# Properties

 Label 1792.2.m.h.1345.5 Level $1792$ Weight $2$ Character 1792.1345 Analytic conductor $14.309$ Analytic rank $0$ Dimension $16$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$1792 = 2^{8} \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1792.m (of order $$4$$, degree $$2$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$14.3091920422$$ Analytic rank: $$0$$ Dimension: $$16$$ Relative dimension: $$8$$ over $$\Q(i)$$ Coefficient field: $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ Defining polynomial: $$x^{16} - 4 x^{15} + 12 x^{14} - 48 x^{13} + 67 x^{12} - 24 x^{11} + 118 x^{10} - 176 x^{9} + 351 x^{8} - 180 x^{7} + 358 x^{6} - 336 x^{5} + 390 x^{4} - 344 x^{3} + 164 x^{2} - 40 x + 4$$ Coefficient ring: $$\Z[a_1, \ldots, a_{11}]$$ Coefficient ring index: $$2^{14}$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

## Embedding invariants

 Embedding label 1345.5 Root $$-0.424637 - 3.22544i$$ of defining polynomial Character $$\chi$$ $$=$$ 1792.1345 Dual form 1792.2.m.h.449.5

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(0.171192 + 0.171192i) q^{3} +(-0.268425 + 0.268425i) q^{5} -1.00000i q^{7} -2.94139i q^{9} +O(q^{10})$$ $$q+(0.171192 + 0.171192i) q^{3} +(-0.268425 + 0.268425i) q^{5} -1.00000i q^{7} -2.94139i q^{9} +(-1.84927 + 1.84927i) q^{11} +(1.63574 + 1.63574i) q^{13} -0.0919045 q^{15} -7.37134 q^{17} +(3.84975 + 3.84975i) q^{19} +(0.171192 - 0.171192i) q^{21} +6.44892i q^{23} +4.85590i q^{25} +(1.01712 - 1.01712i) q^{27} +(3.58700 + 3.58700i) q^{29} +6.10161 q^{31} -0.633164 q^{33} +(0.268425 + 0.268425i) q^{35} +(7.41852 - 7.41852i) q^{37} +0.560052i q^{39} -0.836588i q^{41} +(3.88949 - 3.88949i) q^{43} +(0.789540 + 0.789540i) q^{45} +6.02070 q^{47} -1.00000 q^{49} +(-1.26192 - 1.26192i) q^{51} +(0.575460 - 0.575460i) q^{53} -0.992782i q^{55} +1.31810i q^{57} +(-5.33013 + 5.33013i) q^{59} +(0.929862 + 0.929862i) q^{61} -2.94139 q^{63} -0.878144 q^{65} +(6.21819 + 6.21819i) q^{67} +(-1.10401 + 1.10401i) q^{69} +11.4285i q^{71} -3.68616i q^{73} +(-0.831293 + 0.831293i) q^{75} +(1.84927 + 1.84927i) q^{77} +4.21672 q^{79} -8.47591 q^{81} +(12.0147 + 12.0147i) q^{83} +(1.97865 - 1.97865i) q^{85} +1.22813i q^{87} -9.32780i q^{89} +(1.63574 - 1.63574i) q^{91} +(1.04455 + 1.04455i) q^{93} -2.06673 q^{95} -13.9032 q^{97} +(5.43943 + 5.43943i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$16q + 4q^{3} + 4q^{5} + O(q^{10})$$ $$16q + 4q^{3} + 4q^{5} - 8q^{11} - 12q^{13} - 8q^{17} + 4q^{19} + 4q^{21} - 56q^{27} - 8q^{31} + 16q^{33} - 4q^{35} + 8q^{37} - 24q^{43} + 36q^{45} - 40q^{47} - 16q^{49} + 24q^{51} + 32q^{53} - 4q^{59} + 20q^{61} + 24q^{63} + 72q^{65} + 32q^{67} - 56q^{69} - 28q^{75} + 8q^{77} - 40q^{81} + 36q^{83} - 12q^{91} - 8q^{93} - 80q^{95} - 72q^{97} - 8q^{99} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1792\mathbb{Z}\right)^\times$$.

 $$n$$ $$1023$$ $$1025$$ $$1541$$ $$\chi(n)$$ $$1$$ $$1$$ $$e\left(\frac{3}{4}\right)$$

## Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0 0
$$3$$ 0.171192 + 0.171192i 0.0988380 + 0.0988380i 0.754797 0.655959i $$-0.227735\pi$$
−0.655959 + 0.754797i $$0.727735\pi$$
$$4$$ 0 0
$$5$$ −0.268425 + 0.268425i −0.120043 + 0.120043i −0.764576 0.644533i $$-0.777052\pi$$
0.644533 + 0.764576i $$0.277052\pi$$
$$6$$ 0 0
$$7$$ 1.00000i 0.377964i
$$8$$ 0 0
$$9$$ 2.94139i 0.980462i
$$10$$ 0 0
$$11$$ −1.84927 + 1.84927i −0.557577 + 0.557577i −0.928617 0.371040i $$-0.879001\pi$$
0.371040 + 0.928617i $$0.379001\pi$$
$$12$$ 0 0
$$13$$ 1.63574 + 1.63574i 0.453672 + 0.453672i 0.896571 0.442899i $$-0.146050\pi$$
−0.442899 + 0.896571i $$0.646050\pi$$
$$14$$ 0 0
$$15$$ −0.0919045 −0.0237296
$$16$$ 0 0
$$17$$ −7.37134 −1.78781 −0.893906 0.448255i $$-0.852046\pi$$
−0.893906 + 0.448255i $$0.852046\pi$$
$$18$$ 0 0
$$19$$ 3.84975 + 3.84975i 0.883193 + 0.883193i 0.993858 0.110665i $$-0.0352979\pi$$
−0.110665 + 0.993858i $$0.535298\pi$$
$$20$$ 0 0
$$21$$ 0.171192 0.171192i 0.0373573 0.0373573i
$$22$$ 0 0
$$23$$ 6.44892i 1.34469i 0.740236 + 0.672347i $$0.234714\pi$$
−0.740236 + 0.672347i $$0.765286\pi$$
$$24$$ 0 0
$$25$$ 4.85590i 0.971179i
$$26$$ 0 0
$$27$$ 1.01712 1.01712i 0.195745 0.195745i
$$28$$ 0 0
$$29$$ 3.58700 + 3.58700i 0.666089 + 0.666089i 0.956808 0.290720i $$-0.0938947\pi$$
−0.290720 + 0.956808i $$0.593895\pi$$
$$30$$ 0 0
$$31$$ 6.10161 1.09588 0.547941 0.836517i $$-0.315412\pi$$
0.547941 + 0.836517i $$0.315412\pi$$
$$32$$ 0 0
$$33$$ −0.633164 −0.110220
$$34$$ 0 0
$$35$$ 0.268425 + 0.268425i 0.0453720 + 0.0453720i
$$36$$ 0 0
$$37$$ 7.41852 7.41852i 1.21960 1.21960i 0.251825 0.967773i $$-0.418969\pi$$
0.967773 0.251825i $$-0.0810307\pi$$
$$38$$ 0 0
$$39$$ 0.560052i 0.0896801i
$$40$$ 0 0
$$41$$ 0.836588i 0.130653i −0.997864 0.0653265i $$-0.979191\pi$$
0.997864 0.0653265i $$-0.0208089\pi$$
$$42$$ 0 0
$$43$$ 3.88949 3.88949i 0.593141 0.593141i −0.345337 0.938479i $$-0.612236\pi$$
0.938479 + 0.345337i $$0.112236\pi$$
$$44$$ 0 0
$$45$$ 0.789540 + 0.789540i 0.117698 + 0.117698i
$$46$$ 0 0
$$47$$ 6.02070 0.878209 0.439104 0.898436i $$-0.355296\pi$$
0.439104 + 0.898436i $$0.355296\pi$$
$$48$$ 0 0
$$49$$ −1.00000 −0.142857
$$50$$ 0 0
$$51$$ −1.26192 1.26192i −0.176704 0.176704i
$$52$$ 0 0
$$53$$ 0.575460 0.575460i 0.0790455 0.0790455i −0.666479 0.745524i $$-0.732199\pi$$
0.745524 + 0.666479i $$0.232199\pi$$
$$54$$ 0 0
$$55$$ 0.992782i 0.133867i
$$56$$ 0 0
$$57$$ 1.31810i 0.174586i
$$58$$ 0 0
$$59$$ −5.33013 + 5.33013i −0.693924 + 0.693924i −0.963093 0.269169i $$-0.913251\pi$$
0.269169 + 0.963093i $$0.413251\pi$$
$$60$$ 0 0
$$61$$ 0.929862 + 0.929862i 0.119057 + 0.119057i 0.764125 0.645068i $$-0.223171\pi$$
−0.645068 + 0.764125i $$0.723171\pi$$
$$62$$ 0 0
$$63$$ −2.94139 −0.370580
$$64$$ 0 0
$$65$$ −0.878144 −0.108920
$$66$$ 0 0
$$67$$ 6.21819 + 6.21819i 0.759672 + 0.759672i 0.976263 0.216590i $$-0.0694935\pi$$
−0.216590 + 0.976263i $$0.569494\pi$$
$$68$$ 0 0
$$69$$ −1.10401 + 1.10401i −0.132907 + 0.132907i
$$70$$ 0 0
$$71$$ 11.4285i 1.35631i 0.734919 + 0.678155i $$0.237220\pi$$
−0.734919 + 0.678155i $$0.762780\pi$$
$$72$$ 0 0
$$73$$ 3.68616i 0.431433i −0.976456 0.215716i $$-0.930791\pi$$
0.976456 0.215716i $$-0.0692087\pi$$
$$74$$ 0 0
$$75$$ −0.831293 + 0.831293i −0.0959895 + 0.0959895i
$$76$$ 0 0
$$77$$ 1.84927 + 1.84927i 0.210744 + 0.210744i
$$78$$ 0 0
$$79$$ 4.21672 0.474418 0.237209 0.971459i $$-0.423767\pi$$
0.237209 + 0.971459i $$0.423767\pi$$
$$80$$ 0 0
$$81$$ −8.47591 −0.941768
$$82$$ 0 0
$$83$$ 12.0147 + 12.0147i 1.31878 + 1.31878i 0.914742 + 0.404038i $$0.132393\pi$$
0.404038 + 0.914742i $$0.367607\pi$$
$$84$$ 0 0
$$85$$ 1.97865 1.97865i 0.214614 0.214614i
$$86$$ 0 0
$$87$$ 1.22813i 0.131670i
$$88$$ 0 0
$$89$$ 9.32780i 0.988745i −0.869250 0.494373i $$-0.835398\pi$$
0.869250 0.494373i $$-0.164602\pi$$
$$90$$ 0 0
$$91$$ 1.63574 1.63574i 0.171472 0.171472i
$$92$$ 0 0
$$93$$ 1.04455 + 1.04455i 0.108315 + 0.108315i
$$94$$ 0 0
$$95$$ −2.06673 −0.212043
$$96$$ 0 0
$$97$$ −13.9032 −1.41166 −0.705828 0.708384i $$-0.749425\pi$$
−0.705828 + 0.708384i $$0.749425\pi$$
$$98$$ 0 0
$$99$$ 5.43943 + 5.43943i 0.546683 + 0.546683i
$$100$$ 0 0
$$101$$ 0.813911 0.813911i 0.0809872 0.0809872i −0.665453 0.746440i $$-0.731762\pi$$
0.746440 + 0.665453i $$0.231762\pi$$
$$102$$ 0 0
$$103$$ 8.39975i 0.827652i 0.910356 + 0.413826i $$0.135808\pi$$
−0.910356 + 0.413826i $$0.864192\pi$$
$$104$$ 0 0
$$105$$ 0.0919045i 0.00896896i
$$106$$ 0 0
$$107$$ 0.705176 0.705176i 0.0681719 0.0681719i −0.672199 0.740371i $$-0.734650\pi$$
0.740371 + 0.672199i $$0.234650\pi$$
$$108$$ 0 0
$$109$$ 12.1263 + 12.1263i 1.16149 + 1.16149i 0.984150 + 0.177337i $$0.0567481\pi$$
0.177337 + 0.984150i $$0.443252\pi$$
$$110$$ 0 0
$$111$$ 2.53999 0.241085
$$112$$ 0 0
$$113$$ −3.51705 −0.330856 −0.165428 0.986222i $$-0.552901\pi$$
−0.165428 + 0.986222i $$0.552901\pi$$
$$114$$ 0 0
$$115$$ −1.73105 1.73105i −0.161421 0.161421i
$$116$$ 0 0
$$117$$ 4.81133 4.81133i 0.444808 0.444808i
$$118$$ 0 0
$$119$$ 7.37134i 0.675729i
$$120$$ 0 0
$$121$$ 4.16036i 0.378215i
$$122$$ 0 0
$$123$$ 0.143218 0.143218i 0.0129135 0.0129135i
$$124$$ 0 0
$$125$$ −2.64556 2.64556i −0.236626 0.236626i
$$126$$ 0 0
$$127$$ 5.86352 0.520303 0.260152 0.965568i $$-0.416227\pi$$
0.260152 + 0.965568i $$0.416227\pi$$
$$128$$ 0 0
$$129$$ 1.33170 0.117250
$$130$$ 0 0
$$131$$ −7.79029 7.79029i −0.680641 0.680641i 0.279504 0.960145i $$-0.409830\pi$$
−0.960145 + 0.279504i $$0.909830\pi$$
$$132$$ 0 0
$$133$$ 3.84975 3.84975i 0.333816 0.333816i
$$134$$ 0 0
$$135$$ 0.546040i 0.0469957i
$$136$$ 0 0
$$137$$ 6.34879i 0.542414i −0.962521 0.271207i $$-0.912577\pi$$
0.962521 0.271207i $$-0.0874228\pi$$
$$138$$ 0 0
$$139$$ −14.1119 + 14.1119i −1.19696 + 1.19696i −0.221885 + 0.975073i $$0.571221\pi$$
−0.975073 + 0.221885i $$0.928779\pi$$
$$140$$ 0 0
$$141$$ 1.03070 + 1.03070i 0.0868004 + 0.0868004i
$$142$$ 0 0
$$143$$ −6.04986 −0.505914
$$144$$ 0 0
$$145$$ −1.92568 −0.159919
$$146$$ 0 0
$$147$$ −0.171192 0.171192i −0.0141197 0.0141197i
$$148$$ 0 0
$$149$$ −7.08686 + 7.08686i −0.580578 + 0.580578i −0.935062 0.354484i $$-0.884657\pi$$
0.354484 + 0.935062i $$0.384657\pi$$
$$150$$ 0 0
$$151$$ 8.28521i 0.674241i −0.941462 0.337120i $$-0.890547\pi$$
0.941462 0.337120i $$-0.109453\pi$$
$$152$$ 0 0
$$153$$ 21.6819i 1.75288i
$$154$$ 0 0
$$155$$ −1.63782 + 1.63782i −0.131553 + 0.131553i
$$156$$ 0 0
$$157$$ −7.68999 7.68999i −0.613728 0.613728i 0.330188 0.943915i $$-0.392888\pi$$
−0.943915 + 0.330188i $$0.892888\pi$$
$$158$$ 0 0
$$159$$ 0.197029 0.0156254
$$160$$ 0 0
$$161$$ 6.44892 0.508246
$$162$$ 0 0
$$163$$ 4.46953 + 4.46953i 0.350081 + 0.350081i 0.860140 0.510059i $$-0.170376\pi$$
−0.510059 + 0.860140i $$0.670376\pi$$
$$164$$ 0 0
$$165$$ 0.169957 0.169957i 0.0132311 0.0132311i
$$166$$ 0 0
$$167$$ 12.8905i 0.997493i −0.866748 0.498747i $$-0.833794\pi$$
0.866748 0.498747i $$-0.166206\pi$$
$$168$$ 0 0
$$169$$ 7.64873i 0.588364i
$$170$$ 0 0
$$171$$ 11.3236 11.3236i 0.865938 0.865938i
$$172$$ 0 0
$$173$$ 6.21257 + 6.21257i 0.472333 + 0.472333i 0.902669 0.430336i $$-0.141605\pi$$
−0.430336 + 0.902669i $$0.641605\pi$$
$$174$$ 0 0
$$175$$ 4.85590 0.367071
$$176$$ 0 0
$$177$$ −1.82496 −0.137172
$$178$$ 0 0
$$179$$ −2.03654 2.03654i −0.152218 0.152218i 0.626890 0.779108i $$-0.284328\pi$$
−0.779108 + 0.626890i $$0.784328\pi$$
$$180$$ 0 0
$$181$$ −16.7116 + 16.7116i −1.24217 + 1.24217i −0.283064 + 0.959101i $$0.591351\pi$$
−0.959101 + 0.283064i $$0.908649\pi$$
$$182$$ 0 0
$$183$$ 0.318371i 0.0235346i
$$184$$ 0 0
$$185$$ 3.98263i 0.292809i
$$186$$ 0 0
$$187$$ 13.6316 13.6316i 0.996843 0.996843i
$$188$$ 0 0
$$189$$ −1.01712 1.01712i −0.0739846 0.0739846i
$$190$$ 0 0
$$191$$ −5.11015 −0.369758 −0.184879 0.982761i $$-0.559189\pi$$
−0.184879 + 0.982761i $$0.559189\pi$$
$$192$$ 0 0
$$193$$ 0.676235 0.0486765 0.0243382 0.999704i $$-0.492252\pi$$
0.0243382 + 0.999704i $$0.492252\pi$$
$$194$$ 0 0
$$195$$ −0.150332 0.150332i −0.0107655 0.0107655i
$$196$$ 0 0
$$197$$ 14.3449 14.3449i 1.02203 1.02203i 0.0222782 0.999752i $$-0.492908\pi$$
0.999752 0.0222782i $$-0.00709197\pi$$
$$198$$ 0 0
$$199$$ 4.94660i 0.350655i 0.984510 + 0.175328i $$0.0560984\pi$$
−0.984510 + 0.175328i $$0.943902\pi$$
$$200$$ 0 0
$$201$$ 2.12901i 0.150169i
$$202$$ 0 0
$$203$$ 3.58700 3.58700i 0.251758 0.251758i
$$204$$ 0 0
$$205$$ 0.224561 + 0.224561i 0.0156840 + 0.0156840i
$$206$$ 0 0
$$207$$ 18.9688 1.31842
$$208$$ 0 0
$$209$$ −14.2385 −0.984897
$$210$$ 0 0
$$211$$ −4.67810 4.67810i −0.322054 0.322054i 0.527501 0.849555i $$-0.323129\pi$$
−0.849555 + 0.527501i $$0.823129\pi$$
$$212$$ 0 0
$$213$$ −1.95647 + 1.95647i −0.134055 + 0.134055i
$$214$$ 0 0
$$215$$ 2.08807i 0.142405i
$$216$$ 0 0
$$217$$ 6.10161i 0.414204i
$$218$$ 0 0
$$219$$ 0.631044 0.631044i 0.0426420 0.0426420i
$$220$$ 0 0
$$221$$ −12.0576 12.0576i −0.811080 0.811080i
$$222$$ 0 0
$$223$$ 4.16691 0.279037 0.139518 0.990219i $$-0.455445\pi$$
0.139518 + 0.990219i $$0.455445\pi$$
$$224$$ 0 0
$$225$$ 14.2831 0.952204
$$226$$ 0 0
$$227$$ 12.1022 + 12.1022i 0.803248 + 0.803248i 0.983602 0.180353i $$-0.0577241\pi$$
−0.180353 + 0.983602i $$0.557724\pi$$
$$228$$ 0 0
$$229$$ 13.5287 13.5287i 0.893999 0.893999i −0.100898 0.994897i $$-0.532171\pi$$
0.994897 + 0.100898i $$0.0321714\pi$$
$$230$$ 0 0
$$231$$ 0.633164i 0.0416591i
$$232$$ 0 0
$$233$$ 13.3857i 0.876924i −0.898750 0.438462i $$-0.855523\pi$$
0.898750 0.438462i $$-0.144477\pi$$
$$234$$ 0 0
$$235$$ −1.61610 + 1.61610i −0.105423 + 0.105423i
$$236$$ 0 0
$$237$$ 0.721871 + 0.721871i 0.0468905 + 0.0468905i
$$238$$ 0 0
$$239$$ −20.6475 −1.33558 −0.667788 0.744352i $$-0.732759\pi$$
−0.667788 + 0.744352i $$0.732759\pi$$
$$240$$ 0 0
$$241$$ −0.401861 −0.0258861 −0.0129431 0.999916i $$-0.504120\pi$$
−0.0129431 + 0.999916i $$0.504120\pi$$
$$242$$ 0 0
$$243$$ −4.50237 4.50237i −0.288827 0.288827i
$$244$$ 0 0
$$245$$ 0.268425 0.268425i 0.0171490 0.0171490i
$$246$$ 0 0
$$247$$ 12.5944i 0.801360i
$$248$$ 0 0
$$249$$ 4.11364i 0.260691i
$$250$$ 0 0
$$251$$ −9.25468 + 9.25468i −0.584150 + 0.584150i −0.936041 0.351891i $$-0.885539\pi$$
0.351891 + 0.936041i $$0.385539\pi$$
$$252$$ 0 0
$$253$$ −11.9258 11.9258i −0.749771 0.749771i
$$254$$ 0 0
$$255$$ 0.677459 0.0424241
$$256$$ 0 0
$$257$$ 16.3273 1.01847 0.509234 0.860628i $$-0.329929\pi$$
0.509234 + 0.860628i $$0.329929\pi$$
$$258$$ 0 0
$$259$$ −7.41852 7.41852i −0.460965 0.460965i
$$260$$ 0 0
$$261$$ 10.5507 10.5507i 0.653075 0.653075i
$$262$$ 0 0
$$263$$ 13.3352i 0.822284i −0.911571 0.411142i $$-0.865130\pi$$
0.911571 0.411142i $$-0.134870\pi$$
$$264$$ 0 0
$$265$$ 0.308935i 0.0189777i
$$266$$ 0 0
$$267$$ 1.59685 1.59685i 0.0977256 0.0977256i
$$268$$ 0 0
$$269$$ 19.3277 + 19.3277i 1.17843 + 1.17843i 0.980145 + 0.198284i $$0.0635367\pi$$
0.198284 + 0.980145i $$0.436463\pi$$
$$270$$ 0 0
$$271$$ −24.5968 −1.49415 −0.747074 0.664741i $$-0.768542\pi$$
−0.747074 + 0.664741i $$0.768542\pi$$
$$272$$ 0 0
$$273$$ 0.560052 0.0338959
$$274$$ 0 0
$$275$$ −8.97989 8.97989i −0.541508 0.541508i
$$276$$ 0 0
$$277$$ −17.9974 + 17.9974i −1.08136 + 1.08136i −0.0849786 + 0.996383i $$0.527082\pi$$
−0.996383 + 0.0849786i $$0.972918\pi$$
$$278$$ 0 0
$$279$$ 17.9472i 1.07447i
$$280$$ 0 0
$$281$$ 13.7357i 0.819404i −0.912219 0.409702i $$-0.865633\pi$$
0.912219 0.409702i $$-0.134367\pi$$
$$282$$ 0 0
$$283$$ −10.0342 + 10.0342i −0.596473 + 0.596473i −0.939372 0.342900i $$-0.888591\pi$$
0.342900 + 0.939372i $$0.388591\pi$$
$$284$$ 0 0
$$285$$ −0.353810 0.353810i −0.0209579 0.0209579i
$$286$$ 0 0
$$287$$ −0.836588 −0.0493822
$$288$$ 0 0
$$289$$ 37.3366 2.19627
$$290$$ 0 0
$$291$$ −2.38012 2.38012i −0.139525 0.139525i
$$292$$ 0 0
$$293$$ −19.7376 + 19.7376i −1.15308 + 1.15308i −0.167151 + 0.985931i $$0.553457\pi$$
−0.985931 + 0.167151i $$0.946543\pi$$
$$294$$ 0 0
$$295$$ 2.86148i 0.166602i
$$296$$ 0 0
$$297$$ 3.76187i 0.218286i
$$298$$ 0 0
$$299$$ −10.5487 + 10.5487i −0.610050 + 0.610050i
$$300$$ 0 0
$$301$$ −3.88949 3.88949i −0.224186 0.224186i
$$302$$ 0 0
$$303$$ 0.278671 0.0160092
$$304$$ 0 0
$$305$$ −0.499195 −0.0285838
$$306$$ 0 0
$$307$$ −3.14804 3.14804i −0.179668 0.179668i 0.611543 0.791211i $$-0.290549\pi$$
−0.791211 + 0.611543i $$0.790549\pi$$
$$308$$ 0 0
$$309$$ −1.43797 + 1.43797i −0.0818035 + 0.0818035i
$$310$$ 0 0
$$311$$ 32.2711i 1.82993i −0.403535 0.914964i $$-0.632219\pi$$
0.403535 0.914964i $$-0.367781\pi$$
$$312$$ 0 0
$$313$$ 22.3372i 1.26257i 0.775550 + 0.631286i $$0.217473\pi$$
−0.775550 + 0.631286i $$0.782527\pi$$
$$314$$ 0 0
$$315$$ 0.789540 0.789540i 0.0444856 0.0444856i
$$316$$ 0 0
$$317$$ 0.148346 + 0.148346i 0.00833196 + 0.00833196i 0.711260 0.702929i $$-0.248125\pi$$
−0.702929 + 0.711260i $$0.748125\pi$$
$$318$$ 0 0
$$319$$ −13.2667 −0.742792
$$320$$ 0 0
$$321$$ 0.241442 0.0134760
$$322$$ 0 0
$$323$$ −28.3778 28.3778i −1.57898 1.57898i
$$324$$ 0 0
$$325$$ −7.94297 + 7.94297i −0.440597 + 0.440597i
$$326$$ 0 0
$$327$$ 4.15186i 0.229598i
$$328$$ 0 0
$$329$$ 6.02070i 0.331932i
$$330$$ 0 0
$$331$$ 20.1427 20.1427i 1.10714 1.10714i 0.113618 0.993525i $$-0.463756\pi$$
0.993525 0.113618i $$-0.0362440\pi$$
$$332$$ 0 0
$$333$$ −21.8207 21.8207i −1.19577 1.19577i
$$334$$ 0 0
$$335$$ −3.33823 −0.182387
$$336$$ 0 0
$$337$$ 6.83335 0.372236 0.186118 0.982527i $$-0.440409\pi$$
0.186118 + 0.982527i $$0.440409\pi$$
$$338$$ 0 0
$$339$$ −0.602092 0.602092i −0.0327012 0.0327012i
$$340$$ 0 0
$$341$$ −11.2836 + 11.2836i −0.611039 + 0.611039i
$$342$$ 0 0
$$343$$ 1.00000i 0.0539949i
$$344$$ 0 0
$$345$$ 0.592685i 0.0319091i
$$346$$ 0 0
$$347$$ −19.8489 + 19.8489i −1.06554 + 1.06554i −0.0678488 + 0.997696i $$0.521614\pi$$
−0.997696 + 0.0678488i $$0.978386\pi$$
$$348$$ 0 0
$$349$$ −16.6099 16.6099i −0.889105 0.889105i 0.105332 0.994437i $$-0.466409\pi$$
−0.994437 + 0.105332i $$0.966409\pi$$
$$350$$ 0 0
$$351$$ 3.32748 0.177608
$$352$$ 0 0
$$353$$ 5.41293 0.288101 0.144051 0.989570i $$-0.453987\pi$$
0.144051 + 0.989570i $$0.453987\pi$$
$$354$$ 0 0
$$355$$ −3.06768 3.06768i −0.162816 0.162816i
$$356$$ 0 0
$$357$$ −1.26192 + 1.26192i −0.0667878 + 0.0667878i
$$358$$ 0 0
$$359$$ 29.1561i 1.53880i 0.638768 + 0.769399i $$0.279444\pi$$
−0.638768 + 0.769399i $$0.720556\pi$$
$$360$$ 0 0
$$361$$ 10.6412i 0.560061i
$$362$$ 0 0
$$363$$ −0.712223 + 0.712223i −0.0373820 + 0.0373820i
$$364$$ 0 0
$$365$$ 0.989457 + 0.989457i 0.0517906 + 0.0517906i
$$366$$ 0 0
$$367$$ −6.14461 −0.320746 −0.160373 0.987056i $$-0.551270\pi$$
−0.160373 + 0.987056i $$0.551270\pi$$
$$368$$ 0 0
$$369$$ −2.46073 −0.128100
$$370$$ 0 0
$$371$$ −0.575460 0.575460i −0.0298764 0.0298764i
$$372$$ 0 0
$$373$$ 20.9348 20.9348i 1.08396 1.08396i 0.0878283 0.996136i $$-0.472007\pi$$
0.996136 0.0878283i $$-0.0279927\pi$$
$$374$$ 0 0
$$375$$ 0.905802i 0.0467754i
$$376$$ 0 0
$$377$$ 11.7348i 0.604371i
$$378$$ 0 0
$$379$$ 23.6398 23.6398i 1.21429 1.21429i 0.244693 0.969601i $$-0.421313\pi$$
0.969601 0.244693i $$-0.0786872\pi$$
$$380$$ 0 0
$$381$$ 1.00379 + 1.00379i 0.0514257 + 0.0514257i
$$382$$ 0 0
$$383$$ 6.99982 0.357674 0.178837 0.983879i $$-0.442767\pi$$
0.178837 + 0.983879i $$0.442767\pi$$
$$384$$ 0 0
$$385$$ −0.992782 −0.0505968
$$386$$ 0 0
$$387$$ −11.4405 11.4405i −0.581552 0.581552i
$$388$$ 0 0
$$389$$ −15.4838 + 15.4838i −0.785060 + 0.785060i −0.980680 0.195620i $$-0.937328\pi$$
0.195620 + 0.980680i $$0.437328\pi$$
$$390$$ 0 0
$$391$$ 47.5372i 2.40406i
$$392$$ 0 0
$$393$$ 2.66728i 0.134546i
$$394$$ 0 0
$$395$$ −1.13187 + 1.13187i −0.0569506 + 0.0569506i
$$396$$ 0 0
$$397$$ −5.65923 5.65923i −0.284029 0.284029i 0.550685 0.834713i $$-0.314367\pi$$
−0.834713 + 0.550685i $$0.814367\pi$$
$$398$$ 0 0
$$399$$ 1.31810 0.0659874
$$400$$ 0 0
$$401$$ 26.7191 1.33429 0.667144 0.744929i $$-0.267517\pi$$
0.667144 + 0.744929i $$0.267517\pi$$
$$402$$ 0 0
$$403$$ 9.98063 + 9.98063i 0.497171 + 0.497171i
$$404$$ 0 0
$$405$$ 2.27514 2.27514i 0.113053 0.113053i
$$406$$ 0 0
$$407$$ 27.4378i 1.36004i
$$408$$ 0 0
$$409$$ 20.7456i 1.02581i 0.858447 + 0.512903i $$0.171430\pi$$
−0.858447 + 0.512903i $$0.828570\pi$$
$$410$$ 0 0
$$411$$ 1.08687 1.08687i 0.0536111 0.0536111i
$$412$$ 0 0
$$413$$ 5.33013 + 5.33013i 0.262279 + 0.262279i
$$414$$ 0 0
$$415$$ −6.45006 −0.316621
$$416$$ 0 0
$$417$$ −4.83171 −0.236610
$$418$$ 0 0
$$419$$ 6.11779 + 6.11779i 0.298874 + 0.298874i 0.840573 0.541699i $$-0.182219\pi$$
−0.541699 + 0.840573i $$0.682219\pi$$
$$420$$ 0 0
$$421$$ 9.03252 9.03252i 0.440218 0.440218i −0.451867 0.892085i $$-0.649242\pi$$
0.892085 + 0.451867i $$0.149242\pi$$
$$422$$ 0 0
$$423$$ 17.7092i 0.861050i
$$424$$ 0 0
$$425$$ 35.7945i 1.73629i
$$426$$ 0 0
$$427$$ 0.929862 0.929862i 0.0449992 0.0449992i
$$428$$ 0 0
$$429$$ −1.03569 1.03569i −0.0500036 0.0500036i
$$430$$ 0 0
$$431$$ −2.81338 −0.135516 −0.0677579 0.997702i $$-0.521585\pi$$
−0.0677579 + 0.997702i $$0.521585\pi$$
$$432$$ 0 0
$$433$$ −20.6954 −0.994558 −0.497279 0.867591i $$-0.665667\pi$$
−0.497279 + 0.867591i $$0.665667\pi$$
$$434$$ 0 0
$$435$$ −0.329661 0.329661i −0.0158060 0.0158060i
$$436$$ 0 0
$$437$$ −24.8267 + 24.8267i −1.18762 + 1.18762i
$$438$$ 0 0
$$439$$ 15.6336i 0.746151i −0.927801 0.373075i $$-0.878303\pi$$
0.927801 0.373075i $$-0.121697\pi$$
$$440$$ 0 0
$$441$$ 2.94139i 0.140066i
$$442$$ 0 0
$$443$$ 18.6608 18.6608i 0.886603 0.886603i −0.107592 0.994195i $$-0.534314\pi$$
0.994195 + 0.107592i $$0.0343141\pi$$
$$444$$ 0 0
$$445$$ 2.50381 + 2.50381i 0.118692 + 0.118692i
$$446$$ 0 0
$$447$$ −2.42643 −0.114766
$$448$$ 0 0
$$449$$ 26.8536 1.26730 0.633650 0.773620i $$-0.281556\pi$$
0.633650 + 0.773620i $$0.281556\pi$$
$$450$$ 0 0
$$451$$ 1.54708 + 1.54708i 0.0728492 + 0.0728492i
$$452$$ 0 0
$$453$$ 1.41837 1.41837i 0.0666406 0.0666406i
$$454$$ 0 0
$$455$$ 0.878144i 0.0411680i
$$456$$ 0 0
$$457$$ 0.385896i 0.0180514i 0.999959 + 0.00902572i $$0.00287302\pi$$
−0.999959 + 0.00902572i $$0.997127\pi$$
$$458$$ 0 0
$$459$$ −7.49754 + 7.49754i −0.349955 + 0.349955i
$$460$$ 0 0
$$461$$ 2.13650 + 2.13650i 0.0995065 + 0.0995065i 0.755108 0.655601i $$-0.227585\pi$$
−0.655601 + 0.755108i $$0.727585\pi$$
$$462$$ 0 0
$$463$$ 32.5560 1.51301 0.756503 0.653991i $$-0.226906\pi$$
0.756503 + 0.653991i $$0.226906\pi$$
$$464$$ 0 0
$$465$$ −0.560766 −0.0260049
$$466$$ 0 0
$$467$$ −8.00295 8.00295i −0.370332 0.370332i 0.497266 0.867598i $$-0.334337\pi$$
−0.867598 + 0.497266i $$0.834337\pi$$
$$468$$ 0 0
$$469$$ 6.21819 6.21819i 0.287129 0.287129i
$$470$$ 0 0
$$471$$ 2.63294i 0.121319i
$$472$$ 0 0
$$473$$ 14.3855i 0.661444i
$$474$$ 0 0
$$475$$ −18.6940 + 18.6940i −0.857739 + 0.857739i
$$476$$ 0 0
$$477$$ −1.69265 1.69265i −0.0775012 0.0775012i
$$478$$ 0 0
$$479$$ −20.2388 −0.924735 −0.462368 0.886688i $$-0.653000\pi$$
−0.462368 + 0.886688i $$0.653000\pi$$
$$480$$ 0 0
$$481$$ 24.2695 1.10659
$$482$$ 0 0
$$483$$ 1.10401 + 1.10401i 0.0502341 + 0.0502341i
$$484$$ 0 0
$$485$$ 3.73196 3.73196i 0.169459 0.169459i
$$486$$ 0 0
$$487$$ 36.6988i 1.66298i −0.555537 0.831492i $$-0.687487\pi$$
0.555537 0.831492i $$-0.312513\pi$$
$$488$$ 0 0
$$489$$ 1.53030i 0.0692026i
$$490$$ 0 0
$$491$$ −13.6015 + 13.6015i −0.613829 + 0.613829i −0.943942 0.330113i $$-0.892913\pi$$
0.330113 + 0.943942i $$0.392913\pi$$
$$492$$ 0 0
$$493$$ −26.4410 26.4410i −1.19084 1.19084i
$$494$$ 0 0
$$495$$ −2.92015 −0.131251
$$496$$ 0 0
$$497$$ 11.4285 0.512637
$$498$$ 0 0
$$499$$ −24.1970 24.1970i −1.08321 1.08321i −0.996209 0.0869972i $$-0.972273\pi$$
−0.0869972 0.996209i $$-0.527727\pi$$
$$500$$ 0 0
$$501$$ 2.20675 2.20675i 0.0985903 0.0985903i
$$502$$ 0 0
$$503$$ 13.4123i 0.598026i −0.954249 0.299013i $$-0.903343\pi$$
0.954249 0.299013i $$-0.0966574\pi$$
$$504$$ 0 0
$$505$$ 0.436947i 0.0194439i
$$506$$ 0 0
$$507$$ 1.30940 1.30940i 0.0581527 0.0581527i
$$508$$ 0 0
$$509$$ −18.9792 18.9792i −0.841240 0.841240i 0.147781 0.989020i $$-0.452787\pi$$
−0.989020 + 0.147781i $$0.952787\pi$$
$$510$$ 0 0
$$511$$ −3.68616 −0.163066
$$512$$ 0 0
$$513$$ 7.83132 0.345761
$$514$$ 0 0
$$515$$ −2.25470 2.25470i −0.0993540 0.0993540i
$$516$$ 0 0
$$517$$ −11.1339 + 11.1339i −0.489669 + 0.489669i
$$518$$ 0 0
$$519$$ 2.12709i 0.0933689i
$$520$$ 0 0
$$521$$ 0.00960703i 0.000420892i −1.00000 0.000210446i $$-0.999933\pi$$
1.00000 0.000210446i $$-6.69870e-5\pi$$
$$522$$ 0 0
$$523$$ 23.5829 23.5829i 1.03121 1.03121i 0.0317098 0.999497i $$-0.489905\pi$$
0.999497 0.0317098i $$-0.0100952\pi$$
$$524$$ 0 0
$$525$$ 0.831293 + 0.831293i 0.0362806 + 0.0362806i
$$526$$ 0 0
$$527$$ −44.9770 −1.95923
$$528$$ 0 0
$$529$$ −18.5886 −0.808201
$$530$$ 0 0
$$531$$ 15.6780 + 15.6780i 0.680366 + 0.680366i
$$532$$ 0 0
$$533$$ 1.36844 1.36844i 0.0592736 0.0592736i
$$534$$ 0 0
$$535$$ 0.378573i 0.0163671i
$$536$$ 0 0
$$537$$ 0.697281i 0.0300899i
$$538$$ 0 0
$$539$$ 1.84927 1.84927i 0.0796539 0.0796539i
$$540$$ 0 0
$$541$$ −11.6478 11.6478i −0.500776 0.500776i 0.410903 0.911679i $$-0.365214\pi$$
−0.911679 + 0.410903i $$0.865214\pi$$
$$542$$ 0 0
$$543$$ −5.72181 −0.245546
$$544$$ 0 0
$$545$$ −6.50998 −0.278857
$$546$$ 0 0
$$547$$ −14.0041 14.0041i −0.598773 0.598773i 0.341213 0.939986i $$-0.389162\pi$$
−0.939986 + 0.341213i $$0.889162\pi$$
$$548$$ 0 0
$$549$$ 2.73508 2.73508i 0.116730 0.116730i
$$550$$ 0 0
$$551$$ 27.6181i 1.17657i
$$552$$ 0 0
$$553$$ 4.21672i 0.179313i
$$554$$ 0 0
$$555$$ −0.681796 + 0.681796i −0.0289406 + 0.0289406i
$$556$$ 0 0
$$557$$ 24.3807 + 24.3807i 1.03305 + 1.03305i 0.999435 + 0.0336103i $$0.0107005\pi$$
0.0336103 + 0.999435i $$0.489299\pi$$
$$558$$ 0 0
$$559$$ 12.7244 0.538183
$$560$$ 0 0
$$561$$ 4.66727 0.197052
$$562$$ 0 0
$$563$$ −26.2789 26.2789i −1.10752 1.10752i −0.993475 0.114046i $$-0.963619\pi$$
−0.114046 0.993475i $$-0.536381\pi$$
$$564$$ 0 0
$$565$$ 0.944062 0.944062i 0.0397170 0.0397170i
$$566$$ 0 0
$$567$$ 8.47591i 0.355955i
$$568$$ 0 0
$$569$$ 36.8053i 1.54296i −0.636255 0.771479i $$-0.719517\pi$$
0.636255 0.771479i $$-0.280483\pi$$
$$570$$ 0 0
$$571$$ 23.0536 23.0536i 0.964762 0.964762i −0.0346376 0.999400i $$-0.511028\pi$$
0.999400 + 0.0346376i $$0.0110277\pi$$
$$572$$ 0 0
$$573$$ −0.874820 0.874820i −0.0365461 0.0365461i
$$574$$ 0 0
$$575$$ −31.3153 −1.30594
$$576$$ 0 0
$$577$$ −3.51057 −0.146147 −0.0730735 0.997327i $$-0.523281\pi$$
−0.0730735 + 0.997327i $$0.523281\pi$$
$$578$$ 0 0
$$579$$ 0.115766 + 0.115766i 0.00481109 + 0.00481109i
$$580$$ 0 0
$$581$$ 12.0147 12.0147i 0.498452 0.498452i
$$582$$ 0 0
$$583$$ 2.12837i 0.0881480i
$$584$$ 0 0
$$585$$ 2.58296i 0.106792i
$$586$$ 0 0
$$587$$ −28.0315 + 28.0315i −1.15699 + 1.15699i −0.171865 + 0.985120i $$0.554979\pi$$
−0.985120 + 0.171865i $$0.945021\pi$$
$$588$$ 0 0
$$589$$ 23.4897 + 23.4897i 0.967876 + 0.967876i
$$590$$ 0 0
$$591$$ 4.91147 0.202031
$$592$$ 0 0
$$593$$ 6.27767 0.257793 0.128896 0.991658i $$-0.458857\pi$$
0.128896 + 0.991658i $$0.458857\pi$$
$$594$$ 0 0
$$595$$ −1.97865 1.97865i −0.0811167 0.0811167i
$$596$$ 0 0
$$597$$ −0.846821 + 0.846821i −0.0346581 + 0.0346581i
$$598$$ 0 0
$$599$$ 10.3600i 0.423300i 0.977346 + 0.211650i $$0.0678836\pi$$
−0.977346 + 0.211650i $$0.932116\pi$$
$$600$$ 0 0
$$601$$ 23.9656i 0.977576i 0.872403 + 0.488788i $$0.162561\pi$$
−0.872403 + 0.488788i $$0.837439\pi$$
$$602$$ 0 0
$$603$$ 18.2901 18.2901i 0.744830 0.744830i
$$604$$ 0 0
$$605$$ −1.11674 1.11674i −0.0454021 0.0454021i
$$606$$ 0 0
$$607$$ 14.4285 0.585633 0.292817 0.956169i $$-0.405407\pi$$
0.292817 + 0.956169i $$0.405407\pi$$
$$608$$ 0 0
$$609$$ 1.22813 0.0497665
$$610$$ 0 0
$$611$$ 9.84828 + 9.84828i 0.398419 + 0.398419i
$$612$$ 0 0
$$613$$ 3.13825 3.13825i 0.126753 0.126753i −0.640885 0.767637i $$-0.721432\pi$$
0.767637 + 0.640885i $$0.221432\pi$$
$$614$$ 0 0
$$615$$ 0.0768862i 0.00310035i
$$616$$ 0 0
$$617$$ 15.7644i 0.634651i −0.948317 0.317325i $$-0.897215\pi$$
0.948317 0.317325i $$-0.102785\pi$$
$$618$$ 0 0
$$619$$ −6.16647 + 6.16647i −0.247851 + 0.247851i −0.820088 0.572237i $$-0.806076\pi$$
0.572237 + 0.820088i $$0.306076\pi$$
$$620$$ 0 0
$$621$$ 6.55934 + 6.55934i 0.263217 + 0.263217i
$$622$$ 0 0
$$623$$ −9.32780 −0.373711
$$624$$ 0 0
$$625$$ −22.8592 −0.914369
$$626$$ 0 0
$$627$$ −2.43752 2.43752i −0.0973453 0.0973453i
$$628$$ 0 0
$$629$$ −54.6844 + 54.6844i −2.18041 + 2.18041i
$$630$$ 0 0
$$631$$ 30.5796i 1.21736i 0.793417 + 0.608678i $$0.208300\pi$$
−0.793417 + 0.608678i $$0.791700\pi$$
$$632$$ 0 0
$$633$$ 1.60171i 0.0636623i
$$634$$ 0 0
$$635$$ −1.57391 + 1.57391i −0.0624588 + 0.0624588i
$$636$$ 0 0
$$637$$ −1.63574 1.63574i −0.0648103 0.0648103i
$$638$$ 0 0
$$639$$ 33.6155 1.32981
$$640$$ 0 0
$$641$$ −18.6228 −0.735556 −0.367778 0.929914i $$-0.619881\pi$$
−0.367778 + 0.929914i $$0.619881\pi$$
$$642$$ 0 0
$$643$$ 27.8340 + 27.8340i 1.09766 + 1.09766i 0.994683 + 0.102981i $$0.0328381\pi$$
0.102981 + 0.994683i $$0.467162\pi$$
$$644$$ 0 0
$$645$$ −0.357461 + 0.357461i −0.0140750 + 0.0140750i
$$646$$ 0 0
$$647$$ 29.2607i 1.15036i 0.818029 + 0.575178i $$0.195067\pi$$
−0.818029 + 0.575178i $$0.804933\pi$$
$$648$$ 0 0
$$649$$ 19.7138i 0.773833i
$$650$$ 0 0
$$651$$ 1.04455 1.04455i 0.0409392 0.0409392i
$$652$$ 0 0
$$653$$ 17.3825 + 17.3825i 0.680229 + 0.680229i 0.960052 0.279822i $$-0.0902756\pi$$
−0.279822 + 0.960052i $$0.590276\pi$$
$$654$$ 0 0
$$655$$ 4.18221 0.163413
$$656$$ 0 0
$$657$$ −10.8424 −0.423004
$$658$$ 0 0
$$659$$ 27.7030 + 27.7030i 1.07916 + 1.07916i 0.996585 + 0.0825717i $$0.0263134\pi$$
0.0825717 + 0.996585i $$0.473687\pi$$
$$660$$ 0 0
$$661$$ 18.7539 18.7539i 0.729443 0.729443i −0.241066 0.970509i $$-0.577497\pi$$
0.970509 + 0.241066i $$0.0774970\pi$$
$$662$$ 0 0
$$663$$ 4.12833i 0.160331i
$$664$$ 0 0
$$665$$ 2.06673i 0.0801445i
$$666$$ 0 0
$$667$$ −23.1323 + 23.1323i −0.895685 + 0.895685i
$$668$$ 0 0
$$669$$ 0.713343 + 0.713343i 0.0275794 + 0.0275794i
$$670$$ 0 0
$$671$$ −3.43914 −0.132767
$$672$$ 0 0
$$673$$ 8.89179 0.342753 0.171377 0.985206i $$-0.445179\pi$$
0.171377 + 0.985206i $$0.445179\pi$$
$$674$$ 0 0
$$675$$ 4.93903 + 4.93903i 0.190103 + 0.190103i
$$676$$ 0 0
$$677$$ 23.0023 23.0023i 0.884049 0.884049i −0.109895 0.993943i $$-0.535051\pi$$
0.993943 + 0.109895i $$0.0350514\pi$$
$$678$$ 0 0
$$679$$ 13.9032i 0.533556i
$$680$$ 0 0
$$681$$ 4.14360i 0.158783i
$$682$$ 0 0
$$683$$ −8.13050 + 8.13050i −0.311105 + 0.311105i −0.845337 0.534233i $$-0.820601\pi$$
0.534233 + 0.845337i $$0.320601\pi$$
$$684$$ 0 0
$$685$$ 1.70417 + 1.70417i 0.0651131 + 0.0651131i
$$686$$ 0 0
$$687$$ 4.63201 0.176722
$$688$$ 0 0
$$689$$ 1.88260 0.0717215
$$690$$ 0 0
$$691$$ 1.09420 + 1.09420i 0.0416253 + 0.0416253i 0.727613 0.685988i $$-0.240630\pi$$
−0.685988 + 0.727613i $$0.740630\pi$$
$$692$$ 0 0
$$693$$ 5.43943 5.43943i 0.206627 0.206627i
$$694$$ 0 0
$$695$$ 7.57597i 0.287373i
$$696$$ 0 0
$$697$$ 6.16677i 0.233583i
$$698$$ 0 0
$$699$$ 2.29152 2.29152i 0.0866734 0.0866734i
$$700$$ 0 0
$$701$$ −11.5656 11.5656i −0.436825 0.436825i 0.454117 0.890942i $$-0.349955\pi$$
−0.890942 + 0.454117i $$0.849955\pi$$
$$702$$ 0 0
$$703$$ 57.1189 2.15428
$$704$$ 0 0
$$705$$ −0.553329 −0.0208396
$$706$$ 0 0
$$707$$ −0.813911 0.813911i −0.0306103 0.0306103i
$$708$$ 0 0
$$709$$ 2.69651 2.69651i 0.101270 0.101270i −0.654657 0.755926i $$-0.727187\pi$$
0.755926 + 0.654657i $$0.227187\pi$$
$$710$$ 0 0
$$711$$ 12.4030i 0.465149i
$$712$$ 0 0
$$713$$ 39.3488i 1.47363i
$$714$$ 0 0
$$715$$ 1.62393 1.62393i 0.0607315 0.0607315i
$$716$$ 0 0
$$717$$ −3.53470 3.53470i −0.132006 0.132006i
$$718$$ 0 0
$$719$$ 6.08527 0.226942 0.113471 0.993541i $$-0.463803\pi$$
0.113471 + 0.993541i $$0.463803\pi$$
$$720$$ 0 0
$$721$$ 8.39975 0.312823
$$722$$ 0 0
$$723$$ −0.0687956 0.0687956i −0.00255854 0.00255854i
$$724$$ 0 0
$$725$$ −17.4181 + 17.4181i −0.646891 + 0.646891i
$$726$$ 0 0
$$727$$ 41.6162i 1.54346i −0.635951 0.771729i $$-0.719392\pi$$
0.635951 0.771729i $$-0.280608\pi$$
$$728$$ 0 0
$$729$$ 23.8862i 0.884674i
$$730$$ 0 0
$$731$$ −28.6707 + 28.6707i −1.06042 + 1.06042i
$$732$$ 0 0
$$733$$ 23.5929 + 23.5929i 0.871422 + 0.871422i 0.992627 0.121206i $$-0.0386760\pi$$
−0.121206 + 0.992627i $$0.538676\pi$$
$$734$$ 0 0
$$735$$ 0.0919045 0.00338995
$$736$$ 0 0
$$737$$ −22.9983 −0.847152
$$738$$ 0 0
$$739$$ −7.53135 7.53135i −0.277045 0.277045i 0.554883 0.831928i $$-0.312763\pi$$
−0.831928 + 0.554883i $$0.812763\pi$$
$$740$$ 0 0
$$741$$ −2.15606 + 2.15606i −0.0792048 + 0.0792048i
$$742$$ 0 0
$$743$$ 14.4179i 0.528943i −0.964393 0.264472i $$-0.914802\pi$$
0.964393 0.264472i $$-0.0851975\pi$$
$$744$$ 0 0
$$745$$ 3.80457i 0.139389i
$$746$$ 0 0
$$747$$ 35.3397 35.3397i 1.29301 1.29301i
$$748$$ 0 0
$$749$$ −0.705176 0.705176i −0.0257666 0.0257666i
$$750$$ 0 0
$$751$$ 17.6760 0.645008 0.322504 0.946568i $$-0.395475\pi$$
0.322504 + 0.946568i $$0.395475\pi$$
$$752$$ 0 0
$$753$$ −3.16866 −0.115472
$$754$$ 0 0
$$755$$ 2.22395 + 2.22395i 0.0809379 + 0.0809379i
$$756$$ 0 0
$$757$$ 21.3351 21.3351i 0.775437 0.775437i −0.203614 0.979051i $$-0.565269\pi$$
0.979051 + 0.203614i $$0.0652687\pi$$
$$758$$ 0 0
$$759$$ 4.08323i 0.148212i
$$760$$ 0 0
$$761$$ 22.2510i 0.806597i −0.915068 0.403299i $$-0.867864\pi$$
0.915068 0.403299i $$-0.132136\pi$$
$$762$$ 0 0
$$763$$ 12.1263 12.1263i 0.439001 0.439001i
$$764$$ 0 0
$$765$$ −5.81997 5.81997i −0.210421 0.210421i
$$766$$ 0 0
$$767$$ −17.4374 −0.629628
$$768$$ 0 0
$$769$$ −30.5537 −1.10179 −0.550897 0.834573i $$-0.685714\pi$$
−0.550897 + 0.834573i $$0.685714\pi$$
$$770$$ 0 0
$$771$$ 2.79511 + 2.79511i 0.100663 + 0.100663i
$$772$$ 0 0
$$773$$ 19.1590 19.1590i 0.689100 0.689100i −0.272933 0.962033i $$-0.587994\pi$$
0.962033 + 0.272933i $$0.0879938\pi$$
$$774$$ 0 0
$$775$$ 29.6288i 1.06430i
$$776$$ 0 0
$$777$$ 2.53999i 0.0911217i
$$778$$ 0 0
$$779$$ 3.22065 3.22065i 0.115392 0.115392i
$$780$$ 0 0
$$781$$ −21.1344 21.1344i −0.756247 0.756247i
$$782$$ 0 0
$$783$$ 7.29682 0.260767
$$784$$ 0 0
$$785$$ 4.12836 0.147348
$$786$$ 0 0
$$787$$ 13.8172 + 13.8172i 0.492528 + 0.492528i 0.909102 0.416574i $$-0.136769\pi$$
−0.416574 + 0.909102i $$0.636769\pi$$
$$788$$ 0 0
$$789$$ 2.28289 2.28289i 0.0812729 0.0812729i
$$790$$ 0 0
$$791$$ 3.51705i 0.125052i
$$792$$ 0 0
$$793$$ 3.04202i 0.108025i
$$794$$ 0 0
$$795$$ −0.0528874 + 0.0528874i −0.00187572 + 0.00187572i
$$796$$ 0 0
$$797$$ 8.78511 + 8.78511i 0.311185 + 0.311185i 0.845368 0.534184i $$-0.179381\pi$$
−0.534184 + 0.845368i $$0.679381\pi$$
$$798$$ 0 0
$$799$$ −44.3806