Properties

 Label 75.3.d.b.74.3 Level $75$ Weight $3$ Character 75.74 Analytic conductor $2.044$ Analytic rank $0$ Dimension $4$ CM no Inner twists $4$

Related objects

Newspace parameters

 Level: $$N$$ $$=$$ $$75 = 3 \cdot 5^{2}$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 75.d (of order $$2$$, degree $$1$$, not minimal)

Newform invariants

 Self dual: no Analytic conductor: $$2.04360198270$$ Analytic rank: $$0$$ Dimension: $$4$$ Coefficient field: $$\Q(i, \sqrt{5})$$ Defining polynomial: $$x^{4} + 3 x^{2} + 1$$ Coefficient ring: $$\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$2^{4}$$ Twist minimal: no (minimal twist has level 15) Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

 Embedding label 74.3 Root $$1.61803i$$ of defining polynomial Character $$\chi$$ $$=$$ 75.74 Dual form 75.3.d.b.74.4

$q$-expansion

 $$f(q)$$ $$=$$ $$q+2.23607 q^{2} +(2.23607 - 2.00000i) q^{3} +1.00000 q^{4} +(5.00000 - 4.47214i) q^{6} +6.00000i q^{7} -6.70820 q^{8} +(1.00000 - 8.94427i) q^{9} +O(q^{10})$$ $$q+2.23607 q^{2} +(2.23607 - 2.00000i) q^{3} +1.00000 q^{4} +(5.00000 - 4.47214i) q^{6} +6.00000i q^{7} -6.70820 q^{8} +(1.00000 - 8.94427i) q^{9} -4.47214i q^{11} +(2.23607 - 2.00000i) q^{12} +16.0000i q^{13} +13.4164i q^{14} -19.0000 q^{16} -4.47214 q^{17} +(2.23607 - 20.0000i) q^{18} +2.00000 q^{19} +(12.0000 + 13.4164i) q^{21} -10.0000i q^{22} +13.4164 q^{23} +(-15.0000 + 13.4164i) q^{24} +35.7771i q^{26} +(-15.6525 - 22.0000i) q^{27} +6.00000i q^{28} -31.3050i q^{29} -18.0000 q^{31} -15.6525 q^{32} +(-8.94427 - 10.0000i) q^{33} -10.0000 q^{34} +(1.00000 - 8.94427i) q^{36} +16.0000i q^{37} +4.47214 q^{38} +(32.0000 + 35.7771i) q^{39} -62.6099i q^{41} +(26.8328 + 30.0000i) q^{42} +16.0000i q^{43} -4.47214i q^{44} +30.0000 q^{46} +49.1935 q^{47} +(-42.4853 + 38.0000i) q^{48} +13.0000 q^{49} +(-10.0000 + 8.94427i) q^{51} +16.0000i q^{52} +4.47214 q^{53} +(-35.0000 - 49.1935i) q^{54} -40.2492i q^{56} +(4.47214 - 4.00000i) q^{57} -70.0000i q^{58} +4.47214i q^{59} +82.0000 q^{61} -40.2492 q^{62} +(53.6656 + 6.00000i) q^{63} +41.0000 q^{64} +(-20.0000 - 22.3607i) q^{66} -24.0000i q^{67} -4.47214 q^{68} +(30.0000 - 26.8328i) q^{69} +125.220i q^{71} +(-6.70820 + 60.0000i) q^{72} -74.0000i q^{73} +35.7771i q^{74} +2.00000 q^{76} +26.8328 q^{77} +(71.5542 + 80.0000i) q^{78} -138.000 q^{79} +(-79.0000 - 17.8885i) q^{81} -140.000i q^{82} -93.9149 q^{83} +(12.0000 + 13.4164i) q^{84} +35.7771i q^{86} +(-62.6099 - 70.0000i) q^{87} +30.0000i q^{88} +107.331i q^{89} -96.0000 q^{91} +13.4164 q^{92} +(-40.2492 + 36.0000i) q^{93} +110.000 q^{94} +(-35.0000 + 31.3050i) q^{96} +166.000i q^{97} +29.0689 q^{98} +(-40.0000 - 4.47214i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4q + 4q^{4} + 20q^{6} + 4q^{9} + O(q^{10})$$ $$4q + 4q^{4} + 20q^{6} + 4q^{9} - 76q^{16} + 8q^{19} + 48q^{21} - 60q^{24} - 72q^{31} - 40q^{34} + 4q^{36} + 128q^{39} + 120q^{46} + 52q^{49} - 40q^{51} - 140q^{54} + 328q^{61} + 164q^{64} - 80q^{66} + 120q^{69} + 8q^{76} - 552q^{79} - 316q^{81} + 48q^{84} - 384q^{91} + 440q^{94} - 140q^{96} - 160q^{99} + O(q^{100})$$

Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/75\mathbb{Z}\right)^\times$$.

 $$n$$ $$26$$ $$52$$ $$\chi(n)$$ $$-1$$ $$-1$$

Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 2.23607 1.11803 0.559017 0.829156i $$-0.311179\pi$$
0.559017 + 0.829156i $$0.311179\pi$$
$$3$$ 2.23607 2.00000i 0.745356 0.666667i
$$4$$ 1.00000 0.250000
$$5$$ 0 0
$$6$$ 5.00000 4.47214i 0.833333 0.745356i
$$7$$ 6.00000i 0.857143i 0.903508 + 0.428571i $$0.140983\pi$$
−0.903508 + 0.428571i $$0.859017\pi$$
$$8$$ −6.70820 −0.838525
$$9$$ 1.00000 8.94427i 0.111111 0.993808i
$$10$$ 0 0
$$11$$ 4.47214i 0.406558i −0.979121 0.203279i $$-0.934840\pi$$
0.979121 0.203279i $$-0.0651598\pi$$
$$12$$ 2.23607 2.00000i 0.186339 0.166667i
$$13$$ 16.0000i 1.23077i 0.788227 + 0.615385i $$0.210999\pi$$
−0.788227 + 0.615385i $$0.789001\pi$$
$$14$$ 13.4164i 0.958315i
$$15$$ 0 0
$$16$$ −19.0000 −1.18750
$$17$$ −4.47214 −0.263067 −0.131533 0.991312i $$-0.541990\pi$$
−0.131533 + 0.991312i $$0.541990\pi$$
$$18$$ 2.23607 20.0000i 0.124226 1.11111i
$$19$$ 2.00000 0.105263 0.0526316 0.998614i $$-0.483239\pi$$
0.0526316 + 0.998614i $$0.483239\pi$$
$$20$$ 0 0
$$21$$ 12.0000 + 13.4164i 0.571429 + 0.638877i
$$22$$ 10.0000i 0.454545i
$$23$$ 13.4164 0.583322 0.291661 0.956522i $$-0.405792\pi$$
0.291661 + 0.956522i $$0.405792\pi$$
$$24$$ −15.0000 + 13.4164i −0.625000 + 0.559017i
$$25$$ 0 0
$$26$$ 35.7771i 1.37604i
$$27$$ −15.6525 22.0000i −0.579721 0.814815i
$$28$$ 6.00000i 0.214286i
$$29$$ 31.3050i 1.07948i −0.841831 0.539741i $$-0.818522\pi$$
0.841831 0.539741i $$-0.181478\pi$$
$$30$$ 0 0
$$31$$ −18.0000 −0.580645 −0.290323 0.956929i $$-0.593763\pi$$
−0.290323 + 0.956929i $$0.593763\pi$$
$$32$$ −15.6525 −0.489140
$$33$$ −8.94427 10.0000i −0.271039 0.303030i
$$34$$ −10.0000 −0.294118
$$35$$ 0 0
$$36$$ 1.00000 8.94427i 0.0277778 0.248452i
$$37$$ 16.0000i 0.432432i 0.976346 + 0.216216i $$0.0693716\pi$$
−0.976346 + 0.216216i $$0.930628\pi$$
$$38$$ 4.47214 0.117688
$$39$$ 32.0000 + 35.7771i 0.820513 + 0.917361i
$$40$$ 0 0
$$41$$ 62.6099i 1.52707i −0.645766 0.763535i $$-0.723462\pi$$
0.645766 0.763535i $$-0.276538\pi$$
$$42$$ 26.8328 + 30.0000i 0.638877 + 0.714286i
$$43$$ 16.0000i 0.372093i 0.982541 + 0.186047i $$0.0595675\pi$$
−0.982541 + 0.186047i $$0.940432\pi$$
$$44$$ 4.47214i 0.101639i
$$45$$ 0 0
$$46$$ 30.0000 0.652174
$$47$$ 49.1935 1.04667 0.523335 0.852127i $$-0.324688\pi$$
0.523335 + 0.852127i $$0.324688\pi$$
$$48$$ −42.4853 + 38.0000i −0.885110 + 0.791667i
$$49$$ 13.0000 0.265306
$$50$$ 0 0
$$51$$ −10.0000 + 8.94427i −0.196078 + 0.175378i
$$52$$ 16.0000i 0.307692i
$$53$$ 4.47214 0.0843799 0.0421900 0.999110i $$-0.486567\pi$$
0.0421900 + 0.999110i $$0.486567\pi$$
$$54$$ −35.0000 49.1935i −0.648148 0.910991i
$$55$$ 0 0
$$56$$ 40.2492i 0.718736i
$$57$$ 4.47214 4.00000i 0.0784585 0.0701754i
$$58$$ 70.0000i 1.20690i
$$59$$ 4.47214i 0.0757989i 0.999282 + 0.0378995i $$0.0120667\pi$$
−0.999282 + 0.0378995i $$0.987933\pi$$
$$60$$ 0 0
$$61$$ 82.0000 1.34426 0.672131 0.740432i $$-0.265379\pi$$
0.672131 + 0.740432i $$0.265379\pi$$
$$62$$ −40.2492 −0.649181
$$63$$ 53.6656 + 6.00000i 0.851835 + 0.0952381i
$$64$$ 41.0000 0.640625
$$65$$ 0 0
$$66$$ −20.0000 22.3607i −0.303030 0.338798i
$$67$$ 24.0000i 0.358209i −0.983830 0.179104i $$-0.942680\pi$$
0.983830 0.179104i $$-0.0573200\pi$$
$$68$$ −4.47214 −0.0657667
$$69$$ 30.0000 26.8328i 0.434783 0.388881i
$$70$$ 0 0
$$71$$ 125.220i 1.76366i 0.471568 + 0.881830i $$0.343688\pi$$
−0.471568 + 0.881830i $$0.656312\pi$$
$$72$$ −6.70820 + 60.0000i −0.0931695 + 0.833333i
$$73$$ 74.0000i 1.01370i −0.862035 0.506849i $$-0.830810\pi$$
0.862035 0.506849i $$-0.169190\pi$$
$$74$$ 35.7771i 0.483474i
$$75$$ 0 0
$$76$$ 2.00000 0.0263158
$$77$$ 26.8328 0.348478
$$78$$ 71.5542 + 80.0000i 0.917361 + 1.02564i
$$79$$ −138.000 −1.74684 −0.873418 0.486972i $$-0.838101\pi$$
−0.873418 + 0.486972i $$0.838101\pi$$
$$80$$ 0 0
$$81$$ −79.0000 17.8885i −0.975309 0.220846i
$$82$$ 140.000i 1.70732i
$$83$$ −93.9149 −1.13150 −0.565752 0.824575i $$-0.691414\pi$$
−0.565752 + 0.824575i $$0.691414\pi$$
$$84$$ 12.0000 + 13.4164i 0.142857 + 0.159719i
$$85$$ 0 0
$$86$$ 35.7771i 0.416013i
$$87$$ −62.6099 70.0000i −0.719654 0.804598i
$$88$$ 30.0000i 0.340909i
$$89$$ 107.331i 1.20597i 0.797753 + 0.602985i $$0.206022\pi$$
−0.797753 + 0.602985i $$0.793978\pi$$
$$90$$ 0 0
$$91$$ −96.0000 −1.05495
$$92$$ 13.4164 0.145831
$$93$$ −40.2492 + 36.0000i −0.432787 + 0.387097i
$$94$$ 110.000 1.17021
$$95$$ 0 0
$$96$$ −35.0000 + 31.3050i −0.364583 + 0.326093i
$$97$$ 166.000i 1.71134i 0.517522 + 0.855670i $$0.326855\pi$$
−0.517522 + 0.855670i $$0.673145\pi$$
$$98$$ 29.0689 0.296621
$$99$$ −40.0000 4.47214i −0.404040 0.0451731i
$$100$$ 0 0
$$101$$ 67.0820i 0.664179i −0.943248 0.332089i $$-0.892246\pi$$
0.943248 0.332089i $$-0.107754\pi$$
$$102$$ −22.3607 + 20.0000i −0.219222 + 0.196078i
$$103$$ 26.0000i 0.252427i 0.992003 + 0.126214i $$0.0402825\pi$$
−0.992003 + 0.126214i $$0.959718\pi$$
$$104$$ 107.331i 1.03203i
$$105$$ 0 0
$$106$$ 10.0000 0.0943396
$$107$$ −201.246 −1.88080 −0.940402 0.340064i $$-0.889551\pi$$
−0.940402 + 0.340064i $$0.889551\pi$$
$$108$$ −15.6525 22.0000i −0.144930 0.203704i
$$109$$ −38.0000 −0.348624 −0.174312 0.984690i $$-0.555770\pi$$
−0.174312 + 0.984690i $$0.555770\pi$$
$$110$$ 0 0
$$111$$ 32.0000 + 35.7771i 0.288288 + 0.322316i
$$112$$ 114.000i 1.01786i
$$113$$ 31.3050 0.277035 0.138517 0.990360i $$-0.455766\pi$$
0.138517 + 0.990360i $$0.455766\pi$$
$$114$$ 10.0000 8.94427i 0.0877193 0.0784585i
$$115$$ 0 0
$$116$$ 31.3050i 0.269870i
$$117$$ 143.108 + 16.0000i 1.22315 + 0.136752i
$$118$$ 10.0000i 0.0847458i
$$119$$ 26.8328i 0.225486i
$$120$$ 0 0
$$121$$ 101.000 0.834711
$$122$$ 183.358 1.50293
$$123$$ −125.220 140.000i −1.01805 1.13821i
$$124$$ −18.0000 −0.145161
$$125$$ 0 0
$$126$$ 120.000 + 13.4164i 0.952381 + 0.106479i
$$127$$ 26.0000i 0.204724i 0.994747 + 0.102362i $$0.0326401\pi$$
−0.994747 + 0.102362i $$0.967360\pi$$
$$128$$ 154.289 1.20538
$$129$$ 32.0000 + 35.7771i 0.248062 + 0.277342i
$$130$$ 0 0
$$131$$ 13.4164i 0.102415i −0.998688 0.0512077i $$-0.983693\pi$$
0.998688 0.0512077i $$-0.0163070\pi$$
$$132$$ −8.94427 10.0000i −0.0677596 0.0757576i
$$133$$ 12.0000i 0.0902256i
$$134$$ 53.6656i 0.400490i
$$135$$ 0 0
$$136$$ 30.0000 0.220588
$$137$$ 120.748 0.881370 0.440685 0.897662i $$-0.354736\pi$$
0.440685 + 0.897662i $$0.354736\pi$$
$$138$$ 67.0820 60.0000i 0.486102 0.434783i
$$139$$ 82.0000 0.589928 0.294964 0.955508i $$-0.404692\pi$$
0.294964 + 0.955508i $$0.404692\pi$$
$$140$$ 0 0
$$141$$ 110.000 98.3870i 0.780142 0.697780i
$$142$$ 280.000i 1.97183i
$$143$$ 71.5542 0.500379
$$144$$ −19.0000 + 169.941i −0.131944 + 1.18015i
$$145$$ 0 0
$$146$$ 165.469i 1.13335i
$$147$$ 29.0689 26.0000i 0.197748 0.176871i
$$148$$ 16.0000i 0.108108i
$$149$$ 111.803i 0.750358i −0.926952 0.375179i $$-0.877581\pi$$
0.926952 0.375179i $$-0.122419\pi$$
$$150$$ 0 0
$$151$$ −158.000 −1.04636 −0.523179 0.852223i $$-0.675254\pi$$
−0.523179 + 0.852223i $$0.675254\pi$$
$$152$$ −13.4164 −0.0882658
$$153$$ −4.47214 + 40.0000i −0.0292296 + 0.261438i
$$154$$ 60.0000 0.389610
$$155$$ 0 0
$$156$$ 32.0000 + 35.7771i 0.205128 + 0.229340i
$$157$$ 164.000i 1.04459i −0.852766 0.522293i $$-0.825077\pi$$
0.852766 0.522293i $$-0.174923\pi$$
$$158$$ −308.577 −1.95302
$$159$$ 10.0000 8.94427i 0.0628931 0.0562533i
$$160$$ 0 0
$$161$$ 80.4984i 0.499990i
$$162$$ −176.649 40.0000i −1.09043 0.246914i
$$163$$ 236.000i 1.44785i 0.689877 + 0.723926i $$0.257664\pi$$
−0.689877 + 0.723926i $$0.742336\pi$$
$$164$$ 62.6099i 0.381768i
$$165$$ 0 0
$$166$$ −210.000 −1.26506
$$167$$ −93.9149 −0.562364 −0.281182 0.959654i $$-0.590727\pi$$
−0.281182 + 0.959654i $$0.590727\pi$$
$$168$$ −80.4984 90.0000i −0.479157 0.535714i
$$169$$ −87.0000 −0.514793
$$170$$ 0 0
$$171$$ 2.00000 17.8885i 0.0116959 0.104611i
$$172$$ 16.0000i 0.0930233i
$$173$$ 13.4164 0.0775515 0.0387757 0.999248i $$-0.487654\pi$$
0.0387757 + 0.999248i $$0.487654\pi$$
$$174$$ −140.000 156.525i −0.804598 0.899568i
$$175$$ 0 0
$$176$$ 84.9706i 0.482787i
$$177$$ 8.94427 + 10.0000i 0.0505326 + 0.0564972i
$$178$$ 240.000i 1.34831i
$$179$$ 192.302i 1.07431i 0.843483 + 0.537156i $$0.180501\pi$$
−0.843483 + 0.537156i $$0.819499\pi$$
$$180$$ 0 0
$$181$$ 2.00000 0.0110497 0.00552486 0.999985i $$-0.498241\pi$$
0.00552486 + 0.999985i $$0.498241\pi$$
$$182$$ −214.663 −1.17946
$$183$$ 183.358 164.000i 1.00195 0.896175i
$$184$$ −90.0000 −0.489130
$$185$$ 0 0
$$186$$ −90.0000 + 80.4984i −0.483871 + 0.432787i
$$187$$ 20.0000i 0.106952i
$$188$$ 49.1935 0.261668
$$189$$ 132.000 93.9149i 0.698413 0.496904i
$$190$$ 0 0
$$191$$ 205.718i 1.07706i 0.842607 + 0.538529i $$0.181020\pi$$
−0.842607 + 0.538529i $$0.818980\pi$$
$$192$$ 91.6788 82.0000i 0.477494 0.427083i
$$193$$ 214.000i 1.10881i −0.832248 0.554404i $$-0.812946\pi$$
0.832248 0.554404i $$-0.187054\pi$$
$$194$$ 371.187i 1.91334i
$$195$$ 0 0
$$196$$ 13.0000 0.0663265
$$197$$ 93.9149 0.476725 0.238363 0.971176i $$-0.423389\pi$$
0.238363 + 0.971176i $$0.423389\pi$$
$$198$$ −89.4427 10.0000i −0.451731 0.0505051i
$$199$$ 242.000 1.21608 0.608040 0.793906i $$-0.291956\pi$$
0.608040 + 0.793906i $$0.291956\pi$$
$$200$$ 0 0
$$201$$ −48.0000 53.6656i −0.238806 0.266993i
$$202$$ 150.000i 0.742574i
$$203$$ 187.830 0.925270
$$204$$ −10.0000 + 8.94427i −0.0490196 + 0.0438445i
$$205$$ 0 0
$$206$$ 58.1378i 0.282222i
$$207$$ 13.4164 120.000i 0.0648136 0.579710i
$$208$$ 304.000i 1.46154i
$$209$$ 8.94427i 0.0427956i
$$210$$ 0 0
$$211$$ 2.00000 0.00947867 0.00473934 0.999989i $$-0.498491\pi$$
0.00473934 + 0.999989i $$0.498491\pi$$
$$212$$ 4.47214 0.0210950
$$213$$ 250.440 + 280.000i 1.17577 + 1.31455i
$$214$$ −450.000 −2.10280
$$215$$ 0 0
$$216$$ 105.000 + 147.580i 0.486111 + 0.683243i
$$217$$ 108.000i 0.497696i
$$218$$ −84.9706 −0.389773
$$219$$ −148.000 165.469i −0.675799 0.755566i
$$220$$ 0 0
$$221$$ 71.5542i 0.323775i
$$222$$ 71.5542 + 80.0000i 0.322316 + 0.360360i
$$223$$ 86.0000i 0.385650i 0.981233 + 0.192825i $$0.0617650\pi$$
−0.981233 + 0.192825i $$0.938235\pi$$
$$224$$ 93.9149i 0.419263i
$$225$$ 0 0
$$226$$ 70.0000 0.309735
$$227$$ 58.1378 0.256114 0.128057 0.991767i $$-0.459126\pi$$
0.128057 + 0.991767i $$0.459126\pi$$
$$228$$ 4.47214 4.00000i 0.0196146 0.0175439i
$$229$$ 282.000 1.23144 0.615721 0.787965i $$-0.288865\pi$$
0.615721 + 0.787965i $$0.288865\pi$$
$$230$$ 0 0
$$231$$ 60.0000 53.6656i 0.259740 0.232319i
$$232$$ 210.000i 0.905172i
$$233$$ −362.243 −1.55469 −0.777346 0.629074i $$-0.783434\pi$$
−0.777346 + 0.629074i $$0.783434\pi$$
$$234$$ 320.000 + 35.7771i 1.36752 + 0.152894i
$$235$$ 0 0
$$236$$ 4.47214i 0.0189497i
$$237$$ −308.577 + 276.000i −1.30201 + 1.16456i
$$238$$ 60.0000i 0.252101i
$$239$$ 250.440i 1.04786i −0.851760 0.523932i $$-0.824464\pi$$
0.851760 0.523932i $$-0.175536\pi$$
$$240$$ 0 0
$$241$$ 262.000 1.08714 0.543568 0.839365i $$-0.317073\pi$$
0.543568 + 0.839365i $$0.317073\pi$$
$$242$$ 225.843 0.933235
$$243$$ −212.426 + 118.000i −0.874183 + 0.485597i
$$244$$ 82.0000 0.336066
$$245$$ 0 0
$$246$$ −280.000 313.050i −1.13821 1.27256i
$$247$$ 32.0000i 0.129555i
$$248$$ 120.748 0.486886
$$249$$ −210.000 + 187.830i −0.843373 + 0.754336i
$$250$$ 0 0
$$251$$ 469.574i 1.87081i −0.353573 0.935407i $$-0.615033\pi$$
0.353573 0.935407i $$-0.384967\pi$$
$$252$$ 53.6656 + 6.00000i 0.212959 + 0.0238095i
$$253$$ 60.0000i 0.237154i
$$254$$ 58.1378i 0.228889i
$$255$$ 0 0
$$256$$ 181.000 0.707031
$$257$$ −201.246 −0.783059 −0.391529 0.920166i $$-0.628054\pi$$
−0.391529 + 0.920166i $$0.628054\pi$$
$$258$$ 71.5542 + 80.0000i 0.277342 + 0.310078i
$$259$$ −96.0000 −0.370656
$$260$$ 0 0
$$261$$ −280.000 31.3050i −1.07280 0.119942i
$$262$$ 30.0000i 0.114504i
$$263$$ −58.1378 −0.221056 −0.110528 0.993873i $$-0.535254\pi$$
−0.110528 + 0.993873i $$0.535254\pi$$
$$264$$ 60.0000 + 67.0820i 0.227273 + 0.254099i
$$265$$ 0 0
$$266$$ 26.8328i 0.100875i
$$267$$ 214.663 + 240.000i 0.803979 + 0.898876i
$$268$$ 24.0000i 0.0895522i
$$269$$ 371.187i 1.37988i −0.723867 0.689939i $$-0.757637\pi$$
0.723867 0.689939i $$-0.242363\pi$$
$$270$$ 0 0
$$271$$ 82.0000 0.302583 0.151292 0.988489i $$-0.451657\pi$$
0.151292 + 0.988489i $$0.451657\pi$$
$$272$$ 84.9706 0.312392
$$273$$ −214.663 + 192.000i −0.786310 + 0.703297i
$$274$$ 270.000 0.985401
$$275$$ 0 0
$$276$$ 30.0000 26.8328i 0.108696 0.0972203i
$$277$$ 24.0000i 0.0866426i −0.999061 0.0433213i $$-0.986206\pi$$
0.999061 0.0433213i $$-0.0137939\pi$$
$$278$$ 183.358 0.659560
$$279$$ −18.0000 + 160.997i −0.0645161 + 0.577050i
$$280$$ 0 0
$$281$$ 187.830i 0.668433i 0.942496 + 0.334217i $$0.108472\pi$$
−0.942496 + 0.334217i $$0.891528\pi$$
$$282$$ 245.967 220.000i 0.872225 0.780142i
$$283$$ 144.000i 0.508834i −0.967095 0.254417i $$-0.918116\pi$$
0.967095 0.254417i $$-0.0818836\pi$$
$$284$$ 125.220i 0.440915i
$$285$$ 0 0
$$286$$ 160.000 0.559441
$$287$$ 375.659 1.30892
$$288$$ −15.6525 + 140.000i −0.0543489 + 0.486111i
$$289$$ −269.000 −0.930796
$$290$$ 0 0
$$291$$ 332.000 + 371.187i 1.14089 + 1.27556i
$$292$$ 74.0000i 0.253425i
$$293$$ 469.574 1.60264 0.801321 0.598234i $$-0.204131\pi$$
0.801321 + 0.598234i $$0.204131\pi$$
$$294$$ 65.0000 58.1378i 0.221088 0.197748i
$$295$$ 0 0
$$296$$ 107.331i 0.362606i
$$297$$ −98.3870 + 70.0000i −0.331269 + 0.235690i
$$298$$ 250.000i 0.838926i
$$299$$ 214.663i 0.717935i
$$300$$ 0 0
$$301$$ −96.0000 −0.318937
$$302$$ −353.299 −1.16986
$$303$$ −134.164 150.000i −0.442786 0.495050i
$$304$$ −38.0000 −0.125000
$$305$$ 0 0
$$306$$ −10.0000 + 89.4427i −0.0326797 + 0.292296i
$$307$$ 184.000i 0.599349i −0.954042 0.299674i $$-0.903122\pi$$
0.954042 0.299674i $$-0.0968780\pi$$
$$308$$ 26.8328 0.0871195
$$309$$ 52.0000 + 58.1378i 0.168285 + 0.188148i
$$310$$ 0 0
$$311$$ 160.997i 0.517675i −0.965921 0.258837i $$-0.916661\pi$$
0.965921 0.258837i $$-0.0833394\pi$$
$$312$$ −214.663 240.000i −0.688021 0.769231i
$$313$$ 394.000i 1.25879i −0.777087 0.629393i $$-0.783304\pi$$
0.777087 0.629393i $$-0.216696\pi$$
$$314$$ 366.715i 1.16788i
$$315$$ 0 0
$$316$$ −138.000 −0.436709
$$317$$ −451.686 −1.42488 −0.712438 0.701735i $$-0.752409\pi$$
−0.712438 + 0.701735i $$0.752409\pi$$
$$318$$ 22.3607 20.0000i 0.0703166 0.0628931i
$$319$$ −140.000 −0.438871
$$320$$ 0 0
$$321$$ −450.000 + 402.492i −1.40187 + 1.25387i
$$322$$ 180.000i 0.559006i
$$323$$ −8.94427 −0.0276912
$$324$$ −79.0000 17.8885i −0.243827 0.0552116i
$$325$$ 0 0
$$326$$ 527.712i 1.61875i
$$327$$ −84.9706 + 76.0000i −0.259849 + 0.232416i
$$328$$ 420.000i 1.28049i
$$329$$ 295.161i 0.897146i
$$330$$ 0 0
$$331$$ −198.000 −0.598187 −0.299094 0.954224i $$-0.596684\pi$$
−0.299094 + 0.954224i $$0.596684\pi$$
$$332$$ −93.9149 −0.282876
$$333$$ 143.108 + 16.0000i 0.429755 + 0.0480480i
$$334$$ −210.000 −0.628743
$$335$$ 0 0
$$336$$ −228.000 254.912i −0.678571 0.758666i
$$337$$ 394.000i 1.16914i −0.811343 0.584570i $$-0.801263\pi$$
0.811343 0.584570i $$-0.198737\pi$$
$$338$$ −194.538 −0.575556
$$339$$ 70.0000 62.6099i 0.206490 0.184690i
$$340$$ 0 0
$$341$$ 80.4984i 0.236066i
$$342$$ 4.47214 40.0000i 0.0130764 0.116959i
$$343$$ 372.000i 1.08455i
$$344$$ 107.331i 0.312009i
$$345$$ 0 0
$$346$$ 30.0000 0.0867052
$$347$$ 183.358 0.528408 0.264204 0.964467i $$-0.414891\pi$$
0.264204 + 0.964467i $$0.414891\pi$$
$$348$$ −62.6099 70.0000i −0.179914 0.201149i
$$349$$ 362.000 1.03725 0.518625 0.855002i $$-0.326444\pi$$
0.518625 + 0.855002i $$0.326444\pi$$
$$350$$ 0 0
$$351$$ 352.000 250.440i 1.00285 0.713503i
$$352$$ 70.0000i 0.198864i
$$353$$ −308.577 −0.874157 −0.437078 0.899423i $$-0.643987\pi$$
−0.437078 + 0.899423i $$0.643987\pi$$
$$354$$ 20.0000 + 22.3607i 0.0564972 + 0.0631658i
$$355$$ 0 0
$$356$$ 107.331i 0.301492i
$$357$$ −53.6656 60.0000i −0.150324 0.168067i
$$358$$ 430.000i 1.20112i
$$359$$ 295.161i 0.822175i 0.911596 + 0.411088i $$0.134851\pi$$
−0.911596 + 0.411088i $$0.865149\pi$$
$$360$$ 0 0
$$361$$ −357.000 −0.988920
$$362$$ 4.47214 0.0123540
$$363$$ 225.843 202.000i 0.622157 0.556474i
$$364$$ −96.0000 −0.263736
$$365$$ 0 0
$$366$$ 410.000 366.715i 1.12022 1.00195i
$$367$$ 186.000i 0.506812i 0.967360 + 0.253406i $$0.0815509\pi$$
−0.967360 + 0.253406i $$0.918449\pi$$
$$368$$ −254.912 −0.692695
$$369$$ −560.000 62.6099i −1.51762 0.169675i
$$370$$ 0 0
$$371$$ 26.8328i 0.0723256i
$$372$$ −40.2492 + 36.0000i −0.108197 + 0.0967742i
$$373$$ 44.0000i 0.117962i −0.998259 0.0589812i $$-0.981215\pi$$
0.998259 0.0589812i $$-0.0187852\pi$$
$$374$$ 44.7214i 0.119576i
$$375$$ 0 0
$$376$$ −330.000 −0.877660
$$377$$ 500.879 1.32859
$$378$$ 295.161 210.000i 0.780849 0.555556i
$$379$$ 362.000 0.955145 0.477573 0.878592i $$-0.341517\pi$$
0.477573 + 0.878592i $$0.341517\pi$$
$$380$$ 0 0
$$381$$ 52.0000 + 58.1378i 0.136483 + 0.152593i
$$382$$ 460.000i 1.20419i
$$383$$ −362.243 −0.945804 −0.472902 0.881115i $$-0.656794\pi$$
−0.472902 + 0.881115i $$0.656794\pi$$
$$384$$ 345.000 308.577i 0.898438 0.803587i
$$385$$ 0 0
$$386$$ 478.519i 1.23969i
$$387$$ 143.108 + 16.0000i 0.369789 + 0.0413437i
$$388$$ 166.000i 0.427835i
$$389$$ 442.741i 1.13815i 0.822285 + 0.569076i $$0.192699\pi$$
−0.822285 + 0.569076i $$0.807301\pi$$
$$390$$ 0 0
$$391$$ −60.0000 −0.153453
$$392$$ −87.2067 −0.222466
$$393$$ −26.8328 30.0000i −0.0682769 0.0763359i
$$394$$ 210.000 0.532995
$$395$$ 0 0
$$396$$ −40.0000 4.47214i −0.101010 0.0112933i
$$397$$ 124.000i 0.312343i −0.987730 0.156171i $$-0.950085\pi$$
0.987730 0.156171i $$-0.0499152\pi$$
$$398$$ 541.128 1.35962
$$399$$ 24.0000 + 26.8328i 0.0601504 + 0.0672502i
$$400$$ 0 0
$$401$$ 268.328i 0.669148i 0.942370 + 0.334574i $$0.108592\pi$$
−0.942370 + 0.334574i $$0.891408\pi$$
$$402$$ −107.331 120.000i −0.266993 0.298507i
$$403$$ 288.000i 0.714640i
$$404$$ 67.0820i 0.166045i
$$405$$ 0 0
$$406$$ 420.000 1.03448
$$407$$ 71.5542 0.175809
$$408$$ 67.0820 60.0000i 0.164417 0.147059i
$$409$$ −458.000 −1.11980 −0.559902 0.828559i $$-0.689161\pi$$
−0.559902 + 0.828559i $$0.689161\pi$$
$$410$$ 0 0
$$411$$ 270.000 241.495i 0.656934 0.587580i
$$412$$ 26.0000i 0.0631068i
$$413$$ −26.8328 −0.0649705
$$414$$ 30.0000 268.328i 0.0724638 0.648136i
$$415$$ 0 0
$$416$$ 250.440i 0.602018i
$$417$$ 183.358 164.000i 0.439706 0.393285i
$$418$$ 20.0000i 0.0478469i
$$419$$ 594.794i 1.41956i −0.704425 0.709778i $$-0.748795\pi$$
0.704425 0.709778i $$-0.251205\pi$$
$$420$$ 0 0
$$421$$ 562.000 1.33492 0.667458 0.744647i $$-0.267382\pi$$
0.667458 + 0.744647i $$0.267382\pi$$
$$422$$ 4.47214 0.0105975
$$423$$ 49.1935 440.000i 0.116297 1.04019i
$$424$$ −30.0000 −0.0707547
$$425$$ 0 0
$$426$$ 560.000 + 626.099i 1.31455 + 1.46972i
$$427$$ 492.000i 1.15222i
$$428$$ −201.246 −0.470201
$$429$$ 160.000 143.108i 0.372960 0.333586i
$$430$$ 0 0
$$431$$ 348.827i 0.809342i −0.914462 0.404671i $$-0.867386\pi$$
0.914462 0.404671i $$-0.132614\pi$$
$$432$$ 297.397 + 418.000i 0.688419 + 0.967593i
$$433$$ 226.000i 0.521940i 0.965347 + 0.260970i $$0.0840424\pi$$
−0.965347 + 0.260970i $$0.915958\pi$$
$$434$$ 241.495i 0.556441i
$$435$$ 0 0
$$436$$ −38.0000 −0.0871560
$$437$$ 26.8328 0.0614023
$$438$$ −330.938 370.000i −0.755566 0.844749i
$$439$$ 2.00000 0.00455581 0.00227790 0.999997i $$-0.499275\pi$$
0.00227790 + 0.999997i $$0.499275\pi$$
$$440$$ 0 0
$$441$$ 13.0000 116.276i 0.0294785 0.263663i
$$442$$ 160.000i 0.361991i
$$443$$ 201.246 0.454280 0.227140 0.973862i $$-0.427062\pi$$
0.227140 + 0.973862i $$0.427062\pi$$
$$444$$ 32.0000 + 35.7771i 0.0720721 + 0.0805790i
$$445$$ 0 0
$$446$$ 192.302i 0.431170i
$$447$$ −223.607 250.000i −0.500239 0.559284i
$$448$$ 246.000i 0.549107i
$$449$$ 313.050i 0.697215i 0.937269 + 0.348607i $$0.113345\pi$$
−0.937269 + 0.348607i $$0.886655\pi$$
$$450$$ 0 0
$$451$$ −280.000 −0.620843
$$452$$ 31.3050 0.0692587
$$453$$ −353.299 + 316.000i −0.779909 + 0.697572i
$$454$$ 130.000 0.286344
$$455$$ 0 0
$$456$$ −30.0000 + 26.8328i −0.0657895 + 0.0588439i
$$457$$ 334.000i 0.730853i −0.930840 0.365427i $$-0.880923\pi$$
0.930840 0.365427i $$-0.119077\pi$$
$$458$$ 630.571 1.37679
$$459$$ 70.0000 + 98.3870i 0.152505 + 0.214351i
$$460$$ 0 0
$$461$$ 93.9149i 0.203720i −0.994799 0.101860i $$-0.967521\pi$$
0.994799 0.101860i $$-0.0324794\pi$$
$$462$$ 134.164 120.000i 0.290398 0.259740i
$$463$$ 366.000i 0.790497i 0.918574 + 0.395248i $$0.129341\pi$$
−0.918574 + 0.395248i $$0.870659\pi$$
$$464$$ 594.794i 1.28188i
$$465$$ 0 0
$$466$$ −810.000 −1.73820
$$467$$ −451.686 −0.967207 −0.483604 0.875287i $$-0.660672\pi$$
−0.483604 + 0.875287i $$0.660672\pi$$
$$468$$ 143.108 + 16.0000i 0.305787 + 0.0341880i
$$469$$ 144.000 0.307036
$$470$$ 0 0
$$471$$ −328.000 366.715i −0.696391 0.778588i
$$472$$ 30.0000i 0.0635593i
$$473$$ 71.5542 0.151277
$$474$$ −690.000 + 617.155i −1.45570 + 1.30201i
$$475$$ 0 0
$$476$$ 26.8328i 0.0563715i
$$477$$ 4.47214 40.0000i 0.00937555 0.0838574i
$$478$$ 560.000i 1.17155i
$$479$$ 590.322i 1.23240i −0.787588 0.616202i $$-0.788670\pi$$
0.787588 0.616202i $$-0.211330\pi$$
$$480$$ 0 0
$$481$$ −256.000 −0.532225
$$482$$ 585.850 1.21546
$$483$$ 160.997 + 180.000i 0.333327 + 0.372671i
$$484$$ 101.000 0.208678
$$485$$ 0 0
$$486$$ −475.000 + 263.856i −0.977366 + 0.542914i
$$487$$ 886.000i 1.81930i 0.415374 + 0.909651i $$0.363651\pi$$
−0.415374 + 0.909651i $$0.636349\pi$$
$$488$$ −550.073 −1.12720
$$489$$ 472.000 + 527.712i 0.965235 + 1.07917i
$$490$$ 0 0
$$491$$ 406.964i 0.828848i 0.910084 + 0.414424i $$0.136017\pi$$
−0.910084 + 0.414424i $$0.863983\pi$$
$$492$$ −125.220 140.000i −0.254512 0.284553i
$$493$$ 140.000i 0.283976i
$$494$$ 71.5542i 0.144847i
$$495$$ 0 0
$$496$$ 342.000 0.689516
$$497$$ −751.319 −1.51171
$$498$$ −469.574 + 420.000i −0.942920 + 0.843373i
$$499$$ 2.00000 0.00400802 0.00200401 0.999998i $$-0.499362\pi$$
0.00200401 + 0.999998i $$0.499362\pi$$
$$500$$ 0 0
$$501$$ −210.000 + 187.830i −0.419162 + 0.374910i
$$502$$ 1050.00i 2.09163i
$$503$$ −219.135 −0.435655 −0.217828 0.975987i $$-0.569897\pi$$
−0.217828 + 0.975987i $$0.569897\pi$$
$$504$$ −360.000 40.2492i −0.714286 0.0798596i
$$505$$ 0 0
$$506$$ 134.164i 0.265146i
$$507$$ −194.538 + 174.000i −0.383704 + 0.343195i
$$508$$ 26.0000i 0.0511811i
$$509$$ 800.512i 1.57272i −0.617771 0.786358i $$-0.711964\pi$$
0.617771 0.786358i $$-0.288036\pi$$
$$510$$ 0 0
$$511$$ 444.000 0.868885
$$512$$ −212.426 −0.414895
$$513$$ −31.3050 44.0000i −0.0610233 0.0857700i
$$514$$ −450.000 −0.875486
$$515$$ 0 0
$$516$$ 32.0000 + 35.7771i 0.0620155 + 0.0693354i
$$517$$ 220.000i 0.425532i
$$518$$ −214.663 −0.414406
$$519$$ 30.0000 26.8328i 0.0578035 0.0517010i
$$520$$ 0 0
$$521$$ 527.712i 1.01288i 0.862274 + 0.506441i $$0.169039\pi$$
−0.862274 + 0.506441i $$0.830961\pi$$
$$522$$ −626.099 70.0000i −1.19942 0.134100i
$$523$$ 376.000i 0.718929i 0.933159 + 0.359465i $$0.117041\pi$$
−0.933159 + 0.359465i $$0.882959\pi$$
$$524$$ 13.4164i 0.0256038i
$$525$$ 0 0
$$526$$ −130.000 −0.247148
$$527$$ 80.4984 0.152748
$$528$$ 169.941 + 190.000i 0.321858 + 0.359848i
$$529$$ −349.000 −0.659735
$$530$$ 0 0
$$531$$ 40.0000 + 4.47214i 0.0753296 + 0.00842210i
$$532$$ 12.0000i 0.0225564i
$$533$$ 1001.76 1.87947
$$534$$ 480.000 + 536.656i 0.898876 + 1.00497i
$$535$$ 0 0
$$536$$ 160.997i 0.300367i
$$537$$ 384.604 + 430.000i 0.716208 + 0.800745i
$$538$$ 830.000i 1.54275i
$$539$$ 58.1378i 0.107862i
$$540$$ 0 0
$$541$$ −198.000 −0.365989 −0.182994 0.983114i $$-0.558579\pi$$
−0.182994 + 0.983114i $$0.558579\pi$$
$$542$$ 183.358 0.338298
$$543$$ 4.47214 4.00000i 0.00823598 0.00736648i
$$544$$ 70.0000 0.128676
$$545$$ 0 0
$$546$$ −480.000 + 429.325i −0.879121 + 0.786310i
$$547$$ 1024.00i 1.87203i −0.351961 0.936015i $$-0.614485\pi$$
0.351961 0.936015i $$-0.385515\pi$$
$$548$$ 120.748 0.220342
$$549$$ 82.0000 733.430i 0.149362 1.33594i
$$550$$ 0 0
$$551$$ 62.6099i 0.113630i
$$552$$ −201.246 + 180.000i −0.364576 + 0.326087i
$$553$$ 828.000i 1.49729i
$$554$$ 53.6656i 0.0968694i
$$555$$ 0 0
$$556$$ 82.0000 0.147482
$$557$$ −67.0820 −0.120435 −0.0602173 0.998185i $$-0.519179\pi$$
−0.0602173 + 0.998185i $$0.519179\pi$$
$$558$$ −40.2492 + 360.000i −0.0721312 + 0.645161i
$$559$$ −256.000 −0.457961
$$560$$ 0 0
$$561$$ 40.0000 + 44.7214i 0.0713012 + 0.0797172i
$$562$$ 420.000i 0.747331i
$$563$$ 254.912 0.452774 0.226387 0.974037i $$-0.427309\pi$$
0.226387 + 0.974037i $$0.427309\pi$$
$$564$$ 110.000 98.3870i 0.195035 0.174445i
$$565$$ 0 0
$$566$$ 321.994i 0.568894i
$$567$$ 107.331 474.000i 0.189297 0.835979i
$$568$$ 840.000i 1.47887i
$$569$$ 858.650i 1.50905i 0.656271 + 0.754526i $$0.272133\pi$$
−0.656271 + 0.754526i $$0.727867\pi$$
$$570$$ 0 0
$$571$$ 962.000 1.68476 0.842382 0.538881i $$-0.181153\pi$$
0.842382 + 0.538881i $$0.181153\pi$$
$$572$$ 71.5542 0.125095
$$573$$ 411.437 + 460.000i 0.718039 + 0.802792i
$$574$$ 840.000 1.46341
$$575$$ 0 0
$$576$$ 41.0000 366.715i 0.0711806 0.636658i
$$577$$ 886.000i 1.53553i 0.640732 + 0.767764i $$0.278631\pi$$
−0.640732 + 0.767764i $$0.721369\pi$$
$$578$$ −601.502 −1.04066
$$579$$ −428.000 478.519i −0.739206 0.826457i
$$580$$ 0 0
$$581$$ 563.489i 0.969861i
$$582$$ 742.375 + 830.000i 1.27556 + 1.42612i
$$583$$ 20.0000i 0.0343053i
$$584$$ 496.407i 0.850012i
$$585$$ 0 0
$$586$$ 1050.00 1.79181
$$587$$ 657.404 1.11994 0.559969 0.828513i $$-0.310813\pi$$
0.559969 + 0.828513i $$0.310813\pi$$
$$588$$ 29.0689 26.0000i 0.0494369 0.0442177i
$$589$$ −36.0000 −0.0611205
$$590$$ 0 0
$$591$$ 210.000 187.830i 0.355330 0.317817i
$$592$$ 304.000i 0.513514i
$$593$$ −111.803 −0.188539 −0.0942693 0.995547i $$-0.530051\pi$$
−0.0942693 + 0.995547i $$0.530051\pi$$
$$594$$ −220.000 + 156.525i −0.370370 + 0.263510i
$$595$$ 0 0
$$596$$ 111.803i 0.187590i
$$597$$ 541.128 484.000i 0.906413 0.810720i
$$598$$ 480.000i 0.802676i
$$599$$ 223.607i 0.373300i 0.982426 + 0.186650i $$0.0597631\pi$$
−0.982426 + 0.186650i $$0.940237\pi$$
$$600$$ 0 0
$$601$$ 2.00000 0.00332779 0.00166389 0.999999i $$-0.499470\pi$$
0.00166389 + 0.999999i $$0.499470\pi$$
$$602$$ −214.663 −0.356582
$$603$$ −214.663 24.0000i −0.355991 0.0398010i
$$604$$ −158.000 −0.261589
$$605$$ 0 0
$$606$$ −300.000 335.410i −0.495050 0.553482i
$$607$$ 506.000i 0.833608i 0.908996 + 0.416804i $$0.136850\pi$$
−0.908996 + 0.416804i $$0.863150\pi$$
$$608$$ −31.3050 −0.0514884
$$609$$ 420.000 375.659i 0.689655 0.616846i
$$610$$ 0 0
$$611$$ 787.096i 1.28821i
$$612$$ −4.47214 + 40.0000i −0.00730741 + 0.0653595i
$$613$$ 556.000i 0.907015i 0.891253 + 0.453507i $$0.149827\pi$$
−0.891253 + 0.453507i $$0.850173\pi$$
$$614$$ 411.437i 0.670092i
$$615$$ 0 0
$$616$$ −180.000 −0.292208
$$617$$ −93.9149 −0.152212 −0.0761060 0.997100i $$-0.524249\pi$$
−0.0761060 + 0.997100i $$0.524249\pi$$
$$618$$ 116.276 + 130.000i 0.188148 + 0.210356i
$$619$$ 802.000 1.29564 0.647819 0.761794i $$-0.275681\pi$$
0.647819 + 0.761794i $$0.275681\pi$$
$$620$$ 0 0
$$621$$ −210.000 295.161i −0.338164 0.475299i
$$622$$ 360.000i 0.578778i
$$623$$ −643.988 −1.03369
$$624$$ −608.000 679.765i −0.974359 1.08937i
$$625$$ 0 0
$$626$$ 881.011i 1.40737i
$$627$$ −17.8885 20.0000i −0.0285304 0.0318979i
$$628$$ 164.000i 0.261146i
$$629$$ 71.5542i 0.113759i
$$630$$ 0 0
$$631$$ −698.000 −1.10618 −0.553090 0.833121i $$-0.686552\pi$$
−0.553090 + 0.833121i $$0.686552\pi$$
$$632$$ 925.732 1.46477
$$633$$ 4.47214 4.00000i 0.00706499 0.00631912i
$$634$$ −1010.00 −1.59306
$$635$$ 0 0
$$636$$ 10.0000 8.94427i 0.0157233 0.0140633i
$$637$$ 208.000i 0.326531i
$$638$$ −313.050 −0.490673
$$639$$ 1120.00 + 125.220i 1.75274 + 0.195962i
$$640$$ 0 0
$$641$$ 912.316i 1.42327i −0.702550 0.711635i $$-0.747955\pi$$
0.702550 0.711635i $$-0.252045\pi$$
$$642$$ −1006.23 + 900.000i −1.56734 + 1.40187i
$$643$$ 156.000i 0.242613i 0.992615 + 0.121306i $$0.0387084\pi$$
−0.992615 + 0.121306i $$0.961292\pi$$
$$644$$ 80.4984i 0.124998i
$$645$$ 0 0
$$646$$ −20.0000 −0.0309598
$$647$$ −755.791 −1.16815 −0.584073 0.811701i $$-0.698542\pi$$
−0.584073 + 0.811701i $$0.698542\pi$$
$$648$$ 529.948 + 120.000i 0.817821 + 0.185185i
$$649$$ 20.0000 0.0308166
$$650$$ 0 0
$$651$$ −216.000 241.495i −0.331797 0.370961i
$$652$$ 236.000i 0.361963i
$$653$$ −487.463 −0.746497 −0.373249 0.927731i $$-0.621756\pi$$
−0.373249 + 0.927731i $$0.621756\pi$$
$$654$$ −190.000 + 169.941i −0.290520 + 0.259849i
$$655$$ 0 0
$$656$$ 1189.59i 1.81340i
$$657$$ −661.876 74.0000i −1.00742 0.112633i
$$658$$ 660.000i 1.00304i
$$659$$ 406.964i 0.617548i 0.951135 + 0.308774i $$0.0999187\pi$$
−0.951135 + 0.308774i $$0.900081\pi$$
$$660$$ 0 0
$$661$$ 682.000 1.03177 0.515885 0.856658i $$-0.327463\pi$$
0.515885 + 0.856658i $$0.327463\pi$$
$$662$$ −442.741 −0.668794
$$663$$ −143.108 160.000i −0.215850 0.241327i
$$664$$ 630.000 0.948795
$$665$$ 0 0
$$666$$ 320.000 + 35.7771i 0.480480 + 0.0537194i
$$667$$ 420.000i 0.629685i
$$668$$ −93.9149 −0.140591
$$669$$ 172.000 + 192.302i 0.257100 + 0.287447i
$$670$$ 0 0
$$671$$ 366.715i 0.546520i
$$672$$ −187.830 210.000i −0.279508 0.312500i
$$673$$ 894.000i 1.32838i −0.747564 0.664190i $$-0.768777\pi$$
0.747564 0.664190i $$-0.231223\pi$$
$$674$$ 881.011i 1.30714i
$$675$$ 0 0
$$676$$ −87.0000 −0.128698
$$677$$ 550.073 0.812515 0.406258 0.913759i $$-0.366834\pi$$
0.406258 + 0.913759i $$0.366834\pi$$
$$678$$ 156.525 140.000i 0.230862 0.206490i
$$679$$ −996.000 −1.46686
$$680$$ 0 0
$$681$$ 130.000 116.276i 0.190896 0.170742i
$$682$$ 180.000i 0.263930i
$$683$$ 442.741 0.648231 0.324115 0.946018i $$-0.394933\pi$$
0.324115 + 0.946018i $$0.394933\pi$$
$$684$$ 2.00000 17.8885i 0.00292398 0.0261528i
$$685$$ 0 0
$$686$$ 831.817i 1.21256i
$$687$$ 630.571 564.000i 0.917862 0.820961i
$$688$$ 304.000i 0.441860i
$$689$$ 71.5542i 0.103852i
$$690$$ 0 0
$$691$$ −758.000 −1.09696 −0.548480 0.836163i $$-0.684793\pi$$
−0.548480 + 0.836163i $$0.684793\pi$$
$$692$$ 13.4164 0.0193879
$$693$$ 26.8328 240.000i 0.0387198 0.346320i
$$694$$ 410.000 0.590778
$$695$$ 0 0
$$696$$ 420.000 + 469.574i 0.603448 + 0.674676i
$$697$$ 280.000i 0.401722i
$$698$$ 809.457 1.15968
$$699$$ −810.000 + 724.486i −1.15880 + 1.03646i
$$700$$ 0 0
$$701$$ 782.624i 1.11644i 0.829693 + 0.558220i $$0.188515\pi$$
−0.829693 + 0.558220i $$0.811485\pi$$
$$702$$ 787.096 560.000i 1.12122 0.797721i
$$703$$ 32.0000i 0.0455192i
$$704$$ 183.358i 0.260451i
$$705$$ 0 0
$$706$$ −690.000 −0.977337
$$707$$ 402.492 0.569296
$$708$$ 8.94427 + 10.0000i 0.0126332 + 0.0141243i
$$709$$ 2.00000 0.00282087 0.00141044 0.999999i $$-0.499551\pi$$
0.00141044 + 0.999999i $$0.499551\pi$$
$$710$$ 0 0
$$711$$ −138.000 + 1234.31i −0.194093 + 1.73602i
$$712$$ 720.000i 1.01124i
$$713$$ −241.495 −0.338703
$$714$$ −120.000 134.164i −0.168067 0.187905i
$$715$$ 0 0
$$716$$ 192.302i 0.268578i
$$717$$ −500.879 560.000i −0.698576 0.781032i
$$718$$ 660.000i 0.919220i
$$719$$ 858.650i 1.19423i 0.802156 + 0.597114i $$0.203686\pi$$
−0.802156 + 0.597114i $$0.796314\pi$$
$$720$$ 0 0
$$721$$ −156.000 −0.216366
$$722$$ −798.276 −1.10565
$$723$$ 585.850 524.000i 0.810304 0.724758i
$$724$$ 2.00000 0.00276243
$$725$$ 0 0
$$726$$ 505.000 451.686i 0.695592 0.622157i
$$727$$ 674.000i 0.927098i −0.886071 0.463549i $$-0.846576\pi$$
0.886071 0.463549i $$-0.153424\pi$$
$$728$$ 643.988 0.884598
$$729$$ −239.000 + 688.709i −0.327846 + 0.944731i
$$730$$ 0 0
$$731$$ 71.5542i 0.0978853i
$$732$$ 183.358 164.000i 0.250488 0.224044i
$$733$$ 656.000i 0.894952i 0.894296 + 0.447476i $$0.147677\pi$$
−0.894296 + 0.447476i $$0.852323\pi$$
$$734$$ 415.909i 0.566633i
$$735$$ 0 0
$$736$$ −210.000 −0.285326
$$737$$ −107.331 −0.145633
$$738$$ −1252.20 140.000i −1.69675 0.189702i
$$739$$ −598.000 −0.809202 −0.404601 0.914493i $$-0.632590\pi$$
−0.404601 + 0.914493i $$0.632590\pi$$
$$740$$ 0 0
$$741$$ 64.0000 + 71.5542i 0.0863698 + 0.0965643i
$$742$$ 60.0000i 0.0808625i
$$743$$ 782.624 1.05333 0.526665 0.850073i $$-0.323442\pi$$
0.526665 + 0.850073i $$0.323442\pi$$
$$744$$ 270.000 241.495i 0.362903 0.324591i
$$745$$ 0 0
$$746$$ 98.3870i 0.131886i
$$747$$ −93.9149 + 840.000i −0.125723 + 1.12450i
$$748$$ 20.0000i 0.0267380i
$$749$$ 1207.48i 1.61212i
$$750$$ 0 0
$$751$$ −338.000 −0.450067 −0.225033 0.974351i $$-0.572249\pi$$
−0.225033 + 0.974351i $$0.572249\pi$$
$$752$$ −934.676 −1.24292
$$753$$ −939.149 1050.00i −1.24721 1.39442i
$$754$$ 1120.00 1.48541
$$755$$ 0 0
$$756$$ 132.000 93.9149i 0.174603 0.124226i
$$757$$ 656.000i 0.866579i 0.901255 + 0.433289i $$0.142647\pi$$
−0.901255 + 0.433289i $$0.857353\pi$$
$$758$$ 809.457 1.06788
$$759$$ −120.000 134.164i −0.158103 0.176764i
$$760$$ 0 0
$$761$$ 295.161i 0.387859i −0.981015 0.193930i $$-0.937877\pi$$
0.981015 0.193930i $$-0.0621234\pi$$
$$762$$ 116.276 + 130.000i 0.152593 + 0.170604i
$$763$$ 228.000i 0.298820i
$$764$$ 205.718i 0.269265i
$$765$$ 0 0
$$766$$ −810.000 −1.05744
$$767$$ −71.5542 −0.0932910
$$768$$ 404.728 362.000i 0.526990 0.471354i
$$769$$ 82.0000 0.106632 0.0533160 0.998578i $$-0.483021\pi$$
0.0533160 + 0.998578i $$0.483021\pi$$
$$770$$ 0 0
$$771$$ −450.000 + 402.492i −0.583658 + 0.522039i
$$772$$ 214.000i 0.277202i
$$773$$ −1059.90 −1.37115 −0.685573 0.728004i $$-0.740448\pi$$
−0.685573 + 0.728004i $$0.740448\pi$$
$$774$$ 320.000 + 35.7771i 0.413437 + 0.0462236i
$$775$$ 0 0
$$776$$ 1113.56i 1.43500i
$$777$$ −214.663 + 192.000i −0.276271 + 0.247104i
$$778$$ 990.000i 1.27249i
$$779$$ 125.220i 0.160744i
$$780$$ 0 0
$$781$$ 560.000 0.717029
$$782$$ −134.164 −0.171565
$$783$$ −688.709 + 490.000i −0.879577 + 0.625798i
$$784$$ −247.000 −0.315051
$$785$$ 0 0
$$786$$ −60.0000 67.0820i −0.0763359 0.0853461i
$$787$$ 536.000i 0.681067i 0.940232 + 0.340534i $$0.110608\pi$$
−0.940232 + 0.340534i $$0.889392\pi$$
$$788$$ 93.9149 0.119181