# Properties

 Label 105.4.d.b.64.5 Level $105$ Weight $4$ Character 105.64 Analytic conductor $6.195$ Analytic rank $0$ Dimension $10$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$105 = 3 \cdot 5 \cdot 7$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 105.d (of order $$2$$, degree $$1$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$6.19520055060$$ Analytic rank: $$0$$ Dimension: $$10$$ Coefficient field: $$\mathbb{Q}[x]/(x^{10} + \cdots)$$ Defining polynomial: $$x^{10} + 37 x^{8} + 398 x^{6} + 1149 x^{4} + 1040 x^{2} + 100$$ Coefficient ring: $$\Z[a_1, \ldots, a_{5}]$$ Coefficient ring index: $$2^{9}\cdot 5$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

## Embedding invariants

 Embedding label 64.5 Root $$0.329739i$$ of defining polynomial Character $$\chi$$ $$=$$ 105.64 Dual form 105.4.d.b.64.6

## $q$-expansion

 $$f(q)$$ $$=$$ $$q-0.428319i q^{2} +3.00000i q^{3} +7.81654 q^{4} +(-1.76884 + 11.0395i) q^{5} +1.28496 q^{6} +7.00000i q^{7} -6.77452i q^{8} -9.00000 q^{9} +O(q^{10})$$ $$q-0.428319i q^{2} +3.00000i q^{3} +7.81654 q^{4} +(-1.76884 + 11.0395i) q^{5} +1.28496 q^{6} +7.00000i q^{7} -6.77452i q^{8} -9.00000 q^{9} +(4.72844 + 0.757628i) q^{10} -27.4721 q^{11} +23.4496i q^{12} +46.5524i q^{13} +2.99823 q^{14} +(-33.1186 - 5.30652i) q^{15} +59.6307 q^{16} +5.20546i q^{17} +3.85487i q^{18} +91.0007 q^{19} +(-13.8262 + 86.2910i) q^{20} -21.0000 q^{21} +11.7668i q^{22} +111.563i q^{23} +20.3236 q^{24} +(-118.742 - 39.0544i) q^{25} +19.9393 q^{26} -27.0000i q^{27} +54.7158i q^{28} -0.0763413 q^{29} +(-2.27288 + 14.1853i) q^{30} +201.784 q^{31} -79.7371i q^{32} -82.4163i q^{33} +2.22960 q^{34} +(-77.2767 - 12.3819i) q^{35} -70.3489 q^{36} -312.859i q^{37} -38.9773i q^{38} -139.657 q^{39} +(74.7876 + 11.9831i) q^{40} +102.432 q^{41} +8.99470i q^{42} -257.280i q^{43} -214.737 q^{44} +(15.9196 - 99.3558i) q^{45} +47.7847 q^{46} -350.994i q^{47} +178.892i q^{48} -49.0000 q^{49} +(-16.7277 + 50.8596i) q^{50} -15.6164 q^{51} +363.879i q^{52} -196.260i q^{53} -11.5646 q^{54} +(48.5938 - 303.279i) q^{55} +47.4217 q^{56} +273.002i q^{57} +0.0326984i q^{58} -881.060 q^{59} +(-258.873 - 41.4787i) q^{60} +737.897 q^{61} -86.4280i q^{62} -63.0000i q^{63} +442.893 q^{64} +(-513.917 - 82.3439i) q^{65} -35.3004 q^{66} +365.021i q^{67} +40.6887i q^{68} -334.690 q^{69} +(-5.30340 + 33.0991i) q^{70} +1112.53 q^{71} +60.9707i q^{72} -261.995i q^{73} -134.004 q^{74} +(117.163 - 356.227i) q^{75} +711.311 q^{76} -192.305i q^{77} +59.8179i q^{78} -273.829 q^{79} +(-105.477 + 658.295i) q^{80} +81.0000 q^{81} -43.8735i q^{82} +87.1353i q^{83} -164.147 q^{84} +(-57.4658 - 9.20763i) q^{85} -110.198 q^{86} -0.229024i q^{87} +186.110i q^{88} +1090.99 q^{89} +(-42.5559 - 6.81865i) q^{90} -325.867 q^{91} +872.039i q^{92} +605.353i q^{93} -150.337 q^{94} +(-160.966 + 1004.61i) q^{95} +239.211 q^{96} +228.830i q^{97} +20.9876i q^{98} +247.249 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$10q - 54q^{4} - 14q^{5} - 6q^{6} - 90q^{9} + O(q^{10})$$ $$10q - 54q^{4} - 14q^{5} - 6q^{6} - 90q^{9} + 92q^{10} + 132q^{11} - 14q^{14} + 310q^{16} - 348q^{19} + 366q^{20} - 210q^{21} + 198q^{24} - 374q^{25} + 892q^{26} - 740q^{29} - 378q^{30} + 684q^{31} - 224q^{34} + 486q^{36} - 12q^{39} - 2156q^{40} + 1604q^{41} - 580q^{44} + 126q^{45} + 1280q^{46} - 490q^{49} - 2504q^{50} - 648q^{51} + 54q^{54} - 452q^{55} + 462q^{56} - 1408q^{59} - 852q^{60} + 1300q^{61} - 150q^{64} - 3296q^{65} + 3036q^{66} - 696q^{69} - 882q^{70} + 2940q^{71} + 2624q^{74} - 408q^{75} + 8740q^{76} + 1640q^{79} - 4126q^{80} + 810q^{81} + 1134q^{84} - 1704q^{85} + 1664q^{86} - 572q^{89} - 828q^{90} - 28q^{91} - 5080q^{94} + 1268q^{95} + 330q^{96} - 1188q^{99} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/105\mathbb{Z}\right)^\times$$.

 $$n$$ $$22$$ $$31$$ $$71$$ $$\chi(n)$$ $$-1$$ $$1$$ $$1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0.428319i 0.151434i −0.997129 0.0757168i $$-0.975876\pi$$
0.997129 0.0757168i $$-0.0241245\pi$$
$$3$$ 3.00000i 0.577350i
$$4$$ 7.81654 0.977068
$$5$$ −1.76884 + 11.0395i −0.158210 + 0.987405i
$$6$$ 1.28496 0.0874302
$$7$$ 7.00000i 0.377964i
$$8$$ 6.77452i 0.299394i
$$9$$ −9.00000 −0.333333
$$10$$ 4.72844 + 0.757628i 0.149526 + 0.0239583i
$$11$$ −27.4721 −0.753013 −0.376507 0.926414i $$-0.622875\pi$$
−0.376507 + 0.926414i $$0.622875\pi$$
$$12$$ 23.4496i 0.564110i
$$13$$ 46.5524i 0.993179i 0.867986 + 0.496589i $$0.165414\pi$$
−0.867986 + 0.496589i $$0.834586\pi$$
$$14$$ 2.99823 0.0572365
$$15$$ −33.1186 5.30652i −0.570079 0.0913426i
$$16$$ 59.6307 0.931729
$$17$$ 5.20546i 0.0742653i 0.999310 + 0.0371326i $$0.0118224\pi$$
−0.999310 + 0.0371326i $$0.988178\pi$$
$$18$$ 3.85487i 0.0504779i
$$19$$ 91.0007 1.09879 0.549395 0.835563i $$-0.314858\pi$$
0.549395 + 0.835563i $$0.314858\pi$$
$$20$$ −13.8262 + 86.2910i −0.154582 + 0.964762i
$$21$$ −21.0000 −0.218218
$$22$$ 11.7668i 0.114032i
$$23$$ 111.563i 1.01142i 0.862705 + 0.505708i $$0.168769\pi$$
−0.862705 + 0.505708i $$0.831231\pi$$
$$24$$ 20.3236 0.172855
$$25$$ −118.742 39.0544i −0.949939 0.312435i
$$26$$ 19.9393 0.150401
$$27$$ 27.0000i 0.192450i
$$28$$ 54.7158i 0.369297i
$$29$$ −0.0763413 −0.000488835 −0.000244418 1.00000i $$-0.500078\pi$$
−0.000244418 1.00000i $$0.500078\pi$$
$$30$$ −2.27288 + 14.1853i −0.0138323 + 0.0863291i
$$31$$ 201.784 1.16908 0.584541 0.811364i $$-0.301275\pi$$
0.584541 + 0.811364i $$0.301275\pi$$
$$32$$ 79.7371i 0.440490i
$$33$$ 82.4163i 0.434752i
$$34$$ 2.22960 0.0112463
$$35$$ −77.2767 12.3819i −0.373204 0.0597978i
$$36$$ −70.3489 −0.325689
$$37$$ 312.859i 1.39010i −0.718960 0.695051i $$-0.755382\pi$$
0.718960 0.695051i $$-0.244618\pi$$
$$38$$ 38.9773i 0.166394i
$$39$$ −139.657 −0.573412
$$40$$ 74.7876 + 11.9831i 0.295624 + 0.0473672i
$$41$$ 102.432 0.390175 0.195087 0.980786i $$-0.437501\pi$$
0.195087 + 0.980786i $$0.437501\pi$$
$$42$$ 8.99470i 0.0330455i
$$43$$ 257.280i 0.912439i −0.889867 0.456219i $$-0.849203\pi$$
0.889867 0.456219i $$-0.150797\pi$$
$$44$$ −214.737 −0.735745
$$45$$ 15.9196 99.3558i 0.0527367 0.329135i
$$46$$ 47.7847 0.153162
$$47$$ 350.994i 1.08931i −0.838659 0.544657i $$-0.816660\pi$$
0.838659 0.544657i $$-0.183340\pi$$
$$48$$ 178.892i 0.537934i
$$49$$ −49.0000 −0.142857
$$50$$ −16.7277 + 50.8596i −0.0473131 + 0.143853i
$$51$$ −15.6164 −0.0428771
$$52$$ 363.879i 0.970403i
$$53$$ 196.260i 0.508649i −0.967119 0.254324i $$-0.918147\pi$$
0.967119 0.254324i $$-0.0818531\pi$$
$$54$$ −11.5646 −0.0291434
$$55$$ 48.5938 303.279i 0.119134 0.743530i
$$56$$ 47.4217 0.113160
$$57$$ 273.002i 0.634386i
$$58$$ 0.0326984i 7.40261e-5i
$$59$$ −881.060 −1.94414 −0.972070 0.234692i $$-0.924592\pi$$
−0.972070 + 0.234692i $$0.924592\pi$$
$$60$$ −258.873 41.4787i −0.557006 0.0892479i
$$61$$ 737.897 1.54882 0.774410 0.632684i $$-0.218047\pi$$
0.774410 + 0.632684i $$0.218047\pi$$
$$62$$ 86.4280i 0.177038i
$$63$$ 63.0000i 0.125988i
$$64$$ 442.893 0.865025
$$65$$ −513.917 82.3439i −0.980670 0.157131i
$$66$$ −35.3004 −0.0658361
$$67$$ 365.021i 0.665589i 0.942999 + 0.332794i $$0.107991\pi$$
−0.942999 + 0.332794i $$0.892009\pi$$
$$68$$ 40.6887i 0.0725622i
$$69$$ −334.690 −0.583941
$$70$$ −5.30340 + 33.0991i −0.00905539 + 0.0565157i
$$71$$ 1112.53 1.85962 0.929809 0.368042i $$-0.119972\pi$$
0.929809 + 0.368042i $$0.119972\pi$$
$$72$$ 60.9707i 0.0997982i
$$73$$ 261.995i 0.420057i −0.977695 0.210029i $$-0.932644\pi$$
0.977695 0.210029i $$-0.0673558\pi$$
$$74$$ −134.004 −0.210508
$$75$$ 117.163 356.227i 0.180384 0.548448i
$$76$$ 711.311 1.07359
$$77$$ 192.305i 0.284612i
$$78$$ 59.8179i 0.0868338i
$$79$$ −273.829 −0.389977 −0.194988 0.980806i $$-0.562467\pi$$
−0.194988 + 0.980806i $$0.562467\pi$$
$$80$$ −105.477 + 658.295i −0.147409 + 0.919995i
$$81$$ 81.0000 0.111111
$$82$$ 43.8735i 0.0590856i
$$83$$ 87.1353i 0.115233i 0.998339 + 0.0576165i $$0.0183501\pi$$
−0.998339 + 0.0576165i $$0.981650\pi$$
$$84$$ −164.147 −0.213214
$$85$$ −57.4658 9.20763i −0.0733299 0.0117495i
$$86$$ −110.198 −0.138174
$$87$$ 0.229024i 0.000282229i
$$88$$ 186.110i 0.225448i
$$89$$ 1090.99 1.29938 0.649690 0.760199i $$-0.274899\pi$$
0.649690 + 0.760199i $$0.274899\pi$$
$$90$$ −42.5559 6.81865i −0.0498421 0.00798610i
$$91$$ −325.867 −0.375386
$$92$$ 872.039i 0.988221i
$$93$$ 605.353i 0.674969i
$$94$$ −150.337 −0.164959
$$95$$ −160.966 + 1004.61i −0.173839 + 1.08495i
$$96$$ 239.211 0.254317
$$97$$ 228.830i 0.239527i 0.992802 + 0.119764i $$0.0382137\pi$$
−0.992802 + 0.119764i $$0.961786\pi$$
$$98$$ 20.9876i 0.0216334i
$$99$$ 247.249 0.251004
$$100$$ −928.155 305.270i −0.928155 0.305270i
$$101$$ −590.728 −0.581976 −0.290988 0.956727i $$-0.593984\pi$$
−0.290988 + 0.956727i $$0.593984\pi$$
$$102$$ 6.68879i 0.00649303i
$$103$$ 1471.06i 1.40726i 0.710568 + 0.703629i $$0.248438\pi$$
−0.710568 + 0.703629i $$0.751562\pi$$
$$104$$ 315.371 0.297352
$$105$$ 37.1457 231.830i 0.0345243 0.215470i
$$106$$ −84.0619 −0.0770265
$$107$$ 1223.29i 1.10523i 0.833435 + 0.552617i $$0.186371\pi$$
−0.833435 + 0.552617i $$0.813629\pi$$
$$108$$ 211.047i 0.188037i
$$109$$ −1280.64 −1.12535 −0.562674 0.826679i $$-0.690227\pi$$
−0.562674 + 0.826679i $$0.690227\pi$$
$$110$$ −129.900 20.8136i −0.112595 0.0180409i
$$111$$ 938.578 0.802576
$$112$$ 417.415i 0.352161i
$$113$$ 1805.38i 1.50297i −0.659748 0.751487i $$-0.729337\pi$$
0.659748 0.751487i $$-0.270663\pi$$
$$114$$ 116.932 0.0960674
$$115$$ −1231.61 197.338i −0.998677 0.160016i
$$116$$ −0.596725 −0.000477625
$$117$$ 418.972i 0.331060i
$$118$$ 377.375i 0.294408i
$$119$$ −36.4382 −0.0280696
$$120$$ −35.9492 + 224.363i −0.0273475 + 0.170678i
$$121$$ −576.284 −0.432971
$$122$$ 316.055i 0.234543i
$$123$$ 307.296i 0.225268i
$$124$$ 1577.26 1.14227
$$125$$ 641.178 1241.78i 0.458790 0.888545i
$$126$$ −26.9841 −0.0190788
$$127$$ 1642.42i 1.14757i −0.819005 0.573786i $$-0.805474\pi$$
0.819005 0.573786i $$-0.194526\pi$$
$$128$$ 827.596i 0.571483i
$$129$$ 771.841 0.526797
$$130$$ −35.2694 + 220.120i −0.0237949 + 0.148506i
$$131$$ 2371.85 1.58190 0.790951 0.611879i $$-0.209586\pi$$
0.790951 + 0.611879i $$0.209586\pi$$
$$132$$ 644.210i 0.424783i
$$133$$ 637.005i 0.415303i
$$134$$ 156.345 0.100792
$$135$$ 298.067 + 47.7587i 0.190026 + 0.0304475i
$$136$$ 35.2645 0.0222346
$$137$$ 762.828i 0.475714i −0.971300 0.237857i $$-0.923555\pi$$
0.971300 0.237857i $$-0.0764450\pi$$
$$138$$ 143.354i 0.0884283i
$$139$$ −2025.84 −1.23618 −0.618092 0.786105i $$-0.712094\pi$$
−0.618092 + 0.786105i $$0.712094\pi$$
$$140$$ −604.037 96.7836i −0.364646 0.0584265i
$$141$$ 1052.98 0.628916
$$142$$ 476.517i 0.281609i
$$143$$ 1278.89i 0.747877i
$$144$$ −536.676 −0.310576
$$145$$ 0.135036 0.842772i 7.73386e−5 0.000482679i
$$146$$ −112.217 −0.0636108
$$147$$ 147.000i 0.0824786i
$$148$$ 2445.48i 1.35822i
$$149$$ 10.7903 0.00593272 0.00296636 0.999996i $$-0.499056\pi$$
0.00296636 + 0.999996i $$0.499056\pi$$
$$150$$ −152.579 50.1832i −0.0830534 0.0273162i
$$151$$ −2404.48 −1.29585 −0.647925 0.761704i $$-0.724363\pi$$
−0.647925 + 0.761704i $$0.724363\pi$$
$$152$$ 616.487i 0.328972i
$$153$$ 46.8491i 0.0247551i
$$154$$ −82.3677 −0.0430999
$$155$$ −356.924 + 2227.60i −0.184960 + 1.15436i
$$156$$ −1091.64 −0.560262
$$157$$ 396.624i 0.201618i −0.994906 0.100809i $$-0.967857\pi$$
0.994906 0.100809i $$-0.0321431\pi$$
$$158$$ 117.286i 0.0590556i
$$159$$ 588.780 0.293669
$$160$$ 880.260 + 141.042i 0.434942 + 0.0696899i
$$161$$ −780.943 −0.382279
$$162$$ 34.6938i 0.0168260i
$$163$$ 2751.69i 1.32226i 0.750270 + 0.661132i $$0.229923\pi$$
−0.750270 + 0.661132i $$0.770077\pi$$
$$164$$ 800.663 0.381227
$$165$$ 909.837 + 145.781i 0.429277 + 0.0687822i
$$166$$ 37.3217 0.0174501
$$167$$ 2079.43i 0.963541i 0.876297 + 0.481771i $$0.160006\pi$$
−0.876297 + 0.481771i $$0.839994\pi$$
$$168$$ 142.265i 0.0653332i
$$169$$ 29.8706 0.0135961
$$170$$ −3.94380 + 24.6137i −0.00177927 + 0.0111046i
$$171$$ −819.007 −0.366263
$$172$$ 2011.04i 0.891515i
$$173$$ 1929.59i 0.848000i −0.905662 0.424000i $$-0.860626\pi$$
0.905662 0.424000i $$-0.139374\pi$$
$$174$$ −0.0980953 −4.27390e−5
$$175$$ 273.380 831.197i 0.118089 0.359043i
$$176$$ −1638.18 −0.701605
$$177$$ 2643.18i 1.12245i
$$178$$ 467.292i 0.196770i
$$179$$ −1638.15 −0.684027 −0.342014 0.939695i $$-0.611109\pi$$
−0.342014 + 0.939695i $$0.611109\pi$$
$$180$$ 124.436 776.619i 0.0515273 0.321587i
$$181$$ −36.6604 −0.0150550 −0.00752749 0.999972i $$-0.502396\pi$$
−0.00752749 + 0.999972i $$0.502396\pi$$
$$182$$ 139.575i 0.0568461i
$$183$$ 2213.69i 0.894212i
$$184$$ 755.788 0.302812
$$185$$ 3453.82 + 553.399i 1.37259 + 0.219928i
$$186$$ 259.284 0.102213
$$187$$ 143.005i 0.0559227i
$$188$$ 2743.56i 1.06433i
$$189$$ 189.000 0.0727393
$$190$$ 430.291 + 68.9447i 0.164298 + 0.0263251i
$$191$$ 1054.82 0.399603 0.199801 0.979836i $$-0.435970\pi$$
0.199801 + 0.979836i $$0.435970\pi$$
$$192$$ 1328.68i 0.499422i
$$193$$ 213.661i 0.0796873i −0.999206 0.0398436i $$-0.987314\pi$$
0.999206 0.0398436i $$-0.0126860\pi$$
$$194$$ 98.0121 0.0362725
$$195$$ 247.032 1541.75i 0.0907195 0.566190i
$$196$$ −383.011 −0.139581
$$197$$ 3953.62i 1.42987i 0.699193 + 0.714933i $$0.253543\pi$$
−0.699193 + 0.714933i $$0.746457\pi$$
$$198$$ 105.901i 0.0380105i
$$199$$ −929.168 −0.330990 −0.165495 0.986211i $$-0.552922\pi$$
−0.165495 + 0.986211i $$0.552922\pi$$
$$200$$ −264.575 + 804.423i −0.0935413 + 0.284407i
$$201$$ −1095.06 −0.384278
$$202$$ 253.020i 0.0881308i
$$203$$ 0.534389i 0.000184762i
$$204$$ −122.066 −0.0418938
$$205$$ −181.186 + 1130.80i −0.0617295 + 0.385261i
$$206$$ 630.081 0.213106
$$207$$ 1004.07i 0.337138i
$$208$$ 2775.95i 0.925374i
$$209$$ −2499.98 −0.827403
$$210$$ −99.2972 15.9102i −0.0326293 0.00522813i
$$211$$ −926.806 −0.302388 −0.151194 0.988504i $$-0.548312\pi$$
−0.151194 + 0.988504i $$0.548312\pi$$
$$212$$ 1534.07i 0.496984i
$$213$$ 3337.59i 1.07365i
$$214$$ 523.959 0.167370
$$215$$ 2840.25 + 455.088i 0.900947 + 0.144357i
$$216$$ −182.912 −0.0576185
$$217$$ 1412.49i 0.441871i
$$218$$ 548.521i 0.170415i
$$219$$ 785.985 0.242520
$$220$$ 379.835 2370.59i 0.116402 0.726479i
$$221$$ −242.327 −0.0737587
$$222$$ 402.011i 0.121537i
$$223$$ 5351.73i 1.60708i 0.595253 + 0.803538i $$0.297052\pi$$
−0.595253 + 0.803538i $$0.702948\pi$$
$$224$$ 558.160 0.166489
$$225$$ 1068.68 + 351.489i 0.316646 + 0.104145i
$$226$$ −773.279 −0.227601
$$227$$ 6016.48i 1.75915i 0.475758 + 0.879576i $$0.342174\pi$$
−0.475758 + 0.879576i $$0.657826\pi$$
$$228$$ 2133.93i 0.619839i
$$229$$ −1210.84 −0.349408 −0.174704 0.984621i $$-0.555897\pi$$
−0.174704 + 0.984621i $$0.555897\pi$$
$$230$$ −84.5235 + 527.520i −0.0242318 + 0.151233i
$$231$$ 576.914 0.164321
$$232$$ 0.517176i 0.000146355i
$$233$$ 3517.31i 0.988957i −0.869190 0.494478i $$-0.835359\pi$$
0.869190 0.494478i $$-0.164641\pi$$
$$234$$ −179.454 −0.0501335
$$235$$ 3874.81 + 620.853i 1.07559 + 0.172340i
$$236$$ −6886.84 −1.89956
$$237$$ 821.487i 0.225153i
$$238$$ 15.6072i 0.00425068i
$$239$$ 6715.89 1.81764 0.908818 0.417194i $$-0.136986\pi$$
0.908818 + 0.417194i $$0.136986\pi$$
$$240$$ −1974.88 316.432i −0.531159 0.0851066i
$$241$$ −1715.70 −0.458582 −0.229291 0.973358i $$-0.573641\pi$$
−0.229291 + 0.973358i $$0.573641\pi$$
$$242$$ 246.833i 0.0655663i
$$243$$ 243.000i 0.0641500i
$$244$$ 5767.80 1.51330
$$245$$ 86.6732 540.937i 0.0226014 0.141058i
$$246$$ 131.620 0.0341131
$$247$$ 4236.31i 1.09129i
$$248$$ 1366.99i 0.350017i
$$249$$ −261.406 −0.0665298
$$250$$ −531.877 274.629i −0.134556 0.0694762i
$$251$$ −2464.48 −0.619748 −0.309874 0.950778i $$-0.600287\pi$$
−0.309874 + 0.950778i $$0.600287\pi$$
$$252$$ 492.442i 0.123099i
$$253$$ 3064.88i 0.761609i
$$254$$ −703.482 −0.173781
$$255$$ 27.6229 172.397i 0.00678358 0.0423370i
$$256$$ 3188.67 0.778483
$$257$$ 1873.99i 0.454850i −0.973796 0.227425i $$-0.926969\pi$$
0.973796 0.227425i $$-0.0730307\pi$$
$$258$$ 330.594i 0.0797747i
$$259$$ 2190.02 0.525409
$$260$$ −4017.05 643.644i −0.958181 0.153527i
$$261$$ 0.687072 0.000162945
$$262$$ 1015.91i 0.239553i
$$263$$ 2064.39i 0.484013i −0.970275 0.242007i $$-0.922194\pi$$
0.970275 0.242007i $$-0.0778056\pi$$
$$264$$ −558.331 −0.130162
$$265$$ 2166.62 + 347.153i 0.502243 + 0.0804733i
$$266$$ 272.841 0.0628909
$$267$$ 3272.97i 0.750197i
$$268$$ 2853.20i 0.650325i
$$269$$ −5649.86 −1.28059 −0.640294 0.768130i $$-0.721188\pi$$
−0.640294 + 0.768130i $$0.721188\pi$$
$$270$$ 20.4560 127.668i 0.00461078 0.0287764i
$$271$$ −3094.93 −0.693739 −0.346870 0.937913i $$-0.612755\pi$$
−0.346870 + 0.937913i $$0.612755\pi$$
$$272$$ 310.405i 0.0691951i
$$273$$ 977.601i 0.216729i
$$274$$ −326.734 −0.0720391
$$275$$ 3262.10 + 1072.90i 0.715317 + 0.235268i
$$276$$ −2616.12 −0.570550
$$277$$ 8962.93i 1.94415i −0.234665 0.972076i $$-0.575399\pi$$
0.234665 0.972076i $$-0.424601\pi$$
$$278$$ 867.706i 0.187200i
$$279$$ −1816.06 −0.389694
$$280$$ −83.8814 + 523.513i −0.0179031 + 0.111735i
$$281$$ −5858.94 −1.24383 −0.621913 0.783086i $$-0.713644\pi$$
−0.621913 + 0.783086i $$0.713644\pi$$
$$282$$ 451.012i 0.0952390i
$$283$$ 5819.46i 1.22237i −0.791487 0.611186i $$-0.790693\pi$$
0.791487 0.611186i $$-0.209307\pi$$
$$284$$ 8696.13 1.81697
$$285$$ −3013.82 482.898i −0.626397 0.100366i
$$286$$ −547.774 −0.113254
$$287$$ 717.023i 0.147472i
$$288$$ 717.634i 0.146830i
$$289$$ 4885.90 0.994485
$$290$$ −0.360975 0.0578383i −7.30938e−5 1.17117e-5i
$$291$$ −686.489 −0.138291
$$292$$ 2047.90i 0.410425i
$$293$$ 5678.78i 1.13228i −0.824310 0.566139i $$-0.808436\pi$$
0.824310 0.566139i $$-0.191564\pi$$
$$294$$ −62.9629 −0.0124900
$$295$$ 1558.46 9726.49i 0.307582 1.91965i
$$296$$ −2119.47 −0.416189
$$297$$ 741.746i 0.144917i
$$298$$ 4.62169i 0.000898413i
$$299$$ −5193.54 −1.00452
$$300$$ 915.810 2784.47i 0.176248 0.535871i
$$301$$ 1800.96 0.344869
$$302$$ 1029.88i 0.196235i
$$303$$ 1772.18i 0.336004i
$$304$$ 5426.44 1.02377
$$305$$ −1305.22 + 8146.04i −0.245039 + 1.52931i
$$306$$ −20.0664 −0.00374875
$$307$$ 9184.53i 1.70745i 0.520720 + 0.853727i $$0.325663\pi$$
−0.520720 + 0.853727i $$0.674337\pi$$
$$308$$ 1503.16i 0.278086i
$$309$$ −4413.17 −0.812480
$$310$$ 954.125 + 152.877i 0.174808 + 0.0280092i
$$311$$ 4410.22 0.804119 0.402059 0.915614i $$-0.368295\pi$$
0.402059 + 0.915614i $$0.368295\pi$$
$$312$$ 946.112i 0.171676i
$$313$$ 4405.28i 0.795530i 0.917487 + 0.397765i $$0.130214\pi$$
−0.917487 + 0.397765i $$0.869786\pi$$
$$314$$ −169.882 −0.0305318
$$315$$ 695.490 + 111.437i 0.124401 + 0.0199326i
$$316$$ −2140.40 −0.381034
$$317$$ 7486.86i 1.32651i −0.748393 0.663256i $$-0.769174\pi$$
0.748393 0.663256i $$-0.230826\pi$$
$$318$$ 252.186i 0.0444713i
$$319$$ 2.09726 0.000368100
$$320$$ −783.407 + 4889.33i −0.136856 + 0.854130i
$$321$$ −3669.87 −0.638107
$$322$$ 334.493i 0.0578899i
$$323$$ 473.701i 0.0816019i
$$324$$ 633.140 0.108563
$$325$$ 1818.08 5527.75i 0.310304 0.943459i
$$326$$ 1178.60 0.200235
$$327$$ 3841.91i 0.649719i
$$328$$ 693.927i 0.116816i
$$329$$ 2456.96 0.411722
$$330$$ 62.4409 389.700i 0.0104159 0.0650070i
$$331$$ 8860.56 1.47136 0.735680 0.677329i $$-0.236863\pi$$
0.735680 + 0.677329i $$0.236863\pi$$
$$332$$ 681.097i 0.112590i
$$333$$ 2815.74i 0.463367i
$$334$$ 890.660 0.145912
$$335$$ −4029.66 645.665i −0.657206 0.105303i
$$336$$ −1252.24 −0.203320
$$337$$ 8742.01i 1.41308i −0.707674 0.706539i $$-0.750255\pi$$
0.707674 0.706539i $$-0.249745\pi$$
$$338$$ 12.7942i 0.00205891i
$$339$$ 5416.15 0.867742
$$340$$ −449.184 71.9719i −0.0716483 0.0114801i
$$341$$ −5543.44 −0.880334
$$342$$ 350.796i 0.0554646i
$$343$$ 343.000i 0.0539949i
$$344$$ −1742.95 −0.273179
$$345$$ 592.013 3694.82i 0.0923853 0.576586i
$$346$$ −826.480 −0.128416
$$347$$ 7285.82i 1.12716i −0.826063 0.563579i $$-0.809424\pi$$
0.826063 0.563579i $$-0.190576\pi$$
$$348$$ 1.79018i 0.000275757i
$$349$$ −12610.9 −1.93423 −0.967117 0.254330i $$-0.918145\pi$$
−0.967117 + 0.254330i $$0.918145\pi$$
$$350$$ −356.017 117.094i −0.0543712 0.0178827i
$$351$$ 1256.92 0.191137
$$352$$ 2190.55i 0.331695i
$$353$$ 1202.59i 0.181325i 0.995882 + 0.0906623i $$0.0288984\pi$$
−0.995882 + 0.0906623i $$0.971102\pi$$
$$354$$ −1132.12 −0.169977
$$355$$ −1967.89 + 12281.8i −0.294210 + 1.83620i
$$356$$ 8527.78 1.26958
$$357$$ 109.315i 0.0162060i
$$358$$ 701.649i 0.103585i
$$359$$ −3216.35 −0.472848 −0.236424 0.971650i $$-0.575975\pi$$
−0.236424 + 0.971650i $$0.575975\pi$$
$$360$$ −673.088 107.848i −0.0985413 0.0157891i
$$361$$ 1422.14 0.207339
$$362$$ 15.7024i 0.00227983i
$$363$$ 1728.85i 0.249976i
$$364$$ −2547.15 −0.366778
$$365$$ 2892.30 + 463.428i 0.414767 + 0.0664573i
$$366$$ 948.166 0.135414
$$367$$ 1259.66i 0.179165i −0.995979 0.0895824i $$-0.971447\pi$$
0.995979 0.0895824i $$-0.0285532\pi$$
$$368$$ 6652.59i 0.942365i
$$369$$ −921.887 −0.130058
$$370$$ 237.031 1479.34i 0.0333045 0.207857i
$$371$$ 1373.82 0.192251
$$372$$ 4731.77i 0.659491i
$$373$$ 386.230i 0.0536145i 0.999641 + 0.0268073i $$0.00853404\pi$$
−0.999641 + 0.0268073i $$0.991466\pi$$
$$374$$ −61.2517 −0.00846858
$$375$$ 3725.34 + 1923.53i 0.513002 + 0.264882i
$$376$$ −2377.82 −0.326135
$$377$$ 3.55387i 0.000485501i
$$378$$ 80.9523i 0.0110152i
$$379$$ −14246.0 −1.93079 −0.965395 0.260794i $$-0.916016\pi$$
−0.965395 + 0.260794i $$0.916016\pi$$
$$380$$ −1258.20 + 7852.54i −0.169853 + 1.06007i
$$381$$ 4927.27 0.662551
$$382$$ 451.800i 0.0605133i
$$383$$ 9298.85i 1.24060i −0.784365 0.620299i $$-0.787011\pi$$
0.784365 0.620299i $$-0.212989\pi$$
$$384$$ 2482.79 0.329946
$$385$$ 2122.95 + 340.156i 0.281028 + 0.0450285i
$$386$$ −91.5150 −0.0120673
$$387$$ 2315.52i 0.304146i
$$388$$ 1788.66i 0.234034i
$$389$$ 1043.80 0.136049 0.0680244 0.997684i $$-0.478330\pi$$
0.0680244 + 0.997684i $$0.478330\pi$$
$$390$$ −660.361 105.808i −0.0857402 0.0137380i
$$391$$ −580.738 −0.0751130
$$392$$ 331.952i 0.0427706i
$$393$$ 7115.54i 0.913312i
$$394$$ 1693.41 0.216530
$$395$$ 484.360 3022.94i 0.0616982 0.385065i
$$396$$ 1932.63 0.245248
$$397$$ 4482.04i 0.566617i 0.959029 + 0.283309i $$0.0914321\pi$$
−0.959029 + 0.283309i $$0.908568\pi$$
$$398$$ 397.980i 0.0501230i
$$399$$ −1911.02 −0.239776
$$400$$ −7080.69 2328.84i −0.885086 0.291105i
$$401$$ 12686.2 1.57984 0.789921 0.613209i $$-0.210122\pi$$
0.789921 + 0.613209i $$0.210122\pi$$
$$402$$ 469.036i 0.0581926i
$$403$$ 9393.55i 1.16111i
$$404$$ −4617.45 −0.568630
$$405$$ −143.276 + 894.202i −0.0175789 + 0.109712i
$$406$$ −0.228889 −2.79792e−5
$$407$$ 8594.90i 1.04677i
$$408$$ 105.794i 0.0128372i
$$409$$ 6836.54 0.826516 0.413258 0.910614i $$-0.364391\pi$$
0.413258 + 0.910614i $$0.364391\pi$$
$$410$$ 484.343 + 77.6052i 0.0583414 + 0.00934793i
$$411$$ 2288.48 0.274654
$$412$$ 11498.6i 1.37499i
$$413$$ 6167.42i 0.734816i
$$414$$ −430.062 −0.0510541
$$415$$ −961.932 154.128i −0.113782 0.0182310i
$$416$$ 3711.96 0.437485
$$417$$ 6077.53i 0.713712i
$$418$$ 1070.79i 0.125297i
$$419$$ 5091.64 0.593659 0.296829 0.954930i $$-0.404071\pi$$
0.296829 + 0.954930i $$0.404071\pi$$
$$420$$ 290.351 1812.11i 0.0337325 0.210528i
$$421$$ 8373.48 0.969355 0.484677 0.874693i $$-0.338937\pi$$
0.484677 + 0.874693i $$0.338937\pi$$
$$422$$ 396.968i 0.0457918i
$$423$$ 3158.95i 0.363105i
$$424$$ −1329.57 −0.152287
$$425$$ 203.296 618.109i 0.0232031 0.0705475i
$$426$$ 1429.55 0.162587
$$427$$ 5165.28i 0.585399i
$$428$$ 9561.91i 1.07989i
$$429$$ 3836.68 0.431787
$$430$$ 194.923 1216.53i 0.0218605 0.136434i
$$431$$ 6027.75 0.673657 0.336829 0.941566i $$-0.390646\pi$$
0.336829 + 0.941566i $$0.390646\pi$$
$$432$$ 1610.03i 0.179311i
$$433$$ 11927.5i 1.32379i −0.749597 0.661894i $$-0.769753\pi$$
0.749597 0.661894i $$-0.230247\pi$$
$$434$$ 604.996 0.0669141
$$435$$ 2.52832 + 0.405107i 0.000278675 + 4.46515e-5i
$$436$$ −10010.2 −1.09954
$$437$$ 10152.3i 1.11133i
$$438$$ 336.652i 0.0367257i
$$439$$ −7914.93 −0.860499 −0.430250 0.902710i $$-0.641574\pi$$
−0.430250 + 0.902710i $$0.641574\pi$$
$$440$$ −2054.57 329.200i −0.222609 0.0356681i
$$441$$ 441.000 0.0476190
$$442$$ 103.793i 0.0111695i
$$443$$ 2522.71i 0.270559i 0.990807 + 0.135279i $$0.0431932\pi$$
−0.990807 + 0.135279i $$0.956807\pi$$
$$444$$ 7336.44 0.784171
$$445$$ −1929.79 + 12044.0i −0.205575 + 1.28302i
$$446$$ 2292.24 0.243365
$$447$$ 32.3709i 0.00342526i
$$448$$ 3100.25i 0.326949i
$$449$$ 5339.89 0.561258 0.280629 0.959816i $$-0.409457\pi$$
0.280629 + 0.959816i $$0.409457\pi$$
$$450$$ 150.549 457.737i 0.0157710 0.0479509i
$$451$$ −2814.02 −0.293807
$$452$$ 14111.8i 1.46851i
$$453$$ 7213.43i 0.748160i
$$454$$ 2576.97 0.266395
$$455$$ 576.407 3597.42i 0.0593899 0.370658i
$$456$$ 1849.46 0.189932
$$457$$ 13765.8i 1.40905i −0.709679 0.704526i $$-0.751160\pi$$
0.709679 0.704526i $$-0.248840\pi$$
$$458$$ 518.625i 0.0529122i
$$459$$ 140.547 0.0142924
$$460$$ −9626.90 1542.50i −0.975775 0.156346i
$$461$$ −12501.1 −1.26298 −0.631489 0.775384i $$-0.717556\pi$$
−0.631489 + 0.775384i $$0.717556\pi$$
$$462$$ 247.103i 0.0248837i
$$463$$ 3566.32i 0.357972i −0.983852 0.178986i $$-0.942718\pi$$
0.983852 0.178986i $$-0.0572817\pi$$
$$464$$ −4.55229 −0.000455462
$$465$$ −6682.81 1070.77i −0.666469 0.106787i
$$466$$ −1506.53 −0.149761
$$467$$ 4078.17i 0.404101i −0.979375 0.202050i $$-0.935240\pi$$
0.979375 0.202050i $$-0.0647605\pi$$
$$468$$ 3274.91i 0.323468i
$$469$$ −2555.15 −0.251569
$$470$$ 265.923 1659.65i 0.0260981 0.162881i
$$471$$ 1189.87 0.116404
$$472$$ 5968.76i 0.582065i
$$473$$ 7068.03i 0.687079i
$$474$$ −351.858 −0.0340958
$$475$$ −10805.6 3553.98i −1.04378 0.343300i
$$476$$ −284.821 −0.0274259
$$477$$ 1766.34i 0.169550i
$$478$$ 2876.54i 0.275251i
$$479$$ −19078.0 −1.81982 −0.909911 0.414803i $$-0.863850\pi$$
−0.909911 + 0.414803i $$0.863850\pi$$
$$480$$ −423.127 + 2640.78i −0.0402355 + 0.251114i
$$481$$ 14564.4 1.38062
$$482$$ 734.868i 0.0694447i
$$483$$ 2342.83i 0.220709i
$$484$$ −4504.55 −0.423042
$$485$$ −2526.17 404.764i −0.236511 0.0378956i
$$486$$ 104.081 0.00971447
$$487$$ 15616.4i 1.45307i −0.687128 0.726537i $$-0.741129\pi$$
0.687128 0.726537i $$-0.258871\pi$$
$$488$$ 4998.90i 0.463708i
$$489$$ −8255.07 −0.763409
$$490$$ −231.693 37.1238i −0.0213609 0.00342262i
$$491$$ 7547.46 0.693711 0.346856 0.937919i $$-0.387249\pi$$
0.346856 + 0.937919i $$0.387249\pi$$
$$492$$ 2401.99i 0.220102i
$$493$$ 0.397392i 3.63035e-5i
$$494$$ 1814.49 0.165259
$$495$$ −437.344 + 2729.51i −0.0397114 + 0.247843i
$$496$$ 12032.5 1.08927
$$497$$ 7787.70i 0.702870i
$$498$$ 111.965i 0.0100748i
$$499$$ −3288.10 −0.294982 −0.147491 0.989063i $$-0.547120\pi$$
−0.147491 + 0.989063i $$0.547120\pi$$
$$500$$ 5011.80 9706.42i 0.448269 0.868169i
$$501$$ −6238.30 −0.556301
$$502$$ 1055.58i 0.0938506i
$$503$$ 1044.67i 0.0926032i −0.998928 0.0463016i $$-0.985256\pi$$
0.998928 0.0463016i $$-0.0147435\pi$$
$$504$$ −426.795 −0.0377202
$$505$$ 1044.90 6521.36i 0.0920745 0.574647i
$$506$$ −1312.74 −0.115333
$$507$$ 89.6119i 0.00784972i
$$508$$ 12838.1i 1.12126i
$$509$$ 8783.91 0.764912 0.382456 0.923974i $$-0.375078\pi$$
0.382456 + 0.923974i $$0.375078\pi$$
$$510$$ −73.8411 11.8314i −0.00641125 0.00102726i
$$511$$ 1833.97 0.158767
$$512$$ 7986.54i 0.689372i
$$513$$ 2457.02i 0.211462i
$$514$$ −802.666 −0.0688796
$$515$$ −16239.8 2602.07i −1.38953 0.222642i
$$516$$ 6033.13 0.514716
$$517$$ 9642.54i 0.820268i
$$518$$ 938.025i 0.0795646i
$$519$$ 5788.77 0.489593
$$520$$ −557.841 + 3481.54i −0.0470441 + 0.293607i
$$521$$ 9983.79 0.839535 0.419767 0.907632i $$-0.362112\pi$$
0.419767 + 0.907632i $$0.362112\pi$$
$$522$$ 0.294286i 2.46754e-5i
$$523$$ 8177.52i 0.683706i 0.939754 + 0.341853i $$0.111054\pi$$
−0.939754 + 0.341853i $$0.888946\pi$$
$$524$$ 18539.6 1.54563
$$525$$ 2493.59 + 820.141i 0.207294 + 0.0681789i
$$526$$ −884.215 −0.0732958
$$527$$ 1050.38i 0.0868221i
$$528$$ 4914.54i 0.405072i
$$529$$ −279.364 −0.0229608
$$530$$ 148.692 928.003i 0.0121864 0.0760564i
$$531$$ 7929.54 0.648046
$$532$$ 4979.18i 0.405780i
$$533$$ 4768.45i 0.387513i
$$534$$ 1401.88 0.113605
$$535$$ −13504.6 2163.81i −1.09131 0.174859i
$$536$$ 2472.85 0.199274
$$537$$ 4914.44i 0.394923i
$$538$$ 2419.94i 0.193924i
$$539$$ 1346.13 0.107573
$$540$$ 2329.86 + 373.308i 0.185669 + 0.0297493i
$$541$$ −3425.16 −0.272198 −0.136099 0.990695i $$-0.543457\pi$$
−0.136099 + 0.990695i $$0.543457\pi$$
$$542$$ 1325.61i 0.105055i
$$543$$ 109.981i 0.00869199i
$$544$$ 415.068 0.0327131
$$545$$ 2265.24 14137.6i 0.178041 1.11117i
$$546$$ −418.725 −0.0328201
$$547$$ 5955.72i 0.465536i −0.972532 0.232768i $$-0.925222\pi$$
0.972532 0.232768i $$-0.0747783\pi$$
$$548$$ 5962.68i 0.464805i
$$549$$ −6641.07 −0.516273
$$550$$ 459.545 1397.22i 0.0356274 0.108323i
$$551$$ −6.94712 −0.000537127
$$552$$ 2267.36i 0.174829i
$$553$$ 1916.80i 0.147397i
$$554$$ −3838.99 −0.294410
$$555$$ −1660.20 + 10361.5i −0.126976 + 0.792468i
$$556$$ −15835.1 −1.20784
$$557$$ 2506.35i 0.190660i −0.995446 0.0953298i $$-0.969609\pi$$
0.995446 0.0953298i $$-0.0303906\pi$$
$$558$$ 777.852i 0.0590127i
$$559$$ 11977.0 0.906215
$$560$$ −4608.06 738.341i −0.347725 0.0557153i
$$561$$ 429.015 0.0322870
$$562$$ 2509.50i 0.188357i
$$563$$ 3460.79i 0.259068i −0.991575 0.129534i $$-0.958652\pi$$
0.991575 0.129534i $$-0.0413481\pi$$
$$564$$ 8230.68 0.614493
$$565$$ 19930.6 + 3193.43i 1.48404 + 0.237786i
$$566$$ −2492.59 −0.185108
$$567$$ 567.000i 0.0419961i
$$568$$ 7536.86i 0.556760i
$$569$$ −22561.2 −1.66224 −0.831119 0.556095i $$-0.812299\pi$$
−0.831119 + 0.556095i $$0.812299\pi$$
$$570$$ −206.834 + 1290.87i −0.0151988 + 0.0948575i
$$571$$ −992.585 −0.0727467 −0.0363734 0.999338i $$-0.511581\pi$$
−0.0363734 + 0.999338i $$0.511581\pi$$
$$572$$ 9996.52i 0.730726i
$$573$$ 3164.46i 0.230711i
$$574$$ 307.114 0.0223322
$$575$$ 4357.03 13247.3i 0.316001 0.960783i
$$576$$ −3986.03 −0.288342
$$577$$ 9202.70i 0.663975i 0.943284 + 0.331987i $$0.107719\pi$$
−0.943284 + 0.331987i $$0.892281\pi$$
$$578$$ 2092.72i 0.150598i
$$579$$ 640.983 0.0460075
$$580$$ 1.05551 6.58756i 7.55651e−5 0.000471610i
$$581$$ −609.947 −0.0435540
$$582$$ 294.036i 0.0209419i
$$583$$ 5391.67i 0.383019i
$$584$$ −1774.89 −0.125763
$$585$$ 4625.25 + 741.095i 0.326890 + 0.0523769i
$$586$$ −2432.33 −0.171465
$$587$$ 27046.3i 1.90174i 0.309593 + 0.950869i $$0.399807\pi$$
−0.309593 + 0.950869i $$0.600193\pi$$
$$588$$ 1149.03i 0.0805872i
$$589$$ 18362.5 1.28457
$$590$$ −4166.04 667.516i −0.290700 0.0465783i
$$591$$ −11860.9 −0.825534
$$592$$ 18656.0i 1.29520i
$$593$$ 26364.0i 1.82570i 0.408298 + 0.912849i $$0.366123\pi$$
−0.408298 + 0.912849i $$0.633877\pi$$
$$594$$ 317.704 0.0219454
$$595$$ 64.4534 402.261i 0.00444090 0.0277161i
$$596$$ 84.3428 0.00579667
$$597$$ 2787.50i 0.191097i
$$598$$ 2224.49i 0.152117i
$$599$$ −6624.09 −0.451841 −0.225921 0.974146i $$-0.572539\pi$$
−0.225921 + 0.974146i $$0.572539\pi$$
$$600$$ −2413.27 793.724i −0.164202 0.0540061i
$$601$$ −3984.03 −0.270403 −0.135201 0.990818i $$-0.543168\pi$$
−0.135201 + 0.990818i $$0.543168\pi$$
$$602$$ 771.386i 0.0522248i
$$603$$ 3285.19i 0.221863i
$$604$$ −18794.7 −1.26613
$$605$$ 1019.36 6361.91i 0.0685003 0.427518i
$$606$$ −759.060 −0.0508823
$$607$$ 8605.79i 0.575450i −0.957713 0.287725i $$-0.907101\pi$$
0.957713 0.287725i $$-0.0928990\pi$$
$$608$$ 7256.14i 0.484005i
$$609$$ 1.60317 0.000106673
$$610$$ 3489.10 + 559.052i 0.231589 + 0.0371071i
$$611$$ 16339.6 1.08188
$$612$$ 366.198i 0.0241874i
$$613$$ 22070.4i 1.45418i 0.686541 + 0.727091i $$0.259128\pi$$
−0.686541 + 0.727091i $$0.740872\pi$$
$$614$$ 3933.91 0.258566
$$615$$ −3392.40 543.557i −0.222430 0.0356396i
$$616$$ −1302.77 −0.0852114
$$617$$ 17328.8i 1.13068i 0.824858 + 0.565340i $$0.191255\pi$$
−0.824858 + 0.565340i $$0.808745\pi$$
$$618$$ 1890.24i 0.123037i
$$619$$ −1240.99 −0.0805808 −0.0402904 0.999188i $$-0.512828\pi$$
−0.0402904 + 0.999188i $$0.512828\pi$$
$$620$$ −2789.91 + 17412.2i −0.180719 + 1.12789i
$$621$$ 3012.21 0.194647
$$622$$ 1888.98i 0.121771i
$$623$$ 7636.94i 0.491119i
$$624$$ −8327.86 −0.534265
$$625$$ 12574.5 + 9274.82i 0.804769 + 0.593588i
$$626$$ 1886.86 0.120470
$$627$$ 7499.94i 0.477701i
$$628$$ 3100.23i 0.196995i
$$629$$ 1628.58 0.103236
$$630$$ 47.7306 297.892i 0.00301846 0.0188386i
$$631$$ 10004.0 0.631143 0.315572 0.948902i $$-0.397804\pi$$
0.315572 + 0.948902i $$0.397804\pi$$
$$632$$ 1855.06i 0.116757i
$$633$$ 2780.42i 0.174584i
$$634$$ −3206.76 −0.200878
$$635$$ 18131.6 + 2905.19i 1.13312 + 0.181557i
$$636$$ 4602.22 0.286934
$$637$$ 2281.07i 0.141883i
$$638$$ 0.898294i 5.57426e-5i
$$639$$ −10012.8 −0.619873
$$640$$ 9136.27 + 1463.89i 0.564286 + 0.0904144i
$$641$$ −23107.3 −1.42384 −0.711921 0.702260i $$-0.752174\pi$$
−0.711921 + 0.702260i $$0.752174\pi$$
$$642$$ 1571.88i 0.0966308i
$$643$$ 11629.9i 0.713281i −0.934242 0.356641i $$-0.883922\pi$$
0.934242 0.356641i $$-0.116078\pi$$
$$644$$ −6104.27 −0.373513
$$645$$ −1365.26 + 8520.76i −0.0833445 + 0.520162i
$$646$$ 202.895 0.0123573
$$647$$ 6371.50i 0.387156i 0.981085 + 0.193578i $$0.0620092\pi$$
−0.981085 + 0.193578i $$0.937991\pi$$
$$648$$ 548.736i 0.0332661i
$$649$$ 24204.6 1.46396
$$650$$ −2367.64 778.716i −0.142871 0.0469904i
$$651$$ −4237.47 −0.255114
$$652$$ 21508.7i 1.29194i
$$653$$ 20264.5i 1.21441i 0.794544 + 0.607207i $$0.207710\pi$$
−0.794544 + 0.607207i $$0.792290\pi$$
$$654$$ −1645.56 −0.0983893
$$655$$ −4195.42 + 26184.1i −0.250273 + 1.56198i
$$656$$ 6108.08 0.363537
$$657$$ 2357.96i 0.140019i
$$658$$ 1052.36i 0.0623485i
$$659$$ 7132.74 0.421627 0.210813 0.977526i $$-0.432389\pi$$
0.210813 + 0.977526i $$0.432389\pi$$
$$660$$ 7111.78 + 1139.51i 0.419433 + 0.0672049i
$$661$$ 10555.8 0.621140 0.310570 0.950550i $$-0.399480\pi$$
0.310570 + 0.950550i $$0.399480\pi$$
$$662$$ 3795.14i 0.222813i
$$663$$ 726.980i 0.0425846i
$$664$$ 590.300 0.0345001
$$665$$ −7032.24 1126.76i −0.410073 0.0657052i
$$666$$ 1206.03 0.0701694
$$667$$ 8.51689i 0.000494416i
$$668$$ 16254.0i 0.941445i
$$669$$ −16055.2 −0.927846
$$670$$ −276.550 + 1725.98i −0.0159464 + 0.0995231i
$$671$$ −20271.6 −1.16628
$$672$$ 1674.48i 0.0961227i
$$673$$ 3828.08i 0.219259i −0.993973 0.109630i $$-0.965034\pi$$
0.993973 0.109630i $$-0.0349665\pi$$
$$674$$ −3744.37 −0.213988
$$675$$ −1054.47 + 3206.04i −0.0601281 + 0.182816i
$$676$$ 233.485 0.0132843
$$677$$ 24660.6i 1.39998i −0.714154 0.699989i $$-0.753188\pi$$
0.714154 0.699989i $$-0.246812\pi$$
$$678$$ 2319.84i 0.131405i
$$679$$ −1601.81 −0.0905328
$$680$$ −62.3773 + 389.304i −0.00351774 + 0.0219546i
$$681$$ −18049.4 −1.01565
$$682$$ 2374.36i 0.133312i
$$683$$ 18562.2i 1.03992i 0.854192 + 0.519958i $$0.174052\pi$$
−0.854192 + 0.519958i $$0.825948\pi$$
$$684$$ −6401.80 −0.357864
$$685$$ 8421.26 + 1349.32i 0.469723 + 0.0752627i
$$686$$ −146.913 −0.00817665
$$687$$ 3632.52i 0.201731i
$$688$$ 15341.8i 0.850146i
$$689$$ 9136.38 0.505179
$$690$$ −1582.56 253.570i −0.0873146 0.0139902i
$$691$$ 27335.9 1.50493 0.752465 0.658632i $$-0.228865\pi$$
0.752465 + 0.658632i $$0.228865\pi$$
$$692$$ 15082.7i 0.828554i
$$693$$ 1730.74i 0.0948708i
$$694$$ −3120.66 −0.170689
$$695$$ 3583.39 22364.3i 0.195577 1.22062i
$$696$$ −1.55153 −8.44979e−5
$$697$$ 533.205i 0.0289764i
$$698$$ 5401.50i 0.292908i
$$699$$ 10551.9 0.570974
$$700$$ 2136.89 6497.09i 0.115381 0.350810i
$$701$$ −30924.1 −1.66617 −0.833087 0.553142i $$-0.813429\pi$$
−0.833087 + 0.553142i $$0.813429\pi$$
$$702$$ 538.361i 0.0289446i
$$703$$ 28470.4i 1.52743i
$$704$$ −12167.2 −0.651375
$$705$$ −1862.56 + 11624.4i −0.0995008 + 0.620995i
$$706$$ 515.093 0.0274586
$$707$$ 4135.09i 0.219966i
$$708$$ 20660.5i 1.09671i
$$709$$ 28329.0 1.50059 0.750295 0.661103i $$-0.229912\pi$$
0.750295 + 0.661103i $$0.229912\pi$$
$$710$$ 5260.53 + 842.883i 0.278062 + 0.0445533i
$$711$$ 2464.46 0.129992
$$712$$ 7390.95i 0.389027i
$$713$$ 22511.7i 1.18243i
$$714$$ −46.8215 −0.00245413
$$715$$ 14118.4 + 2262.16i 0.738458 + 0.118322i
$$716$$ −12804.6 −0.668341
$$717$$ 20147.7i 1.04941i
$$718$$ 1377.62i 0.0716051i
$$719$$ 12563.4 0.651651 0.325825 0.945430i $$-0.394358\pi$$
0.325825 + 0.945430i $$0.394358\pi$$
$$720$$ 949.295 5924.65i 0.0491363 0.306665i
$$721$$ −10297.4 −0.531893
$$722$$ 609.127i 0.0313980i
$$723$$ 5147.11i 0.264762i
$$724$$ −286.558 −0.0147097
$$725$$ 9.06495 + 2.98146i 0.000464364 + 0.000152729i
$$726$$ −740.500 −0.0378547
$$727$$ 13523.2i 0.689888i −0.938623 0.344944i $$-0.887898\pi$$
0.938623 0.344944i $$-0.112102\pi$$
$$728$$ 2207.59i 0.112389i
$$729$$ −729.000 −0.0370370
$$730$$ 198.495 1238.83i 0.0100639 0.0628097i
$$731$$ 1339.26 0.0677625
$$732$$ 17303.4i 0.873706i
$$733$$ 21325.0i 1.07457i −0.843402 0.537284i $$-0.819450\pi$$
0.843402 0.537284i $$-0.180550\pi$$
$$734$$ −539.534 −0.0271316
$$735$$ 1622.81 + 260.020i 0.0814398 + 0.0130489i
$$736$$ 8895.74 0.445518
$$737$$ 10027.9i 0.501197i
$$738$$ 394.861i 0.0196952i
$$739$$ 7403.75 0.368540 0.184270 0.982876i $$-0.441008\pi$$
0.184270 + 0.982876i $$0.441008\pi$$
$$740$$ 26996.9 + 4325.67i 1.34112 + 0.214885i
$$741$$ −12708.9 −0.630059
$$742$$ 588.433i 0.0291133i
$$743$$ 27131.6i 1.33965i −0.742519 0.669825i $$-0.766369\pi$$
0.742519 0.669825i $$-0.233631\pi$$
$$744$$ 4100.98 0.202082
$$745$$ −19.0863 + 119.120i −0.000938616 + 0.00585800i
$$746$$ 165.430 0.00811904
$$747$$ 784.217i 0.0384110i
$$748$$ 1117.80i 0.0546403i
$$749$$ −8563.04 −0.417739
$$750$$ 823.886 1595.63i 0.0401121 0.0776857i
$$751$$ −29393.3 −1.42820 −0.714098 0.700046i $$-0.753163\pi$$
−0.714098 + 0.700046i $$0.753163\pi$$
$$752$$ 20930.0i 1.01495i
$$753$$ 7393.44i 0.357811i
$$754$$ −1.52219 −7.35211e−5
$$755$$ 4253.14 26544.3i 0.205017 1.27953i
$$756$$ 1477.33 0.0710712
$$757$$ 37648.5i 1.80761i 0.427946 + 0.903804i $$0.359237\pi$$
−0.427946 + 0.903804i $$0.640763\pi$$
$$758$$ 6101.84i 0.292386i
$$759$$ 9194.63 0.439715
$$760$$ 6805.72 + 1090.47i 0.324828 + 0.0520466i
$$761$$ −35633.2 −1.69738 −0.848688 0.528894i $$-0.822607\pi$$
−0.848688 + 0.528894i $$0.822607\pi$$
$$762$$ 2110.44i 0.100332i
$$763$$ 8964.46i 0.425341i
$$764$$ 8245.05 0.390439
$$765$$ 517.192 + 82.8687i 0.0244433 + 0.00391650i
$$766$$ −3982.87 −0.187868
$$767$$ 41015.5i 1.93088i
$$768$$ 9566.00i 0.449457i
$$769$$ 3571.28 0.167469 0.0837345 0.996488i $$-0.473315\pi$$
0.0837345 + 0.996488i $$0.473315\pi$$
$$770$$ 145.695 909.301i 0.00681883 0.0425570i
$$771$$ 5621.98 0.262608
$$772$$ 1670.09i 0.0778599i
$$773$$ 16250.3i 0.756122i −0.925781 0.378061i $$-0.876591\pi$$
0.925781 0.378061i $$-0.123409\pi$$
$$774$$ 991.782 0.0460580
$$775$$ −23960.3 7880.55i −1.11056 0.365262i
$$776$$ 1550.21 0.0717131
$$777$$ 6570.05i 0.303345i
$$778$$ 447.081i 0.0206024i
$$779$$ 9321.37 0.428720
$$780$$ 1930.93 12051.2i 0.0886391 0.553206i
$$781$$ −30563.5 −1.40032
$$782$$ 248.741i 0.0113746i
$$783$$ 2.06122i 9.40764e-5i