# Properties

 Label 128.4.g.a.17.8 Level $128$ Weight $4$ Character 128.17 Analytic conductor $7.552$ Analytic rank $0$ Dimension $44$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$128 = 2^{7}$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 128.g (of order $$8$$, degree $$4$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$7.55224448073$$ Analytic rank: $$0$$ Dimension: $$44$$ Relative dimension: $$11$$ over $$\Q(\zeta_{8})$$ Twist minimal: no (minimal twist has level 32) Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

## Embedding invariants

 Embedding label 17.8 Character $$\chi$$ $$=$$ 128.17 Dual form 128.4.g.a.113.8

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(1.20185 - 2.90153i) q^{3} +(-3.98512 + 1.65069i) q^{5} +(-22.4050 + 22.4050i) q^{7} +(12.1174 + 12.1174i) q^{9} +O(q^{10})$$ $$q+(1.20185 - 2.90153i) q^{3} +(-3.98512 + 1.65069i) q^{5} +(-22.4050 + 22.4050i) q^{7} +(12.1174 + 12.1174i) q^{9} +(16.5161 + 39.8735i) q^{11} +(17.9201 + 7.42277i) q^{13} +13.5469i q^{15} -45.9852i q^{17} +(25.0023 + 10.3563i) q^{19} +(38.0813 + 91.9364i) q^{21} +(40.3415 + 40.3415i) q^{23} +(-75.2319 + 75.2319i) q^{25} +(128.064 - 53.0458i) q^{27} +(-88.6955 + 214.130i) q^{29} -260.478 q^{31} +135.544 q^{33} +(52.3029 - 126.270i) q^{35} +(70.4470 - 29.1801i) q^{37} +(43.0748 - 43.0748i) q^{39} +(-251.246 - 251.246i) q^{41} +(95.7143 + 231.075i) q^{43} +(-68.2916 - 28.2873i) q^{45} -15.5684i q^{47} -660.968i q^{49} +(-133.428 - 55.2676i) q^{51} +(171.815 + 414.797i) q^{53} +(-131.638 - 131.638i) q^{55} +(60.0981 - 60.0981i) q^{57} +(-53.3294 + 22.0897i) q^{59} +(297.690 - 718.686i) q^{61} -542.983 q^{63} -83.6667 q^{65} +(377.382 - 911.080i) q^{67} +(165.537 - 68.5675i) q^{69} +(359.297 - 359.297i) q^{71} +(605.446 + 605.446i) q^{73} +(127.870 + 308.706i) q^{75} +(-1263.41 - 523.321i) q^{77} +380.220i q^{79} +27.3544i q^{81} +(-235.183 - 97.4158i) q^{83} +(75.9074 + 183.257i) q^{85} +(514.706 + 514.706i) q^{87} +(-949.793 + 949.793i) q^{89} +(-567.808 + 235.194i) q^{91} +(-313.056 + 755.785i) q^{93} -116.732 q^{95} +663.589 q^{97} +(-283.031 + 683.298i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$44q + 4q^{3} - 4q^{5} + 4q^{7} - 4q^{9} + O(q^{10})$$ $$44q + 4q^{3} - 4q^{5} + 4q^{7} - 4q^{9} + 4q^{11} - 4q^{13} + 4q^{19} - 4q^{21} - 324q^{23} - 4q^{25} + 268q^{27} - 4q^{29} + 752q^{31} - 8q^{33} + 460q^{35} - 4q^{37} - 596q^{39} - 4q^{41} - 804q^{43} + 104q^{45} + 1384q^{51} + 748q^{53} + 292q^{55} - 4q^{57} - 1372q^{59} - 1828q^{61} - 2512q^{63} - 8q^{65} - 2036q^{67} - 1060q^{69} - 220q^{71} - 4q^{73} + 1712q^{75} + 1900q^{77} - 2436q^{83} + 496q^{85} + 1292q^{87} - 4q^{89} + 3604q^{91} - 112q^{93} + 6088q^{95} - 8q^{97} + 5424q^{99} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/128\mathbb{Z}\right)^\times$$.

 $$n$$ $$5$$ $$127$$ $$\chi(n)$$ $$e\left(\frac{7}{8}\right)$$ $$1$$

## Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0 0
$$3$$ 1.20185 2.90153i 0.231297 0.558400i −0.765033 0.643991i $$-0.777278\pi$$
0.996330 + 0.0855902i $$0.0272776\pi$$
$$4$$ 0 0
$$5$$ −3.98512 + 1.65069i −0.356440 + 0.147642i −0.553716 0.832706i $$-0.686791\pi$$
0.197276 + 0.980348i $$0.436791\pi$$
$$6$$ 0 0
$$7$$ −22.4050 + 22.4050i −1.20976 + 1.20976i −0.238651 + 0.971105i $$0.576705\pi$$
−0.971105 + 0.238651i $$0.923295\pi$$
$$8$$ 0 0
$$9$$ 12.1174 + 12.1174i 0.448794 + 0.448794i
$$10$$ 0 0
$$11$$ 16.5161 + 39.8735i 0.452709 + 1.09294i 0.971288 + 0.237907i $$0.0764614\pi$$
−0.518578 + 0.855030i $$0.673539\pi$$
$$12$$ 0 0
$$13$$ 17.9201 + 7.42277i 0.382320 + 0.158362i 0.565562 0.824706i $$-0.308659\pi$$
−0.183242 + 0.983068i $$0.558659\pi$$
$$14$$ 0 0
$$15$$ 13.5469i 0.233185i
$$16$$ 0 0
$$17$$ 45.9852i 0.656062i −0.944667 0.328031i $$-0.893615\pi$$
0.944667 0.328031i $$-0.106385\pi$$
$$18$$ 0 0
$$19$$ 25.0023 + 10.3563i 0.301890 + 0.125047i 0.528486 0.848942i $$-0.322760\pi$$
−0.226596 + 0.973989i $$0.572760\pi$$
$$20$$ 0 0
$$21$$ 38.0813 + 91.9364i 0.395715 + 0.955341i
$$22$$ 0 0
$$23$$ 40.3415 + 40.3415i 0.365729 + 0.365729i 0.865917 0.500188i $$-0.166736\pi$$
−0.500188 + 0.865917i $$0.666736\pi$$
$$24$$ 0 0
$$25$$ −75.2319 + 75.2319i −0.601856 + 0.601856i
$$26$$ 0 0
$$27$$ 128.064 53.0458i 0.912812 0.378099i
$$28$$ 0 0
$$29$$ −88.6955 + 214.130i −0.567943 + 1.37113i 0.335344 + 0.942096i $$0.391148\pi$$
−0.903286 + 0.429039i $$0.858852\pi$$
$$30$$ 0 0
$$31$$ −260.478 −1.50913 −0.754567 0.656223i $$-0.772153\pi$$
−0.754567 + 0.656223i $$0.772153\pi$$
$$32$$ 0 0
$$33$$ 135.544 0.715007
$$34$$ 0 0
$$35$$ 52.3029 126.270i 0.252594 0.609817i
$$36$$ 0 0
$$37$$ 70.4470 29.1801i 0.313011 0.129654i −0.220647 0.975354i $$-0.570817\pi$$
0.533658 + 0.845700i $$0.320817\pi$$
$$38$$ 0 0
$$39$$ 43.0748 43.0748i 0.176859 0.176859i
$$40$$ 0 0
$$41$$ −251.246 251.246i −0.957026 0.957026i 0.0420884 0.999114i $$-0.486599\pi$$
−0.999114 + 0.0420884i $$0.986599\pi$$
$$42$$ 0 0
$$43$$ 95.7143 + 231.075i 0.339449 + 0.819501i 0.997769 + 0.0667635i $$0.0212673\pi$$
−0.658320 + 0.752738i $$0.728733\pi$$
$$44$$ 0 0
$$45$$ −68.2916 28.2873i −0.226229 0.0937072i
$$46$$ 0 0
$$47$$ 15.5684i 0.0483167i −0.999708 0.0241584i $$-0.992309\pi$$
0.999708 0.0241584i $$-0.00769059\pi$$
$$48$$ 0 0
$$49$$ 660.968i 1.92702i
$$50$$ 0 0
$$51$$ −133.428 55.2676i −0.366345 0.151745i
$$52$$ 0 0
$$53$$ 171.815 + 414.797i 0.445294 + 1.07503i 0.974065 + 0.226270i $$0.0726531\pi$$
−0.528771 + 0.848765i $$0.677347\pi$$
$$54$$ 0 0
$$55$$ −131.638 131.638i −0.322728 0.322728i
$$56$$ 0 0
$$57$$ 60.0981 60.0981i 0.139652 0.139652i
$$58$$ 0 0
$$59$$ −53.3294 + 22.0897i −0.117676 + 0.0487431i −0.440745 0.897633i $$-0.645286\pi$$
0.323069 + 0.946376i $$0.395286\pi$$
$$60$$ 0 0
$$61$$ 297.690 718.686i 0.624840 1.50850i −0.221118 0.975247i $$-0.570971\pi$$
0.845958 0.533250i $$-0.179029\pi$$
$$62$$ 0 0
$$63$$ −542.983 −1.08586
$$64$$ 0 0
$$65$$ −83.6667 −0.159655
$$66$$ 0 0
$$67$$ 377.382 911.080i 0.688127 1.66128i −0.0603949 0.998175i $$-0.519236\pi$$
0.748522 0.663110i $$-0.230764\pi$$
$$68$$ 0 0
$$69$$ 165.537 68.5675i 0.288815 0.119631i
$$70$$ 0 0
$$71$$ 359.297 359.297i 0.600574 0.600574i −0.339891 0.940465i $$-0.610390\pi$$
0.940465 + 0.339891i $$0.110390\pi$$
$$72$$ 0 0
$$73$$ 605.446 + 605.446i 0.970714 + 0.970714i 0.999583 0.0288694i $$-0.00919069\pi$$
−0.0288694 + 0.999583i $$0.509191\pi$$
$$74$$ 0 0
$$75$$ 127.870 + 308.706i 0.196869 + 0.475284i
$$76$$ 0 0
$$77$$ −1263.41 523.321i −1.86986 0.774520i
$$78$$ 0 0
$$79$$ 380.220i 0.541494i 0.962650 + 0.270747i $$0.0872707\pi$$
−0.962650 + 0.270747i $$0.912729\pi$$
$$80$$ 0 0
$$81$$ 27.3544i 0.0375232i
$$82$$ 0 0
$$83$$ −235.183 97.4158i −0.311020 0.128829i 0.221713 0.975112i $$-0.428835\pi$$
−0.532733 + 0.846283i $$0.678835\pi$$
$$84$$ 0 0
$$85$$ 75.9074 + 183.257i 0.0968625 + 0.233847i
$$86$$ 0 0
$$87$$ 514.706 + 514.706i 0.634279 + 0.634279i
$$88$$ 0 0
$$89$$ −949.793 + 949.793i −1.13121 + 1.13121i −0.141237 + 0.989976i $$0.545108\pi$$
−0.989976 + 0.141237i $$0.954892\pi$$
$$90$$ 0 0
$$91$$ −567.808 + 235.194i −0.654093 + 0.270934i
$$92$$ 0 0
$$93$$ −313.056 + 755.785i −0.349058 + 0.842701i
$$94$$ 0 0
$$95$$ −116.732 −0.126068
$$96$$ 0 0
$$97$$ 663.589 0.694611 0.347305 0.937752i $$-0.387097\pi$$
0.347305 + 0.937752i $$0.387097\pi$$
$$98$$ 0 0
$$99$$ −283.031 + 683.298i −0.287331 + 0.693677i
$$100$$ 0 0
$$101$$ 937.978 388.523i 0.924082 0.382767i 0.130651 0.991428i $$-0.458293\pi$$
0.793430 + 0.608661i $$0.208293\pi$$
$$102$$ 0 0
$$103$$ 954.756 954.756i 0.913348 0.913348i −0.0831859 0.996534i $$-0.526510\pi$$
0.996534 + 0.0831859i $$0.0265095\pi$$
$$104$$ 0 0
$$105$$ −303.517 303.517i −0.282098 0.282098i
$$106$$ 0 0
$$107$$ 172.355 + 416.102i 0.155721 + 0.375945i 0.982416 0.186706i $$-0.0597813\pi$$
−0.826694 + 0.562651i $$0.809781\pi$$
$$108$$ 0 0
$$109$$ 253.241 + 104.896i 0.222533 + 0.0921761i 0.491164 0.871067i $$-0.336571\pi$$
−0.268632 + 0.963243i $$0.586571\pi$$
$$110$$ 0 0
$$111$$ 239.475i 0.204774i
$$112$$ 0 0
$$113$$ 1164.80i 0.969690i 0.874600 + 0.484845i $$0.161124\pi$$
−0.874600 + 0.484845i $$0.838876\pi$$
$$114$$ 0 0
$$115$$ −227.357 94.1743i −0.184358 0.0763635i
$$116$$ 0 0
$$117$$ 127.201 + 307.091i 0.100511 + 0.242655i
$$118$$ 0 0
$$119$$ 1030.30 + 1030.30i 0.793675 + 0.793675i
$$120$$ 0 0
$$121$$ −375.954 + 375.954i −0.282459 + 0.282459i
$$122$$ 0 0
$$123$$ −1030.96 + 427.038i −0.755760 + 0.313046i
$$124$$ 0 0
$$125$$ 381.960 922.133i 0.273308 0.659825i
$$126$$ 0 0
$$127$$ 624.520 0.436356 0.218178 0.975909i $$-0.429989\pi$$
0.218178 + 0.975909i $$0.429989\pi$$
$$128$$ 0 0
$$129$$ 785.506 0.536123
$$130$$ 0 0
$$131$$ −370.999 + 895.672i −0.247438 + 0.597368i −0.997985 0.0634490i $$-0.979790\pi$$
0.750547 + 0.660817i $$0.229790\pi$$
$$132$$ 0 0
$$133$$ −792.208 + 328.143i −0.516490 + 0.213937i
$$134$$ 0 0
$$135$$ −422.788 + 422.788i −0.269539 + 0.269539i
$$136$$ 0 0
$$137$$ 1408.41 + 1408.41i 0.878308 + 0.878308i 0.993360 0.115051i $$-0.0367032\pi$$
−0.115051 + 0.993360i $$0.536703\pi$$
$$138$$ 0 0
$$139$$ 127.491 + 307.790i 0.0777958 + 0.187816i 0.957992 0.286794i $$-0.0925894\pi$$
−0.880197 + 0.474609i $$0.842589\pi$$
$$140$$ 0 0
$$141$$ −45.1722 18.7110i −0.0269801 0.0111755i
$$142$$ 0 0
$$143$$ 837.134i 0.489543i
$$144$$ 0 0
$$145$$ 999.742i 0.572580i
$$146$$ 0 0
$$147$$ −1917.82 794.387i −1.07605 0.445714i
$$148$$ 0 0
$$149$$ −765.994 1849.27i −0.421159 1.01677i −0.982006 0.188849i $$-0.939524\pi$$
0.560847 0.827919i $$-0.310476\pi$$
$$150$$ 0 0
$$151$$ −773.796 773.796i −0.417024 0.417024i 0.467153 0.884177i $$-0.345280\pi$$
−0.884177 + 0.467153i $$0.845280\pi$$
$$152$$ 0 0
$$153$$ 557.223 557.223i 0.294437 0.294437i
$$154$$ 0 0
$$155$$ 1038.04 429.968i 0.537916 0.222812i
$$156$$ 0 0
$$157$$ 640.806 1547.04i 0.325745 0.786417i −0.673154 0.739502i $$-0.735061\pi$$
0.998899 0.0469150i $$-0.0149390\pi$$
$$158$$ 0 0
$$159$$ 1410.04 0.703295
$$160$$ 0 0
$$161$$ −1807.70 −0.884887
$$162$$ 0 0
$$163$$ 636.715 1537.17i 0.305959 0.738651i −0.693869 0.720102i $$-0.744095\pi$$
0.999828 0.0185496i $$-0.00590487\pi$$
$$164$$ 0 0
$$165$$ −540.160 + 223.742i −0.254857 + 0.105565i
$$166$$ 0 0
$$167$$ −1241.93 + 1241.93i −0.575469 + 0.575469i −0.933651 0.358183i $$-0.883396\pi$$
0.358183 + 0.933651i $$0.383396\pi$$
$$168$$ 0 0
$$169$$ −1287.48 1287.48i −0.586017 0.586017i
$$170$$ 0 0
$$171$$ 177.472 + 428.455i 0.0793661 + 0.191607i
$$172$$ 0 0
$$173$$ 1247.56 + 516.757i 0.548268 + 0.227100i 0.639583 0.768722i $$-0.279107\pi$$
−0.0913149 + 0.995822i $$0.529107\pi$$
$$174$$ 0 0
$$175$$ 3371.14i 1.45620i
$$176$$ 0 0
$$177$$ 181.286i 0.0769845i
$$178$$ 0 0
$$179$$ 985.168 + 408.070i 0.411368 + 0.170394i 0.578763 0.815496i $$-0.303536\pi$$
−0.167395 + 0.985890i $$0.553536\pi$$
$$180$$ 0 0
$$181$$ −120.962 292.028i −0.0496742 0.119924i 0.897095 0.441839i $$-0.145674\pi$$
−0.946769 + 0.321914i $$0.895674\pi$$
$$182$$ 0 0
$$183$$ −1727.51 1727.51i −0.697822 0.697822i
$$184$$ 0 0
$$185$$ −232.573 + 232.573i −0.0924274 + 0.0924274i
$$186$$ 0 0
$$187$$ 1833.59 759.499i 0.717035 0.297006i
$$188$$ 0 0
$$189$$ −1680.78 + 4057.76i −0.646872 + 1.56169i
$$190$$ 0 0
$$191$$ −584.594 −0.221465 −0.110732 0.993850i $$-0.535320\pi$$
−0.110732 + 0.993850i $$0.535320\pi$$
$$192$$ 0 0
$$193$$ 660.360 0.246289 0.123145 0.992389i $$-0.460702\pi$$
0.123145 + 0.992389i $$0.460702\pi$$
$$194$$ 0 0
$$195$$ −100.555 + 242.762i −0.0369277 + 0.0891514i
$$196$$ 0 0
$$197$$ −827.877 + 342.918i −0.299410 + 0.124020i −0.527331 0.849660i $$-0.676807\pi$$
0.227921 + 0.973680i $$0.426807\pi$$
$$198$$ 0 0
$$199$$ 153.764 153.764i 0.0547742 0.0547742i −0.679189 0.733963i $$-0.737668\pi$$
0.733963 + 0.679189i $$0.237668\pi$$
$$200$$ 0 0
$$201$$ −2189.97 2189.97i −0.768500 0.768500i
$$202$$ 0 0
$$203$$ −2810.36 6784.80i −0.971667 2.34581i
$$204$$ 0 0
$$205$$ 1415.98 + 586.516i 0.482420 + 0.199825i
$$206$$ 0 0
$$207$$ 977.671i 0.328274i
$$208$$ 0 0
$$209$$ 1167.97i 0.386557i
$$210$$ 0 0
$$211$$ 5199.68 + 2153.78i 1.69650 + 0.702712i 0.999891 0.0147412i $$-0.00469245\pi$$
0.696606 + 0.717454i $$0.254692\pi$$
$$212$$ 0 0
$$213$$ −610.690 1474.34i −0.196450 0.474272i
$$214$$ 0 0
$$215$$ −762.866 762.866i −0.241986 0.241986i
$$216$$ 0 0
$$217$$ 5836.00 5836.00i 1.82568 1.82568i
$$218$$ 0 0
$$219$$ 2484.38 1029.06i 0.766570 0.317524i
$$220$$ 0 0
$$221$$ 341.338 824.062i 0.103895 0.250825i
$$222$$ 0 0
$$223$$ −998.982 −0.299986 −0.149993 0.988687i $$-0.547925\pi$$
−0.149993 + 0.988687i $$0.547925\pi$$
$$224$$ 0 0
$$225$$ −1823.24 −0.540218
$$226$$ 0 0
$$227$$ −1393.39 + 3363.95i −0.407413 + 0.983583i 0.578402 + 0.815752i $$0.303676\pi$$
−0.985816 + 0.167831i $$0.946324\pi$$
$$228$$ 0 0
$$229$$ 941.495 389.980i 0.271684 0.112535i −0.242682 0.970106i $$-0.578027\pi$$
0.514366 + 0.857571i $$0.328027\pi$$
$$230$$ 0 0
$$231$$ −3036.87 + 3036.87i −0.864984 + 0.864984i
$$232$$ 0 0
$$233$$ 540.109 + 540.109i 0.151861 + 0.151861i 0.778949 0.627088i $$-0.215753\pi$$
−0.627088 + 0.778949i $$0.715753\pi$$
$$234$$ 0 0
$$235$$ 25.6986 + 62.0420i 0.00713359 + 0.0172220i
$$236$$ 0 0
$$237$$ 1103.22 + 456.969i 0.302371 + 0.125246i
$$238$$ 0 0
$$239$$ 2875.66i 0.778287i 0.921177 + 0.389144i $$0.127229\pi$$
−0.921177 + 0.389144i $$0.872771\pi$$
$$240$$ 0 0
$$241$$ 179.902i 0.0480851i −0.999711 0.0240425i $$-0.992346\pi$$
0.999711 0.0240425i $$-0.00765371\pi$$
$$242$$ 0 0
$$243$$ 3537.10 + 1465.11i 0.933765 + 0.386778i
$$244$$ 0 0
$$245$$ 1091.05 + 2634.04i 0.284510 + 0.686867i
$$246$$ 0 0
$$247$$ 371.172 + 371.172i 0.0956158 + 0.0956158i
$$248$$ 0 0
$$249$$ −565.311 + 565.311i −0.143876 + 0.143876i
$$250$$ 0 0
$$251$$ −5834.77 + 2416.84i −1.46728 + 0.607767i −0.966237 0.257655i $$-0.917050\pi$$
−0.501043 + 0.865422i $$0.667050\pi$$
$$252$$ 0 0
$$253$$ −942.270 + 2274.84i −0.234150 + 0.565288i
$$254$$ 0 0
$$255$$ 622.955 0.152984
$$256$$ 0 0
$$257$$ −5382.92 −1.30653 −0.653263 0.757131i $$-0.726600\pi$$
−0.653263 + 0.757131i $$0.726600\pi$$
$$258$$ 0 0
$$259$$ −924.585 + 2232.15i −0.221818 + 0.535516i
$$260$$ 0 0
$$261$$ −3669.47 + 1519.94i −0.870247 + 0.360468i
$$262$$ 0 0
$$263$$ −1725.28 + 1725.28i −0.404508 + 0.404508i −0.879818 0.475311i $$-0.842336\pi$$
0.475311 + 0.879818i $$0.342336\pi$$
$$264$$ 0 0
$$265$$ −1369.40 1369.40i −0.317441 0.317441i
$$266$$ 0 0
$$267$$ 1614.34 + 3897.37i 0.370023 + 0.893315i
$$268$$ 0 0
$$269$$ 7959.26 + 3296.83i 1.80403 + 0.747255i 0.984776 + 0.173826i $$0.0556130\pi$$
0.819256 + 0.573428i $$0.194387\pi$$
$$270$$ 0 0
$$271$$ 1049.81i 0.235320i 0.993054 + 0.117660i $$0.0375393\pi$$
−0.993054 + 0.117660i $$0.962461\pi$$
$$272$$ 0 0
$$273$$ 1930.18i 0.427912i
$$274$$ 0 0
$$275$$ −4242.30 1757.22i −0.930256 0.385325i
$$276$$ 0 0
$$277$$ 1433.09 + 3459.78i 0.310852 + 0.750463i 0.999674 + 0.0255326i $$0.00812818\pi$$
−0.688822 + 0.724931i $$0.741872\pi$$
$$278$$ 0 0
$$279$$ −3156.32 3156.32i −0.677291 0.677291i
$$280$$ 0 0
$$281$$ 1634.94 1634.94i 0.347089 0.347089i −0.511935 0.859024i $$-0.671071\pi$$
0.859024 + 0.511935i $$0.171071\pi$$
$$282$$ 0 0
$$283$$ 4367.76 1809.19i 0.917443 0.380017i 0.126542 0.991961i $$-0.459612\pi$$
0.790901 + 0.611944i $$0.209612\pi$$
$$284$$ 0 0
$$285$$ −140.295 + 338.702i −0.0291591 + 0.0703963i
$$286$$ 0 0
$$287$$ 11258.3 2.31553
$$288$$ 0 0
$$289$$ 2798.36 0.569582
$$290$$ 0 0
$$291$$ 797.537 1925.43i 0.160661 0.387871i
$$292$$ 0 0
$$293$$ −440.173 + 182.326i −0.0877651 + 0.0363535i −0.426134 0.904660i $$-0.640125\pi$$
0.338369 + 0.941014i $$0.390125\pi$$
$$294$$ 0 0
$$295$$ 176.061 176.061i 0.0347480 0.0347480i
$$296$$ 0 0
$$297$$ 4230.25 + 4230.25i 0.826477 + 0.826477i
$$298$$ 0 0
$$299$$ 423.480 + 1022.37i 0.0819079 + 0.197743i
$$300$$ 0 0
$$301$$ −7321.71 3032.75i −1.40205 0.580747i
$$302$$ 0 0
$$303$$ 3188.52i 0.604540i
$$304$$ 0 0
$$305$$ 3355.44i 0.629942i
$$306$$ 0 0
$$307$$ −20.2214 8.37598i −0.00375927 0.00155714i 0.380803 0.924656i $$-0.375648\pi$$
−0.384562 + 0.923099i $$0.625648\pi$$
$$308$$ 0 0
$$309$$ −1622.78 3917.73i −0.298759 0.721269i
$$310$$ 0 0
$$311$$ 390.934 + 390.934i 0.0712791 + 0.0712791i 0.741848 0.670568i $$-0.233950\pi$$
−0.670568 + 0.741848i $$0.733950\pi$$
$$312$$ 0 0
$$313$$ −3353.24 + 3353.24i −0.605548 + 0.605548i −0.941779 0.336231i $$-0.890848\pi$$
0.336231 + 0.941779i $$0.390848\pi$$
$$314$$ 0 0
$$315$$ 2163.85 896.296i 0.387045 0.160319i
$$316$$ 0 0
$$317$$ 1362.73 3289.92i 0.241447 0.582904i −0.755980 0.654594i $$-0.772839\pi$$
0.997427 + 0.0716906i $$0.0228394\pi$$
$$318$$ 0 0
$$319$$ −10003.0 −1.75568
$$320$$ 0 0
$$321$$ 1414.48 0.245946
$$322$$ 0 0
$$323$$ 476.236 1149.73i 0.0820386 0.198059i
$$324$$ 0 0
$$325$$ −1906.60 + 789.738i −0.325412 + 0.134790i
$$326$$ 0 0
$$327$$ 608.717 608.717i 0.102942 0.102942i
$$328$$ 0 0
$$329$$ 348.810 + 348.810i 0.0584514 + 0.0584514i
$$330$$ 0 0
$$331$$ −3035.45 7328.23i −0.504059 1.21691i −0.947255 0.320481i $$-0.896155\pi$$
0.443196 0.896425i $$-0.353845\pi$$
$$332$$ 0 0
$$333$$ 1207.23 + 500.049i 0.198665 + 0.0822899i
$$334$$ 0 0
$$335$$ 4253.70i 0.693745i
$$336$$ 0 0
$$337$$ 2973.12i 0.480582i 0.970701 + 0.240291i $$0.0772429\pi$$
−0.970701 + 0.240291i $$0.922757\pi$$
$$338$$ 0 0
$$339$$ 3379.70 + 1399.92i 0.541475 + 0.224286i
$$340$$ 0 0
$$341$$ −4302.09 10386.2i −0.683200 1.64939i
$$342$$ 0 0
$$343$$ 7124.07 + 7124.07i 1.12147 + 1.12147i
$$344$$ 0 0
$$345$$ −546.500 + 546.500i −0.0852828 + 0.0852828i
$$346$$ 0 0
$$347$$ −1239.20 + 513.294i −0.191711 + 0.0794094i −0.476474 0.879189i $$-0.658085\pi$$
0.284762 + 0.958598i $$0.408085\pi$$
$$348$$ 0 0
$$349$$ 618.263 1492.62i 0.0948276 0.228934i −0.869347 0.494202i $$-0.835460\pi$$
0.964175 + 0.265268i $$0.0854604\pi$$
$$350$$ 0 0
$$351$$ 2688.67 0.408862
$$352$$ 0 0
$$353$$ 2669.91 0.402563 0.201282 0.979533i $$-0.435489\pi$$
0.201282 + 0.979533i $$0.435489\pi$$
$$354$$ 0 0
$$355$$ −838.754 + 2024.93i −0.125398 + 0.302739i
$$356$$ 0 0
$$357$$ 4227.72 1751.18i 0.626763 0.259614i
$$358$$ 0 0
$$359$$ 6834.40 6834.40i 1.00475 1.00475i 0.00476246 0.999989i $$-0.498484\pi$$
0.999989 0.00476246i $$-0.00151595\pi$$
$$360$$ 0 0
$$361$$ −4332.19 4332.19i −0.631606 0.631606i
$$362$$ 0 0
$$363$$ 639.000 + 1542.68i 0.0923934 + 0.223057i
$$364$$ 0 0
$$365$$ −3412.18 1413.37i −0.489320 0.202683i
$$366$$ 0 0
$$367$$ 12688.1i 1.80467i −0.431034 0.902336i $$-0.641851\pi$$
0.431034 0.902336i $$-0.358149\pi$$
$$368$$ 0 0
$$369$$ 6088.92i 0.859015i
$$370$$ 0 0
$$371$$ −13143.0 5444.03i −1.83923 0.761832i
$$372$$ 0 0
$$373$$ 921.648 + 2225.05i 0.127939 + 0.308871i 0.974850 0.222863i $$-0.0715404\pi$$
−0.846911 + 0.531735i $$0.821540\pi$$
$$374$$ 0 0
$$375$$ −2216.54 2216.54i −0.305231 0.305231i
$$376$$ 0 0
$$377$$ −3178.87 + 3178.87i −0.434271 + 0.434271i
$$378$$ 0 0
$$379$$ −13206.6 + 5470.36i −1.78992 + 0.741407i −0.799955 + 0.600060i $$0.795143\pi$$
−0.989960 + 0.141348i $$0.954857\pi$$
$$380$$ 0 0
$$381$$ 750.582 1812.06i 0.100928 0.243661i
$$382$$ 0 0
$$383$$ −1489.39 −0.198706 −0.0993529 0.995052i $$-0.531677\pi$$
−0.0993529 + 0.995052i $$0.531677\pi$$
$$384$$ 0 0
$$385$$ 5898.68 0.780843
$$386$$ 0 0
$$387$$ −1640.22 + 3959.85i −0.215445 + 0.520130i
$$388$$ 0 0
$$389$$ 11998.3 4969.86i 1.56385 0.647768i 0.578097 0.815968i $$-0.303795\pi$$
0.985753 + 0.168200i $$0.0537954\pi$$
$$390$$ 0 0
$$391$$ 1855.11 1855.11i 0.239941 0.239941i
$$392$$ 0 0
$$393$$ 2152.93 + 2152.93i 0.276339 + 0.276339i
$$394$$ 0 0
$$395$$ −627.625 1515.22i −0.0799475 0.193010i
$$396$$ 0 0
$$397$$ −8675.83 3593.64i −1.09679 0.454307i −0.240423 0.970668i $$-0.577286\pi$$
−0.856371 + 0.516361i $$0.827286\pi$$
$$398$$ 0 0
$$399$$ 2693.00i 0.337891i
$$400$$ 0 0
$$401$$ 3772.26i 0.469769i −0.972023 0.234885i $$-0.924529\pi$$
0.972023 0.234885i $$-0.0754713\pi$$
$$402$$ 0 0
$$403$$ −4667.80 1933.47i −0.576972 0.238990i
$$404$$ 0 0
$$405$$ −45.1537 109.011i −0.00554001 0.0133748i
$$406$$ 0 0
$$407$$ 2327.03 + 2327.03i 0.283406 + 0.283406i
$$408$$ 0 0
$$409$$ −9020.80 + 9020.80i −1.09059 + 1.09059i −0.0951210 + 0.995466i $$0.530324\pi$$
−0.995466 + 0.0951210i $$0.969676\pi$$
$$410$$ 0 0
$$411$$ 5779.24 2393.84i 0.693598 0.287298i
$$412$$ 0 0
$$413$$ 699.924 1689.77i 0.0833922 0.201327i
$$414$$ 0 0
$$415$$ 1098.03 0.129880
$$416$$ 0 0
$$417$$ 1046.29 0.122870
$$418$$ 0 0
$$419$$ 3925.38 9476.72i 0.457679 1.10494i −0.511655 0.859191i $$-0.670968\pi$$
0.969335 0.245745i $$-0.0790325\pi$$
$$420$$ 0 0
$$421$$ −4298.89 + 1780.66i −0.497660 + 0.206138i −0.617372 0.786671i $$-0.711803\pi$$
0.119712 + 0.992809i $$0.461803\pi$$
$$422$$ 0 0
$$423$$ 188.649 188.649i 0.0216843 0.0216843i
$$424$$ 0 0
$$425$$ 3459.56 + 3459.56i 0.394855 + 0.394855i
$$426$$ 0 0
$$427$$ 9432.43 + 22771.9i 1.06901 + 2.58082i
$$428$$ 0 0
$$429$$ 2428.97 + 1006.11i 0.273361 + 0.113230i
$$430$$ 0 0
$$431$$ 2281.76i 0.255008i 0.991838 + 0.127504i $$0.0406966\pi$$
−0.991838 + 0.127504i $$0.959303\pi$$
$$432$$ 0 0
$$433$$ 8491.53i 0.942441i −0.882016 0.471220i $$-0.843814\pi$$
0.882016 0.471220i $$-0.156186\pi$$
$$434$$ 0 0
$$435$$ −2900.78 1201.54i −0.319729 0.132436i
$$436$$ 0 0
$$437$$ 590.840 + 1426.41i 0.0646767 + 0.156143i
$$438$$ 0 0
$$439$$ 3417.05 + 3417.05i 0.371496 + 0.371496i 0.868022 0.496526i $$-0.165391\pi$$
−0.496526 + 0.868022i $$0.665391\pi$$
$$440$$ 0 0
$$441$$ 8009.24 8009.24i 0.864835 0.864835i
$$442$$ 0 0
$$443$$ 984.558 407.817i 0.105593 0.0437381i −0.329261 0.944239i $$-0.606800\pi$$
0.434855 + 0.900501i $$0.356800\pi$$
$$444$$ 0 0
$$445$$ 2217.23 5352.86i 0.236195 0.570224i
$$446$$ 0 0
$$447$$ −6286.34 −0.665176
$$448$$ 0 0
$$449$$ −6407.14 −0.673434 −0.336717 0.941606i $$-0.609317\pi$$
−0.336717 + 0.941606i $$0.609317\pi$$
$$450$$ 0 0
$$451$$ 5868.44 14167.7i 0.612714 1.47922i
$$452$$ 0 0
$$453$$ −3175.18 + 1315.20i −0.329323 + 0.136410i
$$454$$ 0 0
$$455$$ 1874.55 1874.55i 0.193144 0.193144i
$$456$$ 0 0
$$457$$ 6405.90 + 6405.90i 0.655701 + 0.655701i 0.954360 0.298659i $$-0.0965393\pi$$
−0.298659 + 0.954360i $$0.596539\pi$$
$$458$$ 0 0
$$459$$ −2439.32 5889.05i −0.248057 0.598861i
$$460$$ 0 0
$$461$$ −11209.2 4642.99i −1.13246 0.469080i −0.263843 0.964566i $$-0.584990\pi$$
−0.868616 + 0.495486i $$0.834990\pi$$
$$462$$ 0 0
$$463$$ 10213.2i 1.02515i 0.858642 + 0.512576i $$0.171309\pi$$
−0.858642 + 0.512576i $$0.828691\pi$$
$$464$$ 0 0
$$465$$ 3528.65i 0.351908i
$$466$$ 0 0
$$467$$ 8301.10 + 3438.43i 0.822546 + 0.340710i 0.753948 0.656935i $$-0.228147\pi$$
0.0685986 + 0.997644i $$0.478147\pi$$
$$468$$ 0 0
$$469$$ 11957.5 + 28868.0i 1.17728 + 2.84222i
$$470$$ 0 0
$$471$$ −3718.64 3718.64i −0.363792 0.363792i
$$472$$ 0 0
$$473$$ −7632.93 + 7632.93i −0.741992 + 0.741992i
$$474$$ 0 0
$$475$$ −2660.09 + 1101.85i −0.256954 + 0.106434i
$$476$$ 0 0
$$477$$ −2944.33 + 7108.24i −0.282624 + 0.682314i
$$478$$ 0 0
$$479$$ 1983.62 0.189215 0.0946075 0.995515i $$-0.469840\pi$$
0.0946075 + 0.995515i $$0.469840\pi$$
$$480$$ 0 0
$$481$$ 1479.02 0.140203
$$482$$ 0 0
$$483$$ −2172.59 + 5245.10i −0.204672 + 0.494121i
$$484$$ 0 0
$$485$$ −2644.48 + 1095.38i −0.247587 + 0.102554i
$$486$$ 0 0
$$487$$ 2241.43 2241.43i 0.208561 0.208561i −0.595095 0.803655i $$-0.702886\pi$$
0.803655 + 0.595095i $$0.202886\pi$$
$$488$$ 0 0
$$489$$ −3694.90 3694.90i −0.341696 0.341696i
$$490$$ 0 0
$$491$$ 1553.51 + 3750.50i 0.142788 + 0.344720i 0.979053 0.203605i $$-0.0652657\pi$$
−0.836265 + 0.548325i $$0.815266\pi$$
$$492$$ 0 0
$$493$$ 9846.81 + 4078.68i 0.899550 + 0.372606i
$$494$$ 0 0
$$495$$ 3190.22i 0.289677i
$$496$$ 0 0
$$497$$ 16100.1i 1.45310i
$$498$$ 0 0
$$499$$ 8740.71 + 3620.52i 0.784144 + 0.324803i 0.738587 0.674159i $$-0.235494\pi$$
0.0455575 + 0.998962i $$0.485494\pi$$
$$500$$ 0 0
$$501$$ 2110.88 + 5096.11i 0.188238 + 0.454446i
$$502$$ 0 0
$$503$$ 3856.31 + 3856.31i 0.341838 + 0.341838i 0.857058 0.515220i $$-0.172290\pi$$
−0.515220 + 0.857058i $$0.672290\pi$$
$$504$$ 0 0
$$505$$ −3096.62 + 3096.62i −0.272867 + 0.272867i
$$506$$ 0 0
$$507$$ −5283.03 + 2188.30i −0.462776 + 0.191688i
$$508$$ 0 0
$$509$$ −776.546 + 1874.75i −0.0676224 + 0.163255i −0.954078 0.299559i $$-0.903160\pi$$
0.886455 + 0.462814i $$0.153160\pi$$
$$510$$ 0 0
$$511$$ −27130.0 −2.34865
$$512$$ 0 0
$$513$$ 3751.24 0.322849
$$514$$ 0 0
$$515$$ −2228.81 + 5380.82i −0.190705 + 0.460403i
$$516$$ 0 0
$$517$$ 620.767 257.130i 0.0528071 0.0218734i
$$518$$ 0 0
$$519$$ 2998.78 2998.78i 0.253626 0.253626i
$$520$$ 0 0
$$521$$ −4528.26 4528.26i −0.380780 0.380780i 0.490603 0.871383i $$-0.336777\pi$$
−0.871383 + 0.490603i $$0.836777\pi$$
$$522$$ 0 0
$$523$$ 1376.98 + 3324.33i 0.115127 + 0.277940i 0.970931 0.239359i $$-0.0769373\pi$$
−0.855804 + 0.517300i $$0.826937\pi$$
$$524$$ 0 0
$$525$$ −9781.48 4051.62i −0.813141 0.336814i
$$526$$ 0 0
$$527$$ 11978.1i 0.990086i
$$528$$ 0 0
$$529$$ 8912.13i 0.732484i
$$530$$ 0 0
$$531$$ −913.887 378.544i −0.0746880 0.0309368i
$$532$$ 0 0
$$533$$ −2637.43 6367.31i −0.214333 0.517446i
$$534$$ 0 0
$$535$$ −1373.71 1373.71i −0.111011 0.111011i
$$536$$ 0 0
$$537$$ 2368.06 2368.06i 0.190296 0.190296i
$$538$$ 0 0
$$539$$ 26355.1 10916.6i 2.10611 0.872380i
$$540$$ 0 0
$$541$$ −3507.90 + 8468.82i −0.278773 + 0.673018i −0.999802 0.0198866i $$-0.993669\pi$$
0.721029 + 0.692905i $$0.243669\pi$$
$$542$$ 0 0
$$543$$ −992.708 −0.0784552
$$544$$ 0 0
$$545$$ −1182.35 −0.0929287
$$546$$ 0 0
$$547$$ 2578.26 6224.46i 0.201532 0.486542i −0.790510 0.612450i $$-0.790184\pi$$
0.992042 + 0.125907i $$0.0401842\pi$$
$$548$$ 0 0
$$549$$ 12315.9 5101.40i 0.957429 0.396580i
$$550$$ 0 0
$$551$$ −4435.17 + 4435.17i −0.342912 + 0.342912i
$$552$$ 0 0
$$553$$ −8518.82 8518.82i −0.655076 0.655076i
$$554$$ 0 0
$$555$$ 395.299 + 954.335i 0.0302333 + 0.0729897i
$$556$$ 0 0
$$557$$ 8187.07 + 3391.19i 0.622796 + 0.257970i 0.671689 0.740834i $$-0.265569\pi$$
−0.0488930 + 0.998804i $$0.515569\pi$$
$$558$$ 0 0
$$559$$ 4851.36i 0.367067i
$$560$$ 0 0
$$561$$ 6233.04i 0.469089i
$$562$$ 0 0
$$563$$ 5205.06 + 2156.00i 0.389639 + 0.161394i 0.568898 0.822408i $$-0.307370\pi$$
−0.179259 + 0.983802i $$0.557370\pi$$
$$564$$ 0 0
$$565$$ −1922.72 4641.86i −0.143167 0.345636i
$$566$$ 0 0
$$567$$ −612.876 612.876i −0.0453939 0.0453939i
$$568$$ 0 0
$$569$$ 13921.3 13921.3i 1.02568 1.02568i 0.0260140 0.999662i $$-0.491719\pi$$
0.999662 0.0260140i $$-0.00828146\pi$$
$$570$$ 0 0
$$571$$ −18276.2 + 7570.27i −1.33947 + 0.554826i −0.933341 0.358990i $$-0.883121\pi$$
−0.406128 + 0.913816i $$0.633121\pi$$
$$572$$ 0 0
$$573$$ −702.597 + 1696.22i −0.0512241 + 0.123666i
$$574$$ 0 0
$$575$$ −6069.93 −0.440232
$$576$$ 0 0
$$577$$ 24309.7 1.75394 0.876972 0.480542i $$-0.159560\pi$$
0.876972 + 0.480542i $$0.159560\pi$$
$$578$$ 0 0
$$579$$ 793.657 1916.06i 0.0569659 0.137528i
$$580$$ 0 0
$$581$$ 7451.87 3086.66i 0.532109 0.220407i
$$582$$ 0 0
$$583$$ −13701.7 + 13701.7i −0.973356 + 0.973356i
$$584$$ 0 0
$$585$$ −1013.83 1013.83i −0.0716522 0.0716522i
$$586$$ 0 0
$$587$$ −6035.14 14570.1i −0.424356 1.02449i −0.981048 0.193767i $$-0.937929\pi$$
0.556691 0.830719i $$-0.312071\pi$$
$$588$$ 0 0
$$589$$ −6512.53 2697.58i −0.455593 0.188713i
$$590$$ 0 0
$$591$$ 2814.25i 0.195876i
$$592$$ 0 0
$$593$$ 14290.4i 0.989608i −0.869005 0.494804i $$-0.835240\pi$$
0.869005 0.494804i $$-0.164760\pi$$
$$594$$ 0 0
$$595$$ −5806.57 2405.16i −0.400078 0.165718i
$$596$$ 0 0
$$597$$ −261.350 630.954i −0.0179168 0.0432550i
$$598$$ 0 0
$$599$$ −2752.47 2752.47i −0.187751 0.187751i 0.606972 0.794723i $$-0.292384\pi$$
−0.794723 + 0.606972i $$0.792384\pi$$
$$600$$ 0 0
$$601$$ −10680.0 + 10680.0i −0.724871 + 0.724871i −0.969593 0.244722i $$-0.921303\pi$$
0.244722 + 0.969593i $$0.421303\pi$$
$$602$$ 0 0
$$603$$ 15612.9 6467.06i 1.05440 0.436748i
$$604$$ 0 0
$$605$$ 877.637 2118.80i 0.0589769 0.142383i
$$606$$ 0 0
$$607$$ 13933.7 0.931719 0.465859 0.884859i $$-0.345745\pi$$
0.465859 + 0.884859i $$0.345745\pi$$
$$608$$ 0 0
$$609$$ −23064.0 −1.53464
$$610$$ 0 0
$$611$$ 115.561 278.988i 0.00765153 0.0184724i
$$612$$ 0 0
$$613$$ −20129.3 + 8337.81i −1.32629 + 0.549366i −0.929594 0.368586i $$-0.879842\pi$$
−0.396692 + 0.917952i $$0.629842\pi$$
$$614$$ 0 0
$$615$$ 3403.59 3403.59i 0.223164 0.223164i
$$616$$ 0 0
$$617$$ 4886.46 + 4886.46i 0.318836 + 0.318836i 0.848320 0.529484i $$-0.177615\pi$$
−0.529484 + 0.848320i $$0.677615\pi$$
$$618$$ 0 0
$$619$$ 7135.77 + 17227.3i 0.463345 + 1.11861i 0.967015 + 0.254718i $$0.0819827\pi$$
−0.503670 + 0.863896i $$0.668017\pi$$
$$620$$ 0 0
$$621$$ 7306.23 + 3026.34i 0.472124 + 0.195560i
$$622$$ 0 0
$$623$$ 42560.2i 2.73698i
$$624$$ 0 0
$$625$$ 8993.94i 0.575612i
$$626$$ 0 0
$$627$$ 3388.91 + 1403.73i 0.215853 + 0.0894094i
$$628$$ 0 0
$$629$$ −1341.85 3239.52i −0.0850608 0.205355i
$$630$$ 0 0
$$631$$ −9484.77 9484.77i −0.598388 0.598388i 0.341496 0.939883i $$-0.389067\pi$$
−0.939883 + 0.341496i $$0.889067\pi$$
$$632$$ 0 0
$$633$$ 12498.5 12498.5i 0.784790 0.784790i
$$634$$ 0 0
$$635$$ −2488.79 + 1030.89i −0.155535 + 0.0644245i
$$636$$ 0 0
$$637$$ 4906.21 11844.6i 0.305167 0.736737i
$$638$$ 0 0
$$639$$ 8707.53 0.539068
$$640$$ 0 0
$$641$$ −26621.4 −1.64038 −0.820189 0.572092i $$-0.806132\pi$$
−0.820189 + 0.572092i $$0.806132\pi$$
$$642$$ 0 0
$$643$$ 3206.34 7740.79i 0.196650 0.474754i −0.794539 0.607213i $$-0.792287\pi$$
0.991188 + 0.132459i $$0.0422873\pi$$
$$644$$ 0 0
$$645$$ −3130.33 + 1296.63i −0.191096 + 0.0791545i
$$646$$ 0 0
$$647$$ 11415.8 11415.8i 0.693664 0.693664i −0.269373 0.963036i $$-0.586816\pi$$
0.963036 + 0.269373i $$0.0868163\pi$$
$$648$$ 0 0
$$649$$ −1761.59 1761.59i −0.106546 0.106546i
$$650$$ 0 0
$$651$$ −9919.33 23947.4i −0.597188 1.44174i
$$652$$ 0 0
$$653$$ 24638.3 + 10205.5i 1.47652 + 0.611596i 0.968336 0.249650i $$-0.0803156\pi$$
0.508188 + 0.861246i $$0.330316\pi$$
$$654$$ 0 0
$$655$$ 4181.76i 0.249458i
$$656$$ 0 0
$$657$$ 14672.9i 0.871301i
$$658$$ 0 0
$$659$$ −13287.3 5503.77i −0.785430 0.325336i −0.0463255 0.998926i $$-0.514751\pi$$
−0.739105 + 0.673591i $$0.764751\pi$$
$$660$$ 0 0
$$661$$ −1075.25 2595.89i −0.0632716 0.152751i 0.889081 0.457749i $$-0.151344\pi$$
−0.952353 + 0.304998i $$0.901344\pi$$
$$662$$ 0 0
$$663$$ −1980.81 1980.81i −0.116030 0.116030i
$$664$$ 0 0
$$665$$ 2615.38 2615.38i 0.152511 0.152511i
$$666$$ 0 0
$$667$$ −12216.4 + 5060.20i −0.709177 + 0.293751i
$$668$$ 0 0
$$669$$ −1200.63 + 2898.58i −0.0693858 + 0.167512i
$$670$$ 0 0
$$671$$ 33573.2 1.93156
$$672$$ 0 0
$$673$$ 2416.06 0.138384 0.0691920 0.997603i $$-0.477958\pi$$
0.0691920 + 0.997603i $$0.477958\pi$$
$$674$$ 0 0
$$675$$ −5643.76 + 13625.2i −0.321820 + 0.776942i
$$676$$ 0 0
$$677$$ −10314.0 + 4272.22i −0.585526 + 0.242533i −0.655724 0.755000i $$-0.727637\pi$$
0.0701988 + 0.997533i $$0.477637\pi$$
$$678$$ 0 0
$$679$$ −14867.7 + 14867.7i −0.840310 + 0.840310i
$$680$$ 0 0
$$681$$ 8085.96 + 8085.96i 0.455000 + 0.455000i
$$682$$ 0 0
$$683$$ −3410.41 8233.45i −0.191062 0.461265i 0.799098 0.601200i $$-0.205311\pi$$
−0.990161 + 0.139935i $$0.955311\pi$$
$$684$$ 0 0
$$685$$ −7937.51 3287.83i −0.442740 0.183389i
$$686$$ 0 0
$$687$$ 3200.48i 0.177738i
$$688$$ 0 0
$$689$$ 8708.57i 0.481524i
$$690$$ 0 0
$$691$$ 3706.50 + 1535.28i 0.204055 + 0.0845224i 0.482370 0.875967i $$-0.339776\pi$$
−0.278315 + 0.960490i $$0.589776\pi$$
$$692$$ 0 0
$$693$$ −8967.98 21650.6i −0.491580 1.18678i
$$694$$ 0 0
$$695$$ −1016.13 1016.13i −0.0554591 0.0554591i
$$696$$ 0 0
$$697$$ −11553.6 + 11553.6i −0.627868 + 0.627868i
$$698$$ 0 0
$$699$$ 2216.27 918.011i 0.119924 0.0496743i
$$700$$ 0 0
$$701$$ −6159.04 + 14869.2i −0.331846 + 0.801146i 0.666600 + 0.745415i $$0.267749\pi$$
−0.998446 + 0.0557306i $$0.982251\pi$$
$$702$$ 0 0
$$703$$ 2063.53 0.110708
$$704$$ 0 0
$$705$$ 210.903 0.0112668
$$706$$ 0 0
$$707$$ −12310.5 + 29720.2i −0.654859 + 1.58097i
$$708$$ 0 0
$$709$$ −1554.84 + 644.034i −0.0823598 + 0.0341145i −0.423483 0.905904i $$-0.639193\pi$$
0.341123 + 0.940019i $$0.389193\pi$$
$$710$$ 0 0
$$711$$ −4607.29 + 4607.29i −0.243020 + 0.243020i
$$712$$ 0 0
$$713$$ −10508.0 10508.0i −0.551935 0.551935i
$$714$$ 0 0
$$715$$ −1381.85 3336.08i −0.0722773 0.174493i
$$716$$ 0 0
$$717$$ 8343.81 + 3456.12i 0.434596 + 0.180016i
$$718$$ 0 0
$$719$$ 33535.5i 1.73945i 0.493540 + 0.869723i $$0.335703\pi$$
−0.493540 + 0.869723i $$0.664297\pi$$
$$720$$ 0 0
$$721$$ 42782.6i 2.20986i
$$722$$ 0 0
$$723$$ −521.991 216.216i −0.0268507 0.0111219i
$$724$$ 0 0
$$725$$ −9436.67 22782.1i −0.483406 1.16704i
$$726$$ 0 0
$$727$$ 15842.6 + 15842.6i 0.808210 + 0.808210i 0.984363 0.176153i $$-0.0563654\pi$$
−0.176153 + 0.984363i $$0.556365\pi$$
$$728$$ 0 0
$$729$$ 7979.90 7979.90i 0.405421 0.405421i
$$730$$ 0 0
$$731$$ 10626.0 4401.44i 0.537644 0.222699i
$$732$$ 0 0
$$733$$ 10693.1 25815.3i 0.538823 1.30083i −0.386722 0.922196i $$-0.626393\pi$$
0.925545 0.378638i $$-0.123607\pi$$
$$734$$ 0 0
$$735$$ 8954.03 0.449353
$$736$$ 0 0
$$737$$ 42560.8 2.12720
$$738$$ 0 0
$$739$$ 2894.05 6986.86i 0.144059 0.347789i −0.835337 0.549738i $$-0.814728\pi$$
0.979396 + 0.201949i $$0.0647276\pi$$
$$740$$ 0 0
$$741$$ 1523.06 630.873i 0.0755075 0.0312762i
$$742$$ 0 0
$$743$$ −15149.2 + 15149.2i −0.748009 + 0.748009i −0.974105 0.226096i $$-0.927404\pi$$
0.226096 + 0.974105i $$0.427404\pi$$
$$744$$ 0 0
$$745$$ 6105.16 + 6105.16i 0.300236 + 0.300236i
$$746$$ 0 0
$$747$$ −1669.38 4030.24i −0.0817664 0.197401i
$$748$$ 0 0
$$749$$ −13184.4 5461.15i −0.643187 0.266417i
$$750$$ 0 0
$$751$$ 23633.7i 1.14834i −0.818735 0.574171i $$-0.805324\pi$$
0.818735 0.574171i $$-0.194676\pi$$
$$752$$ 0 0
$$753$$ 19834.5i 0.959905i
$$754$$ 0 0
$$755$$ 4360.97 + 1806.37i 0.210214 + 0.0870736i
$$756$$ 0 0
$$757$$ −8369.97 20206.9i −0.401865 0.970188i −0.987213 0.159406i $$-0.949042\pi$$
0.585348 0.810782i $$-0.300958\pi$$
$$758$$ 0 0
$$759$$ 5468.05 + 5468.05i 0.261499 + 0.261499i
$$760$$ 0 0
$$761$$ 4475.11 4475.11i 0.213170 0.213170i −0.592442 0.805613i $$-0.701836\pi$$
0.805613 + 0.592442i $$0.201836\pi$$
$$762$$ 0 0
$$763$$ −8024.05 + 3323.67i −0.380721 + 0.157700i
$$764$$ 0 0
$$765$$ −1300.80 + 3140.41i −0.0614778 + 0.148420i
$$766$$ 0 0
$$767$$ −1119.64 −0.0527089
$$768$$ 0 0
$$769$$ −6556.87 −0.307473 −0.153736 0.988112i $$-0.549131\pi$$
−0.153736 + 0.988112i $$0.549131\pi$$
$$770$$ 0 0
$$771$$ −6469.48 + 15618.7i −0.302195 + 0.729564i
$$772$$ 0 0
$$773$$ 16437.5 6808.62i 0.764832 0.316804i 0.0340547 0.999420i $$-0.489158\pi$$
0.730777 + 0.682616i $$0.239158\pi$$
$$774$$ 0 0
$$775$$ 19596.2 19596.2i 0.908281 0.908281i
$$776$$ 0 0
$$777$$ 5365.43 + 5365.43i 0.247727 + 0.247727i
$$778$$ 0 0
$$779$$ −3679.74 8883.69i −0.169243 0.408590i
$$780$$ 0 0
$$781$$ 20260.6 + 8392.23i 0.928275 + 0.384504i
$$782$$ 0 0
$$783$$ 32127.2i 1.46633i
$$784$$ 0 0
$$785$$ 7222.93i 0.328404i
$$786$$ 0 0