# Properties

 Label 1960.2.g.c.1569.3 Level $1960$ Weight $2$ Character 1960.1569 Analytic conductor $15.651$ Analytic rank $0$ Dimension $6$ CM no Inner twists $2$

# Learn more about

## Newspace parameters

 Level: $$N$$ $$=$$ $$1960 = 2^{3} \cdot 5 \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1960.g (of order $$2$$, degree $$1$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$15.6506787962$$ Analytic rank: $$0$$ Dimension: $$6$$ Coefficient field: 6.0.5161984.1 Defining polynomial: $$x^{6} - 4 x^{3} + 25 x^{2} - 20 x + 8$$ Coefficient ring: $$\Z[a_1, \ldots, a_{5}]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 280) Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

## Embedding invariants

 Embedding label 1569.3 Root $$-1.75233 + 1.75233i$$ of defining polynomial Character $$\chi$$ $$=$$ 1960.1569 Dual form 1960.2.g.c.1569.4

## $q$-expansion

 $$f(q)$$ $$=$$ $$q-0.363328i q^{3} +(1.75233 + 1.38900i) q^{5} +2.86799 q^{9} +O(q^{10})$$ $$q-0.363328i q^{3} +(1.75233 + 1.38900i) q^{5} +2.86799 q^{9} +5.14134 q^{11} +4.64600i q^{13} +(0.504664 - 0.636672i) q^{15} +3.86799i q^{17} -0.778008 q^{19} +5.00933i q^{23} +(1.14134 + 4.86799i) q^{25} -2.13201i q^{27} -9.42401 q^{29} -4.72666 q^{31} -1.86799i q^{33} -6.00000i q^{37} +1.68802 q^{39} +1.00933 q^{41} -7.00933i q^{43} +(5.02568 + 3.98365i) q^{45} -11.4240i q^{47} +1.40535 q^{51} +7.55602i q^{53} +(9.00933 + 7.14134i) q^{55} +0.282672i q^{57} +12.5140 q^{59} -11.5047 q^{61} +(-6.45331 + 8.14134i) q^{65} +11.7360i q^{67} +1.82003 q^{69} +2.72666 q^{71} -5.00933i q^{73} +(1.76868 - 0.414680i) q^{75} -5.68802 q^{79} +7.82936 q^{81} +4.67531i q^{83} +(-5.37266 + 6.77801i) q^{85} +3.42401i q^{87} -2.82936 q^{89} +1.71733i q^{93} +(-1.36333 - 1.08066i) q^{95} -1.58532i q^{97} +14.7453 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$6q - 8q^{9} + O(q^{10})$$ $$6q - 8q^{9} + 14q^{11} - 18q^{15} + 8q^{19} - 10q^{25} - 6q^{29} - 20q^{31} + 10q^{39} - 36q^{41} + 28q^{45} + 42q^{51} + 12q^{55} + 12q^{59} - 48q^{61} - 22q^{65} + 36q^{69} + 8q^{71} + 40q^{75} - 34q^{79} + 30q^{81} + 14q^{85} - 4q^{95} - 4q^{99} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1960\mathbb{Z}\right)^\times$$.

 $$n$$ $$981$$ $$1081$$ $$1177$$ $$1471$$ $$\chi(n)$$ $$1$$ $$1$$ $$-1$$ $$1$$

## Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0 0
$$3$$ 0.363328i 0.209768i −0.994484 0.104884i $$-0.966553\pi$$
0.994484 0.104884i $$-0.0334471\pi$$
$$4$$ 0 0
$$5$$ 1.75233 + 1.38900i 0.783667 + 0.621181i
$$6$$ 0 0
$$7$$ 0 0
$$8$$ 0 0
$$9$$ 2.86799 0.955998
$$10$$ 0 0
$$11$$ 5.14134 1.55017 0.775086 0.631856i $$-0.217707\pi$$
0.775086 + 0.631856i $$0.217707\pi$$
$$12$$ 0 0
$$13$$ 4.64600i 1.28857i 0.764786 + 0.644284i $$0.222845\pi$$
−0.764786 + 0.644284i $$0.777155\pi$$
$$14$$ 0 0
$$15$$ 0.504664 0.636672i 0.130304 0.164388i
$$16$$ 0 0
$$17$$ 3.86799i 0.938126i 0.883165 + 0.469063i $$0.155408\pi$$
−0.883165 + 0.469063i $$0.844592\pi$$
$$18$$ 0 0
$$19$$ −0.778008 −0.178487 −0.0892436 0.996010i $$-0.528445\pi$$
−0.0892436 + 0.996010i $$0.528445\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 0 0
$$23$$ 5.00933i 1.04452i 0.852787 + 0.522259i $$0.174910\pi$$
−0.852787 + 0.522259i $$0.825090\pi$$
$$24$$ 0 0
$$25$$ 1.14134 + 4.86799i 0.228267 + 0.973599i
$$26$$ 0 0
$$27$$ 2.13201i 0.410305i
$$28$$ 0 0
$$29$$ −9.42401 −1.74999 −0.874997 0.484128i $$-0.839137\pi$$
−0.874997 + 0.484128i $$0.839137\pi$$
$$30$$ 0 0
$$31$$ −4.72666 −0.848933 −0.424466 0.905444i $$-0.639538\pi$$
−0.424466 + 0.905444i $$0.639538\pi$$
$$32$$ 0 0
$$33$$ 1.86799i 0.325176i
$$34$$ 0 0
$$35$$ 0 0
$$36$$ 0 0
$$37$$ 6.00000i 0.986394i −0.869918 0.493197i $$-0.835828\pi$$
0.869918 0.493197i $$-0.164172\pi$$
$$38$$ 0 0
$$39$$ 1.68802 0.270300
$$40$$ 0 0
$$41$$ 1.00933 0.157631 0.0788153 0.996889i $$-0.474886\pi$$
0.0788153 + 0.996889i $$0.474886\pi$$
$$42$$ 0 0
$$43$$ 7.00933i 1.06891i −0.845196 0.534456i $$-0.820516\pi$$
0.845196 0.534456i $$-0.179484\pi$$
$$44$$ 0 0
$$45$$ 5.02568 + 3.98365i 0.749184 + 0.593848i
$$46$$ 0 0
$$47$$ 11.4240i 1.66636i −0.553000 0.833181i $$-0.686517\pi$$
0.553000 0.833181i $$-0.313483\pi$$
$$48$$ 0 0
$$49$$ 0 0
$$50$$ 0 0
$$51$$ 1.40535 0.196788
$$52$$ 0 0
$$53$$ 7.55602i 1.03790i 0.854805 + 0.518949i $$0.173677\pi$$
−0.854805 + 0.518949i $$0.826323\pi$$
$$54$$ 0 0
$$55$$ 9.00933 + 7.14134i 1.21482 + 0.962938i
$$56$$ 0 0
$$57$$ 0.282672i 0.0374409i
$$58$$ 0 0
$$59$$ 12.5140 1.62918 0.814592 0.580035i $$-0.196961\pi$$
0.814592 + 0.580035i $$0.196961\pi$$
$$60$$ 0 0
$$61$$ −11.5047 −1.47302 −0.736511 0.676426i $$-0.763528\pi$$
−0.736511 + 0.676426i $$0.763528\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 0 0
$$65$$ −6.45331 + 8.14134i −0.800435 + 1.00981i
$$66$$ 0 0
$$67$$ 11.7360i 1.43378i 0.697187 + 0.716889i $$0.254435\pi$$
−0.697187 + 0.716889i $$0.745565\pi$$
$$68$$ 0 0
$$69$$ 1.82003 0.219106
$$70$$ 0 0
$$71$$ 2.72666 0.323595 0.161797 0.986824i $$-0.448271\pi$$
0.161797 + 0.986824i $$0.448271\pi$$
$$72$$ 0 0
$$73$$ 5.00933i 0.586298i −0.956067 0.293149i $$-0.905297\pi$$
0.956067 0.293149i $$-0.0947031\pi$$
$$74$$ 0 0
$$75$$ 1.76868 0.414680i 0.204229 0.0478831i
$$76$$ 0 0
$$77$$ 0 0
$$78$$ 0 0
$$79$$ −5.68802 −0.639953 −0.319976 0.947426i $$-0.603675\pi$$
−0.319976 + 0.947426i $$0.603675\pi$$
$$80$$ 0 0
$$81$$ 7.82936 0.869929
$$82$$ 0 0
$$83$$ 4.67531i 0.513181i 0.966520 + 0.256591i $$0.0825992\pi$$
−0.966520 + 0.256591i $$0.917401\pi$$
$$84$$ 0 0
$$85$$ −5.37266 + 6.77801i −0.582746 + 0.735178i
$$86$$ 0 0
$$87$$ 3.42401i 0.367092i
$$88$$ 0 0
$$89$$ −2.82936 −0.299911 −0.149956 0.988693i $$-0.547913\pi$$
−0.149956 + 0.988693i $$0.547913\pi$$
$$90$$ 0 0
$$91$$ 0 0
$$92$$ 0 0
$$93$$ 1.71733i 0.178079i
$$94$$ 0 0
$$95$$ −1.36333 1.08066i −0.139875 0.110873i
$$96$$ 0 0
$$97$$ 1.58532i 0.160965i −0.996756 0.0804824i $$-0.974354\pi$$
0.996756 0.0804824i $$-0.0256461\pi$$
$$98$$ 0 0
$$99$$ 14.7453 1.48196
$$100$$ 0 0
$$101$$ 9.06068 0.901571 0.450786 0.892632i $$-0.351144\pi$$
0.450786 + 0.892632i $$0.351144\pi$$
$$102$$ 0 0
$$103$$ 5.14134i 0.506591i −0.967389 0.253295i $$-0.918486\pi$$
0.967389 0.253295i $$-0.0815145\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$108$$ 0 0
$$109$$ 3.97070 0.380324 0.190162 0.981753i $$-0.439099\pi$$
0.190162 + 0.981753i $$0.439099\pi$$
$$110$$ 0 0
$$111$$ −2.17997 −0.206914
$$112$$ 0 0
$$113$$ 4.54669i 0.427716i 0.976865 + 0.213858i $$0.0686030\pi$$
−0.976865 + 0.213858i $$0.931397\pi$$
$$114$$ 0 0
$$115$$ −6.95798 + 8.77801i −0.648835 + 0.818553i
$$116$$ 0 0
$$117$$ 13.3247i 1.23187i
$$118$$ 0 0
$$119$$ 0 0
$$120$$ 0 0
$$121$$ 15.4333 1.40303
$$122$$ 0 0
$$123$$ 0.366718i 0.0330658i
$$124$$ 0 0
$$125$$ −4.76166 + 10.1157i −0.425896 + 0.904772i
$$126$$ 0 0
$$127$$ 16.1214i 1.43054i −0.698849 0.715270i $$-0.746304\pi$$
0.698849 0.715270i $$-0.253696\pi$$
$$128$$ 0 0
$$129$$ −2.54669 −0.224223
$$130$$ 0 0
$$131$$ −0.0513514 −0.00448659 −0.00224330 0.999997i $$-0.500714\pi$$
−0.00224330 + 0.999997i $$0.500714\pi$$
$$132$$ 0 0
$$133$$ 0 0
$$134$$ 0 0
$$135$$ 2.96137 3.73599i 0.254874 0.321542i
$$136$$ 0 0
$$137$$ 14.0187i 1.19769i 0.800863 + 0.598847i $$0.204374\pi$$
−0.800863 + 0.598847i $$0.795626\pi$$
$$138$$ 0 0
$$139$$ 12.6167 1.07013 0.535067 0.844810i $$-0.320286\pi$$
0.535067 + 0.844810i $$0.320286\pi$$
$$140$$ 0 0
$$141$$ −4.15066 −0.349549
$$142$$ 0 0
$$143$$ 23.8867i 1.99750i
$$144$$ 0 0
$$145$$ −16.5140 13.0900i −1.37141 1.08706i
$$146$$ 0 0
$$147$$ 0 0
$$148$$ 0 0
$$149$$ 11.4533 0.938292 0.469146 0.883121i $$-0.344562\pi$$
0.469146 + 0.883121i $$0.344562\pi$$
$$150$$ 0 0
$$151$$ 5.86799 0.477530 0.238765 0.971077i $$-0.423257\pi$$
0.238765 + 0.971077i $$0.423257\pi$$
$$152$$ 0 0
$$153$$ 11.0934i 0.896846i
$$154$$ 0 0
$$155$$ −8.28267 6.56534i −0.665280 0.527341i
$$156$$ 0 0
$$157$$ 5.78734i 0.461880i −0.972968 0.230940i $$-0.925820\pi$$
0.972968 0.230940i $$-0.0741801\pi$$
$$158$$ 0 0
$$159$$ 2.74531 0.217718
$$160$$ 0 0
$$161$$ 0 0
$$162$$ 0 0
$$163$$ 3.27334i 0.256388i 0.991749 + 0.128194i $$0.0409180\pi$$
−0.991749 + 0.128194i $$0.959082\pi$$
$$164$$ 0 0
$$165$$ 2.59465 3.27334i 0.201993 0.254829i
$$166$$ 0 0
$$167$$ 24.8773i 1.92506i −0.271166 0.962532i $$-0.587409\pi$$
0.271166 0.962532i $$-0.412591\pi$$
$$168$$ 0 0
$$169$$ −8.58532 −0.660409
$$170$$ 0 0
$$171$$ −2.23132 −0.170633
$$172$$ 0 0
$$173$$ 6.62734i 0.503868i −0.967744 0.251934i $$-0.918933\pi$$
0.967744 0.251934i $$-0.0810665\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 0 0
$$177$$ 4.54669i 0.341750i
$$178$$ 0 0
$$179$$ 10.0187 0.748830 0.374415 0.927261i $$-0.377844\pi$$
0.374415 + 0.927261i $$0.377844\pi$$
$$180$$ 0 0
$$181$$ −1.78734 −0.132852 −0.0664258 0.997791i $$-0.521160\pi$$
−0.0664258 + 0.997791i $$0.521160\pi$$
$$182$$ 0 0
$$183$$ 4.17997i 0.308992i
$$184$$ 0 0
$$185$$ 8.33402 10.5140i 0.612730 0.773004i
$$186$$ 0 0
$$187$$ 19.8867i 1.45426i
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ −8.59465 −0.621887 −0.310943 0.950428i $$-0.600645\pi$$
−0.310943 + 0.950428i $$0.600645\pi$$
$$192$$ 0 0
$$193$$ 5.17064i 0.372191i −0.982532 0.186095i $$-0.940417\pi$$
0.982532 0.186095i $$-0.0595834\pi$$
$$194$$ 0 0
$$195$$ 2.95798 + 2.34467i 0.211825 + 0.167905i
$$196$$ 0 0
$$197$$ 23.9160i 1.70394i −0.523590 0.851971i $$-0.675407\pi$$
0.523590 0.851971i $$-0.324593\pi$$
$$198$$ 0 0
$$199$$ −15.3107 −1.08534 −0.542672 0.839945i $$-0.682587\pi$$
−0.542672 + 0.839945i $$0.682587\pi$$
$$200$$ 0 0
$$201$$ 4.26401 0.300760
$$202$$ 0 0
$$203$$ 0 0
$$204$$ 0 0
$$205$$ 1.76868 + 1.40196i 0.123530 + 0.0979172i
$$206$$ 0 0
$$207$$ 14.3667i 0.998556i
$$208$$ 0 0
$$209$$ −4.00000 −0.276686
$$210$$ 0 0
$$211$$ −1.03863 −0.0715025 −0.0357512 0.999361i $$-0.511382\pi$$
−0.0357512 + 0.999361i $$0.511382\pi$$
$$212$$ 0 0
$$213$$ 0.990671i 0.0678797i
$$214$$ 0 0
$$215$$ 9.73599 12.2827i 0.663989 0.837671i
$$216$$ 0 0
$$217$$ 0 0
$$218$$ 0 0
$$219$$ −1.82003 −0.122986
$$220$$ 0 0
$$221$$ −17.9707 −1.20884
$$222$$ 0 0
$$223$$ 9.86799i 0.660810i 0.943839 + 0.330405i $$0.107185\pi$$
−0.943839 + 0.330405i $$0.892815\pi$$
$$224$$ 0 0
$$225$$ 3.27334 + 13.9614i 0.218223 + 0.930758i
$$226$$ 0 0
$$227$$ 21.6553i 1.43731i −0.695364 0.718657i $$-0.744757\pi$$
0.695364 0.718657i $$-0.255243\pi$$
$$228$$ 0 0
$$229$$ 20.2313 1.33692 0.668462 0.743747i $$-0.266953\pi$$
0.668462 + 0.743747i $$0.266953\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ 5.45331i 0.357258i −0.983916 0.178629i $$-0.942834\pi$$
0.983916 0.178629i $$-0.0571663\pi$$
$$234$$ 0 0
$$235$$ 15.8680 20.0187i 1.03511 1.30587i
$$236$$ 0 0
$$237$$ 2.06662i 0.134241i
$$238$$ 0 0
$$239$$ 11.5853 0.749392 0.374696 0.927148i $$-0.377747\pi$$
0.374696 + 0.927148i $$0.377747\pi$$
$$240$$ 0 0
$$241$$ 5.00933 0.322679 0.161340 0.986899i $$-0.448419\pi$$
0.161340 + 0.986899i $$0.448419\pi$$
$$242$$ 0 0
$$243$$ 9.24065i 0.592788i
$$244$$ 0 0
$$245$$ 0 0
$$246$$ 0 0
$$247$$ 3.61462i 0.229993i
$$248$$ 0 0
$$249$$ 1.69867 0.107649
$$250$$ 0 0
$$251$$ 23.4206 1.47830 0.739148 0.673543i $$-0.235228\pi$$
0.739148 + 0.673543i $$0.235228\pi$$
$$252$$ 0 0
$$253$$ 25.7546i 1.61918i
$$254$$ 0 0
$$255$$ 2.46264 + 1.95204i 0.154217 + 0.122241i
$$256$$ 0 0
$$257$$ 13.0093i 0.811500i 0.913984 + 0.405750i $$0.132990\pi$$
−0.913984 + 0.405750i $$0.867010\pi$$
$$258$$ 0 0
$$259$$ 0 0
$$260$$ 0 0
$$261$$ −27.0280 −1.67299
$$262$$ 0 0
$$263$$ 6.01866i 0.371126i 0.982632 + 0.185563i $$0.0594109\pi$$
−0.982632 + 0.185563i $$0.940589\pi$$
$$264$$ 0 0
$$265$$ −10.4953 + 13.2406i −0.644723 + 0.813367i
$$266$$ 0 0
$$267$$ 1.02799i 0.0629117i
$$268$$ 0 0
$$269$$ 3.24065 0.197586 0.0987929 0.995108i $$-0.468502\pi$$
0.0987929 + 0.995108i $$0.468502\pi$$
$$270$$ 0 0
$$271$$ 29.1307 1.76956 0.884782 0.466006i $$-0.154307\pi$$
0.884782 + 0.466006i $$0.154307\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ 5.86799 + 25.0280i 0.353853 + 1.50924i
$$276$$ 0 0
$$277$$ 4.44398i 0.267013i 0.991048 + 0.133507i $$0.0426237\pi$$
−0.991048 + 0.133507i $$0.957376\pi$$
$$278$$ 0 0
$$279$$ −13.5560 −0.811577
$$280$$ 0 0
$$281$$ −24.6974 −1.47332 −0.736660 0.676263i $$-0.763598\pi$$
−0.736660 + 0.676263i $$0.763598\pi$$
$$282$$ 0 0
$$283$$ 7.73937i 0.460058i −0.973184 0.230029i $$-0.926118\pi$$
0.973184 0.230029i $$-0.0738821\pi$$
$$284$$ 0 0
$$285$$ −0.392633 + 0.495336i −0.0232576 + 0.0293412i
$$286$$ 0 0
$$287$$ 0 0
$$288$$ 0 0
$$289$$ 2.03863 0.119920
$$290$$ 0 0
$$291$$ −0.575992 −0.0337652
$$292$$ 0 0
$$293$$ 25.1086i 1.46686i −0.679764 0.733431i $$-0.737918\pi$$
0.679764 0.733431i $$-0.262082\pi$$
$$294$$ 0 0
$$295$$ 21.9287 + 17.3820i 1.27674 + 1.01202i
$$296$$ 0 0
$$297$$ 10.9614i 0.636043i
$$298$$ 0 0
$$299$$ −23.2733 −1.34593
$$300$$ 0 0
$$301$$ 0 0
$$302$$ 0 0
$$303$$ 3.29200i 0.189121i
$$304$$ 0 0
$$305$$ −20.1600 15.9800i −1.15436 0.915014i
$$306$$ 0 0
$$307$$ 33.9193i 1.93588i −0.251183 0.967940i $$-0.580820\pi$$
0.251183 0.967940i $$-0.419180\pi$$
$$308$$ 0 0
$$309$$ −1.86799 −0.106266
$$310$$ 0 0
$$311$$ −0.565344 −0.0320577 −0.0160289 0.999872i $$-0.505102\pi$$
−0.0160289 + 0.999872i $$0.505102\pi$$
$$312$$ 0 0
$$313$$ 27.3400i 1.54535i 0.634804 + 0.772673i $$0.281081\pi$$
−0.634804 + 0.772673i $$0.718919\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ 22.7267i 1.27646i −0.769847 0.638228i $$-0.779668\pi$$
0.769847 0.638228i $$-0.220332\pi$$
$$318$$ 0 0
$$319$$ −48.4520 −2.71279
$$320$$ 0 0
$$321$$ 0 0
$$322$$ 0 0
$$323$$ 3.00933i 0.167444i
$$324$$ 0 0
$$325$$ −22.6167 + 5.30265i −1.25455 + 0.294138i
$$326$$ 0 0
$$327$$ 1.44267i 0.0797796i
$$328$$ 0 0
$$329$$ 0 0
$$330$$ 0 0
$$331$$ 0.462642 0.0254291 0.0127145 0.999919i $$-0.495953\pi$$
0.0127145 + 0.999919i $$0.495953\pi$$
$$332$$ 0 0
$$333$$ 17.2080i 0.942990i
$$334$$ 0 0
$$335$$ −16.3013 + 20.5653i −0.890637 + 1.12360i
$$336$$ 0 0
$$337$$ 10.5653i 0.575531i 0.957701 + 0.287765i $$0.0929124\pi$$
−0.957701 + 0.287765i $$0.907088\pi$$
$$338$$ 0 0
$$339$$ 1.65194 0.0897211
$$340$$ 0 0
$$341$$ −24.3013 −1.31599
$$342$$ 0 0
$$343$$ 0 0
$$344$$ 0 0
$$345$$ 3.18930 + 2.52803i 0.171706 + 0.136105i
$$346$$ 0 0
$$347$$ 31.8760i 1.71119i −0.517643 0.855597i $$-0.673190\pi$$
0.517643 0.855597i $$-0.326810\pi$$
$$348$$ 0 0
$$349$$ −9.62602 −0.515269 −0.257635 0.966242i $$-0.582943\pi$$
−0.257635 + 0.966242i $$0.582943\pi$$
$$350$$ 0 0
$$351$$ 9.90531 0.528706
$$352$$ 0 0
$$353$$ 26.2534i 1.39733i 0.715451 + 0.698663i $$0.246221\pi$$
−0.715451 + 0.698663i $$0.753779\pi$$
$$354$$ 0 0
$$355$$ 4.77801 + 3.78734i 0.253590 + 0.201011i
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ 4.56534 0.240950 0.120475 0.992716i $$-0.461558\pi$$
0.120475 + 0.992716i $$0.461558\pi$$
$$360$$ 0 0
$$361$$ −18.3947 −0.968142
$$362$$ 0 0
$$363$$ 5.60737i 0.294310i
$$364$$ 0 0
$$365$$ 6.95798 8.77801i 0.364197 0.459462i
$$366$$ 0 0
$$367$$ 3.79073i 0.197874i 0.995094 + 0.0989371i $$0.0315443\pi$$
−0.995094 + 0.0989371i $$0.968456\pi$$
$$368$$ 0 0
$$369$$ 2.89475 0.150695
$$370$$ 0 0
$$371$$ 0 0
$$372$$ 0 0
$$373$$ 20.7453i 1.07415i 0.843534 + 0.537076i $$0.180471\pi$$
−0.843534 + 0.537076i $$0.819529\pi$$
$$374$$ 0 0
$$375$$ 3.67531 + 1.73005i 0.189792 + 0.0893392i
$$376$$ 0 0
$$377$$ 43.7839i 2.25499i
$$378$$ 0 0
$$379$$ −3.00933 −0.154579 −0.0772894 0.997009i $$-0.524627\pi$$
−0.0772894 + 0.997009i $$0.524627\pi$$
$$380$$ 0 0
$$381$$ −5.85735 −0.300081
$$382$$ 0 0
$$383$$ 7.00933i 0.358160i −0.983835 0.179080i $$-0.942688\pi$$
0.983835 0.179080i $$-0.0573121\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 0 0
$$387$$ 20.1027i 1.02188i
$$388$$ 0 0
$$389$$ 19.7653 1.00214 0.501070 0.865407i $$-0.332940\pi$$
0.501070 + 0.865407i $$0.332940\pi$$
$$390$$ 0 0
$$391$$ −19.3760 −0.979889
$$392$$ 0 0
$$393$$ 0.0186574i 0.000941142i
$$394$$ 0 0
$$395$$ −9.96731 7.90069i −0.501510 0.397527i
$$396$$ 0 0
$$397$$ 9.37266i 0.470400i −0.971947 0.235200i $$-0.924425\pi$$
0.971947 0.235200i $$-0.0755745\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0 0
$$401$$ −16.1507 −0.806526 −0.403263 0.915084i $$-0.632124\pi$$
−0.403263 + 0.915084i $$0.632124\pi$$
$$402$$ 0 0
$$403$$ 21.9600i 1.09391i
$$404$$ 0 0
$$405$$ 13.7196 + 10.8750i 0.681734 + 0.540384i
$$406$$ 0 0
$$407$$ 30.8480i 1.52908i
$$408$$ 0 0
$$409$$ 15.2920 0.756141 0.378070 0.925777i $$-0.376588\pi$$
0.378070 + 0.925777i $$0.376588\pi$$
$$410$$ 0 0
$$411$$ 5.09337 0.251238
$$412$$ 0 0
$$413$$ 0 0
$$414$$ 0 0
$$415$$ −6.49402 + 8.19269i −0.318779 + 0.402163i
$$416$$ 0 0
$$417$$ 4.58400i 0.224480i
$$418$$ 0 0
$$419$$ −33.1820 −1.62105 −0.810524 0.585705i $$-0.800818\pi$$
−0.810524 + 0.585705i $$0.800818\pi$$
$$420$$ 0 0
$$421$$ 27.8094 1.35535 0.677673 0.735363i $$-0.262988\pi$$
0.677673 + 0.735363i $$0.262988\pi$$
$$422$$ 0 0
$$423$$ 32.7640i 1.59304i
$$424$$ 0 0
$$425$$ −18.8294 + 4.41468i −0.913358 + 0.214143i
$$426$$ 0 0
$$427$$ 0 0
$$428$$ 0 0
$$429$$ 8.67869 0.419011
$$430$$ 0 0
$$431$$ −21.5454 −1.03780 −0.518902 0.854834i $$-0.673659\pi$$
−0.518902 + 0.854834i $$0.673659\pi$$
$$432$$ 0 0
$$433$$ 36.0187i 1.73095i 0.500955 + 0.865473i $$0.332982\pi$$
−0.500955 + 0.865473i $$0.667018\pi$$
$$434$$ 0 0
$$435$$ −4.75596 + 6.00000i −0.228031 + 0.287678i
$$436$$ 0 0
$$437$$ 3.89730i 0.186433i
$$438$$ 0 0
$$439$$ −21.1893 −1.01131 −0.505655 0.862736i $$-0.668749\pi$$
−0.505655 + 0.862736i $$0.668749\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 0 0
$$443$$ 11.1120i 0.527949i −0.964530 0.263974i $$-0.914967\pi$$
0.964530 0.263974i $$-0.0850334\pi$$
$$444$$ 0 0
$$445$$ −4.95798 3.92999i −0.235031 0.186299i
$$446$$ 0 0
$$447$$ 4.16131i 0.196823i
$$448$$ 0 0
$$449$$ −0.961367 −0.0453697 −0.0226848 0.999743i $$-0.507221\pi$$
−0.0226848 + 0.999743i $$0.507221\pi$$
$$450$$ 0 0
$$451$$ 5.18930 0.244355
$$452$$ 0 0
$$453$$ 2.13201i 0.100170i
$$454$$ 0 0
$$455$$ 0 0
$$456$$ 0 0
$$457$$ 28.2241i 1.32027i −0.751149 0.660133i $$-0.770500\pi$$
0.751149 0.660133i $$-0.229500\pi$$
$$458$$ 0 0
$$459$$ 8.24659 0.384918
$$460$$ 0 0
$$461$$ −26.0887 −1.21507 −0.607535 0.794293i $$-0.707842\pi$$
−0.607535 + 0.794293i $$0.707842\pi$$
$$462$$ 0 0
$$463$$ 2.90663i 0.135082i −0.997716 0.0675412i $$-0.978485\pi$$
0.997716 0.0675412i $$-0.0215154\pi$$
$$464$$ 0 0
$$465$$ −2.38538 + 3.00933i −0.110619 + 0.139554i
$$466$$ 0 0
$$467$$ 12.2020i 0.564642i 0.959320 + 0.282321i $$0.0911043\pi$$
−0.959320 + 0.282321i $$0.908896\pi$$
$$468$$ 0 0
$$469$$ 0 0
$$470$$ 0 0
$$471$$ −2.10270 −0.0968874
$$472$$ 0 0
$$473$$ 36.0373i 1.65700i
$$474$$ 0 0
$$475$$ −0.887968 3.78734i −0.0407428 0.173775i
$$476$$ 0 0
$$477$$ 21.6706i 0.992228i
$$478$$ 0 0
$$479$$ −17.6519 −0.806538 −0.403269 0.915082i $$-0.632126\pi$$
−0.403269 + 0.915082i $$0.632126\pi$$
$$480$$ 0 0
$$481$$ 27.8760 1.27104
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 0 0
$$485$$ 2.20202 2.77801i 0.0999884 0.126143i
$$486$$ 0 0
$$487$$ 1.57467i 0.0713553i 0.999363 + 0.0356776i $$0.0113590\pi$$
−0.999363 + 0.0356776i $$0.988641\pi$$
$$488$$ 0 0
$$489$$ 1.18930 0.0537819
$$490$$ 0 0
$$491$$ −3.26270 −0.147243 −0.0736217 0.997286i $$-0.523456\pi$$
−0.0736217 + 0.997286i $$0.523456\pi$$
$$492$$ 0 0
$$493$$ 36.4520i 1.64172i
$$494$$ 0 0
$$495$$ 25.8387 + 20.4813i 1.16136 + 0.920566i
$$496$$ 0 0
$$497$$ 0 0
$$498$$ 0 0
$$499$$ −42.5293 −1.90387 −0.951936 0.306298i $$-0.900910\pi$$
−0.951936 + 0.306298i $$0.900910\pi$$
$$500$$ 0 0
$$501$$ −9.03863 −0.403816
$$502$$ 0 0
$$503$$ 18.6974i 0.833674i 0.908981 + 0.416837i $$0.136861\pi$$
−0.908981 + 0.416837i $$0.863139\pi$$
$$504$$ 0 0
$$505$$ 15.8773 + 12.5853i 0.706532 + 0.560039i
$$506$$ 0 0
$$507$$ 3.11929i 0.138533i
$$508$$ 0 0
$$509$$ 20.2313 0.896738 0.448369 0.893849i $$-0.352005\pi$$
0.448369 + 0.893849i $$0.352005\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ 0 0
$$513$$ 1.65872i 0.0732342i
$$514$$ 0 0
$$515$$ 7.14134 9.00933i 0.314685 0.396998i
$$516$$ 0 0
$$517$$ 58.7347i 2.58315i
$$518$$ 0 0
$$519$$ −2.40790 −0.105695
$$520$$ 0 0
$$521$$ −21.8387 −0.956770 −0.478385 0.878150i $$-0.658778\pi$$
−0.478385 + 0.878150i $$0.658778\pi$$
$$522$$ 0 0
$$523$$ 20.4554i 0.894451i 0.894421 + 0.447226i $$0.147588\pi$$
−0.894421 + 0.447226i $$0.852412\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ 18.2827i 0.796406i
$$528$$ 0 0
$$529$$ −2.09337 −0.0910163
$$530$$ 0 0
$$531$$ 35.8900 1.55750
$$532$$ 0 0
$$533$$ 4.68934i 0.203118i
$$534$$ 0 0
$$535$$ 0 0
$$536$$ 0 0
$$537$$ 3.64006i 0.157080i
$$538$$ 0 0
$$539$$ 0 0
$$540$$ 0 0
$$541$$ 27.3400 1.17544 0.587718 0.809066i $$-0.300026\pi$$
0.587718 + 0.809066i $$0.300026\pi$$
$$542$$ 0 0
$$543$$ 0.649390i 0.0278680i
$$544$$ 0 0
$$545$$ 6.95798 + 5.51531i 0.298047 + 0.236250i
$$546$$ 0 0
$$547$$ 22.6867i 0.970013i 0.874510 + 0.485007i $$0.161183\pi$$
−0.874510 + 0.485007i $$0.838817\pi$$
$$548$$ 0 0
$$549$$ −32.9953 −1.40820
$$550$$ 0 0
$$551$$ 7.33195 0.312352
$$552$$ 0 0
$$553$$ 0 0
$$554$$ 0 0
$$555$$ −3.82003 3.02799i −0.162151 0.128531i
$$556$$ 0 0
$$557$$ 12.7453i 0.540036i 0.962855 + 0.270018i $$0.0870297\pi$$
−0.962855 + 0.270018i $$0.912970\pi$$
$$558$$ 0 0
$$559$$ 32.5653 1.37737
$$560$$ 0 0
$$561$$ 7.22538 0.305056
$$562$$ 0 0
$$563$$ 5.20333i 0.219294i 0.993971 + 0.109647i $$0.0349721\pi$$
−0.993971 + 0.109647i $$0.965028\pi$$
$$564$$ 0 0
$$565$$ −6.31537 + 7.96731i −0.265689 + 0.335187i
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 0 0
$$569$$ 7.37605 0.309220 0.154610 0.987976i $$-0.450588\pi$$
0.154610 + 0.987976i $$0.450588\pi$$
$$570$$ 0 0
$$571$$ 15.8973 0.665281 0.332641 0.943054i $$-0.392060\pi$$
0.332641 + 0.943054i $$0.392060\pi$$
$$572$$ 0 0
$$573$$ 3.12268i 0.130452i
$$574$$ 0 0
$$575$$ −24.3854 + 5.71733i −1.01694 + 0.238429i
$$576$$ 0 0
$$577$$ 19.9707i 0.831391i −0.909504 0.415695i $$-0.863538\pi$$
0.909504 0.415695i $$-0.136462\pi$$
$$578$$ 0 0
$$579$$ −1.87864 −0.0780736
$$580$$ 0 0
$$581$$ 0 0
$$582$$ 0 0
$$583$$ 38.8480i 1.60892i
$$584$$ 0 0
$$585$$ −18.5081 + 23.3493i −0.765214 + 0.965374i
$$586$$ 0 0
$$587$$ 13.8060i 0.569834i −0.958552 0.284917i $$-0.908034\pi$$
0.958552 0.284917i $$-0.0919661\pi$$
$$588$$ 0 0
$$589$$ 3.67738 0.151524
$$590$$ 0 0
$$591$$ −8.68934 −0.357432
$$592$$ 0 0
$$593$$ 20.0666i 0.824037i −0.911175 0.412019i $$-0.864824\pi$$
0.911175 0.412019i $$-0.135176\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 0 0
$$597$$ 5.56279i 0.227670i
$$598$$ 0 0
$$599$$ −46.0267 −1.88060 −0.940299 0.340349i $$-0.889455\pi$$
−0.940299 + 0.340349i $$0.889455\pi$$
$$600$$ 0 0
$$601$$ 1.37605 0.0561301 0.0280651 0.999606i $$-0.491065\pi$$
0.0280651 + 0.999606i $$0.491065\pi$$
$$602$$ 0 0
$$603$$ 33.6587i 1.37069i
$$604$$ 0 0
$$605$$ 27.0443 + 21.4370i 1.09951 + 0.871537i
$$606$$ 0 0
$$607$$ 18.7933i 0.762796i 0.924411 + 0.381398i $$0.124557\pi$$
−0.924411 + 0.381398i $$0.875443\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 53.0759 2.14722
$$612$$ 0 0
$$613$$ 24.8480i 1.00360i 0.864983 + 0.501801i $$0.167329\pi$$
−0.864983 + 0.501801i $$0.832671\pi$$
$$614$$ 0 0
$$615$$ 0.509372 0.642611i 0.0205399 0.0259126i
$$616$$ 0 0
$$617$$ 43.1680i 1.73788i −0.494919 0.868939i $$-0.664802\pi$$
0.494919 0.868939i $$-0.335198\pi$$
$$618$$ 0 0
$$619$$ 31.9486 1.28412 0.642062 0.766652i $$-0.278079\pi$$
0.642062 + 0.766652i $$0.278079\pi$$
$$620$$ 0 0
$$621$$ 10.6799 0.428571
$$622$$ 0 0
$$623$$ 0 0
$$624$$ 0 0
$$625$$ −22.3947 + 11.1120i −0.895788 + 0.444481i
$$626$$ 0 0
$$627$$ 1.45331i 0.0580397i
$$628$$ 0 0
$$629$$ 23.2080 0.925362
$$630$$ 0 0
$$631$$ −8.59465 −0.342148 −0.171074 0.985258i $$-0.554724\pi$$
−0.171074 + 0.985258i $$0.554724\pi$$
$$632$$ 0 0
$$633$$ 0.377365i 0.0149989i
$$634$$ 0 0
$$635$$ 22.3926 28.2500i 0.888625 1.12107i
$$636$$ 0 0
$$637$$ 0 0
$$638$$ 0 0
$$639$$ 7.82003 0.309356
$$640$$ 0 0
$$641$$ 33.2266 1.31237 0.656186 0.754599i $$-0.272169\pi$$
0.656186 + 0.754599i $$0.272169\pi$$
$$642$$ 0 0
$$643$$ 17.4940i 0.689897i −0.938622 0.344948i $$-0.887896\pi$$
0.938622 0.344948i $$-0.112104\pi$$
$$644$$ 0 0
$$645$$ −4.46264 3.53736i −0.175716 0.139283i
$$646$$ 0 0
$$647$$ 9.91595i 0.389836i 0.980820 + 0.194918i $$0.0624441\pi$$
−0.980820 + 0.194918i $$0.937556\pi$$
$$648$$ 0 0
$$649$$ 64.3386 2.52551
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ 14.6240i 0.572280i 0.958188 + 0.286140i $$0.0923722\pi$$
−0.958188 + 0.286140i $$0.907628\pi$$
$$654$$ 0 0
$$655$$ −0.0899847 0.0713273i −0.00351599 0.00278699i
$$656$$ 0 0
$$657$$ 14.3667i 0.560499i
$$658$$ 0 0
$$659$$ −20.2534 −0.788959 −0.394480 0.918905i $$-0.629075\pi$$
−0.394480 + 0.918905i $$0.629075\pi$$
$$660$$ 0 0
$$661$$ 12.4299 0.483469 0.241734 0.970342i $$-0.422284\pi$$
0.241734 + 0.970342i $$0.422284\pi$$
$$662$$ 0 0
$$663$$ 6.52926i 0.253575i
$$664$$ 0 0
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 47.2080i 1.82790i
$$668$$ 0 0
$$669$$ 3.58532 0.138616
$$670$$ 0 0
$$671$$ −59.1493 −2.28344
$$672$$ 0 0
$$673$$ 47.6774i 1.83783i −0.394458 0.918914i $$-0.629068\pi$$
0.394458 0.918914i $$-0.370932\pi$$
$$674$$ 0 0
$$675$$ 10.3786 2.43334i 0.399472 0.0936592i
$$676$$ 0 0
$$677$$ 6.00339i 0.230729i 0.993323 + 0.115364i $$0.0368036\pi$$
−0.993323 + 0.115364i $$0.963196\pi$$
$$678$$ 0 0
$$679$$ 0 0
$$680$$ 0 0
$$681$$ −7.86799 −0.301502
$$682$$ 0 0
$$683$$ 28.5653i 1.09302i −0.837452 0.546511i $$-0.815956\pi$$
0.837452 0.546511i $$-0.184044\pi$$
$$684$$ 0 0
$$685$$ −19.4720 + 24.5653i −0.743986 + 0.938594i
$$686$$ 0 0
$$687$$ 7.35061i 0.280443i
$$688$$ 0 0
$$689$$ −35.1053 −1.33740
$$690$$ 0 0
$$691$$ −47.8247 −1.81934 −0.909668 0.415337i $$-0.863664\pi$$
−0.909668 + 0.415337i $$0.863664\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ 22.1086 + 17.5246i 0.838629 + 0.664747i
$$696$$ 0 0
$$697$$ 3.90408i 0.147877i
$$698$$ 0 0
$$699$$ −1.98134 −0.0749413
$$700$$ 0 0
$$701$$ −4.80005 −0.181296 −0.0906478 0.995883i $$-0.528894\pi$$
−0.0906478 + 0.995883i $$0.528894\pi$$
$$702$$ 0 0
$$703$$ 4.66805i 0.176059i
$$704$$ 0 0
$$705$$ −7.27334 5.76529i −0.273930 0.217133i
$$706$$ 0 0
$$707$$ 0 0
$$708$$ 0 0
$$709$$ −11.7653 −0.441855 −0.220927 0.975290i $$-0.570908\pi$$
−0.220927 + 0.975290i $$0.570908\pi$$
$$710$$ 0 0
$$711$$ −16.3132 −0.611793
$$712$$ 0 0
$$713$$ 23.6774i 0.886725i
$$714$$ 0 0
$$715$$ −33.1787 + 41.8573i −1.24081 + 1.56538i
$$716$$ 0 0
$$717$$ 4.20927i 0.157198i
$$718$$ 0 0
$$719$$ −40.7640 −1.52024 −0.760120 0.649783i $$-0.774860\pi$$
−0.760120 + 0.649783i $$0.774860\pi$$
$$720$$ 0 0
$$721$$ 0 0
$$722$$ 0 0
$$723$$ 1.82003i 0.0676877i
$$724$$ 0 0
$$725$$ −10.7560 45.8760i −0.399466 1.70379i
$$726$$ 0 0
$$727$$ 22.1214i 0.820436i 0.911988 + 0.410218i $$0.134547\pi$$
−0.911988 + 0.410218i $$0.865453\pi$$
$$728$$ 0 0
$$729$$ 20.1307 0.745581
$$730$$ 0 0
$$731$$ 27.1120 1.00277
$$732$$ 0 0
$$733$$ 13.0500i 0.482014i −0.970523 0.241007i $$-0.922522\pi$$
0.970523 0.241007i $$-0.0774777\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 60.3386i 2.22260i
$$738$$ 0 0
$$739$$ 34.5734 1.27180 0.635901 0.771771i $$-0.280629\pi$$
0.635901 + 0.771771i $$0.280629\pi$$
$$740$$ 0 0
$$741$$ −1.31330 −0.0482451
$$742$$ 0 0
$$743$$ 3.55602i 0.130458i −0.997870 0.0652288i $$-0.979222\pi$$
0.997870 0.0652288i $$-0.0207777\pi$$
$$744$$ 0 0
$$745$$ 20.0700 + 15.9087i 0.735308 + 0.582850i
$$746$$ 0 0
$$747$$ 13.4087i 0.490600i
$$748$$ 0 0
$$749$$ 0 0
$$750$$ 0 0
$$751$$ −23.6226 −0.862002 −0.431001 0.902351i $$-0.641839\pi$$
−0.431001 + 0.902351i $$0.641839\pi$$
$$752$$ 0 0
$$753$$ 8.50937i 0.310099i
$$754$$ 0 0
$$755$$ 10.2827 + 8.15066i 0.374225 + 0.296633i
$$756$$ 0 0
$$757$$ 15.1893i 0.552064i −0.961148 0.276032i $$-0.910980\pi$$
0.961148 0.276032i $$-0.0890196\pi$$
$$758$$ 0 0
$$759$$ 9.35739 0.339652
$$760$$ 0 0
$$761$$ −34.4626 −1.24927 −0.624635 0.780917i $$-0.714752\pi$$
−0.624635 + 0.780917i $$0.714752\pi$$
$$762$$ 0 0
$$763$$ 0 0
$$764$$ 0 0
$$765$$ −15.4087 + 19.4393i −0.557104 + 0.702829i
$$766$$ 0 0
$$767$$ 58.1400i 2.09931i
$$768$$ 0 0
$$769$$ 40.3854 1.45633 0.728167 0.685400i $$-0.240373\pi$$
0.728167 + 0.685400i $$0.240373\pi$$
$$770$$ 0 0
$$771$$ 4.72666 0.170226
$$772$$ 0 0
$$773$$ 10.7674i 0.387275i 0.981073 + 0.193638i $$0.0620286\pi$$
−0.981073 + 0.193638i $$0.937971\pi$$
$$774$$ 0 0
$$775$$ −5.39470 23.0093i −0.193783 0.826519i
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ −0.785266 −0.0281351
$$780$$ 0 0
$$781$$ 14.0187 0.501627
$$782$$ 0 0
$$783$$ 20.0921i 0.718031i
$$784$$ 0 0
$$785$$ 8.03863 10.1413i 0.286911 0.361960i
$$786$$ 0 0
$$787$$ 9.19269i 0.327684i −0.986487 0.163842i $$-0.947611\pi$$
0.986487 0.163842i $$-0.0523887\pi$$
$$788$$ 0 0
$$789$$ 2.18675 0.0778503
$$790$$ 0 0
$$791$$ 0 0
$$792$$ 0 0
$$793$$ 53.4507i 1.89809i
$$794$$ 0 0
$$795$$ 4.81070 + 3.81325i 0.170618 + 0.135242i
$$796$$ 0 0
$$797$$ 21.1086i 0.747706i 0.927488 + 0.373853i $$0.121964\pi$$
−0.927488 + 0.373853i $$0.878036\pi$$
$$798$$ 0 0
$$799$$ 44.1880 1.56326
$$800$$ 0 0
$$801$$ −8.11458 −0.286715
$$802$$ 0 0
$$803$$ 25.7546i 0.908862i
$$804$$ 0 0