# Properties

 Label 3150.2.b.e.251.5 Level 3150 Weight 2 Character 3150.251 Analytic conductor 25.153 Analytic rank 0 Dimension 8 CM no Inner twists 2

# Related objects

## Newspace parameters

 Level: $$N$$ = $$3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 3150.b (of order $$2$$, degree $$1$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$25.1528766367$$ Analytic rank: $$0$$ Dimension: $$8$$ Coefficient field: 8.0.7442857984.4 Coefficient ring: $$\Z[a_1, \ldots, a_{17}]$$ Coefficient ring index: $$2^{2}\cdot 3^{2}$$ Twist minimal: no (minimal twist has level 630) Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

## Embedding invariants

 Embedding label 251.5 Root $$1.91681i$$ Character $$\chi$$ = 3150.251 Dual form 3150.2.b.e.251.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+1.00000i q^{2} -1.00000 q^{4} +(-2.27220 + 1.35539i) q^{7} -1.00000i q^{8} +O(q^{10})$$ $$q+1.00000i q^{2} -1.00000 q^{4} +(-2.27220 + 1.35539i) q^{7} -1.00000i q^{8} +2.71078i q^{11} +6.54441i q^{13} +(-1.35539 - 2.27220i) q^{14} +1.00000 q^{16} -1.53186 q^{17} -2.30177i q^{19} -2.71078 q^{22} +3.83363i q^{23} -6.54441 q^{26} +(2.27220 - 1.35539i) q^{28} -3.83363i q^{29} -3.25519i q^{31} +1.00000i q^{32} -1.53186i q^{34} -3.01255 q^{37} +2.30177 q^{38} -6.54441 q^{41} +0.468142 q^{43} -2.71078i q^{44} -3.83363 q^{46} +9.11980 q^{47} +(3.32583 - 6.15945i) q^{49} -6.54441i q^{52} +9.25519i q^{53} +(1.35539 + 2.27220i) q^{56} +3.83363 q^{58} +11.1961 q^{59} +4.78705i q^{61} +3.25519 q^{62} -1.00000 q^{64} -13.5570 q^{67} +1.53186 q^{68} +2.30177i q^{71} -11.4216i q^{73} -3.01255i q^{74} +2.30177i q^{76} +(-3.67417 - 6.15945i) q^{77} -12.6768 q^{79} -6.54441i q^{82} -13.0888 q^{83} +0.468142i q^{86} +2.71078 q^{88} -9.60812 q^{89} +(-8.87024 - 14.8702i) q^{91} -3.83363i q^{92} +9.11980i q^{94} -16.9224i q^{97} +(6.15945 + 3.32583i) q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$8q - 8q^{4} + 4q^{7} + O(q^{10})$$ $$8q - 8q^{4} + 4q^{7} + 8q^{16} - 8q^{26} - 4q^{28} + 8q^{37} + 8q^{38} - 8q^{41} + 16q^{43} - 8q^{46} + 40q^{47} + 4q^{49} + 8q^{58} - 40q^{62} - 8q^{64} - 32q^{67} - 52q^{77} + 8q^{79} - 16q^{83} - 8q^{89} - 4q^{91} + 4q^{98} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/3150\mathbb{Z}\right)^\times$$.

 $$n$$ $$127$$ $$451$$ $$2801$$ $$\chi(n)$$ $$1$$ $$-1$$ $$-1$$

## Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 1.00000i 0.707107i
$$3$$ 0 0
$$4$$ −1.00000 −0.500000
$$5$$ 0 0
$$6$$ 0 0
$$7$$ −2.27220 + 1.35539i −0.858813 + 0.512290i
$$8$$ 1.00000i 0.353553i
$$9$$ 0 0
$$10$$ 0 0
$$11$$ 2.71078i 0.817332i 0.912684 + 0.408666i $$0.134006\pi$$
−0.912684 + 0.408666i $$0.865994\pi$$
$$12$$ 0 0
$$13$$ 6.54441i 1.81509i 0.419952 + 0.907546i $$0.362047\pi$$
−0.419952 + 0.907546i $$0.637953\pi$$
$$14$$ −1.35539 2.27220i −0.362244 0.607272i
$$15$$ 0 0
$$16$$ 1.00000 0.250000
$$17$$ −1.53186 −0.371530 −0.185765 0.982594i $$-0.559476\pi$$
−0.185765 + 0.982594i $$0.559476\pi$$
$$18$$ 0 0
$$19$$ 2.30177i 0.528062i −0.964514 0.264031i $$-0.914948\pi$$
0.964514 0.264031i $$-0.0850521\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ −2.71078 −0.577941
$$23$$ 3.83363i 0.799366i 0.916653 + 0.399683i $$0.130880\pi$$
−0.916653 + 0.399683i $$0.869120\pi$$
$$24$$ 0 0
$$25$$ 0 0
$$26$$ −6.54441 −1.28346
$$27$$ 0 0
$$28$$ 2.27220 1.35539i 0.429406 0.256145i
$$29$$ 3.83363i 0.711887i −0.934508 0.355943i $$-0.884160\pi$$
0.934508 0.355943i $$-0.115840\pi$$
$$30$$ 0 0
$$31$$ 3.25519i 0.584650i −0.956319 0.292325i $$-0.905571\pi$$
0.956319 0.292325i $$-0.0944289\pi$$
$$32$$ 1.00000i 0.176777i
$$33$$ 0 0
$$34$$ 1.53186i 0.262711i
$$35$$ 0 0
$$36$$ 0 0
$$37$$ −3.01255 −0.495260 −0.247630 0.968855i $$-0.579652\pi$$
−0.247630 + 0.968855i $$0.579652\pi$$
$$38$$ 2.30177 0.373396
$$39$$ 0 0
$$40$$ 0 0
$$41$$ −6.54441 −1.02207 −0.511033 0.859561i $$-0.670737\pi$$
−0.511033 + 0.859561i $$0.670737\pi$$
$$42$$ 0 0
$$43$$ 0.468142 0.0713910 0.0356955 0.999363i $$-0.488635\pi$$
0.0356955 + 0.999363i $$0.488635\pi$$
$$44$$ 2.71078i 0.408666i
$$45$$ 0 0
$$46$$ −3.83363 −0.565237
$$47$$ 9.11980 1.33026 0.665130 0.746728i $$-0.268376\pi$$
0.665130 + 0.746728i $$0.268376\pi$$
$$48$$ 0 0
$$49$$ 3.32583 6.15945i 0.475118 0.879922i
$$50$$ 0 0
$$51$$ 0 0
$$52$$ 6.54441i 0.907546i
$$53$$ 9.25519i 1.27130i 0.771978 + 0.635649i $$0.219268\pi$$
−0.771978 + 0.635649i $$0.780732\pi$$
$$54$$ 0 0
$$55$$ 0 0
$$56$$ 1.35539 + 2.27220i 0.181122 + 0.303636i
$$57$$ 0 0
$$58$$ 3.83363 0.503380
$$59$$ 11.1961 1.45760 0.728802 0.684725i $$-0.240078\pi$$
0.728802 + 0.684725i $$0.240078\pi$$
$$60$$ 0 0
$$61$$ 4.78705i 0.612919i 0.951884 + 0.306459i $$0.0991444\pi$$
−0.951884 + 0.306459i $$0.900856\pi$$
$$62$$ 3.25519 0.413410
$$63$$ 0 0
$$64$$ −1.00000 −0.125000
$$65$$ 0 0
$$66$$ 0 0
$$67$$ −13.5570 −1.65625 −0.828123 0.560546i $$-0.810591\pi$$
−0.828123 + 0.560546i $$0.810591\pi$$
$$68$$ 1.53186 0.185765
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 2.30177i 0.273170i 0.990628 + 0.136585i $$0.0436126\pi$$
−0.990628 + 0.136585i $$0.956387\pi$$
$$72$$ 0 0
$$73$$ 11.4216i 1.33679i −0.743805 0.668397i $$-0.766981\pi$$
0.743805 0.668397i $$-0.233019\pi$$
$$74$$ 3.01255i 0.350202i
$$75$$ 0 0
$$76$$ 2.30177i 0.264031i
$$77$$ −3.67417 6.15945i −0.418711 0.701935i
$$78$$ 0 0
$$79$$ −12.6768 −1.42625 −0.713123 0.701039i $$-0.752720\pi$$
−0.713123 + 0.701039i $$0.752720\pi$$
$$80$$ 0 0
$$81$$ 0 0
$$82$$ 6.54441i 0.722709i
$$83$$ −13.0888 −1.43668 −0.718342 0.695690i $$-0.755099\pi$$
−0.718342 + 0.695690i $$0.755099\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ 0.468142i 0.0504811i
$$87$$ 0 0
$$88$$ 2.71078 0.288970
$$89$$ −9.60812 −1.01846 −0.509230 0.860631i $$-0.670070\pi$$
−0.509230 + 0.860631i $$0.670070\pi$$
$$90$$ 0 0
$$91$$ −8.87024 14.8702i −0.929853 1.55882i
$$92$$ 3.83363i 0.399683i
$$93$$ 0 0
$$94$$ 9.11980i 0.940635i
$$95$$ 0 0
$$96$$ 0 0
$$97$$ 16.9224i 1.71821i −0.511796 0.859107i $$-0.671020\pi$$
0.511796 0.859107i $$-0.328980\pi$$
$$98$$ 6.15945 + 3.32583i 0.622199 + 0.335959i
$$99$$ 0 0
$$100$$ 0 0
$$101$$ 17.7405 1.76524 0.882622 0.470084i $$-0.155776\pi$$
0.882622 + 0.470084i $$0.155776\pi$$
$$102$$ 0 0
$$103$$ 4.05913i 0.399958i 0.979800 + 0.199979i $$0.0640874\pi$$
−0.979800 + 0.199979i $$0.935913\pi$$
$$104$$ 6.54441 0.641732
$$105$$ 0 0
$$106$$ −9.25519 −0.898944
$$107$$ 6.31891i 0.610872i −0.952213 0.305436i $$-0.901198\pi$$
0.952213 0.305436i $$-0.0988022\pi$$
$$108$$ 0 0
$$109$$ −12.0251 −1.15180 −0.575898 0.817522i $$-0.695347\pi$$
−0.575898 + 0.817522i $$0.695347\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ −2.27220 + 1.35539i −0.214703 + 0.128072i
$$113$$ 9.06372i 0.852643i −0.904572 0.426321i $$-0.859809\pi$$
0.904572 0.426321i $$-0.140191\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ 3.83363i 0.355943i
$$117$$ 0 0
$$118$$ 11.1961i 1.03068i
$$119$$ 3.48069 2.07627i 0.319075 0.190331i
$$120$$ 0 0
$$121$$ 3.65166 0.331969
$$122$$ −4.78705 −0.433399
$$123$$ 0 0
$$124$$ 3.25519i 0.292325i
$$125$$ 0 0
$$126$$ 0 0
$$127$$ −21.6332 −1.91964 −0.959819 0.280619i $$-0.909460\pi$$
−0.959819 + 0.280619i $$0.909460\pi$$
$$128$$ 1.00000i 0.0883883i
$$129$$ 0 0
$$130$$ 0 0
$$131$$ −2.51931 −0.220113 −0.110056 0.993925i $$-0.535103\pi$$
−0.110056 + 0.993925i $$0.535103\pi$$
$$132$$ 0 0
$$133$$ 3.11980 + 5.23009i 0.270521 + 0.453506i
$$134$$ 13.5570i 1.17114i
$$135$$ 0 0
$$136$$ 1.53186i 0.131356i
$$137$$ 1.39646i 0.119308i 0.998219 + 0.0596539i $$0.0189997\pi$$
−0.998219 + 0.0596539i $$0.981000\pi$$
$$138$$ 0 0
$$139$$ 6.13539i 0.520397i −0.965555 0.260199i $$-0.916212\pi$$
0.965555 0.260199i $$-0.0837881\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ −2.30177 −0.193160
$$143$$ −17.7405 −1.48353
$$144$$ 0 0
$$145$$ 0 0
$$146$$ 11.4216 0.945256
$$147$$ 0 0
$$148$$ 3.01255 0.247630
$$149$$ 4.65166i 0.381078i −0.981680 0.190539i $$-0.938976\pi$$
0.981680 0.190539i $$-0.0610236\pi$$
$$150$$ 0 0
$$151$$ −3.58794 −0.291982 −0.145991 0.989286i $$-0.546637\pi$$
−0.145991 + 0.989286i $$0.546637\pi$$
$$152$$ −2.30177 −0.186698
$$153$$ 0 0
$$154$$ 6.15945 3.67417i 0.496343 0.296073i
$$155$$ 0 0
$$156$$ 0 0
$$157$$ 13.1228i 1.04732i −0.851928 0.523658i $$-0.824567\pi$$
0.851928 0.523658i $$-0.175433\pi$$
$$158$$ 12.6768i 1.00851i
$$159$$ 0 0
$$160$$ 0 0
$$161$$ −5.19606 8.71078i −0.409507 0.686506i
$$162$$ 0 0
$$163$$ −16.6207 −1.30183 −0.650916 0.759150i $$-0.725615\pi$$
−0.650916 + 0.759150i $$0.725615\pi$$
$$164$$ 6.54441 0.511033
$$165$$ 0 0
$$166$$ 13.0888i 1.01589i
$$167$$ −8.62068 −0.667088 −0.333544 0.942735i $$-0.608245\pi$$
−0.333544 + 0.942735i $$0.608245\pi$$
$$168$$ 0 0
$$169$$ −29.8293 −2.29456
$$170$$ 0 0
$$171$$ 0 0
$$172$$ −0.468142 −0.0356955
$$173$$ 10.6517 0.809830 0.404915 0.914354i $$-0.367301\pi$$
0.404915 + 0.914354i $$0.367301\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 2.71078i 0.204333i
$$177$$ 0 0
$$178$$ 9.60812i 0.720159i
$$179$$ 23.1961i 1.73376i 0.498521 + 0.866878i $$0.333877\pi$$
−0.498521 + 0.866878i $$0.666123\pi$$
$$180$$ 0 0
$$181$$ 9.11980i 0.677869i 0.940810 + 0.338935i $$0.110067\pi$$
−0.940810 + 0.338935i $$0.889933\pi$$
$$182$$ 14.8702 8.87024i 1.10226 0.657506i
$$183$$ 0 0
$$184$$ 3.83363 0.282619
$$185$$ 0 0
$$186$$ 0 0
$$187$$ 4.15253i 0.303663i
$$188$$ −9.11980 −0.665130
$$189$$ 0 0
$$190$$ 0 0
$$191$$ 9.69823i 0.701739i 0.936424 + 0.350870i $$0.114114\pi$$
−0.936424 + 0.350870i $$0.885886\pi$$
$$192$$ 0 0
$$193$$ 18.1525 1.30665 0.653324 0.757078i $$-0.273374\pi$$
0.653324 + 0.757078i $$0.273374\pi$$
$$194$$ 16.9224 1.21496
$$195$$ 0 0
$$196$$ −3.32583 + 6.15945i −0.237559 + 0.439961i
$$197$$ 4.60354i 0.327988i −0.986461 0.163994i $$-0.947562\pi$$
0.986461 0.163994i $$-0.0524378\pi$$
$$198$$ 0 0
$$199$$ 11.7405i 0.832260i −0.909305 0.416130i $$-0.863386\pi$$
0.909305 0.416130i $$-0.136614\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ 17.7405i 1.24822i
$$203$$ 5.19606 + 8.71078i 0.364692 + 0.611377i
$$204$$ 0 0
$$205$$ 0 0
$$206$$ −4.05913 −0.282813
$$207$$ 0 0
$$208$$ 6.54441i 0.453773i
$$209$$ 6.23960 0.431602
$$210$$ 0 0
$$211$$ 4.00000 0.275371 0.137686 0.990476i $$-0.456034\pi$$
0.137686 + 0.990476i $$0.456034\pi$$
$$212$$ 9.25519i 0.635649i
$$213$$ 0 0
$$214$$ 6.31891 0.431952
$$215$$ 0 0
$$216$$ 0 0
$$217$$ 4.41206 + 7.39646i 0.299510 + 0.502105i
$$218$$ 12.0251i 0.814443i
$$219$$ 0 0
$$220$$ 0 0
$$221$$ 10.0251i 0.674361i
$$222$$ 0 0
$$223$$ 26.4513i 1.77131i −0.464347 0.885654i $$-0.653711\pi$$
0.464347 0.885654i $$-0.346289\pi$$
$$224$$ −1.35539 2.27220i −0.0905609 0.151818i
$$225$$ 0 0
$$226$$ 9.06372 0.602909
$$227$$ −15.0637 −0.999814 −0.499907 0.866079i $$-0.666632\pi$$
−0.499907 + 0.866079i $$0.666632\pi$$
$$228$$ 0 0
$$229$$ 11.3655i 0.751052i −0.926812 0.375526i $$-0.877462\pi$$
0.926812 0.375526i $$-0.122538\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ −3.83363 −0.251690
$$233$$ 20.9957i 1.37547i 0.725961 + 0.687736i $$0.241395\pi$$
−0.725961 + 0.687736i $$0.758605\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ −11.1961 −0.728802
$$237$$ 0 0
$$238$$ 2.07627 + 3.48069i 0.134584 + 0.225620i
$$239$$ 9.69823i 0.627326i −0.949534 0.313663i $$-0.898444\pi$$
0.949534 0.313663i $$-0.101556\pi$$
$$240$$ 0 0
$$241$$ 24.7019i 1.59119i 0.605831 + 0.795593i $$0.292841\pi$$
−0.605831 + 0.795593i $$0.707159\pi$$
$$242$$ 3.65166i 0.234737i
$$243$$ 0 0
$$244$$ 4.78705i 0.306459i
$$245$$ 0 0
$$246$$ 0 0
$$247$$ 15.0637 0.958481
$$248$$ −3.25519 −0.206705
$$249$$ 0 0
$$250$$ 0 0
$$251$$ 3.60812 0.227743 0.113871 0.993495i $$-0.463675\pi$$
0.113871 + 0.993495i $$0.463675\pi$$
$$252$$ 0 0
$$253$$ −10.3921 −0.653348
$$254$$ 21.6332i 1.35739i
$$255$$ 0 0
$$256$$ 1.00000 0.0625000
$$257$$ 28.7983 1.79639 0.898195 0.439598i $$-0.144879\pi$$
0.898195 + 0.439598i $$0.144879\pi$$
$$258$$ 0 0
$$259$$ 6.84513 4.08319i 0.425336 0.253717i
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 2.51931i 0.155643i
$$263$$ 12.7699i 0.787426i 0.919233 + 0.393713i $$0.128810\pi$$
−0.919233 + 0.393713i $$0.871190\pi$$
$$264$$ 0 0
$$265$$ 0 0
$$266$$ −5.23009 + 3.11980i −0.320677 + 0.191287i
$$267$$ 0 0
$$268$$ 13.5570 0.828123
$$269$$ −8.43716 −0.514423 −0.257211 0.966355i $$-0.582804\pi$$
−0.257211 + 0.966355i $$0.582804\pi$$
$$270$$ 0 0
$$271$$ 2.16637i 0.131598i 0.997833 + 0.0657989i $$0.0209596\pi$$
−0.997833 + 0.0657989i $$0.979040\pi$$
$$272$$ −1.53186 −0.0928825
$$273$$ 0 0
$$274$$ −1.39646 −0.0843634
$$275$$ 0 0
$$276$$ 0 0
$$277$$ −5.92373 −0.355923 −0.177961 0.984037i $$-0.556950\pi$$
−0.177961 + 0.984037i $$0.556950\pi$$
$$278$$ 6.13539 0.367977
$$279$$ 0 0
$$280$$ 0 0
$$281$$ 27.3566i 1.63196i −0.578083 0.815978i $$-0.696199\pi$$
0.578083 0.815978i $$-0.303801\pi$$
$$282$$ 0 0
$$283$$ 18.0594i 1.07352i 0.843735 + 0.536759i $$0.180352\pi$$
−0.843735 + 0.536759i $$0.819648\pi$$
$$284$$ 2.30177i 0.136585i
$$285$$ 0 0
$$286$$ 17.7405i 1.04902i
$$287$$ 14.8702 8.87024i 0.877762 0.523594i
$$288$$ 0 0
$$289$$ −14.6534 −0.861965
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 11.4216i 0.668397i
$$293$$ 29.1139 1.70085 0.850427 0.526094i $$-0.176344\pi$$
0.850427 + 0.526094i $$0.176344\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ 3.01255i 0.175101i
$$297$$ 0 0
$$298$$ 4.65166 0.269463
$$299$$ −25.0888 −1.45092
$$300$$ 0 0
$$301$$ −1.06372 + 0.634516i −0.0613115 + 0.0365729i
$$302$$ 3.58794i 0.206463i
$$303$$ 0 0
$$304$$ 2.30177i 0.132015i
$$305$$ 0 0
$$306$$ 0 0
$$307$$ 7.39646i 0.422138i −0.977471 0.211069i $$-0.932305\pi$$
0.977471 0.211069i $$-0.0676945\pi$$
$$308$$ 3.67417 + 6.15945i 0.209355 + 0.350967i
$$309$$ 0 0
$$310$$ 0 0
$$311$$ 1.97490 0.111986 0.0559931 0.998431i $$-0.482168\pi$$
0.0559931 + 0.998431i $$0.482168\pi$$
$$312$$ 0 0
$$313$$ 0.961388i 0.0543409i −0.999631 0.0271704i $$-0.991350\pi$$
0.999631 0.0271704i $$-0.00864968\pi$$
$$314$$ 13.1228 0.740565
$$315$$ 0 0
$$316$$ 12.6768 0.713123
$$317$$ 17.1620i 0.963916i −0.876194 0.481958i $$-0.839926\pi$$
0.876194 0.481958i $$-0.160074\pi$$
$$318$$ 0 0
$$319$$ 10.3921 0.581848
$$320$$ 0 0
$$321$$ 0 0
$$322$$ 8.71078 5.19606i 0.485433 0.289565i
$$323$$ 3.52598i 0.196191i
$$324$$ 0 0
$$325$$ 0 0
$$326$$ 16.6207i 0.920534i
$$327$$ 0 0
$$328$$ 6.54441i 0.361355i
$$329$$ −20.7220 + 12.3609i −1.14244 + 0.681478i
$$330$$ 0 0
$$331$$ 9.74047 0.535385 0.267692 0.963504i $$-0.413739\pi$$
0.267692 + 0.963504i $$0.413739\pi$$
$$332$$ 13.0888 0.718342
$$333$$ 0 0
$$334$$ 8.62068i 0.471702i
$$335$$ 0 0
$$336$$ 0 0
$$337$$ −3.15078 −0.171634 −0.0858169 0.996311i $$-0.527350\pi$$
−0.0858169 + 0.996311i $$0.527350\pi$$
$$338$$ 29.8293i 1.62250i
$$339$$ 0 0
$$340$$ 0 0
$$341$$ 8.82412 0.477853
$$342$$ 0 0
$$343$$ 0.791511 + 18.5033i 0.0427376 + 0.999086i
$$344$$ 0.468142i 0.0252405i
$$345$$ 0 0
$$346$$ 10.6517i 0.572637i
$$347$$ 30.0594i 1.61367i 0.590775 + 0.806836i $$0.298822\pi$$
−0.590775 + 0.806836i $$0.701178\pi$$
$$348$$ 0 0
$$349$$ 27.5180i 1.47301i 0.676434 + 0.736503i $$0.263524\pi$$
−0.676434 + 0.736503i $$0.736476\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ −2.71078 −0.144485
$$353$$ −16.5956 −0.883293 −0.441647 0.897189i $$-0.645605\pi$$
−0.441647 + 0.897189i $$0.645605\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ 9.60812 0.509230
$$357$$ 0 0
$$358$$ −23.1961 −1.22595
$$359$$ 15.0076i 0.792073i −0.918235 0.396036i $$-0.870385\pi$$
0.918235 0.396036i $$-0.129615\pi$$
$$360$$ 0 0
$$361$$ 13.7019 0.721151
$$362$$ −9.11980 −0.479326
$$363$$ 0 0
$$364$$ 8.87024 + 14.8702i 0.464927 + 0.779412i
$$365$$ 0 0
$$366$$ 0 0
$$367$$ 14.2598i 0.744354i 0.928162 + 0.372177i $$0.121389\pi$$
−0.928162 + 0.372177i $$0.878611\pi$$
$$368$$ 3.83363i 0.199842i
$$369$$ 0 0
$$370$$ 0 0
$$371$$ −12.5444 21.0297i −0.651273 1.09181i
$$372$$ 0 0
$$373$$ −8.98745 −0.465352 −0.232676 0.972554i $$-0.574748\pi$$
−0.232676 + 0.972554i $$0.574748\pi$$
$$374$$ 4.15253 0.214722
$$375$$ 0 0
$$376$$ 9.11980i 0.470318i
$$377$$ 25.0888 1.29214
$$378$$ 0 0
$$379$$ −34.5447 −1.77444 −0.887220 0.461346i $$-0.847367\pi$$
−0.887220 + 0.461346i $$0.847367\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ −9.69823 −0.496205
$$383$$ −2.88020 −0.147171 −0.0735857 0.997289i $$-0.523444\pi$$
−0.0735857 + 0.997289i $$0.523444\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 18.1525i 0.923940i
$$387$$ 0 0
$$388$$ 16.9224i 0.859107i
$$389$$ 35.1620i 1.78279i 0.453231 + 0.891393i $$0.350271\pi$$
−0.453231 + 0.891393i $$0.649729\pi$$
$$390$$ 0 0
$$391$$ 5.87257i 0.296989i
$$392$$ −6.15945 3.32583i −0.311099 0.167980i
$$393$$ 0 0
$$394$$ 4.60354 0.231923
$$395$$ 0 0
$$396$$ 0 0
$$397$$ 16.1185i 0.808965i 0.914546 + 0.404482i $$0.132548\pi$$
−0.914546 + 0.404482i $$0.867452\pi$$
$$398$$ 11.7405 0.588497
$$399$$ 0 0
$$400$$ 0 0
$$401$$ 16.6256i 0.830243i −0.909766 0.415121i $$-0.863739\pi$$
0.909766 0.415121i $$-0.136261\pi$$
$$402$$ 0 0
$$403$$ 21.3033 1.06119
$$404$$ −17.7405 −0.882622
$$405$$ 0 0
$$406$$ −8.71078 + 5.19606i −0.432309 + 0.257876i
$$407$$ 8.16637i 0.404792i
$$408$$ 0 0
$$409$$ 12.0000i 0.593362i 0.954977 + 0.296681i $$0.0958798\pi$$
−0.954977 + 0.296681i $$0.904120\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 4.05913i 0.199979i
$$413$$ −25.4397 + 15.1751i −1.25181 + 0.746715i
$$414$$ 0 0
$$415$$ 0 0
$$416$$ −6.54441 −0.320866
$$417$$ 0 0
$$418$$ 6.23960i 0.305189i
$$419$$ −36.2849 −1.77263 −0.886316 0.463080i $$-0.846744\pi$$
−0.886316 + 0.463080i $$0.846744\pi$$
$$420$$ 0 0
$$421$$ 19.2414 0.937766 0.468883 0.883260i $$-0.344657\pi$$
0.468883 + 0.883260i $$0.344657\pi$$
$$422$$ 4.00000i 0.194717i
$$423$$ 0 0
$$424$$ 9.25519 0.449472
$$425$$ 0 0
$$426$$ 0 0
$$427$$ −6.48833 10.8772i −0.313992 0.526383i
$$428$$ 6.31891i 0.305436i
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 17.2974i 0.833188i 0.909093 + 0.416594i $$0.136776\pi$$
−0.909093 + 0.416594i $$0.863224\pi$$
$$432$$ 0 0
$$433$$ 31.6473i 1.52087i −0.649412 0.760437i $$-0.724985\pi$$
0.649412 0.760437i $$-0.275015\pi$$
$$434$$ −7.39646 + 4.41206i −0.355042 + 0.211786i
$$435$$ 0 0
$$436$$ 12.0251 0.575898
$$437$$ 8.82412 0.422115
$$438$$ 0 0
$$439$$ 13.0095i 0.620910i −0.950588 0.310455i $$-0.899519\pi$$
0.950588 0.310455i $$-0.100481\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 10.0251 0.476846
$$443$$ 3.78551i 0.179855i −0.995948 0.0899275i $$-0.971336\pi$$
0.995948 0.0899275i $$-0.0286635\pi$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ 26.4513 1.25250
$$447$$ 0 0
$$448$$ 2.27220 1.35539i 0.107352 0.0640362i
$$449$$ 24.9307i 1.17655i 0.808661 + 0.588275i $$0.200193\pi$$
−0.808661 + 0.588275i $$0.799807\pi$$
$$450$$ 0 0
$$451$$ 17.7405i 0.835366i
$$452$$ 9.06372i 0.426321i
$$453$$ 0 0
$$454$$ 15.0637i 0.706975i
$$455$$ 0 0
$$456$$ 0 0
$$457$$ 31.3535 1.46666 0.733328 0.679875i $$-0.237966\pi$$
0.733328 + 0.679875i $$0.237966\pi$$
$$458$$ 11.3655 0.531074
$$459$$ 0 0
$$460$$ 0 0
$$461$$ 9.52598 0.443669 0.221835 0.975084i $$-0.428795\pi$$
0.221835 + 0.975084i $$0.428795\pi$$
$$462$$ 0 0
$$463$$ −34.0003 −1.58013 −0.790063 0.613026i $$-0.789952\pi$$
−0.790063 + 0.613026i $$0.789952\pi$$
$$464$$ 3.83363i 0.177972i
$$465$$ 0 0
$$466$$ −20.9957 −0.972605
$$467$$ −39.2665 −1.81703 −0.908517 0.417847i $$-0.862785\pi$$
−0.908517 + 0.417847i $$0.862785\pi$$
$$468$$ 0 0
$$469$$ 30.8042 18.3750i 1.42241 0.848478i
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 11.1961i 0.515341i
$$473$$ 1.26903i 0.0583502i
$$474$$ 0 0
$$475$$ 0 0
$$476$$ −3.48069 + 2.07627i −0.159537 + 0.0951655i
$$477$$ 0 0
$$478$$ 9.69823 0.443587
$$479$$ 34.0251 1.55465 0.777323 0.629101i $$-0.216577\pi$$
0.777323 + 0.629101i $$0.216577\pi$$
$$480$$ 0 0
$$481$$ 19.7154i 0.898944i
$$482$$ −24.7019 −1.12514
$$483$$ 0 0
$$484$$ −3.65166 −0.165984
$$485$$ 0 0
$$486$$ 0 0
$$487$$ 12.8091 0.580436 0.290218 0.956961i $$-0.406272\pi$$
0.290218 + 0.956961i $$0.406272\pi$$
$$488$$ 4.78705 0.216700
$$489$$ 0 0
$$490$$ 0 0
$$491$$ 11.6471i 0.525625i 0.964847 + 0.262812i $$0.0846500\pi$$
−0.964847 + 0.262812i $$0.915350\pi$$
$$492$$ 0 0
$$493$$ 5.87257i 0.264487i
$$494$$ 15.0637i 0.677749i
$$495$$ 0 0
$$496$$ 3.25519i 0.146162i
$$497$$ −3.11980 5.23009i −0.139942 0.234602i
$$498$$ 0 0
$$499$$ 35.5511 1.59149 0.795743 0.605635i $$-0.207081\pi$$
0.795743 + 0.605635i $$0.207081\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 3.60812i 0.161038i
$$503$$ −8.23372 −0.367123 −0.183562 0.983008i $$-0.558763\pi$$
−0.183562 + 0.983008i $$0.558763\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ 10.3921i 0.461986i
$$507$$ 0 0
$$508$$ 21.6332 0.959819
$$509$$ 31.0888 1.37799 0.688994 0.724767i $$-0.258053\pi$$
0.688994 + 0.724767i $$0.258053\pi$$
$$510$$ 0 0
$$511$$ 15.4807 + 25.9521i 0.684826 + 1.14805i
$$512$$ 1.00000i 0.0441942i
$$513$$ 0 0
$$514$$ 28.7983i 1.27024i
$$515$$ 0 0
$$516$$ 0 0
$$517$$ 24.7218i 1.08726i
$$518$$ 4.08319 + 6.84513i 0.179405 + 0.300758i
$$519$$ 0 0
$$520$$ 0 0
$$521$$ 1.39363 0.0610561 0.0305281 0.999534i $$-0.490281\pi$$
0.0305281 + 0.999534i $$0.490281\pi$$
$$522$$ 0 0
$$523$$ 20.4853i 0.895759i −0.894094 0.447879i $$-0.852179\pi$$
0.894094 0.447879i $$-0.147821\pi$$
$$524$$ 2.51931 0.110056
$$525$$ 0 0
$$526$$ −12.7699 −0.556795
$$527$$ 4.98649i 0.217215i
$$528$$ 0 0
$$529$$ 8.30331 0.361013
$$530$$ 0 0
$$531$$ 0 0
$$532$$ −3.11980 5.23009i −0.135260 0.226753i
$$533$$ 42.8293i 1.85514i
$$534$$ 0 0
$$535$$ 0 0
$$536$$ 13.5570i 0.585572i
$$537$$ 0 0
$$538$$ 8.43716i 0.363752i
$$539$$ 16.6969 + 9.01560i 0.719188 + 0.388329i
$$540$$ 0 0
$$541$$ −0.0870615 −0.00374306 −0.00187153 0.999998i $$-0.500596\pi$$
−0.00187153 + 0.999998i $$0.500596\pi$$
$$542$$ −2.16637 −0.0930537
$$543$$ 0 0
$$544$$ 1.53186i 0.0656779i
$$545$$ 0 0
$$546$$ 0 0
$$547$$ 5.40443 0.231077 0.115538 0.993303i $$-0.463141\pi$$
0.115538 + 0.993303i $$0.463141\pi$$
$$548$$ 1.39646i 0.0596539i
$$549$$ 0 0
$$550$$ 0 0
$$551$$ −8.82412 −0.375920
$$552$$ 0 0
$$553$$ 28.8042 17.1820i 1.22488 0.730652i
$$554$$ 5.92373i 0.251675i
$$555$$ 0 0
$$556$$ 6.13539i 0.260199i
$$557$$ 0.127431i 0.00539940i 0.999996 + 0.00269970i $$0.000859343\pi$$
−0.999996 + 0.00269970i $$0.999141\pi$$
$$558$$ 0 0
$$559$$ 3.06372i 0.129581i
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 27.3566 1.15397
$$563$$ 6.23960 0.262968 0.131484 0.991318i $$-0.458026\pi$$
0.131484 + 0.991318i $$0.458026\pi$$
$$564$$ 0 0
$$565$$ 0 0
$$566$$ −18.0594 −0.759092
$$567$$ 0 0
$$568$$ 2.30177 0.0965801
$$569$$ 11.6391i 0.487937i −0.969783 0.243968i $$-0.921551\pi$$
0.969783 0.243968i $$-0.0784493\pi$$
$$570$$ 0 0
$$571$$ −35.9181 −1.50313 −0.751563 0.659661i $$-0.770700\pi$$
−0.751563 + 0.659661i $$0.770700\pi$$
$$572$$ 17.7405 0.741766
$$573$$ 0 0
$$574$$ 8.87024 + 14.8702i 0.370237 + 0.620672i
$$575$$ 0 0
$$576$$ 0 0
$$577$$ 7.15687i 0.297944i 0.988841 + 0.148972i $$0.0475965\pi$$
−0.988841 + 0.148972i $$0.952404\pi$$
$$578$$ 14.6534i 0.609502i
$$579$$ 0 0
$$580$$ 0 0
$$581$$ 29.7405 17.7405i 1.23384 0.735999i
$$582$$ 0 0
$$583$$ −25.0888 −1.03907
$$584$$ −11.4216 −0.472628
$$585$$ 0 0
$$586$$ 29.1139i 1.20269i
$$587$$ 4.15253 0.171393 0.0856967 0.996321i $$-0.472688\pi$$
0.0856967 + 0.996321i $$0.472688\pi$$
$$588$$ 0 0
$$589$$ −7.49270 −0.308731
$$590$$ 0 0
$$591$$ 0 0
$$592$$ −3.01255 −0.123815
$$593$$ −29.7966 −1.22360 −0.611799 0.791013i $$-0.709554\pi$$
−0.611799 + 0.791013i $$0.709554\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 4.65166i 0.190539i
$$597$$ 0 0
$$598$$ 25.0888i 1.02596i
$$599$$ 35.4249i 1.44742i 0.690104 + 0.723710i $$0.257565\pi$$
−0.690104 + 0.723710i $$0.742435\pi$$
$$600$$ 0 0
$$601$$ 27.4948i 1.12154i 0.827973 + 0.560768i $$0.189494\pi$$
−0.827973 + 0.560768i $$0.810506\pi$$
$$602$$ −0.634516 1.06372i −0.0258609 0.0433538i
$$603$$ 0 0
$$604$$ 3.58794 0.145991
$$605$$ 0 0
$$606$$ 0 0
$$607$$ 4.76499i 0.193405i 0.995313 + 0.0967025i $$0.0308296\pi$$
−0.995313 + 0.0967025i $$0.969170\pi$$
$$608$$ 2.30177 0.0933490
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 59.6837i 2.41454i
$$612$$ 0 0
$$613$$ −10.7981 −0.436130 −0.218065 0.975934i $$-0.569974\pi$$
−0.218065 + 0.975934i $$0.569974\pi$$
$$614$$ 7.39646 0.298497
$$615$$ 0 0
$$616$$ −6.15945 + 3.67417i −0.248171 + 0.148037i
$$617$$ 34.9025i 1.40512i 0.711623 + 0.702561i $$0.247960\pi$$
−0.711623 + 0.702561i $$0.752040\pi$$
$$618$$ 0 0
$$619$$ 1.26107i 0.0506866i −0.999679 0.0253433i $$-0.991932\pi$$
0.999679 0.0253433i $$-0.00806789\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 1.97490i 0.0791861i
$$623$$ 21.8316 13.0228i 0.874666 0.521746i
$$624$$ 0 0
$$625$$ 0 0
$$626$$ 0.961388 0.0384248
$$627$$ 0 0
$$628$$ 13.1228i 0.523658i
$$629$$ 4.61480 0.184004
$$630$$ 0 0
$$631$$ 16.2145 0.645489 0.322744 0.946486i $$-0.395395\pi$$
0.322744 + 0.946486i $$0.395395\pi$$
$$632$$ 12.6768i 0.504254i
$$633$$ 0 0
$$634$$ 17.1620 0.681592
$$635$$ 0 0
$$636$$ 0 0
$$637$$ 40.3100 + 21.7656i 1.59714 + 0.862384i
$$638$$ 10.3921i 0.411428i
$$639$$ 0 0
$$640$$ 0 0
$$641$$ 19.6893i 0.777681i −0.921305 0.388840i $$-0.872876\pi$$
0.921305 0.388840i $$-0.127124\pi$$
$$642$$ 0 0
$$643$$ 17.1508i 0.676361i 0.941081 + 0.338180i $$0.109811\pi$$
−0.941081 + 0.338180i $$0.890189\pi$$
$$644$$ 5.19606 + 8.71078i 0.204754 + 0.343253i
$$645$$ 0 0
$$646$$ −3.52598 −0.138728
$$647$$ −29.0578 −1.14238 −0.571191 0.820817i $$-0.693518\pi$$
−0.571191 + 0.820817i $$0.693518\pi$$
$$648$$ 0 0
$$649$$ 30.3501i 1.19135i
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 16.6207 0.650916
$$653$$ 9.11183i 0.356574i 0.983979 + 0.178287i $$0.0570555\pi$$
−0.983979 + 0.178287i $$0.942945\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ −6.54441 −0.255516
$$657$$ 0 0
$$658$$ −12.3609 20.7220i −0.481878 0.807829i
$$659$$ 37.5539i 1.46289i −0.681899 0.731446i $$-0.738846\pi$$
0.681899 0.731446i $$-0.261154\pi$$
$$660$$ 0 0
$$661$$ 9.50275i 0.369614i −0.982775 0.184807i $$-0.940834\pi$$
0.982775 0.184807i $$-0.0591660\pi$$
$$662$$ 9.74047i 0.378574i
$$663$$ 0 0
$$664$$ 13.0888i 0.507945i
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 14.6967 0.569058
$$668$$ 8.62068 0.333544
$$669$$ 0 0
$$670$$ 0 0
$$671$$ −12.9767 −0.500958
$$672$$ 0 0
$$673$$ −49.6335 −1.91323 −0.956615 0.291355i $$-0.905894\pi$$
−0.956615 + 0.291355i $$0.905894\pi$$
$$674$$ 3.15078i 0.121363i
$$675$$ 0 0
$$676$$ 29.8293 1.14728
$$677$$ −37.5312 −1.44244 −0.721220 0.692706i $$-0.756418\pi$$
−0.721220 + 0.692706i $$0.756418\pi$$
$$678$$ 0 0
$$679$$ 22.9365 + 38.4513i 0.880224 + 1.47562i
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 8.82412i 0.337893i
$$683$$ 9.01560i 0.344972i 0.985012 + 0.172486i $$0.0551800\pi$$
−0.985012 + 0.172486i $$0.944820\pi$$
$$684$$ 0 0
$$685$$ 0 0
$$686$$ −18.5033 + 0.791511i −0.706461 + 0.0302200i
$$687$$ 0 0
$$688$$ 0.468142 0.0178478
$$689$$ −60.5698 −2.30752
$$690$$ 0 0
$$691$$ 8.15841i 0.310361i 0.987886 + 0.155180i $$0.0495958\pi$$
−0.987886 + 0.155180i $$0.950404\pi$$
$$692$$ −10.6517 −0.404915
$$693$$ 0 0
$$694$$ −30.0594 −1.14104
$$695$$ 0 0
$$696$$ 0 0
$$697$$ 10.0251 0.379728
$$698$$ −27.5180 −1.04157
$$699$$ 0 0
$$700$$ 0 0
$$701$$ 34.3440i 1.29716i 0.761148 + 0.648578i $$0.224636\pi$$
−0.761148 + 0.648578i $$0.775364\pi$$
$$702$$ 0 0
$$703$$ 6.93420i 0.261528i
$$704$$ 2.71078i 0.102166i
$$705$$ 0 0
$$706$$ 16.5956i 0.624583i
$$707$$ −40.3100 + 24.0453i −1.51601 + 0.904316i
$$708$$ 0 0
$$709$$ −5.06372 −0.190172 −0.0950859 0.995469i $$-0.530313\pi$$
−0.0950859 + 0.995469i $$0.530313\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 9.60812i 0.360080i
$$713$$ 12.4792 0.467349
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 23.1961i 0.866878i
$$717$$ 0 0
$$718$$ 15.0076 0.560080
$$719$$ 18.1274 0.676039 0.338020 0.941139i $$-0.390243\pi$$
0.338020 + 0.941139i $$0.390243\pi$$
$$720$$ 0 0
$$721$$ −5.50171 9.22317i −0.204894 0.343489i
$$722$$ 13.7019i 0.509930i
$$723$$ 0 0
$$724$$ 9.11980i 0.338935i
$$725$$ 0 0
$$726$$ 0 0
$$727$$ 11.1168i 0.412298i −0.978521 0.206149i $$-0.933907\pi$$
0.978521 0.206149i $$-0.0660931\pi$$
$$728$$ −14.8702 + 8.87024i −0.551128 + 0.328753i
$$729$$ 0 0
$$730$$ 0 0
$$731$$ −0.717127 −0.0265239
$$732$$ 0 0
$$733$$ 20.8342i 0.769529i 0.923015 + 0.384765i $$0.125717\pi$$
−0.923015 + 0.384765i $$0.874283\pi$$
$$734$$ −14.2598 −0.526338
$$735$$ 0 0
$$736$$ −3.83363 −0.141309
$$737$$ 36.7500i 1.35370i
$$738$$ 0 0
$$739$$ 30.9818 1.13968 0.569842 0.821754i $$-0.307004\pi$$
0.569842 + 0.821754i $$0.307004\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 21.0297 12.5444i 0.772024 0.460520i
$$743$$ 45.8449i 1.68189i −0.541124 0.840943i $$-0.682001\pi$$
0.541124 0.840943i $$-0.317999\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ 8.98745i 0.329054i
$$747$$ 0 0
$$748$$ 4.15253i 0.151832i
$$749$$ 8.56459 + 14.3579i 0.312943 + 0.524624i
$$750$$ 0 0
$$751$$ −35.2665 −1.28689 −0.643446 0.765492i $$-0.722496\pi$$
−0.643446 + 0.765492i $$0.722496\pi$$
$$752$$ 9.11980 0.332565
$$753$$ 0 0
$$754$$ 25.0888i 0.913681i
$$755$$ 0 0
$$756$$ 0 0
$$757$$ 12.3661 0.449452 0.224726 0.974422i $$-0.427851\pi$$
0.224726 + 0.974422i $$0.427851\pi$$
$$758$$ 34.5447i 1.25472i
$$759$$ 0 0
$$760$$ 0 0
$$761$$ −1.50580 −0.0545851 −0.0272926 0.999627i $$-0.508689\pi$$
−0.0272926 + 0.999627i $$0.508689\pi$$
$$762$$ 0 0
$$763$$ 27.3235 16.2987i 0.989177 0.590053i
$$764$$ 9.69823i 0.350870i
$$765$$ 0 0
$$766$$ 2.88020i 0.104066i
$$767$$ 73.2716i 2.64569i
$$768$$ 0 0
$$769$$ 3.76558i 0.135790i 0.997692 + 0.0678951i $$0.0216283\pi$$
−0.997692 + 0.0678951i $$0.978372\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ −18.1525 −0.653324
$$773$$ 15.1911 0.546388 0.273194 0.961959i $$-0.411920\pi$$
0.273194 + 0.961959i $$0.411920\pi$$
$$774$$ 0 0
$$775$$ 0 0
$$776$$ −16.9224 −0.607480
$$777$$ 0 0
$$778$$ −35.1620 −1.26062
$$779$$ 15.0637i 0.539714i
$$780$$ 0 0
$$781$$ −6.23960 −0.223270
$$782$$ 5.87257 0.210003
$$783$$ 0 0
$$784$$ 3.32583 6.15945i 0.118780 0.219980i
$$785$$ 0 0
$$786$$ 0 0
$$787$$ 23.8198i 0.849084i 0.905408 + 0.424542i $$0.139565\pi$$
−0.905408 + 0.424542i $$0.860435\pi$$
$$788$$ 4.60354i 0.163994i
$$789$$ 0 0
$$790$$ 0 0
$$791$$ 12.2849 + 20.5946i 0.436800 + 0.732260i
$$792$$ 0 0
$$793$$ −31.3284 −1.11250
$$794$$ −16.1185 −0.572024
$$795$$ 0 0
$$796$$ 11.7405i 0.416130i
$$797$$ −10.6517 −0.377301 −0.188650 0.982044i $$-0.560411\pi$$
−0.188650 + 0.982044i $$0.560411\pi$$
$$798$$ 0 0
$$799$$ −13.9702 −0.494231
$$800$$ 0 0
$$801$$ 0 0
$$802$$ 16.6256 0.587070
$$803$$ 30.9614 1.09260