 7469.16i −0.436651 + 0.590299i
$$544$$ 3069.26 5316.11i 0.241900 0.418982i
$$545$$ 0 0
$$546$$ −334.544 38.0620i −0.0262219 0.00298334i
$$547$$ 8410.52 + 14567.4i 0.657418 + 1.13868i 0.981282 + 0.192578i $$0.0616848\pi$$
−0.323863 + 0.946104i $$0.604982\pi$$
$$548$$ −2965.70 −0.231183
$$549$$ −10710.1 + 11492.6i −0.832598 + 0.893428i
$$550$$ 0 0
$$551$$ 14846.7 + 25715.2i 1.14790 + 1.98821i
$$552$$ 491.112 + 1128.98i 0.0378680 + 0.0870521i
$$553$$ −2379.50 + 4121.41i −0.182977 + 0.316926i
$$554$$ −440.771 + 763.438i −0.0338025 + 0.0585476i
$$555$$ 0 0
$$556$$ −9570.54 16576.7i −0.730002 1.26440i
$$557$$ −12248.8 −0.931771 −0.465885 0.884845i $$-0.654264\pi$$
−0.465885 + 0.884845i $$0.654264\pi$$
$$558$$ 441.156 + 1441.30i 0.0334688 + 0.109346i
$$559$$ 3222.91 0.243854
$$560$$ 0 0
$$561$$ −572.804 65.1694i −0.0431084 0.00490455i
$$562$$ −1652.28 + 2861.84i −0.124017 + 0.214803i
$$563$$ −4422.86 + 7660.62i −0.331086 + 0.573457i −0.982725 0.185072i $$-0.940748\pi$$
0.651639 + 0.758529i $$0.274082\pi$$
$$564$$ −11708.3 + 15828.1i −0.874127 + 1.18171i
$$565$$ 0 0
$$566$$ 3062.06 0.227399
$$567$$ 8311.39 + 4047.12i 0.615601 + 0.299759i
$$568$$ −8009.40 −0.591667
$$569$$ 4049.35 + 7013.68i 0.298344 + 0.516747i 0.975757 0.218856i $$-0.0702325\pi$$
−0.677413 + 0.735603i $$0.736899\pi$$
$$570$$ 0 0
$$571$$ 8189.02 14183.8i 0.600175 1.03953i −0.392619 0.919701i $$-0.628431\pi$$
0.992794 0.119832i $$-0.0382356\pi$$
$$572$$ −66.3361 + 114.897i −0.00484904 + 0.00839879i
$$573$$ −4053.69 461.200i −0.295542 0.0336246i
$$574$$ −428.218 741.696i −0.0311385 0.0539334i
$$575$$ 0 0
$$576$$ 3374.49 + 11024.8i 0.244104 + 0.797510i
$$577$$ 24920.9 1.79804 0.899020 0.437907i $$-0.144280\pi$$
0.899020 + 0.437907i $$0.144280\pi$$
$$578$$ 10.4558 + 18.1100i 0.000752430 + 0.00130325i
$$579$$ −988.853 2273.21i −0.0709764 0.163163i
$$580$$ 0 0
$$581$$ 8199.69 14202.3i 0.585509 1.01413i
$$582$$ −1560.42 3587.15i −0.111137 0.255484i
$$583$$ 365.034 + 632.257i 0.0259317 + 0.0449150i
$$584$$ −3268.44 −0.231591
$$585$$ 0 0
$$586$$ −3637.76 −0.256441
$$587$$ 4182.25 + 7243.86i 0.294071 + 0.509346i 0.974768 0.223219i $$-0.0716564\pi$$
−0.680697 + 0.732565i $$0.738323\pi$$
$$588$$ −7311.99 831.905i −0.512826 0.0583456i
$$589$$ 5779.56 10010.5i 0.404317 0.700297i
$$590$$ 0 0
$$591$$ −14302.2 + 19334.8i −0.995456 + 1.34573i
$$592$$ 4969.25 + 8607.00i 0.344992 + 0.597543i
$$593$$ 27169.7 1.88150 0.940749 0.339105i $$-0.110124\pi$$
0.940749 + 0.339105i $$0.110124\pi$$
$$594$$ −80.7132 + 69.0030i −0.00557526 + 0.00476637i
$$595$$ 0 0
$$596$$ 1493.83 + 2587.39i 0.102667 + 0.177825i
$$597$$ 7829.88 10585.0i 0.536777 0.725656i
$$598$$ 80.6231 139.643i 0.00551325 0.00954923i
$$599$$ −10666.2 + 18474.4i −0.727560 + 1.26017i 0.230351 + 0.973108i $$0.426013\pi$$
−0.957911 + 0.287064i $$0.907321\pi$$
$$600$$ 0 0
$$601$$ −292.016 505.786i −0.0198196 0.0343285i 0.855946 0.517066i $$-0.172976\pi$$
−0.875765 + 0.482738i $$0.839643\pi$$
$$602$$ 1812.43 0.122706
$$603$$ 13179.6 + 3038.28i 0.890074 + 0.205188i
$$604$$ −6196.17 −0.417415
$$605$$ 0 0
$$606$$ −1139.47 2619.46i −0.0763827 0.175591i
$$607$$ −5635.12 + 9760.32i −0.376808 + 0.652651i −0.990596 0.136820i $$-0.956312\pi$$
0.613788 + 0.789471i $$0.289645\pi$$
$$608$$ −4335.49 + 7509.29i −0.289190 + 0.500891i
$$609$$ −7918.17 18202.5i −0.526864 1.21117i
$$610$$ 0 0
$$611$$ 5232.19 0.346435
$$612$$ 14271.0 + 3289.88i 0.942598 + 0.217297i
$$613$$ 4271.02 0.281411 0.140706 0.990051i $$-0.455063\pi$$
0.140706 + 0.990051i $$0.455063\pi$$
$$614$$ −1075.28 1862.44i −0.0706756 0.122414i
$$615$$ 0 0
$$616$$ −75.6968 + 131.111i −0.00495115 + 0.00857565i
$$617$$ 3598.08 6232.06i 0.234770 0.406634i −0.724436 0.689342i $$-0.757900\pi$$
0.959206 + 0.282708i $$0.0912329\pi$$
$$618$$ −2134.76 + 2885.94i −0.138953 + 0.187847i
$$619$$ −5128.24 8882.36i −0.332991 0.576757i 0.650106 0.759843i $$-0.274724\pi$$
−0.983097 + 0.183087i $$0.941391\pi$$
$$620$$ 0 0
$$621$$ −3365.01 + 2876.80i −0.217445 + 0.185897i
$$622$$ 1872.28 0.120694
$$623$$ 2557.08 + 4428.99i 0.164442 + 0.284822i
$$624$$ 1944.21 2628.33i 0.124729 0.168618i
$$625$$ 0 0
$$626$$ 753.607 1305.29i 0.0481153 0.0833382i
$$627$$ 809.115 + 92.0552i 0.0515358 + 0.00586337i
$$628$$ −3385.28 5863.47i −0.215107 0.372576i
$$629$$ 11831.8 0.750026
$$630$$ 0 0
$$631$$ 15187.7 0.958183 0.479091 0.877765i $$-0.340966\pi$$
0.479091 + 0.877765i $$0.340966\pi$$
$$632$$ 1408.96 + 2440.39i 0.0886795 + 0.153597i
$$633$$ 5731.90 + 13176.7i 0.359909 + 0.827371i
$$634$$ 1866.47 3232.81i 0.116919 0.202510i
$$635$$ 0 0
$$636$$ −7398.14 17007.1i −0.461250 1.06034i
$$637$$ 977.872 + 1693.72i 0.0608237 + 0.105350i
$$638$$ 228.016 0.0141493
$$639$$ −8429.31 27539.3i −0.521844 1.70491i
$$640$$ 0 0
$$641$$ 14196.7 + 24589.4i 0.874783 + 1.51517i 0.856994 + 0.515327i $$0.172329\pi$$
0.0177891 + 0.999842i $$0.494337\pi$$
$$642$$ −336.036 38.2317i −0.0206578 0.00235029i
$$643$$ 5844.00 10122.1i 0.358421 0.620804i −0.629276 0.777182i $$-0.716649\pi$$
0.987697 + 0.156378i $$0.0499818\pi$$
$$644$$ −1555.27 + 2693.80i −0.0951648 + 0.164830i
$$645$$ 0 0
$$646$$ 1637.04 + 2835.44i 0.0997036 + 0.172692i
$$647$$ −12800.8 −0.777822 −0.388911 0.921275i $$-0.627149\pi$$
−0.388911 + 0.921275i $$0.627149\pi$$
$$648$$ 4536.04 3063.85i 0.274989 0.185740i
$$649$$ 795.310 0.0481027
$$650$$ 0 0
$$651$$ −4595.39 + 6212.40i −0.276663 + 0.374014i
$$652$$ −121.500 + 210.443i −0.00729799 + 0.0126405i
$$653$$ 3079.46 5333.78i 0.184546 0.319643i −0.758877 0.651233i $$-0.774252\pi$$
0.943423 + 0.331590i $$0.107585\pi$$
$$654$$ −98.5968 11.2176i −0.00589517 0.000670709i
$$655$$ 0 0
$$656$$ 8315.69 0.494929
$$657$$ −3439.80 11238.1i −0.204261 0.667339i
$$658$$ 2942.36 0.174324
$$659$$ −8289.10 14357.1i −0.489981 0.848672i 0.509953 0.860202i $$-0.329663\pi$$
−0.999934 + 0.0115307i $$0.996330\pi$$
$$660$$ 0 0
$$661$$ 11469.8 19866.4i 0.674925 1.16900i −0.301566 0.953445i $$-0.597509\pi$$
0.976491 0.215559i $$-0.0691573\pi$$
$$662$$ 2583.22 4474.27i 0.151661 0.262685i
$$663$$ −1552.53 3569.01i −0.0909433 0.209063i
$$664$$ −4855.25 8409.53i −0.283765 0.491496i
$$665$$ 0 0
$$666$$ 1485.82 1594.37i 0.0864478 0.0927637i
$$667$$ 9506.20 0.551847
$$668$$ −144.908 250.988i −0.00839319 0.0145374i
$$669$$ −2423.38 275.715i −0.140050 0.0159338i
$$670$$ 0 0
$$671$$ 462.552 801.163i 0.0266119 0.0460932i
$$672$$ 3447.19 4660.18i 0.197884 0.267515i
$$673$$ −1181.62 2046.62i −0.0676790 0.117223i 0.830200 0.557465i $$-0.188226\pi$$
−0.897879 + 0.440242i $$0.854893\pi$$
$$674$$ −3102.46 −0.177303
$$675$$ 0 0
$$676$$ 16182.4 0.920712
$$677$$ 7824.09 + 13551.7i 0.444172 + 0.769328i 0.997994 0.0633068i $$-0.0201647\pi$$
−0.553822 + 0.832635i $$0.686831\pi$$
$$678$$ −2910.33 + 3934.40i −0.164853 + 0.222861i
$$679$$ 10027.2 17367.7i 0.566730 0.981605i
$$680$$ 0 0
$$681$$ 22138.2 + 2518.72i 1.24572 + 0.141729i
$$682$$ −44.3813 76.8706i −0.00249186 0.00431602i
$$683$$ 19626.7 1.09955 0.549777 0.835311i $$-0.314713\pi$$
0.549777 + 0.835311i $$0.314713\pi$$
$$684$$ −20158.5 4647.12i −1.12687 0.259777i
$$685$$ 0 0
$$686$$ 1585.18 + 2745.62i 0.0882253 + 0.152811i
$$687$$ 8507.72 + 19557.8i 0.472474 + 1.08614i
$$688$$ −8799.02 + 15240.3i −0.487586 + 0.844524i
$$689$$ −2464.42 + 4268.51i −0.136266 + 0.236019i
$$690$$ 0 0
$$691$$ 51.5955 + 89.3660i 0.00284050 + 0.00491989i 0.867442 0.497538i $$-0.165763\pi$$
−0.864602 + 0.502458i $$0.832429\pi$$
$$692$$ 9181.78 0.504391
$$693$$ −530.473 122.290i −0.0290779 0.00670332i
$$694$$ 2826.96 0.154625
$$695$$ 0 0
$$696$$ −11678.5 1328.69i −0.636021 0.0723619i
$$697$$ 4949.93 8573.54i 0.268999 0.465920i
$$698$$ 1736.71 3008.06i 0.0941766 0.163119i
$$699$$ −13202.8 + 17848.5i −0.714412 + 0.965797i
$$700$$ 0 0
$$701$$ −17977.8 −0.968631 −0.484316 0.874893i $$-0.660931\pi$$
−0.484316 + 0.874893i $$0.660931\pi$$
$$702$$ −675.898 238.981i −0.0363392 0.0128487i
$$703$$ −16713.1 −0.896651
$$704$$ −339.482 588.000i −0.0181743 0.0314788i
$$705$$ 0 0
$$706$$ −297.692 + 515.617i −0.0158694 + 0.0274865i
$$707$$ 7322.22 12682.5i 0.389506 0.674644i
$$708$$ −20074.4 2283.92i −1.06560 0.121236i
$$709$$ −5385.10 9327.26i −0.285249 0.494066i 0.687421 0.726260i $$-0.258743\pi$$
−0.972670 + 0.232194i $$0.925410\pi$$
$$710$$ 0 0
$$711$$ −6908.16 + 7412.87i −0.364383 + 0.391005i
$$712$$ 3028.23 0.159393
$$713$$ −1850.30 3204.81i −0.0971868 0.168333i
$$714$$ −873.080 2007.06i −0.0457622 0.105200i
$$715$$ 0 0
$$716$$ −1669.27 + 2891.27i −0.0871280 + 0.150910i
$$717$$ −3236.02 7439.06i −0.168551 0.387471i
$$718$$ 2601.12 + 4505.27i 0.135199 + 0.234171i
$$719$$ 24138.7 1.25205 0.626023 0.779804i $$-0.284681\pi$$
0.626023 + 0.779804i $$0.284681\pi$$
$$720$$ 0 0
$$721$$ −18402.9 −0.950568
$$722$$ −679.843 1177.52i −0.0350431 0.0606964i
$$723$$ 24892.9 + 2832.13i 1.28046 + 0.145682i
$$724$$ −6949.28 + 12036.5i −0.356724 + 0.617864i
$$725$$ 0 0
$$726$$ −1954.19 + 2641.82i −0.0998991 + 0.135051i
$$727$$ 5395.46 + 9345.20i 0.275250 + 0.476746i 0.970198 0.242313i $$-0.0779062\pi$$
−0.694949 + 0.719059i $$0.744573\pi$$
$$728$$ −1022.09 −0.0520347
$$729$$ 15308.5 + 12372.1i 0.777753 + 0.628570i
$$730$$ 0 0
$$731$$ 10475.3 + 18143.7i 0.530016 + 0.918015i
$$732$$ −13976.0 + 18893.8i −0.705692 + 0.954009i
$$733$$ 10492.9 18174.3i 0.528738 0.915801i −0.470700 0.882293i $$-0.655999\pi$$
0.999438 0.0335082i $$-0.0106680\pi$$
$$734$$ 1530.77 2651.36i 0.0769776 0.133329i
$$735$$ 0 0
$$736$$ 1387.99 + 2404.06i 0.0695134 + 0.120401i
$$737$$ −796.481 −0.0398084
$$738$$ −533.705 1743.66i −0.0266205 0.0869717i
$$739$$ 1773.47 0.0882790 0.0441395 0.999025i $$-0.485945\pi$$
0.0441395 + 0.999025i $$0.485945\pi$$
$$740$$ 0 0
$$741$$ 2193.03 + 5041.42i 0.108722 + 0.249934i
$$742$$ −1385.89 + 2400.43i −0.0685682 + 0.118764i
$$743$$ 2640.39 4573.28i 0.130372 0.225811i −0.793448 0.608638i $$-0.791716\pi$$
0.923820 + 0.382827i $$0.125050\pi$$
$$744$$ 1825.17 + 4195.76i 0.0899381 + 0.206753i
$$745$$ 0 0
$$746$$ 2338.14 0.114753
$$747$$ 23805.4 25544.6i 1.16599 1.25117i
$$748$$ −862.437 −0.0421575
$$749$$ −866.918 1501.55i −0.0422917 0.0732514i
$$750$$ 0 0
$$751$$ −5514.51 + 9551.40i −0.267946 + 0.464095i −0.968331 0.249669i $$-0.919678\pi$$
0.700386 + 0.713765i $$0.253011\pi$$
$$752$$ −14284.6 + 24741.7i −0.692696 + 1.19978i
$$753$$ −10777.5 + 14569.8i −0.521584 + 0.705117i
$$754$$ 769.692 + 1333.15i 0.0371758 + 0.0643904i
$$755$$ 0 0
$$756$$ 13038.5 + 4610.09i 0.627255 + 0.221782i
$$757$$ −19897.2 −0.955318 −0.477659 0.878545i $$-0.658514\pi$$
−0.477659 + 0.878545i $$0.658514\pi$$
$$758$$ −1143.87 1981.24i −0.0548115 0.0949363i
$$759$$ 155.040 209.595i 0.00741448 0.0100235i
$$760$$ 0 0
$$761$$ 12636.2 21886.5i 0.601920 1.04256i −0.390610 0.920556i $$-0.627736\pi$$
0.992530 0.122000i $$-0.0389307\pi$$
$$762$$ −3240.11 368.636i −0.154038 0.0175253i
$$763$$ −254.364 440.571i −0.0120689 0.0209040i
$$764$$ −6103.40 −0.289023
$$765$$ 0 0
$$766$$ −2014.65 −0.0950292
$$767$$ 2684.65 + 4649.96i 0.126385 + 0.218905i
$$768$$ 6185.87 + 14220.3i 0.290642 + 0.668137i
$$769$$ −15167.1 + 26270.1i −0.711233 + 1.23189i 0.253162 + 0.967424i $$0.418529\pi$$
−0.964395 + 0.264467i $$0.914804\pi$$
$$770$$ 0 0
$$771$$ −10201.4 23451.3i −0.476517 1.09543i
$$772$$ −1854.26 3211.67i −0.0864458 0.149729i
$$773$$ 6671.36 0.310417 0.155208 0.987882i $$-0.450395\pi$$
0.155208 + 0.987882i $$0.450395\pi$$
$$774$$ 3760.37 + 866.877i 0.174630 + 0.0402574i
$$775$$ 0 0
$$776$$ −5937.38 10283.8i −0.274664 0.475732i
$$777$$ 11101.2 + 1263.01i 0.512551 + 0.0583143i
$$778$$ 837.129 1449.95i 0.0385765 0.0668165i
$$779$$ −6992.04 + 12110.6i −0.321586 + 0.557004i