Properties

 Label 378.4.g.f.163.2 Level $378$ Weight $4$ Character 378.163 Analytic conductor $22.303$ Analytic rank $0$ Dimension $8$ CM no Inner twists $2$

Learn more

Newspace parameters

 Level: $$N$$ $$=$$ $$378 = 2 \cdot 3^{3} \cdot 7$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 378.g (of order $$3$$, degree $$2$$, minimal)

Newform invariants

 Self dual: no Analytic conductor: $$22.3027219822$$ Analytic rank: $$0$$ Dimension: $$8$$ Relative dimension: $$4$$ over $$\Q(\zeta_{3})$$ Coefficient field: $$\mathbb{Q}[x]/(x^{8} - \cdots)$$ Defining polynomial: $$x^{8} - x^{7} + 18x^{6} + 9x^{5} + 283x^{4} - 48x^{3} + 186x^{2} + 40x + 100$$ x^8 - x^7 + 18*x^6 + 9*x^5 + 283*x^4 - 48*x^3 + 186*x^2 + 40*x + 100 Coefficient ring: $$\Z[a_1, \ldots, a_{25}]$$ Coefficient ring index: $$2^{4}\cdot 3^{3}$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

 Embedding label 163.2 Root $$-1.84763 + 3.20018i$$ of defining polynomial Character $$\chi$$ $$=$$ 378.163 Dual form 378.4.g.f.109.2

$q$-expansion

 $$f(q)$$ $$=$$ $$q+(1.00000 - 1.73205i) q^{2} +(-2.00000 - 3.46410i) q^{4} +(-5.04834 + 8.74398i) q^{5} +(-5.48778 - 17.6885i) q^{7} -8.00000 q^{8} +O(q^{10})$$ $$q+(1.00000 - 1.73205i) q^{2} +(-2.00000 - 3.46410i) q^{4} +(-5.04834 + 8.74398i) q^{5} +(-5.48778 - 17.6885i) q^{7} -8.00000 q^{8} +(10.0967 + 17.4880i) q^{10} +(18.0748 + 31.3065i) q^{11} -4.01927 q^{13} +(-36.1252 - 8.18341i) q^{14} +(-8.00000 + 13.8564i) q^{16} +(18.9802 + 32.8747i) q^{17} +(-28.5163 + 49.3917i) q^{19} +40.3867 q^{20} +72.2993 q^{22} +(39.2198 - 67.9308i) q^{23} +(11.5285 + 19.9680i) q^{25} +(-4.01927 + 6.96157i) q^{26} +(-50.2993 + 54.3873i) q^{28} +215.332 q^{29} +(91.1642 + 157.901i) q^{31} +(16.0000 + 27.7128i) q^{32} +75.9208 q^{34} +(182.372 + 41.3127i) q^{35} +(-156.279 + 270.683i) q^{37} +(57.0327 + 98.7835i) q^{38} +(40.3867 - 69.9518i) q^{40} +186.557 q^{41} +262.266 q^{43} +(72.2993 - 125.226i) q^{44} +(-78.4397 - 135.862i) q^{46} +(-68.9606 + 119.443i) q^{47} +(-282.768 + 194.142i) q^{49} +46.1142 q^{50} +(8.03853 + 13.9231i) q^{52} +(273.767 + 474.179i) q^{53} -364.991 q^{55} +(43.9023 + 141.508i) q^{56} +(215.332 - 372.967i) q^{58} +(1.86703 + 3.23378i) q^{59} +(57.5008 - 99.5943i) q^{61} +364.657 q^{62} +64.0000 q^{64} +(20.2906 - 35.1444i) q^{65} +(-313.900 - 543.690i) q^{67} +(75.9208 - 131.499i) q^{68} +(253.928 - 274.566i) q^{70} +533.107 q^{71} +(149.197 + 258.417i) q^{73} +(312.557 + 541.365i) q^{74} +228.131 q^{76} +(454.576 - 491.521i) q^{77} +(433.508 - 750.857i) q^{79} +(-80.7734 - 139.904i) q^{80} +(186.557 - 323.126i) q^{82} -244.224 q^{83} -383.274 q^{85} +(262.266 - 454.258i) q^{86} +(-144.599 - 250.452i) q^{88} +(-223.508 + 387.128i) q^{89} +(22.0569 + 71.0949i) q^{91} -313.759 q^{92} +(137.921 + 238.887i) q^{94} +(-287.920 - 498.692i) q^{95} -1803.99 q^{97} +(53.4948 + 683.911i) q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$8 q + 8 q^{2} - 16 q^{4} - 2 q^{5} + 6 q^{7} - 64 q^{8}+O(q^{10})$$ 8 * q + 8 * q^2 - 16 * q^4 - 2 * q^5 + 6 * q^7 - 64 * q^8 $$8 q + 8 q^{2} - 16 q^{4} - 2 q^{5} + 6 q^{7} - 64 q^{8} + 4 q^{10} + 32 q^{11} - 4 q^{13} + 36 q^{14} - 64 q^{16} - 58 q^{17} + 70 q^{19} + 16 q^{20} + 128 q^{22} + 86 q^{23} - 156 q^{25} - 4 q^{26} + 48 q^{28} - 212 q^{29} - 64 q^{31} + 128 q^{32} - 232 q^{34} + 8 q^{35} - 146 q^{37} - 140 q^{38} + 16 q^{40} - 780 q^{41} + 880 q^{43} + 128 q^{44} - 172 q^{46} - 306 q^{47} + 50 q^{49} - 624 q^{50} + 8 q^{52} - 90 q^{53} - 64 q^{55} - 48 q^{56} - 212 q^{58} + 148 q^{59} - 364 q^{61} - 256 q^{62} + 512 q^{64} + 1296 q^{65} - 954 q^{67} - 232 q^{68} + 20 q^{70} - 1360 q^{71} - 54 q^{73} + 292 q^{74} - 560 q^{76} + 2224 q^{77} - 226 q^{79} - 32 q^{80} - 780 q^{82} - 3136 q^{83} + 3920 q^{85} + 880 q^{86} - 256 q^{88} - 1458 q^{89} + 3836 q^{91} - 688 q^{92} + 612 q^{94} + 1310 q^{95} - 4344 q^{97} + 776 q^{98}+O(q^{100})$$ 8 * q + 8 * q^2 - 16 * q^4 - 2 * q^5 + 6 * q^7 - 64 * q^8 + 4 * q^10 + 32 * q^11 - 4 * q^13 + 36 * q^14 - 64 * q^16 - 58 * q^17 + 70 * q^19 + 16 * q^20 + 128 * q^22 + 86 * q^23 - 156 * q^25 - 4 * q^26 + 48 * q^28 - 212 * q^29 - 64 * q^31 + 128 * q^32 - 232 * q^34 + 8 * q^35 - 146 * q^37 - 140 * q^38 + 16 * q^40 - 780 * q^41 + 880 * q^43 + 128 * q^44 - 172 * q^46 - 306 * q^47 + 50 * q^49 - 624 * q^50 + 8 * q^52 - 90 * q^53 - 64 * q^55 - 48 * q^56 - 212 * q^58 + 148 * q^59 - 364 * q^61 - 256 * q^62 + 512 * q^64 + 1296 * q^65 - 954 * q^67 - 232 * q^68 + 20 * q^70 - 1360 * q^71 - 54 * q^73 + 292 * q^74 - 560 * q^76 + 2224 * q^77 - 226 * q^79 - 32 * q^80 - 780 * q^82 - 3136 * q^83 + 3920 * q^85 + 880 * q^86 - 256 * q^88 - 1458 * q^89 + 3836 * q^91 - 688 * q^92 + 612 * q^94 + 1310 * q^95 - 4344 * q^97 + 776 * q^98

Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/378\mathbb{Z}\right)^\times$$.

 $$n$$ $$29$$ $$325$$ $$\chi(n)$$ $$1$$ $$e\left(\frac{1}{3}\right)$$

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 0
$$4$$ −2.00000 3.46410i −0.250000 0.433013i
$$5$$ −5.04834 + 8.74398i −0.451537 + 0.782085i −0.998482 0.0550835i $$-0.982458\pi$$
0.546945 + 0.837169i $$0.315791\pi$$
$$6$$ 0 0
$$7$$ −5.48778 17.6885i −0.296312 0.955091i
$$8$$ −8.00000 −0.353553
$$9$$ 0 0
$$10$$ 10.0967 + 17.4880i 0.319285 + 0.553018i
$$11$$ 18.0748 + 31.3065i 0.495433 + 0.858116i 0.999986 0.00526523i $$-0.00167598\pi$$
−0.504553 + 0.863381i $$0.668343\pi$$
$$12$$ 0 0
$$13$$ −4.01927 −0.0857495 −0.0428748 0.999080i $$-0.513652\pi$$
−0.0428748 + 0.999080i $$0.513652\pi$$
$$14$$ −36.1252 8.18341i −0.689634 0.156222i
$$15$$ 0 0
$$16$$ −8.00000 + 13.8564i −0.125000 + 0.216506i
$$17$$ 18.9802 + 32.8747i 0.270787 + 0.469017i 0.969064 0.246811i $$-0.0793828\pi$$
−0.698277 + 0.715828i $$0.746049\pi$$
$$18$$ 0 0
$$19$$ −28.5163 + 49.3917i −0.344321 + 0.596381i −0.985230 0.171236i $$-0.945224\pi$$
0.640909 + 0.767617i $$0.278557\pi$$
$$20$$ 40.3867 0.451537
$$21$$ 0 0
$$22$$ 72.2993 0.700648
$$23$$ 39.2198 67.9308i 0.355561 0.615850i −0.631653 0.775251i $$-0.717623\pi$$
0.987214 + 0.159402i $$0.0509565\pi$$
$$24$$ 0 0
$$25$$ 11.5285 + 19.9680i 0.0922284 + 0.159744i
$$26$$ −4.01927 + 6.96157i −0.0303170 + 0.0525107i
$$27$$ 0 0
$$28$$ −50.2993 + 54.3873i −0.339488 + 0.367080i
$$29$$ 215.332 1.37884 0.689418 0.724364i $$-0.257866\pi$$
0.689418 + 0.724364i $$0.257866\pi$$
$$30$$ 0 0
$$31$$ 91.1642 + 157.901i 0.528180 + 0.914834i 0.999460 + 0.0328507i $$0.0104586\pi$$
−0.471281 + 0.881983i $$0.656208\pi$$
$$32$$ 16.0000 + 27.7128i 0.0883883 + 0.153093i
$$33$$ 0 0
$$34$$ 75.9208 0.382950
$$35$$ 182.372 + 41.3127i 0.880759 + 0.199518i
$$36$$ 0 0
$$37$$ −156.279 + 270.683i −0.694380 + 1.20270i 0.276010 + 0.961155i $$0.410988\pi$$
−0.970389 + 0.241546i $$0.922346\pi$$
$$38$$ 57.0327 + 98.7835i 0.243472 + 0.421705i
$$39$$ 0 0
$$40$$ 40.3867 69.9518i 0.159642 0.276509i
$$41$$ 186.557 0.710617 0.355308 0.934749i $$-0.384376\pi$$
0.355308 + 0.934749i $$0.384376\pi$$
$$42$$ 0 0
$$43$$ 262.266 0.930121 0.465061 0.885279i $$-0.346033\pi$$
0.465061 + 0.885279i $$0.346033\pi$$
$$44$$ 72.2993 125.226i 0.247717 0.429058i
$$45$$ 0 0
$$46$$ −78.4397 135.862i −0.251420 0.435472i
$$47$$ −68.9606 + 119.443i −0.214020 + 0.370693i −0.952969 0.303068i $$-0.901989\pi$$
0.738949 + 0.673761i $$0.235322\pi$$
$$48$$ 0 0
$$49$$ −282.768 + 194.142i −0.824398 + 0.566011i
$$50$$ 46.1142 0.130431
$$51$$ 0 0
$$52$$ 8.03853 + 13.9231i 0.0214374 + 0.0371306i
$$53$$ 273.767 + 474.179i 0.709526 + 1.22893i 0.965033 + 0.262127i $$0.0844241\pi$$
−0.255508 + 0.966807i $$0.582243\pi$$
$$54$$ 0 0
$$55$$ −364.991 −0.894826
$$56$$ 43.9023 + 141.508i 0.104762 + 0.337676i
$$57$$ 0 0
$$58$$ 215.332 372.967i 0.487492 0.844361i
$$59$$ 1.86703 + 3.23378i 0.00411976 + 0.00713564i 0.868078 0.496428i $$-0.165355\pi$$
−0.863958 + 0.503564i $$0.832022\pi$$
$$60$$ 0 0
$$61$$ 57.5008 99.5943i 0.120692 0.209045i −0.799349 0.600868i $$-0.794822\pi$$
0.920041 + 0.391822i $$0.128155\pi$$
$$62$$ 364.657 0.746959
$$63$$ 0 0
$$64$$ 64.0000 0.125000
$$65$$ 20.2906 35.1444i 0.0387191 0.0670635i
$$66$$ 0 0
$$67$$ −313.900 543.690i −0.572373 0.991378i −0.996322 0.0856924i $$-0.972690\pi$$
0.423949 0.905686i $$-0.360644\pi$$
$$68$$ 75.9208 131.499i 0.135393 0.234508i
$$69$$ 0 0
$$70$$ 253.928 274.566i 0.433574 0.468812i
$$71$$ 533.107 0.891100 0.445550 0.895257i $$-0.353008\pi$$
0.445550 + 0.895257i $$0.353008\pi$$
$$72$$ 0 0
$$73$$ 149.197 + 258.417i 0.239208 + 0.414320i 0.960487 0.278324i $$-0.0897789\pi$$
−0.721279 + 0.692644i $$0.756446\pi$$
$$74$$ 312.557 + 541.365i 0.491001 + 0.850438i
$$75$$ 0 0
$$76$$ 228.131 0.344321
$$77$$ 454.576 491.521i 0.672775 0.727454i
$$78$$ 0 0
$$79$$ 433.508 750.857i 0.617385 1.06934i −0.372576 0.928002i $$-0.621525\pi$$
0.989961 0.141340i $$-0.0451412\pi$$
$$80$$ −80.7734 139.904i −0.112884 0.195521i
$$81$$ 0 0
$$82$$ 186.557 323.126i 0.251241 0.435162i
$$83$$ −244.224 −0.322977 −0.161489 0.986875i $$-0.551630\pi$$
−0.161489 + 0.986875i $$0.551630\pi$$
$$84$$ 0 0
$$85$$ −383.274 −0.489081
$$86$$ 262.266 454.258i 0.328847 0.569580i
$$87$$ 0 0
$$88$$ −144.599 250.452i −0.175162 0.303390i
$$89$$ −223.508 + 387.128i −0.266200 + 0.461073i −0.967877 0.251423i $$-0.919102\pi$$
0.701677 + 0.712495i $$0.252435\pi$$
$$90$$ 0 0
$$91$$ 22.0569 + 71.0949i 0.0254087 + 0.0818986i
$$92$$ −313.759 −0.355561
$$93$$ 0 0
$$94$$ 137.921 + 238.887i 0.151335 + 0.262120i
$$95$$ −287.920 498.692i −0.310947 0.538576i
$$96$$ 0 0
$$97$$ −1803.99 −1.88832 −0.944162 0.329481i $$-0.893126\pi$$
−0.944162 + 0.329481i $$0.893126\pi$$
$$98$$ 53.4948 + 683.911i 0.0551407 + 0.704954i
$$99$$ 0 0
$$100$$ 46.1142 79.8721i 0.0461142 0.0798721i
$$101$$ 842.134 + 1458.62i 0.829658 + 1.43701i 0.898307 + 0.439369i $$0.144798\pi$$
−0.0686484 + 0.997641i $$0.521869\pi$$
$$102$$ 0 0
$$103$$ −820.532 + 1421.20i −0.784946 + 1.35957i 0.144085 + 0.989565i $$0.453976\pi$$
−0.929031 + 0.370001i $$0.879357\pi$$
$$104$$ 32.1541 0.0303170
$$105$$ 0 0
$$106$$ 1095.07 1.00342
$$107$$ 160.547 278.076i 0.145053 0.251239i −0.784340 0.620332i $$-0.786998\pi$$
0.929393 + 0.369092i $$0.120331\pi$$
$$108$$ 0 0
$$109$$ −280.005 484.982i −0.246051 0.426173i 0.716376 0.697715i $$-0.245800\pi$$
−0.962427 + 0.271542i $$0.912466\pi$$
$$110$$ −364.991 + 632.184i −0.316369 + 0.547967i
$$111$$ 0 0
$$112$$ 289.002 + 65.4673i 0.243822 + 0.0552329i
$$113$$ −1870.65 −1.55731 −0.778655 0.627452i $$-0.784098\pi$$
−0.778655 + 0.627452i $$0.784098\pi$$
$$114$$ 0 0
$$115$$ 395.990 + 685.875i 0.321098 + 0.556158i
$$116$$ −430.665 745.934i −0.344709 0.597053i
$$117$$ 0 0
$$118$$ 7.46811 0.00582623
$$119$$ 477.346 516.141i 0.367716 0.397602i
$$120$$ 0 0
$$121$$ 12.1012 20.9598i 0.00909179 0.0157474i
$$122$$ −115.002 199.189i −0.0853423 0.147817i
$$123$$ 0 0
$$124$$ 364.657 631.604i 0.264090 0.457417i
$$125$$ −1494.88 −1.06965
$$126$$ 0 0
$$127$$ 790.048 0.552011 0.276006 0.961156i $$-0.410989\pi$$
0.276006 + 0.961156i $$0.410989\pi$$
$$128$$ 64.0000 110.851i 0.0441942 0.0765466i
$$129$$ 0 0
$$130$$ −40.5812 70.2888i −0.0273785 0.0474210i
$$131$$ 819.041 1418.62i 0.546259 0.946148i −0.452267 0.891882i $$-0.649385\pi$$
0.998527 0.0542661i $$-0.0172819\pi$$
$$132$$ 0 0
$$133$$ 1030.16 + 233.361i 0.671625 + 0.152143i
$$134$$ −1255.60 −0.809457
$$135$$ 0 0
$$136$$ −151.842 262.997i −0.0957376 0.165822i
$$137$$ 994.660 + 1722.80i 0.620289 + 1.07437i 0.989432 + 0.144999i $$0.0463178\pi$$
−0.369143 + 0.929373i $$0.620349\pi$$
$$138$$ 0 0
$$139$$ −655.628 −0.400069 −0.200035 0.979789i $$-0.564105\pi$$
−0.200035 + 0.979789i $$0.564105\pi$$
$$140$$ −221.634 714.382i −0.133796 0.431259i
$$141$$ 0 0
$$142$$ 533.107 923.368i 0.315052 0.545685i
$$143$$ −72.6475 125.829i −0.0424832 0.0735830i
$$144$$ 0 0
$$145$$ −1087.07 + 1882.86i −0.622596 + 1.07837i
$$146$$ 596.788 0.338291
$$147$$ 0 0
$$148$$ 1250.23 0.694380
$$149$$ 1494.77 2589.01i 0.821853 1.42349i −0.0824482 0.996595i $$-0.526274\pi$$
0.904301 0.426895i $$-0.140393\pi$$
$$150$$ 0 0
$$151$$ 547.979 + 949.128i 0.295324 + 0.511516i 0.975060 0.221940i $$-0.0712391\pi$$
−0.679736 + 0.733457i $$0.737906\pi$$
$$152$$ 228.131 395.134i 0.121736 0.210853i
$$153$$ 0 0
$$154$$ −396.763 1278.87i −0.207611 0.669183i
$$155$$ −1840.91 −0.953971
$$156$$ 0 0
$$157$$ −250.513 433.901i −0.127345 0.220567i 0.795302 0.606213i $$-0.207312\pi$$
−0.922647 + 0.385646i $$0.873979\pi$$
$$158$$ −867.015 1501.71i −0.436557 0.756139i
$$159$$ 0 0
$$160$$ −323.094 −0.159642
$$161$$ −1416.83 320.952i −0.693550 0.157109i
$$162$$ 0 0
$$163$$ −1134.21 + 1964.50i −0.545018 + 0.943998i 0.453588 + 0.891211i $$0.350144\pi$$
−0.998606 + 0.0527870i $$0.983190\pi$$
$$164$$ −373.114 646.252i −0.177654 0.307706i
$$165$$ 0 0
$$166$$ −244.224 + 423.009i −0.114190 + 0.197782i
$$167$$ −1369.97 −0.634799 −0.317400 0.948292i $$-0.602810\pi$$
−0.317400 + 0.948292i $$0.602810\pi$$
$$168$$ 0 0
$$169$$ −2180.85 −0.992647
$$170$$ −383.274 + 663.850i −0.172916 + 0.299500i
$$171$$ 0 0
$$172$$ −524.532 908.516i −0.232530 0.402754i
$$173$$ −921.885 + 1596.75i −0.405142 + 0.701727i −0.994338 0.106264i $$-0.966111\pi$$
0.589196 + 0.807990i $$0.299445\pi$$
$$174$$ 0 0
$$175$$ 289.939 313.503i 0.125242 0.135421i
$$176$$ −578.395 −0.247717
$$177$$ 0 0
$$178$$ 447.017 + 774.255i 0.188232 + 0.326028i
$$179$$ −530.785 919.346i −0.221635 0.383884i 0.733669 0.679507i $$-0.237806\pi$$
−0.955305 + 0.295623i $$0.904473\pi$$
$$180$$ 0 0
$$181$$ 2441.54 1.00264 0.501320 0.865262i $$-0.332848\pi$$
0.501320 + 0.865262i $$0.332848\pi$$
$$182$$ 145.197 + 32.8913i 0.0591358 + 0.0133960i
$$183$$ 0 0
$$184$$ −313.759 + 543.446i −0.125710 + 0.217736i
$$185$$ −1577.90 2732.99i −0.627077 1.08613i
$$186$$ 0 0
$$187$$ −686.128 + 1188.41i −0.268314 + 0.464733i
$$188$$ 551.685 0.214020
$$189$$ 0 0
$$190$$ −1151.68 −0.439746
$$191$$ −1846.08 + 3197.50i −0.699359 + 1.21132i 0.269331 + 0.963048i $$0.413198\pi$$
−0.968689 + 0.248277i $$0.920136\pi$$
$$192$$ 0 0
$$193$$ −1571.16 2721.33i −0.585982 1.01495i −0.994752 0.102313i $$-0.967376\pi$$
0.408770 0.912637i $$-0.365958\pi$$
$$194$$ −1803.99 + 3124.60i −0.667623 + 1.15636i
$$195$$ 0 0
$$196$$ 1238.06 + 591.255i 0.451189 + 0.215472i
$$197$$ −2273.51 −0.822236 −0.411118 0.911582i $$-0.634862\pi$$
−0.411118 + 0.911582i $$0.634862\pi$$
$$198$$ 0 0
$$199$$ 1368.26 + 2369.89i 0.487403 + 0.844206i 0.999895 0.0144854i $$-0.00461100\pi$$
−0.512492 + 0.858692i $$0.671278\pi$$
$$200$$ −92.2284 159.744i −0.0326076 0.0564781i
$$201$$ 0 0
$$202$$ 3368.54 1.17331
$$203$$ −1181.70 3808.92i −0.408566 1.31691i
$$204$$ 0 0
$$205$$ −941.803 + 1631.25i −0.320870 + 0.555763i
$$206$$ 1641.06 + 2842.41i 0.555041 + 0.961359i
$$207$$ 0 0
$$208$$ 32.1541 55.6926i 0.0107187 0.0185653i
$$209$$ −2061.71 −0.682352
$$210$$ 0 0
$$211$$ 2915.84 0.951349 0.475675 0.879621i $$-0.342204\pi$$
0.475675 + 0.879621i $$0.342204\pi$$
$$212$$ 1095.07 1896.72i 0.354763 0.614467i
$$213$$ 0 0
$$214$$ −321.094 556.151i −0.102568 0.177653i
$$215$$ −1324.01 + 2293.25i −0.419984 + 0.727434i
$$216$$ 0 0
$$217$$ 2292.75 2479.09i 0.717244 0.775536i
$$218$$ −1120.02 −0.347969
$$219$$ 0 0
$$220$$ 729.983 + 1264.37i 0.223707 + 0.387471i
$$221$$ −76.2865 132.132i −0.0232198 0.0402179i
$$222$$ 0 0
$$223$$ −1875.11 −0.563078 −0.281539 0.959550i $$-0.590845\pi$$
−0.281539 + 0.959550i $$0.590845\pi$$
$$224$$ 402.395 435.098i 0.120027 0.129782i
$$225$$ 0 0
$$226$$ −1870.65 + 3240.06i −0.550592 + 0.953654i
$$227$$ 2019.15 + 3497.27i 0.590377 + 1.02256i 0.994182 + 0.107717i $$0.0343542\pi$$
−0.403805 + 0.914845i $$0.632312\pi$$
$$228$$ 0 0
$$229$$ −686.456 + 1188.98i −0.198089 + 0.343099i −0.947909 0.318542i $$-0.896807\pi$$
0.749820 + 0.661642i $$0.230140\pi$$
$$230$$ 1583.96 0.454101
$$231$$ 0 0
$$232$$ −1722.66 −0.487492
$$233$$ 2087.15 3615.06i 0.586841 1.01644i −0.407802 0.913070i $$-0.633705\pi$$
0.994643 0.103368i $$-0.0329620\pi$$
$$234$$ 0 0
$$235$$ −696.273 1205.98i −0.193276 0.334764i
$$236$$ 7.46811 12.9351i 0.00205988 0.00356782i
$$237$$ 0 0
$$238$$ −416.637 1342.93i −0.113473 0.365753i
$$239$$ −5544.70 −1.50066 −0.750329 0.661065i $$-0.770105\pi$$
−0.750329 + 0.661065i $$0.770105\pi$$
$$240$$ 0 0
$$241$$ −2445.07 4234.98i −0.653530 1.13195i −0.982260 0.187524i $$-0.939954\pi$$
0.328730 0.944424i $$-0.393379\pi$$
$$242$$ −24.2023 41.9197i −0.00642887 0.0111351i
$$243$$ 0 0
$$244$$ −460.007 −0.120692
$$245$$ −270.060 3452.61i −0.0704224 0.900324i
$$246$$ 0 0
$$247$$ 114.615 198.519i 0.0295253 0.0511394i
$$248$$ −729.313 1263.21i −0.186740 0.323443i
$$249$$ 0 0
$$250$$ −1494.88 + 2589.22i −0.378179 + 0.655026i
$$251$$ 7560.15 1.90117 0.950583 0.310470i $$-0.100487\pi$$
0.950583 + 0.310470i $$0.100487\pi$$
$$252$$ 0 0
$$253$$ 2835.57 0.704627
$$254$$ 790.048 1368.40i 0.195165 0.338037i
$$255$$ 0 0
$$256$$ −128.000 221.703i −0.0312500 0.0541266i
$$257$$ 1616.43 2799.74i 0.392335 0.679545i −0.600422 0.799683i $$-0.705001\pi$$
0.992757 + 0.120139i $$0.0383340\pi$$
$$258$$ 0 0
$$259$$ 5645.60 + 1278.89i 1.35444 + 0.306821i
$$260$$ −162.325 −0.0387191
$$261$$ 0 0
$$262$$ −1638.08 2837.24i −0.386263 0.669028i
$$263$$ 2142.26 + 3710.51i 0.502272 + 0.869961i 0.999997 + 0.00262575i $$0.000835803\pi$$
−0.497724 + 0.867335i $$0.665831\pi$$
$$264$$ 0 0
$$265$$ −5528.28 −1.28151
$$266$$ 1434.35 1550.93i 0.330623 0.357494i
$$267$$ 0 0
$$268$$ −1255.60 + 2174.76i −0.286186 + 0.495689i
$$269$$ 3348.26 + 5799.36i 0.758912 + 1.31447i 0.943406 + 0.331640i $$0.107602\pi$$
−0.184495 + 0.982834i $$0.559065\pi$$
$$270$$ 0 0
$$271$$ 3157.89 5469.63i 0.707854 1.22604i −0.257798 0.966199i $$-0.582997\pi$$
0.965652 0.259840i $$-0.0836698\pi$$
$$272$$ −607.367 −0.135393
$$273$$ 0 0
$$274$$ 3978.64 0.877221
$$275$$ −416.753 + 721.837i −0.0913860 + 0.158285i
$$276$$ 0 0
$$277$$ −1377.62 2386.12i −0.298821 0.517573i 0.677045 0.735941i $$-0.263260\pi$$
−0.975866 + 0.218368i $$0.929927\pi$$
$$278$$ −655.628 + 1135.58i −0.141446 + 0.244991i
$$279$$ 0 0
$$280$$ −1458.98 330.501i −0.311395 0.0705401i
$$281$$ 1453.00 0.308464 0.154232 0.988035i $$-0.450710\pi$$
0.154232 + 0.988035i $$0.450710\pi$$
$$282$$ 0 0
$$283$$ −2715.92 4704.11i −0.570476 0.988093i −0.996517 0.0833890i $$-0.973426\pi$$
0.426042 0.904704i $$-0.359908\pi$$
$$284$$ −1066.21 1846.74i −0.222775 0.385858i
$$285$$ 0 0
$$286$$ −290.590 −0.0600803
$$287$$ −1023.78 3299.92i −0.210565 0.678704i
$$288$$ 0 0
$$289$$ 1736.00 3006.85i 0.353349 0.612018i
$$290$$ 2174.14 + 3765.73i 0.440242 + 0.762521i
$$291$$ 0 0
$$292$$ 596.788 1033.67i 0.119604 0.207160i
$$293$$ 6227.21 1.24163 0.620815 0.783957i $$-0.286802\pi$$
0.620815 + 0.783957i $$0.286802\pi$$
$$294$$ 0 0
$$295$$ −37.7015 −0.00744091
$$296$$ 1250.23 2165.46i 0.245500 0.425219i
$$297$$ 0 0
$$298$$ −2989.53 5178.02i −0.581138 1.00656i
$$299$$ −157.635 + 273.032i −0.0304892 + 0.0528088i
$$300$$ 0 0
$$301$$ −1439.26 4639.10i −0.275606 0.888350i
$$302$$ 2191.92 0.417651
$$303$$ 0 0
$$304$$ −456.261 790.268i −0.0860802 0.149095i
$$305$$ 580.567 + 1005.57i 0.108994 + 0.188783i
$$306$$ 0 0
$$307$$ 8621.61 1.60281 0.801403 0.598125i $$-0.204088\pi$$
0.801403 + 0.598125i $$0.204088\pi$$
$$308$$ −2611.83 591.655i −0.483191 0.109457i
$$309$$ 0 0
$$310$$ −1840.91 + 3188.55i −0.337280 + 0.584186i
$$311$$ 3712.11 + 6429.56i 0.676831 + 1.17230i 0.975930 + 0.218083i $$0.0699804\pi$$
−0.299100 + 0.954222i $$0.596686\pi$$
$$312$$ 0 0
$$313$$ −1633.30 + 2828.96i −0.294951 + 0.510870i −0.974974 0.222321i $$-0.928637\pi$$
0.680022 + 0.733191i $$0.261970\pi$$
$$314$$ −1002.05 −0.180092
$$315$$ 0 0
$$316$$ −3468.06 −0.617385
$$317$$ 2440.25 4226.63i 0.432359 0.748868i −0.564717 0.825285i $$-0.691015\pi$$
0.997076 + 0.0764167i $$0.0243479\pi$$
$$318$$ 0 0
$$319$$ 3892.10 + 6741.31i 0.683121 + 1.18320i
$$320$$ −323.094 + 559.615i −0.0564421 + 0.0977607i
$$321$$ 0 0
$$322$$ −1972.73 + 2133.06i −0.341416 + 0.369164i
$$323$$ −2164.98 −0.372950
$$324$$ 0 0
$$325$$ −46.3363 80.2568i −0.00790854 0.0136980i
$$326$$ 2268.41 + 3929.01i 0.385386 + 0.667508i
$$327$$ 0 0
$$328$$ −1492.46 −0.251241
$$329$$ 2491.22 + 564.333i 0.417463 + 0.0945675i
$$330$$ 0 0
$$331$$ 4799.58 8313.11i 0.797005 1.38045i −0.124554 0.992213i $$-0.539750\pi$$
0.921558 0.388240i $$-0.126917\pi$$
$$332$$ 488.449 + 846.018i 0.0807443 + 0.139853i
$$333$$ 0 0
$$334$$ −1369.97 + 2372.86i −0.224436 + 0.388734i
$$335$$ 6338.69 1.03379
$$336$$ 0 0
$$337$$ −2895.79 −0.468082 −0.234041 0.972227i $$-0.575195\pi$$
−0.234041 + 0.972227i $$0.575195\pi$$
$$338$$ −2180.85 + 3777.34i −0.350954 + 0.607870i
$$339$$ 0 0
$$340$$ 766.548 + 1327.70i 0.122270 + 0.211778i
$$341$$ −3295.55 + 5708.07i −0.523356 + 0.906478i
$$342$$ 0 0
$$343$$ 4985.85 + 3936.35i 0.784871 + 0.619659i
$$344$$ −2098.13 −0.328847
$$345$$ 0 0
$$346$$ 1843.77 + 3193.50i 0.286479 + 0.496196i
$$347$$ 2678.81 + 4639.83i 0.414426 + 0.717807i 0.995368 0.0961381i $$-0.0306490\pi$$
−0.580942 + 0.813945i $$0.697316\pi$$
$$348$$ 0 0
$$349$$ −6049.21 −0.927813 −0.463906 0.885884i $$-0.653553\pi$$
−0.463906 + 0.885884i $$0.653553\pi$$
$$350$$ −253.065 815.692i −0.0386482 0.124573i
$$351$$ 0 0
$$352$$ −578.395 + 1001.81i −0.0875811 + 0.151695i
$$353$$ 3440.28 + 5958.74i 0.518718 + 0.898446i 0.999763 + 0.0217505i $$0.00692394\pi$$
−0.481045 + 0.876696i $$0.659743\pi$$
$$354$$ 0 0
$$355$$ −2691.30 + 4661.47i −0.402365 + 0.696916i
$$356$$ 1788.07 0.266200
$$357$$ 0 0
$$358$$ −2123.14 −0.313440
$$359$$ 2995.95 5189.15i 0.440447 0.762876i −0.557276 0.830328i $$-0.688153\pi$$
0.997723 + 0.0674511i $$0.0214867\pi$$
$$360$$ 0 0
$$361$$ 1803.14 + 3123.13i 0.262886 + 0.455333i
$$362$$ 2441.54 4228.86i 0.354487 0.613989i
$$363$$ 0 0
$$364$$ 202.166 218.597i 0.0291110 0.0314769i
$$365$$ −3012.79 −0.432045
$$366$$ 0 0
$$367$$ 3285.52 + 5690.70i 0.467311 + 0.809406i 0.999302 0.0373437i $$-0.0118896\pi$$
−0.531992 + 0.846749i $$0.678556\pi$$
$$368$$ 627.518 + 1086.89i 0.0888903 + 0.153962i
$$369$$ 0 0
$$370$$ −6311.58 −0.886820
$$371$$ 6885.16 7444.74i 0.963503 1.04181i
$$372$$ 0 0
$$373$$ 1866.81 3233.41i 0.259141 0.448846i −0.706871 0.707343i $$-0.749894\pi$$
0.966012 + 0.258497i $$0.0832272\pi$$
$$374$$ 1372.26 + 2376.82i 0.189726 + 0.328616i
$$375$$ 0 0
$$376$$ 551.685 955.546i 0.0756675 0.131060i
$$377$$ −865.479 −0.118235
$$378$$ 0 0
$$379$$ 8419.14 1.14106 0.570531 0.821276i $$-0.306738\pi$$
0.570531 + 0.821276i $$0.306738\pi$$
$$380$$ −1151.68 + 1994.77i −0.155474 + 0.269288i
$$381$$ 0 0
$$382$$ 3692.15 + 6395.00i 0.494521 + 0.856536i
$$383$$ −2665.21 + 4616.28i −0.355577 + 0.615877i −0.987217 0.159385i $$-0.949049\pi$$
0.631640 + 0.775262i $$0.282382\pi$$
$$384$$ 0 0
$$385$$ 2002.99 + 6456.16i 0.265148 + 0.854640i
$$386$$ −6284.64 −0.828704
$$387$$ 0 0
$$388$$ 3607.98 + 6249.21i 0.472081 + 0.817668i
$$389$$ −3905.58 6764.67i −0.509051 0.881703i −0.999945 0.0104832i $$-0.996663\pi$$
0.490894 0.871219i $$-0.336670\pi$$
$$390$$ 0 0
$$391$$ 2977.60 0.385125
$$392$$ 2262.15 1553.13i 0.291469 0.200115i
$$393$$ 0 0
$$394$$ −2273.51 + 3937.83i −0.290704 + 0.503515i
$$395$$ 4376.99 + 7581.16i 0.557544 + 0.965695i
$$396$$ 0 0
$$397$$ −455.847 + 789.550i −0.0576279 + 0.0998145i −0.893400 0.449262i $$-0.851687\pi$$
0.835772 + 0.549076i $$0.185020\pi$$
$$398$$ 5473.03 0.689292
$$399$$ 0 0
$$400$$ −368.913 −0.0461142
$$401$$ −834.008 + 1444.54i −0.103861 + 0.179893i −0.913272 0.407349i $$-0.866453\pi$$
0.809411 + 0.587242i $$0.199786\pi$$
$$402$$ 0 0
$$403$$ −366.413 634.646i −0.0452912 0.0784466i
$$404$$ 3368.54 5834.48i 0.414829 0.718505i
$$405$$ 0 0
$$406$$ −7778.93 1762.15i −0.950892 0.215405i
$$407$$ −11298.8 −1.37608
$$408$$ 0 0
$$409$$ −4555.24 7889.90i −0.550714 0.953864i −0.998223 0.0595852i $$-0.981022\pi$$
0.447509 0.894279i $$-0.352311\pi$$
$$410$$ 1883.61 + 3262.50i 0.226889 + 0.392984i
$$411$$ 0 0
$$412$$ 6564.26 0.784946
$$413$$ 46.9551 50.7713i 0.00559445 0.00604913i
$$414$$ 0 0
$$415$$ 1232.93 2135.49i 0.145836 0.252596i
$$416$$ −64.3083 111.385i −0.00757926 0.0131277i
$$417$$ 0 0
$$418$$ −2061.71 + 3570.99i −0.241248 + 0.417853i
$$419$$ 12626.4 1.47217 0.736085 0.676889i $$-0.236672\pi$$
0.736085 + 0.676889i $$0.236672\pi$$
$$420$$ 0 0
$$421$$ −4805.61 −0.556320 −0.278160 0.960535i $$-0.589725\pi$$
−0.278160 + 0.960535i $$0.589725\pi$$
$$422$$ 2915.84 5050.38i 0.336353 0.582580i
$$423$$ 0 0
$$424$$ −2190.14 3793.43i −0.250855 0.434494i
$$425$$ −437.628 + 757.994i −0.0499484 + 0.0865132i
$$426$$ 0 0
$$427$$ −2077.23 470.553i −0.235420 0.0533294i
$$428$$ −1284.38 −0.145053
$$429$$ 0 0
$$430$$ 2648.02 + 4586.50i 0.296974 + 0.514374i
$$431$$ −3341.06 5786.89i −0.373395 0.646739i 0.616690 0.787206i $$-0.288473\pi$$
−0.990085 + 0.140467i $$0.955140\pi$$
$$432$$ 0 0
$$433$$ −8502.27 −0.943632 −0.471816 0.881697i $$-0.656401\pi$$
−0.471816 + 0.881697i $$0.656401\pi$$
$$434$$ −2001.16 6450.24i −0.221333 0.713414i
$$435$$ 0 0
$$436$$ −1120.02 + 1939.93i −0.123026 + 0.213087i
$$437$$ 2236.81 + 3874.27i 0.244854 + 0.424100i
$$438$$ 0 0
$$439$$ 6814.77 11803.5i 0.740891 1.28326i −0.211199 0.977443i $$-0.567737\pi$$
0.952090 0.305818i $$-0.0989299\pi$$
$$440$$ 2919.93 0.316369
$$441$$ 0 0
$$442$$ −305.146 −0.0328378
$$443$$ 3427.16 5936.02i 0.367561 0.636634i −0.621623 0.783317i $$-0.713526\pi$$
0.989184 + 0.146683i $$0.0468597\pi$$
$$444$$ 0 0
$$445$$ −2256.69 3908.70i −0.240399 0.416383i
$$446$$ −1875.11 + 3247.78i −0.199078 + 0.344813i
$$447$$ 0 0
$$448$$ −351.218 1132.07i −0.0370391 0.119386i
$$449$$ −10372.3 −1.09019 −0.545097 0.838373i $$-0.683507\pi$$
−0.545097 + 0.838373i $$0.683507\pi$$
$$450$$ 0 0
$$451$$ 3371.98 + 5840.45i 0.352063 + 0.609791i
$$452$$ 3741.30 + 6480.13i 0.389328 + 0.674335i
$$453$$ 0 0
$$454$$ 8076.59 0.834919
$$455$$ −733.003 166.047i −0.0755247 0.0171085i
$$456$$ 0 0
$$457$$ 3950.40 6842.30i 0.404359 0.700370i −0.589888 0.807485i $$-0.700828\pi$$
0.994247 + 0.107115i $$0.0341613\pi$$
$$458$$ 1372.91 + 2377.95i 0.140070 + 0.242608i
$$459$$ 0 0
$$460$$ 1583.96 2743.50i 0.160549 0.278079i
$$461$$ −11359.7 −1.14767 −0.573834 0.818972i $$-0.694544\pi$$
−0.573834 + 0.818972i $$0.694544\pi$$
$$462$$ 0 0
$$463$$ 7346.85 0.737445 0.368723 0.929539i $$-0.379795\pi$$
0.368723 + 0.929539i $$0.379795\pi$$
$$464$$ −1722.66 + 2983.73i −0.172354 + 0.298527i
$$465$$ 0 0
$$466$$ −4174.31 7230.11i −0.414959 0.718731i
$$467$$ −473.289 + 819.760i −0.0468976 + 0.0812291i −0.888521 0.458835i $$-0.848267\pi$$
0.841624 + 0.540064i $$0.181600\pi$$
$$468$$ 0 0
$$469$$ −7894.47 + 8536.08i −0.777256 + 0.840426i
$$470$$ −2785.09 −0.273333
$$471$$ 0 0
$$472$$ −14.9362 25.8703i −0.00145656 0.00252283i
$$473$$ 4740.41 + 8210.64i 0.460813 + 0.798151i
$$474$$ 0 0
$$475$$ −1315.01 −0.127025
$$476$$ −2742.66 621.292i −0.264096 0.0598253i
$$477$$ 0 0
$$478$$ −5544.70 + 9603.71i −0.530562 + 0.918961i
$$479$$ −7657.75 13263.6i −0.730462 1.26520i −0.956686 0.291122i $$-0.905971\pi$$
0.226224 0.974075i $$-0.427362\pi$$
$$480$$ 0 0
$$481$$ 628.125 1087.95i 0.0595427 0.103131i
$$482$$ −9780.28 −0.924231
$$483$$ 0 0
$$484$$ −96.8094 −0.00909179
$$485$$ 9107.15 15774.1i 0.852649 1.47683i
$$486$$ 0 0
$$487$$ 4320.19 + 7482.78i 0.401984 + 0.696257i 0.993965 0.109695i $$-0.0349873\pi$$
−0.591981 + 0.805952i $$0.701654\pi$$
$$488$$ −460.007 + 796.755i −0.0426711 + 0.0739086i
$$489$$ 0 0
$$490$$ −6250.16 2984.86i −0.576232 0.275188i
$$491$$ −13425.6 −1.23399 −0.616996 0.786966i $$-0.711651\pi$$
−0.616996 + 0.786966i $$0.711651\pi$$
$$492$$ 0 0
$$493$$ 4087.05 + 7078.99i 0.373371 + 0.646697i
$$494$$ −229.229 397.037i −0.0208776 0.0361610i
$$495$$ 0 0
$$496$$ −2917.25 −0.264090
$$497$$ −2925.57 9429.88i −0.264044 0.851082i
$$498$$ 0 0
$$499$$ 5489.01 9507.24i 0.492429 0.852911i −0.507533 0.861632i $$-0.669443\pi$$
0.999962 + 0.00872085i $$0.00277597\pi$$
$$500$$ 2989.77 + 5178.43i 0.267413 + 0.463173i
$$501$$ 0 0
$$502$$ 7560.15 13094.6i 0.672164 1.16422i
$$503$$ −7829.41 −0.694028 −0.347014 0.937860i $$-0.612804\pi$$
−0.347014 + 0.937860i $$0.612804\pi$$
$$504$$ 0 0
$$505$$ −17005.5 −1.49849
$$506$$ 2835.57 4911.35i 0.249123 0.431494i
$$507$$ 0 0
$$508$$ −1580.10 2736.81i −0.138003 0.239028i
$$509$$ −9091.90 + 15747.6i −0.791732 + 1.37132i 0.133162 + 0.991094i $$0.457487\pi$$
−0.924894 + 0.380225i $$0.875847\pi$$
$$510$$ 0 0
$$511$$ 3752.25 4057.21i 0.324833 0.351234i
$$512$$ −512.000 −0.0441942
$$513$$ 0 0
$$514$$ −3232.86 5599.48i −0.277423 0.480511i
$$515$$ −8284.65 14349.4i −0.708865 1.22779i
$$516$$ 0 0
$$517$$ −4985.80 −0.424130
$$518$$ 7860.71 8499.57i 0.666756 0.720946i
$$519$$ 0 0
$$520$$ −162.325 + 281.155i −0.0136893 + 0.0237105i
$$521$$ 11202.3 + 19402.9i 0.941997 + 1.63159i 0.761656 + 0.647982i $$0.224387\pi$$
0.180341 + 0.983604i $$0.442280\pi$$
$$522$$ 0 0
$$523$$ −2843.67 + 4925.38i −0.237753 + 0.411801i −0.960069 0.279763i $$-0.909744\pi$$
0.722316 + 0.691563i $$0.243078\pi$$
$$524$$ −6552.33 −0.546259
$$525$$ 0 0
$$526$$ 8569.05 0.710320
$$527$$ −3460.63 + 5993.99i −0.286048 + 0.495450i
$$528$$ 0 0
$$529$$ 3007.11 + 5208.46i 0.247153 + 0.428081i
$$530$$ −5528.28 + 9575.27i −0.453082 + 0.784761i
$$531$$ 0 0
$$532$$ −1251.93 4035.30i −0.102027 0.328858i
$$533$$ −749.822 −0.0609351
$$534$$ 0 0
$$535$$ 1620.99 + 2807.64i 0.130994 + 0.226888i
$$536$$ 2511.20 + 4349.52i 0.202364 + 0.350505i
$$537$$ 0 0
$$538$$ 13393.1 1.07326
$$539$$ −11188.9 5343.42i −0.894137 0.427008i
$$540$$ 0 0
$$541$$ 6508.78 11273.5i 0.517254 0.895910i −0.482545 0.875871i $$-0.660288\pi$$
0.999799 0.0200392i $$-0.00637910\pi$$
$$542$$ −6315.79 10939.3i −0.500528 0.866940i
$$543$$ 0 0
$$544$$ −607.367 + 1051.99i −0.0478688 + 0.0829112i
$$545$$ 5654.23 0.444405
$$546$$ 0 0
$$547$$ −6353.31 −0.496614 −0.248307 0.968681i $$-0.579874\pi$$
−0.248307 + 0.968681i $$0.579874\pi$$
$$548$$ 3978.64 6891.21i 0.310144 0.537186i
$$549$$ 0 0
$$550$$ 833.506 + 1443.67i 0.0646197 + 0.111925i
$$551$$ −6140.49 + 10635.6i −0.474762 + 0.822311i
$$552$$ 0 0
$$553$$ −15660.6 3547.57i −1.20426 0.272799i
$$554$$ −5510.50 −0.422597
$$555$$ 0 0
$$556$$ 1311.26 + 2271.16i 0.100017 + 0.173235i
$$557$$ −7759.69 13440.2i −0.590285 1.02240i −0.994194 0.107604i $$-0.965682\pi$$
0.403909 0.914799i $$-0.367651\pi$$
$$558$$ 0 0
$$559$$ −1054.12 −0.0797574
$$560$$ −2031.42 + 2196.52i −0.153292 + 0.165750i
$$561$$ 0 0
$$562$$ 1453.00 2516.66i 0.109059 0.188895i
$$563$$ −9095.49 15753.9i −0.680869 1.17930i −0.974716 0.223448i $$-0.928269\pi$$
0.293847 0.955853i $$-0.405064\pi$$
$$564$$ 0 0
$$565$$ 9443.68 16356.9i 0.703184 1.21795i
$$566$$ −10863.7 −0.806774
$$567$$ 0 0
$$568$$ −4264.85 −0.315052
$$569$$ 6159.38 10668.4i 0.453804 0.786012i −0.544814 0.838557i $$-0.683400\pi$$
0.998619 + 0.0525449i $$0.0167333\pi$$
$$570$$ 0 0
$$571$$ 8694.98 + 15060.2i 0.637257 + 1.10376i 0.986032 + 0.166555i $$0.0532644\pi$$
−0.348775 + 0.937206i $$0.613402\pi$$
$$572$$ −290.590 + 503.317i −0.0212416 + 0.0367915i
$$573$$ 0 0
$$574$$ −6739.41 1526.67i −0.490065 0.111014i
$$575$$ 1808.59 0.131171
$$576$$ 0 0
$$577$$ −1625.45 2815.37i −0.117276 0.203129i 0.801411 0.598114i $$-0.204083\pi$$
−0.918687 + 0.394985i $$0.870750\pi$$
$$578$$ −3472.01 6013.69i −0.249855 0.432762i
$$579$$ 0 0
$$580$$ 8696.57 0.622596
$$581$$ 1340.25 + 4319.97i 0.0957022 + 0.308473i
$$582$$ 0 0
$$583$$ −9896.60 + 17141.4i −0.703045 + 1.21771i
$$584$$ −1193.58 2067.33i −0.0845728 0.146484i
$$585$$ 0 0
$$586$$ 6227.21 10785.8i 0.438982 0.760339i
$$587$$ 6993.54 0.491745 0.245872 0.969302i $$-0.420926\pi$$
0.245872 + 0.969302i $$0.420926\pi$$
$$588$$ 0 0
$$589$$ −10398.7 −0.727453
$$590$$ −37.7015 + 65.3010i −0.00263076 + 0.00455661i
$$591$$ 0 0
$$592$$ −2500.46 4330.92i −0.173595 0.300675i
$$593$$ 5001.10 8662.15i 0.346324 0.599851i −0.639269 0.768983i $$-0.720763\pi$$
0.985593 + 0.169132i $$0.0540963\pi$$
$$594$$ 0 0
$$595$$ 2103.32 + 6779.56i 0.144921 + 0.467117i
$$596$$ −11958.1 −0.821853
$$597$$ 0 0
$$598$$ 315.270 + 546.064i 0.0215591 + 0.0373415i
$$599$$ 12362.1 + 21411.8i 0.843241 + 1.46054i 0.887140 + 0.461500i $$0.152688\pi$$
−0.0438997 + 0.999036i $$0.513978\pi$$
$$600$$ 0 0
$$601$$ −4825.50 −0.327515 −0.163757 0.986501i $$-0.552361\pi$$
−0.163757 + 0.986501i $$0.552361\pi$$
$$602$$ −9474.42 2146.23i −0.641443 0.145305i
$$603$$ 0 0
$$604$$ 2191.92 3796.51i 0.147662 0.255758i
$$605$$ 122.182 + 211.625i 0.00821056 + 0.0142211i
$$606$$ 0 0
$$607$$ −12365.1 + 21417.0i −0.826826 + 1.43210i 0.0736896 + 0.997281i $$0.476523\pi$$
−0.900516 + 0.434824i $$0.856811\pi$$
$$608$$ −1825.04 −0.121736
$$609$$ 0 0
$$610$$ 2322.27 0.154141
$$611$$ 277.171 480.074i 0.0183521 0.0317868i
$$612$$ 0 0
$$613$$ 3804.29 + 6589.22i 0.250659 + 0.434154i 0.963707 0.266961i $$-0.0860195\pi$$
−0.713049 + 0.701115i $$0.752686\pi$$
$$614$$ 8621.61 14933.1i 0.566677 0.981514i
$$615$$ 0 0
$$616$$ −3636.61 + 3932.16i −0.237862 + 0.257194i
$$617$$ −25089.8 −1.63708 −0.818538 0.574452i $$-0.805215\pi$$
−0.818538 + 0.574452i $$0.805215\pi$$
$$618$$ 0 0
$$619$$ −11452.5 19836.3i −0.743642 1.28803i −0.950827 0.309724i $$-0.899763\pi$$
0.207185 0.978302i $$-0.433570\pi$$
$$620$$ 3681.82 + 6377.10i 0.238493 + 0.413082i
$$621$$ 0 0
$$622$$ 14848.4 0.957183
$$623$$ 8074.29 + 1829.06i 0.519245 + 0.117624i
$$624$$ 0 0
$$625$$ 6105.62 10575.2i 0.390760 0.676815i
$$626$$ 3266.61 + 5657.93i 0.208562 + 0.361240i
$$627$$ 0 0
$$628$$ −1002.05 + 1735.60i −0.0636723 + 0.110284i
$$629$$ −11864.8 −0.752116
$$630$$ 0 0
$$631$$ 2253.93 0.142199 0.0710996 0.997469i $$-0.477349\pi$$
0.0710996 + 0.997469i $$0.477349\pi$$
$$632$$ −3468.06 + 6006.86i −0.218279 + 0.378070i
$$633$$ 0 0
$$634$$ −4880.49 8453.26i −0.305724 0.529530i
$$635$$ −3988.43 + 6908.17i −0.249254 + 0.431720i
$$636$$ 0 0
$$637$$ 1136.52 780.307i 0.0706917 0.0485352i
$$638$$ 15568.4 0.966079
$$639$$ 0 0
$$640$$ 646.187 + 1119.23i 0.0399106 + 0.0691272i
$$641$$ 6014.77 + 10417.9i 0.370623 + 0.641938i 0.989661 0.143423i $$-0.0458109\pi$$
−0.619039 + 0.785361i $$0.712478\pi$$
$$642$$ 0 0
$$643$$ −4738.59 −0.290625 −0.145312 0.989386i $$-0.546419\pi$$
−0.145312 + 0.989386i $$0.546419\pi$$
$$644$$ 1721.84 + 5549.93i 0.105357 + 0.339593i
$$645$$ 0 0
$$646$$ −2164.98 + 3749.86i −0.131858 + 0.228384i
$$647$$ −2869.84 4970.71i −0.174382 0.302038i 0.765565 0.643358i $$-0.222459\pi$$
−0.939947 + 0.341320i $$0.889126\pi$$
$$648$$ 0 0
$$649$$ −67.4924 + 116.900i −0.00408214 + 0.00707047i
$$650$$ −185.345 −0.0111844
$$651$$ 0 0
$$652$$ 9073.65 0.545018
$$653$$ −863.084 + 1494.91i −0.0517230 + 0.0895868i −0.890728 0.454537i $$-0.849805\pi$$
0.839005 + 0.544124i $$0.183138\pi$$
$$654$$ 0 0
$$655$$ 8269.59 + 14323.4i 0.493313 + 0.854442i
$$656$$ −1492.46 + 2585.01i −0.0888271 + 0.153853i
$$657$$ 0 0
$$658$$ 3468.67 3750.58i 0.205506 0.222208i
$$659$$ −10987.7 −0.649501 −0.324751 0.945800i $$-0.605280\pi$$
−0.324751 + 0.945800i $$0.605280\pi$$
$$660$$ 0 0
$$661$$ −16020.4 27748.1i −0.942695 1.63280i −0.760302 0.649570i $$-0.774949\pi$$
−0.182393 0.983226i $$-0.558384\pi$$
$$662$$ −9599.15 16626.2i −0.563567 0.976127i
$$663$$ 0 0
$$664$$ 1953.80 0.114190
$$665$$ −7241.09 + 7829.60i −0.422252 + 0.456570i
$$666$$ 0 0
$$667$$ 8445.31 14627.7i 0.490260 0.849156i
$$668$$ 2739.94 + 4745.72i 0.158700 + 0.274876i
$$669$$ 0 0
$$670$$ 6338.69 10978.9i 0.365500 0.633065i
$$671$$ 4157.27 0.239180
$$672$$ 0 0
$$673$$ −13026.7 −0.746124 −0.373062 0.927806i $$-0.621692\pi$$
−0.373062 + 0.927806i $$0.621692\pi$$
$$674$$ −2895.79 + 5015.65i −0.165492 + 0.286641i
$$675$$ 0 0
$$676$$ 4361.69 + 7554.67i 0.248162 + 0.429829i
$$677$$ 2360.39 4088.32i 0.133999 0.232093i −0.791216 0.611537i $$-0.790551\pi$$
0.925215 + 0.379444i $$0.123885\pi$$
$$678$$ 0 0
$$679$$ 9899.91 + 31909.9i 0.559534 + 1.80352i
$$680$$ 3066.19 0.172916
$$681$$ 0 0
$$682$$ 6591.11 + 11416.1i 0.370068 + 0.640977i
$$683$$ 5585.00 + 9673.51i 0.312890 + 0.541942i 0.978987 0.203924i $$-0.0653694\pi$$
−0.666096 + 0.745866i $$0.732036\pi$$
$$684$$ 0 0
$$685$$ −20085.5 −1.12033
$$686$$ 11803.8 4699.40i 0.656956 0.261551i
$$687$$ 0 0
$$688$$ −2098.13 + 3634.07i −0.116265 + 0.201377i
$$689$$ −1100.34 1905.85i −0.0608415 0.105381i
$$690$$ 0 0
$$691$$ 6986.42 12100.8i 0.384625 0.666190i −0.607092 0.794632i $$-0.707664\pi$$
0.991717 + 0.128441i $$0.0409974\pi$$
$$692$$ 7375.08 0.405142
$$693$$ 0 0
$$694$$ 10715.2 0.586087
$$695$$ 3309.83 5732.79i 0.180646 0.312888i
$$696$$ 0 0
$$697$$ 3540.89 + 6133.00i 0.192426 + 0.333291i
$$698$$ −6049.21 + 10477.5i −0.328031 + 0.568167i
$$699$$ 0 0
$$700$$ −1665.88 377.371i −0.0899493 0.0203761i
$$701$$ 9694.83 0.522352 0.261176 0.965291i $$-0.415890\pi$$
0.261176 + 0.965291i $$0.415890\pi$$
$$702$$ 0 0
$$703$$ −8912.99 15437.7i −0.478179 0.828230i
$$704$$ 1156.79 + 2003.62i 0.0619292 + 0.107264i
$$705$$ 0 0
$$706$$ 13761.1 0.733578
$$707$$ 21179.4 22900.7i 1.12664 1.21820i
$$708$$ 0 0
$$709$$ −12712.8 + 22019.3i −0.673399 + 1.16636i 0.303535 + 0.952820i $$0.401833\pi$$
−0.976934 + 0.213541i $$0.931500\pi$$
$$710$$ 5382.61 + 9322.95i 0.284515 + 0.492794i
$$711$$ 0 0
$$712$$ 1788.07 3097.02i 0.0941160 0.163014i
$$713$$ 14301.8 0.751200
$$714$$ 0 0
$$715$$ 1467.00 0.0767309
$$716$$ −2123.14 + 3677.39i −0.110818 + 0.191942i
$$717$$ 0 0
$$718$$ −5991.91 10378.3i −0.311443 0.539435i
$$719$$ 8796.40 15235.8i 0.456259 0.790264i −0.542500 0.840056i $$-0.682522\pi$$
0.998760 + 0.0497912i $$0.0158556\pi$$
$$720$$ 0 0
$$721$$ 29641.9 + 6714.76i 1.53110 + 0.346839i
$$722$$ 7212.55 0.371778
$$723$$ 0 0
$$724$$ −4883.07 8457.73i −0.250660 0.434156i
$$725$$ 2482.47 + 4299.76i 0.127168 + 0.220261i
$$726$$ 0 0
$$727$$ −10087.1 −0.514596 −0.257298 0.966332i $$-0.582832\pi$$
−0.257298 + 0.966332i $$0.582832\pi$$
$$728$$ −176.455 568.759i −0.00898332 0.0289555i
$$729$$ 0 0
$$730$$ −3012.79 + 5218.30i −0.152751 + 0.264572i
$$731$$ 4977.86 + 8621.91i 0.251865 + 0.436242i
$$732$$ 0 0
$$733$$ −15904.3 + 27547.1i −0.801417 + 1.38810i 0.117266 + 0.993101i $$0.462587\pi$$
−0.918683 + 0.394995i $$0.870746\pi$$
$$734$$ 13142.1 0.660877
$$735$$ 0 0
$$736$$ 2510.07 0.125710
$$737$$ 11347.4 19654.2i 0.567145 0.982324i
$$738$$ 0 0
$$739$$ 8287.63 + 14354.6i 0.412538 + 0.714536i 0.995166 0.0982021i $$-0.0313092\pi$$
−0.582629 + 0.812738i $$0.697976\pi$$
$$740$$ −6311.58 + 10932.0i −0.313538 + 0.543064i
$$741$$ 0 0
$$742$$ −6009.51 19370.2i −0.297326 0.958358i
$$743$$ 11053.4 0.545773 0.272886 0.962046i $$-0.412022\pi$$
0.272886 + 0.962046i $$0.412022\pi$$
$$744$$ 0 0
$$745$$ 15092.2 + 26140.4i 0.742194 + 1.28552i
$$746$$ −3733.61 6466.81i −0.183240 0.317382i
$$747$$ 0 0
$$748$$ 5489.02 0.268314
$$749$$ −5799.80 1313.82i −0.282937 0.0640935i
$$750$$ 0 0
$$751$$ −1589.84 + 2753.68i −0.0772490 + 0.133799i −0.902062 0.431606i $$-0.857947\pi$$
0.824813 + 0.565405i $$0.191280\pi$$
$$752$$ −1103.37 1911.09i −0.0535050 0.0926733i
$$753$$ 0 0
$$754$$ −865.479 + 1499.05i −0.0418022 + 0.0724036i
$$755$$ −11065.5 −0.533399
$$756$$ 0 0
$$757$$ −31130.8 −1.49467 −0.747336 0.664446i $$-0.768667\pi$$
−0.747336 + 0.664446i $$0.768667\pi$$
$$758$$ 8419.14 14582.4i 0.403426 0.698755i
$$759$$ 0 0
$$760$$ 2303.36 + 3989.54i 0.109936 + 0.190416i
$$761$$ 3915.15 6781.24i 0.186497 0.323022i −0.757583 0.652739i $$-0.773620\pi$$
0.944080 + 0.329717i $$0.106953\pi$$
$$762$$ 0 0
$$763$$ −7042.02 + 7614.35i −0.334126 + 0.361282i
$$764$$ 14768.6 0.699359
$$765$$ 0 0
$$766$$ 5330.42 + 9232.56i 0.251431 + 0.435491i
$$767$$ −7.50408 12.9974i −0.000353268 0.000611878i
$$768$$ 0 0
$$769$$ 9389.21 0.440291 0.220145 0.975467i $$-0.429347\pi$$
0.220145 + 0.975467i $$0.429347\pi$$
$$770$$ 13185.4 + 2986.88i 0.617102 + 0.139792i
$$771$$ 0 0
$$772$$ −6284.64 + 10885.3i −0.292991 + 0.507475i
$$773$$ 13896.1 + 24068.8i 0.646584 + 1.11992i 0.983933 + 0.178537i $$0.0571363\pi$$
−0.337349 + 0.941380i $$0.609530\pi$$
$$774$$ 0 0
$$775$$ −2101.98 + 3640.74i −0.0974263 + 0.168747i
$$776$$ 14431.9 0.667623
$$777$$ 0 0
$$778$$ −15622.3 −0.719907
$$779$$ −5319.92 + 9214.37i −0.244680 + 0.423798i
$$780$$ 0 0
$$781$$ 9635.81 + 16689.7i 0.441481 + 0.764667i
$$782$$ 2977.60 5157.36i 0.136162 0.235840i
$$783$$ 0 0
$$784$$ −427.958 5471.29i −0.0194952 0.249239i