# Properties

 Label 128.4.g.a.17.7 Level $128$ Weight $4$ Character 128.17 Analytic conductor $7.552$ Analytic rank $0$ Dimension $44$ CM no Inner twists $2$

# Learn more about

## 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 17.7 Character $$\chi$$ $$=$$ 128.17 Dual form 128.4.g.a.113.7

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(0.998206 - 2.40988i) q^{3} +(17.4005 - 7.20752i) q^{5} +(-4.37099 + 4.37099i) q^{7} +(14.2808 + 14.2808i) q^{9} +O(q^{10})$$ $$q+(0.998206 - 2.40988i) q^{3} +(17.4005 - 7.20752i) q^{5} +(-4.37099 + 4.37099i) q^{7} +(14.2808 + 14.2808i) q^{9} +(-11.7977 - 28.4821i) q^{11} +(-12.9230 - 5.35288i) q^{13} -49.1278i q^{15} -72.9239i q^{17} +(143.136 + 59.2889i) q^{19} +(6.17043 + 14.8967i) q^{21} +(-83.6411 - 83.6411i) q^{23} +(162.441 - 162.441i) q^{25} +(113.737 - 47.1114i) q^{27} +(-39.6554 + 95.7367i) q^{29} +29.0324 q^{31} -80.4149 q^{33} +(-44.5534 + 107.562i) q^{35} +(-267.681 + 110.877i) q^{37} +(-25.7996 + 25.7996i) q^{39} +(-124.918 - 124.918i) q^{41} +(27.0156 + 65.2215i) q^{43} +(351.421 + 145.564i) q^{45} +282.627i q^{47} +304.789i q^{49} +(-175.738 - 72.7931i) q^{51} +(-51.4343 - 124.173i) q^{53} +(-410.570 - 410.570i) q^{55} +(285.759 - 285.759i) q^{57} +(222.476 - 92.1524i) q^{59} +(-226.809 + 547.566i) q^{61} -124.842 q^{63} -263.447 q^{65} +(-356.015 + 859.496i) q^{67} +(-285.056 + 118.074i) q^{69} +(-690.837 + 690.837i) q^{71} +(223.345 + 223.345i) q^{73} +(-229.314 - 553.612i) q^{75} +(176.062 + 72.9275i) q^{77} -698.000i q^{79} +224.174i q^{81} +(915.116 + 379.053i) q^{83} +(-525.601 - 1268.91i) q^{85} +(191.130 + 191.130i) q^{87} +(-163.738 + 163.738i) q^{89} +(79.8837 - 33.0889i) q^{91} +(28.9803 - 69.9647i) q^{93} +2917.97 q^{95} -839.460 q^{97} +(238.266 - 575.225i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$44q + 4q^{3} - 4q^{5} + 4q^{7} - 4q^{9} + O(q^{10})$$ $$44q + 4q^{3} - 4q^{5} + 4q^{7} - 4q^{9} + 4q^{11} - 4q^{13} + 4q^{19} - 4q^{21} - 324q^{23} - 4q^{25} + 268q^{27} - 4q^{29} + 752q^{31} - 8q^{33} + 460q^{35} - 4q^{37} - 596q^{39} - 4q^{41} - 804q^{43} + 104q^{45} + 1384q^{51} + 748q^{53} + 292q^{55} - 4q^{57} - 1372q^{59} - 1828q^{61} - 2512q^{63} - 8q^{65} - 2036q^{67} - 1060q^{69} - 220q^{71} - 4q^{73} + 1712q^{75} + 1900q^{77} - 2436q^{83} + 496q^{85} + 1292q^{87} - 4q^{89} + 3604q^{91} - 112q^{93} + 6088q^{95} - 8q^{97} + 5424q^{99} + O(q^{100})$$

## 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
$$3$$ 0.998206 2.40988i 0.192105 0.463782i −0.798252 0.602324i $$-0.794242\pi$$
0.990357 + 0.138542i $$0.0442415\pi$$
$$4$$ 0 0
$$5$$ 17.4005 7.20752i 1.55635 0.644661i 0.571898 0.820325i $$-0.306207\pi$$
0.984450 + 0.175664i $$0.0562073\pi$$
$$6$$ 0 0
$$7$$ −4.37099 + 4.37099i −0.236012 + 0.236012i −0.815196 0.579185i $$-0.803371\pi$$
0.579185 + 0.815196i $$0.303371\pi$$
$$8$$ 0 0
$$9$$ 14.2808 + 14.2808i 0.528917 + 0.528917i
$$10$$ 0 0
$$11$$ −11.7977 28.4821i −0.323375 0.780697i −0.999053 0.0435002i $$-0.986149\pi$$
0.675678 0.737197i $$-0.263851\pi$$
$$12$$ 0 0
$$13$$ −12.9230 5.35288i −0.275707 0.114202i 0.240546 0.970638i $$-0.422674\pi$$
−0.516253 + 0.856436i $$0.672674\pi$$
$$14$$ 0 0
$$15$$ 49.1278i 0.845649i
$$16$$ 0 0
$$17$$ 72.9239i 1.04039i −0.854047 0.520195i $$-0.825859\pi$$
0.854047 0.520195i $$-0.174141\pi$$
$$18$$ 0 0
$$19$$ 143.136 + 59.2889i 1.72830 + 0.715884i 0.999515 + 0.0311397i $$0.00991368\pi$$
0.728783 + 0.684745i $$0.240086\pi$$
$$20$$ 0 0
$$21$$ 6.17043 + 14.8967i 0.0641190 + 0.154797i
$$22$$ 0 0
$$23$$ −83.6411 83.6411i −0.758278 0.758278i 0.217731 0.976009i $$-0.430134\pi$$
−0.976009 + 0.217731i $$0.930134\pi$$
$$24$$ 0 0
$$25$$ 162.441 162.441i 1.29953 1.29953i
$$26$$ 0 0
$$27$$ 113.737 47.1114i 0.810692 0.335800i
$$28$$ 0 0
$$29$$ −39.6554 + 95.7367i −0.253925 + 0.613030i −0.998514 0.0544937i $$-0.982646\pi$$
0.744589 + 0.667523i $$0.232646\pi$$
$$30$$ 0 0
$$31$$ 29.0324 0.168206 0.0841029 0.996457i $$-0.473198\pi$$
0.0841029 + 0.996457i $$0.473198\pi$$
$$32$$ 0 0
$$33$$ −80.4149 −0.424195
$$34$$ 0 0
$$35$$ −44.5534 + 107.562i −0.215169 + 0.519463i
$$36$$ 0 0
$$37$$ −267.681 + 110.877i −1.18936 + 0.492650i −0.887547 0.460716i $$-0.847593\pi$$
−0.301815 + 0.953366i $$0.597593\pi$$
$$38$$ 0 0
$$39$$ −25.7996 + 25.7996i −0.105929 + 0.105929i
$$40$$ 0 0
$$41$$ −124.918 124.918i −0.475827 0.475827i 0.427968 0.903794i $$-0.359230\pi$$
−0.903794 + 0.427968i $$0.859230\pi$$
$$42$$ 0 0
$$43$$ 27.0156 + 65.2215i 0.0958103 + 0.231306i 0.964517 0.264020i $$-0.0850485\pi$$
−0.868707 + 0.495326i $$0.835048\pi$$
$$44$$ 0 0
$$45$$ 351.421 + 145.564i 1.16415 + 0.482207i
$$46$$ 0 0
$$47$$ 282.627i 0.877136i 0.898698 + 0.438568i $$0.144514\pi$$
−0.898698 + 0.438568i $$0.855486\pi$$
$$48$$ 0 0
$$49$$ 304.789i 0.888597i
$$50$$ 0 0
$$51$$ −175.738 72.7931i −0.482515 0.199864i
$$52$$ 0 0
$$53$$ −51.4343 124.173i −0.133303 0.321821i 0.843107 0.537745i $$-0.180724\pi$$
−0.976410 + 0.215924i $$0.930724\pi$$
$$54$$ 0 0
$$55$$ −410.570 410.570i −1.00657 1.00657i
$$56$$ 0 0
$$57$$ 285.759 285.759i 0.664029 0.664029i
$$58$$ 0 0
$$59$$ 222.476 92.1524i 0.490913 0.203343i −0.123474 0.992348i $$-0.539404\pi$$
0.614387 + 0.789005i $$0.289404\pi$$
$$60$$ 0 0
$$61$$ −226.809 + 547.566i −0.476065 + 1.14932i 0.485374 + 0.874306i $$0.338683\pi$$
−0.961440 + 0.275016i $$0.911317\pi$$
$$62$$ 0 0
$$63$$ −124.842 −0.249661
$$64$$ 0 0
$$65$$ −263.447 −0.502717
$$66$$ 0 0
$$67$$ −356.015 + 859.496i −0.649166 + 1.56723i 0.164808 + 0.986326i $$0.447299\pi$$
−0.813975 + 0.580900i $$0.802701\pi$$
$$68$$ 0 0
$$69$$ −285.056 + 118.074i −0.497344 + 0.206007i
$$70$$ 0 0
$$71$$ −690.837 + 690.837i −1.15475 + 1.15475i −0.169163 + 0.985588i $$0.554106\pi$$
−0.985588 + 0.169163i $$0.945894\pi$$
$$72$$ 0 0
$$73$$ 223.345 + 223.345i 0.358089 + 0.358089i 0.863108 0.505019i $$-0.168515\pi$$
−0.505019 + 0.863108i $$0.668515\pi$$
$$74$$ 0 0
$$75$$ −229.314 553.612i −0.353052 0.852342i
$$76$$ 0 0
$$77$$ 176.062 + 72.9275i 0.260574 + 0.107933i
$$78$$ 0 0
$$79$$ 698.000i 0.994065i −0.867732 0.497033i $$-0.834423\pi$$
0.867732 0.497033i $$-0.165577\pi$$
$$80$$ 0 0
$$81$$ 224.174i 0.307509i
$$82$$ 0 0
$$83$$ 915.116 + 379.053i 1.21020 + 0.501283i 0.894283 0.447502i $$-0.147686\pi$$
0.315922 + 0.948785i $$0.397686\pi$$
$$84$$ 0 0
$$85$$ −525.601 1268.91i −0.670699 1.61921i
$$86$$ 0 0
$$87$$ 191.130 + 191.130i 0.235532 + 0.235532i
$$88$$ 0 0
$$89$$ −163.738 + 163.738i −0.195014 + 0.195014i −0.797859 0.602845i $$-0.794034\pi$$
0.602845 + 0.797859i $$0.294034\pi$$
$$90$$ 0 0
$$91$$ 79.8837 33.0889i 0.0920229 0.0381171i
$$92$$ 0 0
$$93$$ 28.9803 69.9647i 0.0323131 0.0780108i
$$94$$ 0 0
$$95$$ 2917.97 3.15134
$$96$$ 0 0
$$97$$ −839.460 −0.878704 −0.439352 0.898315i $$-0.644792\pi$$
−0.439352 + 0.898315i $$0.644792\pi$$
$$98$$ 0 0
$$99$$ 238.266 575.225i 0.241885 0.583963i
$$100$$ 0 0
$$101$$ 1561.02 646.594i 1.53789 0.637015i 0.556814 0.830637i $$-0.312024\pi$$
0.981076 + 0.193622i $$0.0620235\pi$$
$$102$$ 0 0
$$103$$ 80.1481 80.1481i 0.0766721 0.0766721i −0.667731 0.744403i $$-0.732734\pi$$
0.744403 + 0.667731i $$0.232734\pi$$
$$104$$ 0 0
$$105$$ 214.737 + 214.737i 0.199583 + 0.199583i
$$106$$ 0 0
$$107$$ −552.814 1334.61i −0.499463 1.20581i −0.949773 0.312939i $$-0.898687\pi$$
0.450310 0.892872i $$-0.351313\pi$$
$$108$$ 0 0
$$109$$ 490.666 + 203.241i 0.431168 + 0.178596i 0.587703 0.809077i $$-0.300032\pi$$
−0.156535 + 0.987672i $$0.550032\pi$$
$$110$$ 0 0
$$111$$ 755.757i 0.646246i
$$112$$ 0 0
$$113$$ 109.197i 0.0909060i 0.998966 + 0.0454530i $$0.0144731\pi$$
−0.998966 + 0.0454530i $$0.985527\pi$$
$$114$$ 0 0
$$115$$ −2058.24 852.552i −1.66898 0.691312i
$$116$$ 0 0
$$117$$ −108.107 260.993i −0.0854230 0.206229i
$$118$$ 0 0
$$119$$ 318.750 + 318.750i 0.245544 + 0.245544i
$$120$$ 0 0
$$121$$ 269.116 269.116i 0.202191 0.202191i
$$122$$ 0 0
$$123$$ −425.731 + 176.344i −0.312088 + 0.129271i
$$124$$ 0 0
$$125$$ 754.814 1822.28i 0.540101 1.30392i
$$126$$ 0 0
$$127$$ −1519.49 −1.06167 −0.530837 0.847474i $$-0.678122\pi$$
−0.530837 + 0.847474i $$0.678122\pi$$
$$128$$ 0 0
$$129$$ 184.143 0.125681
$$130$$ 0 0
$$131$$ −386.047 + 932.000i −0.257474 + 0.621597i −0.998770 0.0495811i $$-0.984211\pi$$
0.741296 + 0.671178i $$0.234211\pi$$
$$132$$ 0 0
$$133$$ −884.798 + 366.495i −0.576855 + 0.238941i
$$134$$ 0 0
$$135$$ 1639.52 1639.52i 1.04524 1.04524i
$$136$$ 0 0
$$137$$ 121.798 + 121.798i 0.0759557 + 0.0759557i 0.744064 0.668108i $$-0.232896\pi$$
−0.668108 + 0.744064i $$0.732896\pi$$
$$138$$ 0 0
$$139$$ 2.36667 + 5.71364i 0.00144416 + 0.00348651i 0.924600 0.380939i $$-0.124399\pi$$
−0.923156 + 0.384426i $$0.874399\pi$$
$$140$$ 0 0
$$141$$ 681.098 + 282.120i 0.406800 + 0.168502i
$$142$$ 0 0
$$143$$ 431.225i 0.252174i
$$144$$ 0 0
$$145$$ 1951.68i 1.11778i
$$146$$ 0 0
$$147$$ 734.505 + 304.242i 0.412115 + 0.170704i
$$148$$ 0 0
$$149$$ 311.513 + 752.060i 0.171276 + 0.413497i 0.986087 0.166229i $$-0.0531592\pi$$
−0.814811 + 0.579727i $$0.803159\pi$$
$$150$$ 0 0
$$151$$ −571.254 571.254i −0.307868 0.307868i 0.536214 0.844082i $$-0.319854\pi$$
−0.844082 + 0.536214i $$0.819854\pi$$
$$152$$ 0 0
$$153$$ 1041.41 1041.41i 0.550281 0.550281i
$$154$$ 0 0
$$155$$ 505.179 209.252i 0.261787 0.108436i
$$156$$ 0 0
$$157$$ −219.641 + 530.260i −0.111651 + 0.269550i −0.969822 0.243814i $$-0.921601\pi$$
0.858171 + 0.513365i $$0.171601\pi$$
$$158$$ 0 0
$$159$$ −350.585 −0.174863
$$160$$ 0 0
$$161$$ 731.190 0.357924
$$162$$ 0 0
$$163$$ 570.638 1377.64i 0.274207 0.661995i −0.725447 0.688278i $$-0.758367\pi$$
0.999655 + 0.0262826i $$0.00836698\pi$$
$$164$$ 0 0
$$165$$ −1399.26 + 579.593i −0.660196 + 0.273462i
$$166$$ 0 0
$$167$$ −642.374 + 642.374i −0.297655 + 0.297655i −0.840095 0.542440i $$-0.817501\pi$$
0.542440 + 0.840095i $$0.317501\pi$$
$$168$$ 0 0
$$169$$ −1415.16 1415.16i −0.644134 0.644134i
$$170$$ 0 0
$$171$$ 1197.40 + 2890.78i 0.535483 + 1.29277i
$$172$$ 0 0
$$173$$ −1861.21 770.937i −0.817948 0.338805i −0.0658275 0.997831i $$-0.520969\pi$$
−0.752120 + 0.659026i $$0.770969\pi$$
$$174$$ 0 0
$$175$$ 1420.06i 0.613406i
$$176$$ 0 0
$$177$$ 628.127i 0.266740i
$$178$$ 0 0
$$179$$ 317.221 + 131.397i 0.132459 + 0.0548664i 0.447928 0.894069i $$-0.352162\pi$$
−0.315469 + 0.948936i $$0.602162\pi$$
$$180$$ 0 0
$$181$$ 532.578 + 1285.76i 0.218708 + 0.528008i 0.994710 0.102722i $$-0.0327553\pi$$
−0.776002 + 0.630731i $$0.782755\pi$$
$$182$$ 0 0
$$183$$ 1093.17 + 1093.17i 0.441581 + 0.441581i
$$184$$ 0 0
$$185$$ −3858.63 + 3858.63i −1.53347 + 1.53347i
$$186$$ 0 0
$$187$$ −2077.02 + 860.331i −0.812230 + 0.336437i
$$188$$ 0 0
$$189$$ −291.220 + 703.067i −0.112080 + 0.270585i
$$190$$ 0 0
$$191$$ −3161.63 −1.19773 −0.598867 0.800848i $$-0.704382\pi$$
−0.598867 + 0.800848i $$0.704382\pi$$
$$192$$ 0 0
$$193$$ −1428.55 −0.532796 −0.266398 0.963863i $$-0.585834\pi$$
−0.266398 + 0.963863i $$0.585834\pi$$
$$194$$ 0 0
$$195$$ −262.975 + 634.877i −0.0965744 + 0.233151i
$$196$$ 0 0
$$197$$ 1377.48 570.573i 0.498181 0.206353i −0.119421 0.992844i $$-0.538104\pi$$
0.617603 + 0.786490i $$0.288104\pi$$
$$198$$ 0 0
$$199$$ −1207.72 + 1207.72i −0.430217 + 0.430217i −0.888702 0.458485i $$-0.848392\pi$$
0.458485 + 0.888702i $$0.348392\pi$$
$$200$$ 0 0
$$201$$ 1715.91 + 1715.91i 0.602143 + 0.602143i
$$202$$ 0 0
$$203$$ −245.131 591.798i −0.0847528 0.204611i
$$204$$ 0 0
$$205$$ −3073.98 1273.28i −1.04730 0.433805i
$$206$$ 0 0
$$207$$ 2388.92i 0.802132i
$$208$$ 0 0
$$209$$ 4776.28i 1.58078i
$$210$$ 0 0
$$211$$ 627.654 + 259.983i 0.204784 + 0.0848245i 0.482718 0.875776i $$-0.339650\pi$$
−0.277934 + 0.960600i $$0.589650\pi$$
$$212$$ 0 0
$$213$$ 975.239 + 2354.43i 0.313720 + 0.757386i
$$214$$ 0 0
$$215$$ 940.170 + 940.170i 0.298228 + 0.298228i
$$216$$ 0 0
$$217$$ −126.901 + 126.901i −0.0396985 + 0.0396985i
$$218$$ 0 0
$$219$$ 761.178 315.290i 0.234866 0.0972846i
$$220$$ 0 0
$$221$$ −390.353 + 942.394i −0.118814 + 0.286843i
$$222$$ 0 0
$$223$$ −1684.85 −0.505946 −0.252973 0.967473i $$-0.581408\pi$$
−0.252973 + 0.967473i $$0.581408\pi$$
$$224$$ 0 0
$$225$$ 4639.56 1.37468
$$226$$ 0 0
$$227$$ 1751.96 4229.60i 0.512254 1.23669i −0.430315 0.902679i $$-0.641598\pi$$
0.942569 0.334011i $$-0.108402\pi$$
$$228$$ 0 0
$$229$$ 1072.62 444.292i 0.309521 0.128208i −0.222515 0.974929i $$-0.571427\pi$$
0.532037 + 0.846721i $$0.321427\pi$$
$$230$$ 0 0
$$231$$ 351.493 351.493i 0.100115 0.100115i
$$232$$ 0 0
$$233$$ −224.008 224.008i −0.0629840 0.0629840i 0.674913 0.737897i $$-0.264181\pi$$
−0.737897 + 0.674913i $$0.764181\pi$$
$$234$$ 0 0
$$235$$ 2037.04 + 4917.85i 0.565455 + 1.36513i
$$236$$ 0 0
$$237$$ −1682.10 696.748i −0.461030 0.190965i
$$238$$ 0 0
$$239$$ 5695.35i 1.54143i −0.637181 0.770714i $$-0.719899\pi$$
0.637181 0.770714i $$-0.280101\pi$$
$$240$$ 0 0
$$241$$ 5864.62i 1.56752i −0.621061 0.783762i $$-0.713298\pi$$
0.621061 0.783762i $$-0.286702\pi$$
$$242$$ 0 0
$$243$$ 3611.13 + 1495.78i 0.953309 + 0.394874i
$$244$$ 0 0
$$245$$ 2196.77 + 5303.48i 0.572844 + 1.38297i
$$246$$ 0 0
$$247$$ −1532.38 1532.38i −0.394749 0.394749i
$$248$$ 0 0
$$249$$ 1826.95 1826.95i 0.464972 0.464972i
$$250$$ 0 0
$$251$$ −1284.55 + 532.079i −0.323029 + 0.133803i −0.538305 0.842750i $$-0.680935\pi$$
0.215276 + 0.976553i $$0.430935\pi$$
$$252$$ 0 0
$$253$$ −1395.50 + 3369.04i −0.346777 + 0.837193i
$$254$$ 0 0
$$255$$ −3582.59 −0.879805
$$256$$ 0 0
$$257$$ 6068.35 1.47289 0.736446 0.676497i $$-0.236503\pi$$
0.736446 + 0.676497i $$0.236503\pi$$
$$258$$ 0 0
$$259$$ 685.388 1654.67i 0.164432 0.396974i
$$260$$ 0 0
$$261$$ −1933.50 + 800.883i −0.458547 + 0.189937i
$$262$$ 0 0
$$263$$ 1919.51 1919.51i 0.450046 0.450046i −0.445324 0.895370i $$-0.646911\pi$$
0.895370 + 0.445324i $$0.146911\pi$$
$$264$$ 0 0
$$265$$ −1789.97 1789.97i −0.414931 0.414931i
$$266$$ 0 0
$$267$$ 231.146 + 558.035i 0.0529808 + 0.127907i
$$268$$ 0 0
$$269$$ 3969.40 + 1644.18i 0.899697 + 0.372667i 0.784103 0.620630i $$-0.213123\pi$$
0.115593 + 0.993297i $$0.463123\pi$$
$$270$$ 0 0
$$271$$ 4538.69i 1.01736i 0.860954 + 0.508682i $$0.169867\pi$$
−0.860954 + 0.508682i $$0.830133\pi$$
$$272$$ 0 0
$$273$$ 225.540i 0.0500011i
$$274$$ 0 0
$$275$$ −6543.07 2710.23i −1.43477 0.594301i
$$276$$ 0 0
$$277$$ −1889.91 4562.63i −0.409940 0.989683i −0.985153 0.171679i $$-0.945081\pi$$
0.575213 0.818004i $$-0.304919\pi$$
$$278$$ 0 0
$$279$$ 414.605 + 414.605i 0.0889669 + 0.0889669i
$$280$$ 0 0
$$281$$ −30.7223 + 30.7223i −0.00652220 + 0.00652220i −0.710360 0.703838i $$-0.751468\pi$$
0.703838 + 0.710360i $$0.251468\pi$$
$$282$$ 0 0
$$283$$ 5549.45 2298.66i 1.16565 0.482830i 0.285901 0.958259i $$-0.407707\pi$$
0.879754 + 0.475429i $$0.157707\pi$$
$$284$$ 0 0
$$285$$ 2912.73 7031.95i 0.605387 1.46153i
$$286$$ 0 0
$$287$$ 1092.03 0.224601
$$288$$ 0 0
$$289$$ −404.895 −0.0824130
$$290$$ 0 0
$$291$$ −837.954 + 2023.00i −0.168803 + 0.407527i
$$292$$ 0 0
$$293$$ 2663.79 1103.38i 0.531128 0.220000i −0.100969 0.994890i $$-0.532194\pi$$
0.632097 + 0.774889i $$0.282194\pi$$
$$294$$ 0 0
$$295$$ 3207.00 3207.00i 0.632944 0.632944i
$$296$$ 0 0
$$297$$ −2683.66 2683.66i −0.524316 0.524316i
$$298$$ 0 0
$$299$$ 633.173 + 1528.61i 0.122466 + 0.295659i
$$300$$ 0 0
$$301$$ −403.168 166.998i −0.0772033 0.0319787i
$$302$$ 0 0
$$303$$ 4407.30i 0.835620i
$$304$$ 0 0
$$305$$ 11162.7i 2.09565i
$$306$$ 0 0
$$307$$ −401.539 166.323i −0.0746484 0.0309204i 0.345047 0.938585i $$-0.387863\pi$$
−0.419695 + 0.907665i $$0.637863\pi$$
$$308$$ 0 0
$$309$$ −113.143 273.152i −0.0208301 0.0502883i
$$310$$ 0 0
$$311$$ 5345.11 + 5345.11i 0.974577 + 0.974577i 0.999685 0.0251081i $$-0.00799300\pi$$
−0.0251081 + 0.999685i $$0.507993\pi$$
$$312$$ 0 0
$$313$$ −1787.53 + 1787.53i −0.322803 + 0.322803i −0.849841 0.527039i $$-0.823302\pi$$
0.527039 + 0.849841i $$0.323302\pi$$
$$314$$ 0 0
$$315$$ −2172.32 + 899.804i −0.388560 + 0.160947i
$$316$$ 0 0
$$317$$ 2370.77 5723.55i 0.420050 1.01409i −0.562282 0.826945i $$-0.690077\pi$$
0.982332 0.187145i $$-0.0599234\pi$$
$$318$$ 0 0
$$319$$ 3194.62 0.560703
$$320$$ 0 0
$$321$$ −3768.08 −0.655183
$$322$$ 0 0
$$323$$ 4323.58 10438.0i 0.744800 1.79811i
$$324$$ 0 0
$$325$$ −2968.74 + 1229.69i −0.506696 + 0.209880i
$$326$$ 0 0
$$327$$ 979.572 979.572i 0.165659 0.165659i
$$328$$ 0 0
$$329$$ −1235.36 1235.36i −0.207014 0.207014i
$$330$$ 0 0
$$331$$ −1696.86 4096.57i −0.281775 0.680265i 0.718102 0.695938i $$-0.245011\pi$$
−0.999877 + 0.0156724i $$0.995011\pi$$
$$332$$ 0 0
$$333$$ −5406.09 2239.28i −0.889646 0.368503i
$$334$$ 0 0
$$335$$ 17521.6i 2.85764i
$$336$$ 0 0
$$337$$ 927.470i 0.149918i −0.997187 0.0749592i $$-0.976117\pi$$
0.997187 0.0749592i $$-0.0238826\pi$$
$$338$$ 0 0
$$339$$ 263.152 + 109.001i 0.0421606 + 0.0174635i
$$340$$ 0 0
$$341$$ −342.515 826.904i −0.0543936 0.131318i
$$342$$ 0 0
$$343$$ −2831.48 2831.48i −0.445731 0.445731i
$$344$$ 0 0
$$345$$ −4109.10 + 4109.10i −0.641237 + 0.641237i
$$346$$ 0 0
$$347$$ −3765.13 + 1559.57i −0.582487 + 0.241274i −0.654415 0.756136i $$-0.727085\pi$$
0.0719277 + 0.997410i $$0.477085\pi$$
$$348$$ 0 0
$$349$$ −1631.14 + 3937.93i −0.250181 + 0.603990i −0.998218 0.0596662i $$-0.980996\pi$$
0.748037 + 0.663657i $$0.230996\pi$$
$$350$$ 0 0
$$351$$ −1722.00 −0.261862
$$352$$ 0 0
$$353$$ −11289.2 −1.70216 −0.851080 0.525037i $$-0.824052\pi$$
−0.851080 + 0.525037i $$0.824052\pi$$
$$354$$ 0 0
$$355$$ −7041.69 + 17000.1i −1.05277 + 2.54162i
$$356$$ 0 0
$$357$$ 1086.33 449.972i 0.161049 0.0667088i
$$358$$ 0 0
$$359$$ −2970.97 + 2970.97i −0.436774 + 0.436774i −0.890925 0.454151i $$-0.849943\pi$$
0.454151 + 0.890925i $$0.349943\pi$$
$$360$$ 0 0
$$361$$ 12122.7 + 12122.7i 1.76742 + 1.76742i
$$362$$ 0 0
$$363$$ −379.904 917.170i −0.0549306 0.132614i
$$364$$ 0 0
$$365$$ 5496.07 + 2276.55i 0.788157 + 0.326465i
$$366$$ 0 0
$$367$$ 12266.5i 1.74470i −0.488882 0.872350i $$-0.662595\pi$$
0.488882 0.872350i $$-0.337405\pi$$
$$368$$ 0 0
$$369$$ 3567.84i 0.503346i
$$370$$ 0 0
$$371$$ 767.581 + 317.942i 0.107415 + 0.0444926i
$$372$$ 0 0
$$373$$ −905.804 2186.80i −0.125739 0.303561i 0.848457 0.529265i $$-0.177532\pi$$
−0.974196 + 0.225703i $$0.927532\pi$$
$$374$$ 0 0
$$375$$ −3638.03 3638.03i −0.500979 0.500979i
$$376$$ 0 0
$$377$$ 1024.93 1024.93i 0.140018 0.140018i
$$378$$ 0 0
$$379$$ −6881.62 + 2850.46i −0.932679 + 0.386328i −0.796694 0.604383i $$-0.793420\pi$$
−0.135985 + 0.990711i $$0.543420\pi$$
$$380$$ 0 0
$$381$$ −1516.76 + 3661.78i −0.203953 + 0.492385i
$$382$$ 0 0
$$383$$ 2433.37 0.324645 0.162323 0.986738i $$-0.448101\pi$$
0.162323 + 0.986738i $$0.448101\pi$$
$$384$$ 0 0
$$385$$ 3589.20 0.475124
$$386$$ 0 0
$$387$$ −545.609 + 1317.22i −0.0716663 + 0.173018i
$$388$$ 0 0
$$389$$ 4253.32 1761.78i 0.554375 0.229630i −0.0878663 0.996132i $$-0.528005\pi$$
0.642241 + 0.766503i $$0.278005\pi$$
$$390$$ 0 0
$$391$$ −6099.44 + 6099.44i −0.788905 + 0.788905i
$$392$$ 0 0
$$393$$ 1860.66 + 1860.66i 0.238824 + 0.238824i
$$394$$ 0 0
$$395$$ −5030.85 12145.6i −0.640835 1.54711i
$$396$$ 0 0
$$397$$ −306.541 126.974i −0.0387528 0.0160519i 0.363223 0.931702i $$-0.381676\pi$$
−0.401976 + 0.915650i $$0.631676\pi$$
$$398$$ 0 0
$$399$$ 2498.10i 0.313437i
$$400$$ 0 0
$$401$$ 10975.6i 1.36682i 0.730036 + 0.683409i $$0.239503\pi$$
−0.730036 + 0.683409i $$0.760497\pi$$
$$402$$ 0 0
$$403$$ −375.186 155.407i −0.0463755 0.0192094i
$$404$$ 0 0
$$405$$ 1615.74 + 3900.74i 0.198239 + 0.478591i
$$406$$ 0 0
$$407$$ 6316.01 + 6316.01i 0.769221 + 0.769221i
$$408$$ 0 0
$$409$$ 8384.88 8384.88i 1.01371 1.01371i 0.0138007 0.999905i $$-0.495607\pi$$
0.999905 0.0138007i $$-0.00439304\pi$$
$$410$$ 0 0
$$411$$ 415.100 171.940i 0.0498184 0.0206355i
$$412$$ 0 0
$$413$$ −569.642 + 1375.24i −0.0678698 + 0.163852i
$$414$$ 0 0
$$415$$ 18655.5 2.20666
$$416$$ 0 0
$$417$$ 16.1316 0.00189441
$$418$$ 0 0
$$419$$ −533.639 + 1288.32i −0.0622195 + 0.150211i −0.951931 0.306311i $$-0.900905\pi$$
0.889712 + 0.456522i $$0.150905\pi$$
$$420$$ 0 0
$$421$$ 1963.49 813.303i 0.227303 0.0941520i −0.266125 0.963938i $$-0.585744\pi$$
0.493428 + 0.869786i $$0.335744\pi$$
$$422$$ 0 0
$$423$$ −4036.13 + 4036.13i −0.463932 + 0.463932i
$$424$$ 0 0
$$425$$ −11845.8 11845.8i −1.35201 1.35201i
$$426$$ 0 0
$$427$$ −1402.03 3384.79i −0.158897 0.383610i
$$428$$ 0 0
$$429$$ 1039.20 + 430.451i 0.116954 + 0.0484438i
$$430$$ 0 0
$$431$$ 4521.29i 0.505297i −0.967558 0.252649i $$-0.918698\pi$$
0.967558 0.252649i $$-0.0813016\pi$$
$$432$$ 0 0
$$433$$ 2122.80i 0.235601i 0.993037 + 0.117801i $$0.0375844\pi$$
−0.993037 + 0.117801i $$0.962416\pi$$
$$434$$ 0 0
$$435$$ 4703.33 + 1948.18i 0.518408 + 0.214732i
$$436$$ 0 0
$$437$$ −7013.07 16931.1i −0.767691 1.85337i
$$438$$ 0 0
$$439$$ −8028.12 8028.12i −0.872805 0.872805i 0.119972 0.992777i $$-0.461719\pi$$
−0.992777 + 0.119972i $$0.961719\pi$$
$$440$$ 0 0
$$441$$ −4352.62 + 4352.62i −0.469994 + 0.469994i
$$442$$ 0 0
$$443$$ −3136.09 + 1299.01i −0.336343 + 0.139318i −0.544462 0.838786i $$-0.683266\pi$$
0.208119 + 0.978104i $$0.433266\pi$$
$$444$$ 0 0
$$445$$ −1668.98 + 4029.28i −0.177792 + 0.429227i
$$446$$ 0 0
$$447$$ 2123.33 0.224676
$$448$$ 0 0
$$449$$ −16955.9 −1.78218 −0.891088 0.453832i $$-0.850057\pi$$
−0.891088 + 0.453832i $$0.850057\pi$$
$$450$$ 0 0
$$451$$ −2084.18 + 5031.66i −0.217606 + 0.525347i
$$452$$ 0 0
$$453$$ −1946.88 + 806.426i −0.201926 + 0.0836406i
$$454$$ 0 0
$$455$$ 1151.53 1151.53i 0.118647 0.118647i
$$456$$ 0 0
$$457$$ 6223.46 + 6223.46i 0.637027 + 0.637027i 0.949821 0.312794i $$-0.101265\pi$$
−0.312794 + 0.949821i $$0.601265\pi$$
$$458$$ 0 0
$$459$$ −3435.55 8294.14i −0.349363 0.843437i
$$460$$ 0 0
$$461$$ 10872.5 + 4503.54i 1.09844 + 0.454991i 0.856944 0.515410i $$-0.172360\pi$$
0.241501 + 0.970401i $$0.422360\pi$$
$$462$$ 0 0
$$463$$ 13182.5i 1.32320i 0.749858 + 0.661599i $$0.230122\pi$$
−0.749858 + 0.661599i $$0.769878\pi$$
$$464$$ 0 0
$$465$$ 1426.30i 0.142243i
$$466$$ 0 0
$$467$$ −7043.25 2917.41i −0.697907 0.289083i 0.00538305 0.999986i $$-0.498287\pi$$
−0.703290 + 0.710903i $$0.748287\pi$$
$$468$$ 0 0
$$469$$ −2200.71 5312.99i −0.216673 0.523094i
$$470$$ 0 0
$$471$$ 1058.62 + 1058.62i 0.103564 + 0.103564i
$$472$$ 0 0
$$473$$ 1538.92 1538.92i 0.149598 0.149598i
$$474$$ 0 0
$$475$$ 32882.1 13620.2i 3.17628 1.31566i
$$476$$ 0 0
$$477$$ 1038.77 2507.81i 0.0997107 0.240723i
$$478$$ 0 0
$$479$$ −4612.37 −0.439968 −0.219984 0.975503i $$-0.570601\pi$$
−0.219984 + 0.975503i $$0.570601\pi$$
$$480$$ 0 0
$$481$$ 4052.74 0.384177
$$482$$ 0 0
$$483$$ 729.878 1762.08i 0.0687590 0.165999i
$$484$$ 0 0
$$485$$ −14607.0 + 6050.43i −1.36757 + 0.566466i
$$486$$ 0 0
$$487$$ 10988.9 10988.9i 1.02249 1.02249i 0.0227515 0.999741i $$-0.492757\pi$$
0.999741 0.0227515i $$-0.00724266\pi$$
$$488$$ 0 0
$$489$$ −2750.34 2750.34i −0.254345 0.254345i
$$490$$ 0 0
$$491$$ 7836.91 + 18920.0i 0.720316 + 1.73900i 0.672451 + 0.740142i $$0.265242\pi$$
0.0478645 + 0.998854i $$0.484758\pi$$
$$492$$ 0 0
$$493$$ 6981.49 + 2891.83i 0.637790 + 0.264181i
$$494$$ 0 0
$$495$$ 11726.5i 1.06478i
$$496$$ 0 0
$$497$$ 6039.29i 0.545069i
$$498$$ 0 0
$$499$$ 6404.45 + 2652.81i 0.574554 + 0.237988i 0.650990 0.759086i $$-0.274354\pi$$
−0.0764356 + 0.997075i $$0.524354\pi$$
$$500$$ 0 0
$$501$$ 906.824 + 2189.27i 0.0808661 + 0.195228i
$$502$$ 0 0
$$503$$ −2553.60 2553.60i −0.226361 0.226361i 0.584810 0.811171i $$-0.301169\pi$$
−0.811171 + 0.584810i $$0.801169\pi$$
$$504$$ 0 0
$$505$$ 22502.1 22502.1i 1.98283 1.98283i
$$506$$ 0 0
$$507$$ −4823.00 + 1997.75i −0.422479 + 0.174997i
$$508$$ 0 0
$$509$$ 3141.82 7585.02i 0.273593 0.660511i −0.726039 0.687654i $$-0.758641\pi$$
0.999632 + 0.0271425i $$0.00864080\pi$$
$$510$$ 0 0
$$511$$ −1952.48 −0.169026
$$512$$ 0 0
$$513$$ 19073.0 1.64151
$$514$$ 0 0
$$515$$ 816.948 1972.29i 0.0699010 0.168756i
$$516$$ 0 0
$$517$$ 8049.80 3334.34i 0.684777 0.283644i
$$518$$ 0 0
$$519$$ −3715.74 + 3715.74i −0.314263 + 0.314263i
$$520$$ 0 0
$$521$$ −7065.05 7065.05i −0.594099 0.594099i 0.344637 0.938736i $$-0.388002\pi$$
−0.938736 + 0.344637i $$0.888002\pi$$
$$522$$ 0 0
$$523$$ 111.041 + 268.077i 0.00928391 + 0.0224134i 0.928454 0.371449i $$-0.121139\pi$$
−0.919170 + 0.393862i $$0.871139\pi$$
$$524$$ 0 0
$$525$$ 3422.17 + 1417.51i 0.284487 + 0.117838i
$$526$$ 0 0
$$527$$ 2117.16i 0.175000i
$$528$$ 0 0
$$529$$ 1824.68i 0.149970i
$$530$$ 0 0
$$531$$ 4493.13 + 1861.11i 0.367204 + 0.152101i
$$532$$ 0 0
$$533$$ 945.642 + 2282.98i 0.0768486 + 0.185529i
$$534$$ 0 0
$$535$$ −19238.5 19238.5i −1.55468 1.55468i
$$536$$ 0 0
$$537$$ 633.304 633.304i 0.0508921 0.0508921i
$$538$$ 0 0
$$539$$ 8681.02 3595.79i 0.693725 0.287350i
$$540$$ 0 0
$$541$$ −8420.37 + 20328.6i −0.669168 + 1.61552i 0.113837 + 0.993499i $$0.463686\pi$$
−0.783005 + 0.622016i $$0.786314\pi$$
$$542$$ 0 0
$$543$$ 3630.14 0.286896
$$544$$ 0 0
$$545$$ 10002.7 0.786181
$$546$$ 0 0
$$547$$ −646.357 + 1560.44i −0.0505233 + 0.121974i −0.947126 0.320862i $$-0.896028\pi$$
0.896603 + 0.442836i $$0.146028\pi$$
$$548$$ 0 0
$$549$$ −11058.7 + 4580.65i −0.859696 + 0.356098i
$$550$$ 0 0
$$551$$ −11352.2 + 11352.2i −0.877717 + 0.877717i
$$552$$ 0 0
$$553$$ 3050.95 + 3050.95i 0.234611 + 0.234611i
$$554$$ 0 0
$$555$$ 5447.14 + 13150.5i 0.416609 + 1.00578i
$$556$$ 0 0
$$557$$ −6482.01 2684.93i −0.493091 0.204245i 0.122260 0.992498i $$-0.460986\pi$$
−0.615351 + 0.788253i $$0.710986\pi$$
$$558$$ 0 0
$$559$$ 987.467i 0.0747145i
$$560$$ 0 0
$$561$$ 5864.17i 0.441329i
$$562$$ 0 0
$$563$$ 945.289 + 391.551i 0.0707623 + 0.0293107i 0.417784 0.908546i $$-0.362807\pi$$
−0.347022 + 0.937857i $$0.612807\pi$$
$$564$$ 0 0
$$565$$ 787.039 + 1900.08i 0.0586035 + 0.141481i
$$566$$ 0 0
$$567$$ −979.862 979.862i −0.0725756 0.0725756i
$$568$$ 0 0
$$569$$ −3760.45 + 3760.45i −0.277058 + 0.277058i −0.831934 0.554875i $$-0.812766\pi$$
0.554875 + 0.831934i $$0.312766\pi$$
$$570$$ 0 0
$$571$$ −2056.20 + 851.705i −0.150699 + 0.0624216i −0.456758 0.889591i $$-0.650990\pi$$
0.306059 + 0.952013i $$0.400990\pi$$
$$572$$ 0 0
$$573$$ −3155.95 + 7619.15i −0.230091 + 0.555488i
$$574$$ 0 0
$$575$$ −27173.5 −1.97080
$$576$$ 0 0
$$577$$ −23621.3 −1.70427 −0.852137 0.523318i $$-0.824694\pi$$
−0.852137 + 0.523318i $$0.824694\pi$$
$$578$$ 0 0
$$579$$ −1425.99 + 3442.65i −0.102353 + 0.247101i
$$580$$ 0 0
$$581$$ −5656.80 + 2343.13i −0.403931 + 0.167314i
$$582$$ 0 0
$$583$$ −2929.91 + 2929.91i −0.208138 + 0.208138i
$$584$$ 0 0
$$585$$ −3762.23 3762.23i −0.265896 0.265896i
$$586$$ 0 0
$$587$$ −7316.12 17662.7i −0.514427 1.24194i −0.941283 0.337617i $$-0.890379\pi$$
0.426857 0.904319i $$-0.359621\pi$$
$$588$$ 0 0
$$589$$ 4155.59 + 1721.30i 0.290710 + 0.120416i
$$590$$ 0 0
$$591$$ 3889.13i 0.270689i
$$592$$ 0 0
$$593$$ 16542.0i 1.14553i −0.819720 0.572764i $$-0.805871\pi$$
0.819720 0.572764i $$-0.194129\pi$$
$$594$$ 0 0
$$595$$ 7843.81 + 3249.01i 0.540445 + 0.223860i
$$596$$ 0 0
$$597$$ 1704.91 + 4116.02i 0.116880 + 0.282174i
$$598$$ 0 0
$$599$$ 8579.81 + 8579.81i 0.585244 + 0.585244i 0.936340 0.351095i $$-0.114191\pi$$
−0.351095 + 0.936340i $$0.614191\pi$$
$$600$$ 0 0
$$601$$ −13633.8 + 13633.8i −0.925346 + 0.925346i −0.997401 0.0720542i $$-0.977045\pi$$
0.0720542 + 0.997401i $$0.477045\pi$$
$$602$$ 0 0
$$603$$ −17358.4 + 7190.09i −1.17229 + 0.485578i
$$604$$ 0 0
$$605$$ 2743.09 6622.41i 0.184335 0.445023i
$$606$$ 0 0
$$607$$ 23984.1 1.60376 0.801881 0.597484i $$-0.203833\pi$$
0.801881 + 0.597484i $$0.203833\pi$$
$$608$$ 0 0
$$609$$ −1670.86 −0.111176
$$610$$ 0 0
$$611$$ 1512.87 3652.38i 0.100170 0.241833i
$$612$$ 0 0
$$613$$ 18072.9 7486.04i 1.19080 0.493244i 0.302782 0.953060i $$-0.402085\pi$$
0.888014 + 0.459816i $$0.152085\pi$$
$$614$$ 0 0
$$615$$ −6136.93 + 6136.93i −0.402382 + 0.402382i
$$616$$ 0 0
$$617$$ 18674.2 + 18674.2i 1.21847 + 1.21847i 0.968168 + 0.250301i $$0.0805297\pi$$
0.250301 + 0.968168i $$0.419470\pi$$
$$618$$ 0 0
$$619$$ −3214.09 7759.51i −0.208700 0.503846i 0.784519 0.620105i $$-0.212910\pi$$
−0.993219 + 0.116258i $$0.962910\pi$$
$$620$$ 0 0
$$621$$ −13453.5 5572.64i −0.869359 0.360100i
$$622$$ 0 0
$$623$$ 1431.40i 0.0920511i
$$624$$ 0 0
$$625$$ 8433.25i 0.539728i
$$626$$ 0 0
$$627$$ −11510.3 4767.71i −0.733136 0.303675i
$$628$$ 0 0
$$629$$ 8085.58 + 19520.3i 0.512549 + 1.23740i
$$630$$ 0 0
$$631$$ 20023.0 + 20023.0i 1.26324 + 1.26324i 0.949515 + 0.313722i $$0.101576\pi$$
0.313722 + 0.949515i $$0.398424\pi$$
$$632$$ 0 0
$$633$$ 1253.06 1253.06i 0.0786801 0.0786801i
$$634$$ 0 0
$$635$$ −26439.8 + 10951.7i −1.65233 + 0.684419i
$$636$$ 0 0
$$637$$ 1631.50 3938.78i 0.101479 0.244992i
$$638$$ 0 0
$$639$$ −19731.4 −1.22154
$$640$$ 0 0
$$641$$ 8637.88 0.532255 0.266128 0.963938i $$-0.414256\pi$$
0.266128 + 0.963938i $$0.414256\pi$$
$$642$$ 0 0
$$643$$ −5274.73 + 12734.3i −0.323507 + 0.781015i 0.675538 + 0.737325i $$0.263911\pi$$
−0.999045 + 0.0436901i $$0.986089\pi$$
$$644$$ 0 0
$$645$$ 3204.18 1327.22i 0.195604 0.0810219i
$$646$$ 0 0
$$647$$ 14785.3 14785.3i 0.898406 0.898406i −0.0968891 0.995295i $$-0.530889\pi$$
0.995295 + 0.0968891i $$0.0308892\pi$$
$$648$$ 0 0
$$649$$ −5249.38 5249.38i −0.317498 0.317498i
$$650$$ 0 0
$$651$$ 179.143 + 432.488i 0.0107852 + 0.0260377i
$$652$$ 0 0
$$653$$ −25046.7 10374.7i −1.50100 0.621733i −0.527321 0.849666i $$-0.676803\pi$$
−0.973677 + 0.227933i $$0.926803\pi$$
$$654$$ 0 0
$$655$$ 18999.7i 1.13340i
$$656$$ 0 0
$$657$$ 6379.06i 0.378799i
$$658$$ 0 0
$$659$$ 23962.3 + 9925.50i 1.41645 + 0.586711i 0.953965 0.299918i $$-0.0969594\pi$$
0.462481 + 0.886629i $$0.346959\pi$$
$$660$$ 0 0
$$661$$ −398.063 961.010i −0.0234234 0.0565491i 0.911735 0.410779i $$-0.134743\pi$$
−0.935158 + 0.354230i $$0.884743\pi$$
$$662$$ 0 0
$$663$$ 1881.41 + 1881.41i 0.110208 + 0.110208i
$$664$$ 0 0
$$665$$ −12754.4 + 12754.4i −0.743752 + 0.743752i
$$666$$ 0 0
$$667$$ 11324.4 4690.70i 0.657392 0.272301i
$$668$$ 0 0
$$669$$ −1681.83 + 4060.30i −0.0971948 + 0.234649i
$$670$$ 0 0
$$671$$ 18271.6 1.05122
$$672$$ 0 0
$$673$$ −15307.7 −0.876775 −0.438387 0.898786i $$-0.644450\pi$$
−0.438387 + 0.898786i $$0.644450\pi$$
$$674$$ 0 0
$$675$$ 10822.7 26128.3i 0.617135 1.48990i
$$676$$ 0 0
$$677$$ −1043.10 + 432.068i −0.0592168 + 0.0245284i −0.412095 0.911141i $$-0.635203\pi$$
0.352878 + 0.935669i $$0.385203\pi$$
$$678$$ 0 0
$$679$$ 3669.28 3669.28i 0.207384 0.207384i
$$680$$ 0 0
$$681$$ −8444.03 8444.03i −0.475148 0.475148i
$$682$$ 0 0
$$683$$ 8946.40 + 21598.5i 0.501207 + 1.21002i 0.948827 + 0.315797i $$0.102272\pi$$
−0.447619 + 0.894224i $$0.647728\pi$$
$$684$$ 0 0
$$685$$ 2997.22 + 1241.49i 0.167179 + 0.0692479i
$$686$$ 0 0
$$687$$ 3028.37i 0.168180i
$$688$$ 0 0
$$689$$ 1880.01i 0.103952i
$$690$$ 0 0
$$691$$ −19676.4 8150.22i −1.08325 0.448696i −0.231600 0.972811i $$-0.574396\pi$$
−0.851647 + 0.524115i $$0.824396\pi$$
$$692$$ 0 0
$$693$$ 1472.85 + 3555.77i 0.0807342 + 0.194910i
$$694$$ 0 0
$$695$$ 82.3624 + 82.3624i 0.00449523 + 0.00449523i
$$696$$ 0 0
$$697$$ −9109.50 + 9109.50i −0.495046 + 0.495046i
$$698$$ 0 0
$$699$$ −763.440 + 316.227i −0.0413104 + 0.0171113i
$$700$$ 0 0
$$701$$ 2739.27 6613.19i 0.147591 0.356315i −0.832744 0.553658i $$-0.813231\pi$$
0.980334 + 0.197343i $$0.0632313\pi$$
$$702$$ 0 0
$$703$$ −44888.5 −2.40825
$$704$$ 0 0
$$705$$ 13884.8 0.741749
$$706$$ 0 0
$$707$$ −3996.93 + 9649.45i −0.212617 + 0.513303i
$$708$$ 0 0
$$709$$ −2388.26 + 989.248i −0.126506 + 0.0524005i −0.445039 0.895511i $$-0.646810\pi$$
0.318532 + 0.947912i $$0.396810\pi$$
$$710$$ 0 0
$$711$$ 9967.97 9967.97i 0.525778 0.525778i
$$712$$ 0 0
$$713$$ −2428.31 2428.31i −0.127547 0.127547i
$$714$$ 0 0
$$715$$ 3108.06 + 7503.53i 0.162566 + 0.392470i
$$716$$ 0 0
$$717$$ −13725.1 5685.13i −0.714887 0.296116i
$$718$$ 0 0
$$719$$ 11843.1i 0.614288i −0.951663 0.307144i $$-0.900627\pi$$
0.951663 0.307144i $$-0.0993734\pi$$
$$720$$ 0 0
$$721$$ 700.654i 0.0361910i
$$722$$ 0 0
$$723$$ −14133.0 5854.10i −0.726990 0.301129i
$$724$$ 0 0
$$725$$ 9109.88 + 21993.2i 0.466665 + 1.12663i
$$726$$ 0 0
$$727$$ 4691.36 + 4691.36i 0.239330 + 0.239330i 0.816573 0.577243i $$-0.195871\pi$$
−0.577243 + 0.816573i $$0.695871\pi$$
$$728$$ 0 0
$$729$$ 2929.40 2929.40i 0.148829 0.148829i
$$730$$ 0 0
$$731$$ 4756.20 1970.08i 0.240649 0.0996801i
$$732$$ 0 0
$$733$$ 13224.6 31927.0i 0.666386 1.60880i −0.121224 0.992625i $$-0.538682\pi$$
0.787610 0.616174i $$-0.211318\pi$$
$$734$$ 0 0
$$735$$ 14973.6 0.751441
$$736$$ 0 0
$$737$$ 28680.4 1.43345
$$738$$ 0 0
$$739$$ 13199.0 31865.1i 0.657012 1.58617i −0.145383 0.989375i $$-0.546442\pi$$
0.802396 0.596793i $$-0.203558\pi$$
$$740$$ 0 0
$$741$$ −5222.48 + 2163.22i −0.258911 + 0.107244i
$$742$$ 0 0
$$743$$ 14307.6 14307.6i 0.706452 0.706452i −0.259335 0.965787i $$-0.583503\pi$$
0.965787 + 0.259335i $$0.0835035\pi$$
$$744$$ 0 0
$$745$$ 10841.0 + 10841.0i 0.533131 + 0.533131i
$$746$$ 0 0
$$747$$ 7655.38 + 18481.7i 0.374961 + 0.905235i
$$748$$ 0 0
$$749$$ 8249.93 + 3417.23i 0.402464 + 0.166706i
$$750$$ 0 0
$$751$$ 15781.7i 0.766820i 0.923578 + 0.383410i $$0.125250\pi$$
−0.923578 + 0.383410i $$0.874750\pi$$
$$752$$ 0 0
$$753$$ 3626.75i 0.175519i
$$754$$ 0 0
$$755$$ −14057.4 5822.78i −0.677619 0.280679i
$$756$$ 0 0
$$757$$ −15069.9 36382.0i −0.723548 1.74680i −0.662983 0.748635i $$-0.730710\pi$$
−0.0605650 0.998164i $$-0.519290\pi$$
$$758$$ 0 0
$$759$$ 6726.00 + 6726.00i 0.321658 + 0.321658i
$$760$$ 0 0
$$761$$ −12120.7 + 12120.7i −0.577363 + 0.577363i −0.934176 0.356813i $$-0.883863\pi$$
0.356813 + 0.934176i $$0.383863\pi$$
$$762$$ 0 0
$$763$$ −3033.06 + 1256.34i −0.143911 + 0.0596100i
$$764$$ 0 0
$$765$$ 10615.1 25627.0i 0.501684 1.21117i
$$766$$ 0 0
$$767$$ −3368.33 −0.158570
$$768$$ 0 0
$$769$$ 5213.88 0.244496 0.122248 0.992500i $$-0.460990\pi$$
0.122248 + 0.992500i $$0.460990\pi$$
$$770$$ 0 0
$$771$$ 6057.46 14624.0i 0.282950 0.683101i
$$772$$ 0 0
$$773$$ 25960.5 10753.2i 1.20793 0.500343i 0.314380 0.949297i $$-0.398203\pi$$
0.893555 + 0.448954i $$0.148203\pi$$
$$774$$ 0 0
$$775$$ 4716.05 4716.05i 0.218588 0.218588i
$$776$$ 0 0
$$777$$ −3303.41 3303.41i −0.152521 0.152521i
$$778$$ 0 0
$$779$$ −10474.0 25286.5i −0.481733 1.16301i
$$780$$ 0 0
$$781$$ 27826.7 + 11526.2i 1.27493 + 0.528093i
$$782$$ 0 0
$$783$$ 12757.0i 0.582246i
$$784$$ 0 0
$$785$$ 10809.9i 0.491491i
$$786$$ 0 0