# Properties

 Label 370.2.h.e.253.7 Level $370$ Weight $2$ Character 370.253 Analytic conductor $2.954$ Analytic rank $0$ Dimension $20$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$370 = 2 \cdot 5 \cdot 37$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 370.h (of order $$4$$, degree $$2$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$2.95446487479$$ Analytic rank: $$0$$ Dimension: $$20$$ Relative dimension: $$10$$ over $$\Q(i)$$ Coefficient field: $$\mathbb{Q}[x]/(x^{20} - \cdots)$$ Defining polynomial: $$x^{20} - 4 x^{19} + 8 x^{18} + 4 x^{17} + 103 x^{16} - 394 x^{15} + 760 x^{14} + 278 x^{13} + 2009 x^{12} - 7362 x^{11} + 13826 x^{10} + 4848 x^{9} + 13544 x^{8} - 44248 x^{7} + 76384 x^{6} + 24512 x^{5} + 28432 x^{4} - 61952 x^{3} + 61952 x^{2} - 5632 x + 256$$ Coefficient ring: $$\Z[a_1, \ldots, a_{9}]$$ Coefficient ring index: $$2^{6}$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

## Embedding invariants

 Embedding label 253.7 Root $$1.28931 + 1.28931i$$ of defining polynomial Character $$\chi$$ $$=$$ 370.253 Dual form 370.2.h.e.117.7

## $q$-expansion

 $$f(q)$$ $$=$$ $$q-1.00000 q^{2} +(1.28931 - 1.28931i) q^{3} +1.00000 q^{4} +(1.69364 - 1.45999i) q^{5} +(-1.28931 + 1.28931i) q^{6} +(0.579841 - 0.579841i) q^{7} -1.00000 q^{8} -0.324646i q^{9} +O(q^{10})$$ $$q-1.00000 q^{2} +(1.28931 - 1.28931i) q^{3} +1.00000 q^{4} +(1.69364 - 1.45999i) q^{5} +(-1.28931 + 1.28931i) q^{6} +(0.579841 - 0.579841i) q^{7} -1.00000 q^{8} -0.324646i q^{9} +(-1.69364 + 1.45999i) q^{10} -3.64633i q^{11} +(1.28931 - 1.28931i) q^{12} +3.10704 q^{13} +(-0.579841 + 0.579841i) q^{14} +(0.301249 - 4.06602i) q^{15} +1.00000 q^{16} +8.09027i q^{17} +0.324646i q^{18} +(-3.05234 - 3.05234i) q^{19} +(1.69364 - 1.45999i) q^{20} -1.49519i q^{21} +3.64633i q^{22} -7.79067 q^{23} +(-1.28931 + 1.28931i) q^{24} +(0.736849 - 4.94541i) q^{25} -3.10704 q^{26} +(3.44936 + 3.44936i) q^{27} +(0.579841 - 0.579841i) q^{28} +(1.37472 - 1.37472i) q^{29} +(-0.301249 + 4.06602i) q^{30} +(3.23904 + 3.23904i) q^{31} -1.00000 q^{32} +(-4.70126 - 4.70126i) q^{33} -8.09027i q^{34} +(0.135480 - 1.82861i) q^{35} -0.324646i q^{36} +(-4.87870 - 3.63294i) q^{37} +(3.05234 + 3.05234i) q^{38} +(4.00594 - 4.00594i) q^{39} +(-1.69364 + 1.45999i) q^{40} -9.31106i q^{41} +1.49519i q^{42} +10.9160 q^{43} -3.64633i q^{44} +(-0.473980 - 0.549834i) q^{45} +7.79067 q^{46} +(-4.11794 + 4.11794i) q^{47} +(1.28931 - 1.28931i) q^{48} +6.32757i q^{49} +(-0.736849 + 4.94541i) q^{50} +(10.4309 + 10.4309i) q^{51} +3.10704 q^{52} +(0.446555 + 0.446555i) q^{53} +(-3.44936 - 3.44936i) q^{54} +(-5.32361 - 6.17558i) q^{55} +(-0.579841 + 0.579841i) q^{56} -7.87084 q^{57} +(-1.37472 + 1.37472i) q^{58} +(-6.16388 - 6.16388i) q^{59} +(0.301249 - 4.06602i) q^{60} +(8.71382 + 8.71382i) q^{61} +(-3.23904 - 3.23904i) q^{62} +(-0.188243 - 0.188243i) q^{63} +1.00000 q^{64} +(5.26221 - 4.53625i) q^{65} +(4.70126 + 4.70126i) q^{66} +(-2.01024 - 2.01024i) q^{67} +8.09027i q^{68} +(-10.0446 + 10.0446i) q^{69} +(-0.135480 + 1.82861i) q^{70} +0.00151598 q^{71} +0.324646i q^{72} +(-9.32759 + 9.32759i) q^{73} +(4.87870 + 3.63294i) q^{74} +(-5.42614 - 7.32620i) q^{75} +(-3.05234 - 3.05234i) q^{76} +(-2.11429 - 2.11429i) q^{77} +(-4.00594 + 4.00594i) q^{78} +(0.760897 + 0.760897i) q^{79} +(1.69364 - 1.45999i) q^{80} +9.86854 q^{81} +9.31106i q^{82} +(3.16981 + 3.16981i) q^{83} -1.49519i q^{84} +(11.8117 + 13.7020i) q^{85} -10.9160 q^{86} -3.54488i q^{87} +3.64633i q^{88} +(-5.80016 + 5.80016i) q^{89} +(0.473980 + 0.549834i) q^{90} +(1.80159 - 1.80159i) q^{91} -7.79067 q^{92} +8.35226 q^{93} +(4.11794 - 4.11794i) q^{94} +(-9.62597 - 0.713182i) q^{95} +(-1.28931 + 1.28931i) q^{96} +14.6206i q^{97} -6.32757i q^{98} -1.18377 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$20q - 20q^{2} + 4q^{3} + 20q^{4} - 4q^{5} - 4q^{6} - 2q^{7} - 20q^{8} + O(q^{10})$$ $$20q - 20q^{2} + 4q^{3} + 20q^{4} - 4q^{5} - 4q^{6} - 2q^{7} - 20q^{8} + 4q^{10} + 4q^{12} + 2q^{14} - 4q^{15} + 20q^{16} + 6q^{19} - 4q^{20} - 4q^{23} - 4q^{24} + 10q^{25} - 20q^{27} - 2q^{28} + 18q^{29} + 4q^{30} + 12q^{31} - 20q^{32} + 4q^{33} - 12q^{35} - 32q^{37} - 6q^{38} + 6q^{39} + 4q^{40} + 16q^{43} + 22q^{45} + 4q^{46} - 22q^{47} + 4q^{48} - 10q^{50} + 8q^{51} - 4q^{53} + 20q^{54} + 16q^{55} + 2q^{56} + 24q^{57} - 18q^{58} - 10q^{59} - 4q^{60} + 10q^{61} - 12q^{62} - 2q^{63} + 20q^{64} + 20q^{65} - 4q^{66} + 8q^{67} - 34q^{69} + 12q^{70} + 16q^{71} - 6q^{73} + 32q^{74} - 26q^{75} + 6q^{76} - 4q^{77} - 6q^{78} + 12q^{79} - 4q^{80} - 28q^{81} + 6q^{83} + 10q^{85} - 16q^{86} - 44q^{89} - 22q^{90} - 40q^{91} - 4q^{92} - 40q^{93} + 22q^{94} + 50q^{95} - 4q^{96} - 20q^{99} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/370\mathbb{Z}\right)^\times$$.

 $$n$$ $$261$$ $$297$$ $$\chi(n)$$ $$e\left(\frac{1}{4}\right)$$ $$e\left(\frac{3}{4}\right)$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −1.00000 −0.707107
$$3$$ 1.28931 1.28931i 0.744384 0.744384i −0.229034 0.973418i $$-0.573557\pi$$
0.973418 + 0.229034i $$0.0735568\pi$$
$$4$$ 1.00000 0.500000
$$5$$ 1.69364 1.45999i 0.757420 0.652928i
$$6$$ −1.28931 + 1.28931i −0.526359 + 0.526359i
$$7$$ 0.579841 0.579841i 0.219159 0.219159i −0.588985 0.808144i $$-0.700472\pi$$
0.808144 + 0.588985i $$0.200472\pi$$
$$8$$ −1.00000 −0.353553
$$9$$ 0.324646i 0.108215i
$$10$$ −1.69364 + 1.45999i −0.535577 + 0.461690i
$$11$$ 3.64633i 1.09941i −0.835359 0.549705i $$-0.814740\pi$$
0.835359 0.549705i $$-0.185260\pi$$
$$12$$ 1.28931 1.28931i 0.372192 0.372192i
$$13$$ 3.10704 0.861737 0.430868 0.902415i $$-0.358207\pi$$
0.430868 + 0.902415i $$0.358207\pi$$
$$14$$ −0.579841 + 0.579841i −0.154969 + 0.154969i
$$15$$ 0.301249 4.06602i 0.0777820 1.04984i
$$16$$ 1.00000 0.250000
$$17$$ 8.09027i 1.96218i 0.193558 + 0.981089i $$0.437997\pi$$
−0.193558 + 0.981089i $$0.562003\pi$$
$$18$$ 0.324646i 0.0765198i
$$19$$ −3.05234 3.05234i −0.700255 0.700255i 0.264210 0.964465i $$-0.414889\pi$$
−0.964465 + 0.264210i $$0.914889\pi$$
$$20$$ 1.69364 1.45999i 0.378710 0.326464i
$$21$$ 1.49519i 0.326278i
$$22$$ 3.64633i 0.777401i
$$23$$ −7.79067 −1.62447 −0.812233 0.583333i $$-0.801748\pi$$
−0.812233 + 0.583333i $$0.801748\pi$$
$$24$$ −1.28931 + 1.28931i −0.263180 + 0.263180i
$$25$$ 0.736849 4.94541i 0.147370 0.989081i
$$26$$ −3.10704 −0.609340
$$27$$ 3.44936 + 3.44936i 0.663830 + 0.663830i
$$28$$ 0.579841 0.579841i 0.109580 0.109580i
$$29$$ 1.37472 1.37472i 0.255279 0.255279i −0.567852 0.823131i $$-0.692225\pi$$
0.823131 + 0.567852i $$0.192225\pi$$
$$30$$ −0.301249 + 4.06602i −0.0550002 + 0.742349i
$$31$$ 3.23904 + 3.23904i 0.581749 + 0.581749i 0.935384 0.353635i $$-0.115054\pi$$
−0.353635 + 0.935384i $$0.615054\pi$$
$$32$$ −1.00000 −0.176777
$$33$$ −4.70126 4.70126i −0.818384 0.818384i
$$34$$ 8.09027i 1.38747i
$$35$$ 0.135480 1.82861i 0.0229004 0.309091i
$$36$$ 0.324646i 0.0541076i
$$37$$ −4.87870 3.63294i −0.802054 0.597252i
$$38$$ 3.05234 + 3.05234i 0.495155 + 0.495155i
$$39$$ 4.00594 4.00594i 0.641463 0.641463i
$$40$$ −1.69364 + 1.45999i −0.267788 + 0.230845i
$$41$$ 9.31106i 1.45414i −0.686562 0.727072i $$-0.740881\pi$$
0.686562 0.727072i $$-0.259119\pi$$
$$42$$ 1.49519i 0.230713i
$$43$$ 10.9160 1.66467 0.832334 0.554275i $$-0.187004\pi$$
0.832334 + 0.554275i $$0.187004\pi$$
$$44$$ 3.64633i 0.549705i
$$45$$ −0.473980 0.549834i −0.0706568 0.0819644i
$$46$$ 7.79067 1.14867
$$47$$ −4.11794 + 4.11794i −0.600663 + 0.600663i −0.940489 0.339825i $$-0.889632\pi$$
0.339825 + 0.940489i $$0.389632\pi$$
$$48$$ 1.28931 1.28931i 0.186096 0.186096i
$$49$$ 6.32757i 0.903938i
$$50$$ −0.736849 + 4.94541i −0.104206 + 0.699386i
$$51$$ 10.4309 + 10.4309i 1.46061 + 1.46061i
$$52$$ 3.10704 0.430868
$$53$$ 0.446555 + 0.446555i 0.0613390 + 0.0613390i 0.737111 0.675772i $$-0.236190\pi$$
−0.675772 + 0.737111i $$0.736190\pi$$
$$54$$ −3.44936 3.44936i −0.469399 0.469399i
$$55$$ −5.32361 6.17558i −0.717836 0.832715i
$$56$$ −0.579841 + 0.579841i −0.0774846 + 0.0774846i
$$57$$ −7.87084 −1.04252
$$58$$ −1.37472 + 1.37472i −0.180509 + 0.180509i
$$59$$ −6.16388 6.16388i −0.802468 0.802468i 0.181012 0.983481i $$-0.442063\pi$$
−0.983481 + 0.181012i $$0.942063\pi$$
$$60$$ 0.301249 4.06602i 0.0388910 0.524920i
$$61$$ 8.71382 + 8.71382i 1.11569 + 1.11569i 0.992366 + 0.123324i $$0.0393555\pi$$
0.123324 + 0.992366i $$0.460644\pi$$
$$62$$ −3.23904 3.23904i −0.411359 0.411359i
$$63$$ −0.188243 0.188243i −0.0237164 0.0237164i
$$64$$ 1.00000 0.125000
$$65$$ 5.26221 4.53625i 0.652697 0.562652i
$$66$$ 4.70126 + 4.70126i 0.578685 + 0.578685i
$$67$$ −2.01024 2.01024i −0.245590 0.245590i 0.573568 0.819158i $$-0.305559\pi$$
−0.819158 + 0.573568i $$0.805559\pi$$
$$68$$ 8.09027i 0.981089i
$$69$$ −10.0446 + 10.0446i −1.20923 + 1.20923i
$$70$$ −0.135480 + 1.82861i −0.0161930 + 0.218560i
$$71$$ 0.00151598 0.000179913 8.99567e−5 1.00000i $$-0.499971\pi$$
8.99567e−5 1.00000i $$0.499971\pi$$
$$72$$ 0.324646i 0.0382599i
$$73$$ −9.32759 + 9.32759i −1.09171 + 1.09171i −0.0963663 + 0.995346i $$0.530722\pi$$
−0.995346 + 0.0963663i $$0.969278\pi$$
$$74$$ 4.87870 + 3.63294i 0.567138 + 0.422321i
$$75$$ −5.42614 7.32620i −0.626557 0.845956i
$$76$$ −3.05234 3.05234i −0.350128 0.350128i
$$77$$ −2.11429 2.11429i −0.240946 0.240946i
$$78$$ −4.00594 + 4.00594i −0.453583 + 0.453583i
$$79$$ 0.760897 + 0.760897i 0.0856076 + 0.0856076i 0.748614 0.663006i $$-0.230720\pi$$
−0.663006 + 0.748614i $$0.730720\pi$$
$$80$$ 1.69364 1.45999i 0.189355 0.163232i
$$81$$ 9.86854 1.09650
$$82$$ 9.31106i 1.02823i
$$83$$ 3.16981 + 3.16981i 0.347932 + 0.347932i 0.859339 0.511407i $$-0.170875\pi$$
−0.511407 + 0.859339i $$0.670875\pi$$
$$84$$ 1.49519i 0.163139i
$$85$$ 11.8117 + 13.7020i 1.28116 + 1.48619i
$$86$$ −10.9160 −1.17710
$$87$$ 3.54488i 0.380051i
$$88$$ 3.64633i 0.388700i
$$89$$ −5.80016 + 5.80016i −0.614816 + 0.614816i −0.944197 0.329381i $$-0.893160\pi$$
0.329381 + 0.944197i $$0.393160\pi$$
$$90$$ 0.473980 + 0.549834i 0.0499619 + 0.0579576i
$$91$$ 1.80159 1.80159i 0.188858 0.188858i
$$92$$ −7.79067 −0.812233
$$93$$ 8.35226 0.866089
$$94$$ 4.11794 4.11794i 0.424733 0.424733i
$$95$$ −9.62597 0.713182i −0.987604 0.0731710i
$$96$$ −1.28931 + 1.28931i −0.131590 + 0.131590i
$$97$$ 14.6206i 1.48449i 0.670127 + 0.742246i $$0.266240\pi$$
−0.670127 + 0.742246i $$0.733760\pi$$
$$98$$ 6.32757i 0.639181i
$$99$$ −1.18377 −0.118973
$$100$$ 0.736849 4.94541i 0.0736849 0.494541i
$$101$$ 3.68870i 0.367039i −0.983016 0.183520i $$-0.941251\pi$$
0.983016 0.183520i $$-0.0587491\pi$$
$$102$$ −10.4309 10.4309i −1.03281 1.03281i
$$103$$ 11.1543i 1.09907i 0.835471 + 0.549535i $$0.185195\pi$$
−0.835471 + 0.549535i $$0.814805\pi$$
$$104$$ −3.10704 −0.304670
$$105$$ −2.18297 2.53232i −0.213036 0.247129i
$$106$$ −0.446555 0.446555i −0.0433732 0.0433732i
$$107$$ −3.88311 + 3.88311i −0.375394 + 0.375394i −0.869437 0.494043i $$-0.835519\pi$$
0.494043 + 0.869437i $$0.335519\pi$$
$$108$$ 3.44936 + 3.44936i 0.331915 + 0.331915i
$$109$$ 2.01583 + 2.01583i 0.193081 + 0.193081i 0.797026 0.603945i $$-0.206405\pi$$
−0.603945 + 0.797026i $$0.706405\pi$$
$$110$$ 5.32361 + 6.17558i 0.507587 + 0.588819i
$$111$$ −10.9742 + 1.60617i −1.04162 + 0.152451i
$$112$$ 0.579841 0.579841i 0.0547899 0.0547899i
$$113$$ 11.8892i 1.11844i 0.829019 + 0.559220i $$0.188899\pi$$
−0.829019 + 0.559220i $$0.811101\pi$$
$$114$$ 7.87084 0.737171
$$115$$ −13.1946 + 11.3743i −1.23040 + 1.06066i
$$116$$ 1.37472 1.37472i 0.127639 0.127639i
$$117$$ 1.00869i 0.0932531i
$$118$$ 6.16388 + 6.16388i 0.567431 + 0.567431i
$$119$$ 4.69107 + 4.69107i 0.430030 + 0.430030i
$$120$$ −0.301249 + 4.06602i −0.0275001 + 0.371175i
$$121$$ −2.29574 −0.208704
$$122$$ −8.71382 8.71382i −0.788912 0.788912i
$$123$$ −12.0049 12.0049i −1.08244 1.08244i
$$124$$ 3.23904 + 3.23904i 0.290875 + 0.290875i
$$125$$ −5.97229 9.45154i −0.534178 0.845372i
$$126$$ 0.188243 + 0.188243i 0.0167700 + 0.0167700i
$$127$$ 13.9019 13.9019i 1.23359 1.23359i 0.271015 0.962575i $$-0.412641\pi$$
0.962575 0.271015i $$-0.0873593\pi$$
$$128$$ −1.00000 −0.0883883
$$129$$ 14.0741 14.0741i 1.23915 1.23915i
$$130$$ −5.26221 + 4.53625i −0.461526 + 0.397855i
$$131$$ 2.71250 + 2.71250i 0.236992 + 0.236992i 0.815603 0.578611i $$-0.196405\pi$$
−0.578611 + 0.815603i $$0.696405\pi$$
$$132$$ −4.70126 4.70126i −0.409192 0.409192i
$$133$$ −3.53975 −0.306935
$$134$$ 2.01024 + 2.01024i 0.173658 + 0.173658i
$$135$$ 10.8780 + 0.805947i 0.936232 + 0.0693648i
$$136$$ 8.09027i 0.693735i
$$137$$ −11.4519 + 11.4519i −0.978406 + 0.978406i −0.999772 0.0213660i $$-0.993198\pi$$
0.0213660 + 0.999772i $$0.493198\pi$$
$$138$$ 10.0446 10.0446i 0.855053 0.855053i
$$139$$ −2.41427 −0.204775 −0.102388 0.994745i $$-0.532648\pi$$
−0.102388 + 0.994745i $$0.532648\pi$$
$$140$$ 0.135480 1.82861i 0.0114502 0.154546i
$$141$$ 10.6186i 0.894248i
$$142$$ −0.00151598 −0.000127218
$$143$$ 11.3293i 0.947403i
$$144$$ 0.324646i 0.0270538i
$$145$$ 0.321204 4.33536i 0.0266746 0.360032i
$$146$$ 9.32759 9.32759i 0.771957 0.771957i
$$147$$ 8.15820 + 8.15820i 0.672877 + 0.672877i
$$148$$ −4.87870 3.63294i −0.401027 0.298626i
$$149$$ 4.02923i 0.330088i −0.986286 0.165044i $$-0.947223\pi$$
0.986286 0.165044i $$-0.0527765\pi$$
$$150$$ 5.42614 + 7.32620i 0.443043 + 0.598181i
$$151$$ 8.86568i 0.721479i −0.932667 0.360739i $$-0.882524\pi$$
0.932667 0.360739i $$-0.117476\pi$$
$$152$$ 3.05234 + 3.05234i 0.247578 + 0.247578i
$$153$$ 2.62647 0.212338
$$154$$ 2.11429 + 2.11429i 0.170375 + 0.170375i
$$155$$ 10.2148 + 0.756805i 0.820469 + 0.0607880i
$$156$$ 4.00594 4.00594i 0.320732 0.320732i
$$157$$ 6.87897 6.87897i 0.549001 0.549001i −0.377151 0.926152i $$-0.623096\pi$$
0.926152 + 0.377151i $$0.123096\pi$$
$$158$$ −0.760897 0.760897i −0.0605337 0.0605337i
$$159$$ 1.15150 0.0913196
$$160$$ −1.69364 + 1.45999i −0.133894 + 0.115422i
$$161$$ −4.51735 + 4.51735i −0.356017 + 0.356017i
$$162$$ −9.86854 −0.775346
$$163$$ 10.6733i 0.835995i −0.908448 0.417997i $$-0.862732\pi$$
0.908448 0.417997i $$-0.137268\pi$$
$$164$$ 9.31106i 0.727072i
$$165$$ −14.8260 1.09845i −1.15421 0.0855144i
$$166$$ −3.16981 3.16981i −0.246025 0.246025i
$$167$$ 0.864796i 0.0669199i 0.999440 + 0.0334600i $$0.0106526\pi$$
−0.999440 + 0.0334600i $$0.989347\pi$$
$$168$$ 1.49519i 0.115357i
$$169$$ −3.34633 −0.257410
$$170$$ −11.8117 13.7020i −0.905918 1.05090i
$$171$$ −0.990930 + 0.990930i −0.0757783 + 0.0757783i
$$172$$ 10.9160 0.832334
$$173$$ −2.14973 + 2.14973i −0.163441 + 0.163441i −0.784089 0.620648i $$-0.786870\pi$$
0.620648 + 0.784089i $$0.286870\pi$$
$$174$$ 3.54488i 0.268737i
$$175$$ −2.44030 3.29481i −0.184469 0.249064i
$$176$$ 3.64633i 0.274853i
$$177$$ −15.8943 −1.19469
$$178$$ 5.80016 5.80016i 0.434741 0.434741i
$$179$$ −0.313292 + 0.313292i −0.0234165 + 0.0234165i −0.718718 0.695302i $$-0.755271\pi$$
0.695302 + 0.718718i $$0.255271\pi$$
$$180$$ −0.473980 0.549834i −0.0353284 0.0409822i
$$181$$ 16.2161 1.20533 0.602667 0.797993i $$-0.294105\pi$$
0.602667 + 0.797993i $$0.294105\pi$$
$$182$$ −1.80159 + 1.80159i −0.133543 + 0.133543i
$$183$$ 22.4697 1.66100
$$184$$ 7.79067 0.574336
$$185$$ −13.5668 + 0.969960i −0.997454 + 0.0713129i
$$186$$ −8.35226 −0.612418
$$187$$ 29.4998 2.15724
$$188$$ −4.11794 + 4.11794i −0.300332 + 0.300332i
$$189$$ 4.00017 0.290969
$$190$$ 9.62597 + 0.713182i 0.698341 + 0.0517397i
$$191$$ 0.276686 0.276686i 0.0200203 0.0200203i −0.697026 0.717046i $$-0.745494\pi$$
0.717046 + 0.697026i $$0.245494\pi$$
$$192$$ 1.28931 1.28931i 0.0930480 0.0930480i
$$193$$ 8.78779 0.632559 0.316279 0.948666i $$-0.397566\pi$$
0.316279 + 0.948666i $$0.397566\pi$$
$$194$$ 14.6206i 1.04969i
$$195$$ 0.935990 12.6333i 0.0670276 0.904686i
$$196$$ 6.32757i 0.451969i
$$197$$ 8.41487 8.41487i 0.599535 0.599535i −0.340654 0.940189i $$-0.610649\pi$$
0.940189 + 0.340654i $$0.110649\pi$$
$$198$$ 1.18377 0.0841266
$$199$$ 4.20114 4.20114i 0.297811 0.297811i −0.542345 0.840156i $$-0.682463\pi$$
0.840156 + 0.542345i $$0.182463\pi$$
$$200$$ −0.736849 + 4.94541i −0.0521031 + 0.349693i
$$201$$ −5.18365 −0.365627
$$202$$ 3.68870i 0.259536i
$$203$$ 1.59424i 0.111894i
$$204$$ 10.4309 + 10.4309i 0.730307 + 0.730307i
$$205$$ −13.5941 15.7696i −0.949451 1.10140i
$$206$$ 11.1543i 0.777160i
$$207$$ 2.52921i 0.175792i
$$208$$ 3.10704 0.215434
$$209$$ −11.1299 + 11.1299i −0.769868 + 0.769868i
$$210$$ 2.18297 + 2.53232i 0.150639 + 0.174747i
$$211$$ −27.4901 −1.89250 −0.946248 0.323442i $$-0.895160\pi$$
−0.946248 + 0.323442i $$0.895160\pi$$
$$212$$ 0.446555 + 0.446555i 0.0306695 + 0.0306695i
$$213$$ 0.00195457 0.00195457i 0.000133925 0.000133925i
$$214$$ 3.88311 3.88311i 0.265444 0.265444i
$$215$$ 18.4877 15.9372i 1.26085 1.08691i
$$216$$ −3.44936 3.44936i −0.234699 0.234699i
$$217$$ 3.75626 0.254992
$$218$$ −2.01583 2.01583i −0.136529 0.136529i
$$219$$ 24.0523i 1.62531i
$$220$$ −5.32361 6.17558i −0.358918 0.416358i
$$221$$ 25.1367i 1.69088i
$$222$$ 10.9742 1.60617i 0.736537 0.107799i
$$223$$ −9.42660 9.42660i −0.631252 0.631252i 0.317130 0.948382i $$-0.397281\pi$$
−0.948382 + 0.317130i $$0.897281\pi$$
$$224$$ −0.579841 + 0.579841i −0.0387423 + 0.0387423i
$$225$$ −1.60551 0.239215i −0.107034 0.0159477i
$$226$$ 11.8892i 0.790856i
$$227$$ 17.9587i 1.19196i −0.802999 0.595981i $$-0.796763\pi$$
0.802999 0.595981i $$-0.203237\pi$$
$$228$$ −7.87084 −0.521259
$$229$$ 18.1673i 1.20053i −0.799802 0.600264i $$-0.795062\pi$$
0.799802 0.600264i $$-0.204938\pi$$
$$230$$ 13.1946 11.3743i 0.870027 0.750000i
$$231$$ −5.45197 −0.358713
$$232$$ −1.37472 + 1.37472i −0.0902547 + 0.0902547i
$$233$$ 2.23686 2.23686i 0.146541 0.146541i −0.630030 0.776571i $$-0.716957\pi$$
0.776571 + 0.630030i $$0.216957\pi$$
$$234$$ 1.00869i 0.0659399i
$$235$$ −0.962160 + 12.9865i −0.0627644 + 0.847144i
$$236$$ −6.16388 6.16388i −0.401234 0.401234i
$$237$$ 1.96207 0.127450
$$238$$ −4.69107 4.69107i −0.304077 0.304077i
$$239$$ 4.53542 + 4.53542i 0.293372 + 0.293372i 0.838411 0.545039i $$-0.183485\pi$$
−0.545039 + 0.838411i $$0.683485\pi$$
$$240$$ 0.301249 4.06602i 0.0194455 0.262460i
$$241$$ 2.95256 2.95256i 0.190191 0.190191i −0.605587 0.795779i $$-0.707062\pi$$
0.795779 + 0.605587i $$0.207062\pi$$
$$242$$ 2.29574 0.147576
$$243$$ 2.37553 2.37553i 0.152390 0.152390i
$$244$$ 8.71382 + 8.71382i 0.557845 + 0.557845i
$$245$$ 9.23820 + 10.7166i 0.590207 + 0.684661i
$$246$$ 12.0049 + 12.0049i 0.765402 + 0.765402i
$$247$$ −9.48374 9.48374i −0.603436 0.603436i
$$248$$ −3.23904 3.23904i −0.205679 0.205679i
$$249$$ 8.17374 0.517990
$$250$$ 5.97229 + 9.45154i 0.377721 + 0.597768i
$$251$$ −9.93109 9.93109i −0.626845 0.626845i 0.320428 0.947273i $$-0.396173\pi$$
−0.947273 + 0.320428i $$0.896173\pi$$
$$252$$ −0.188243 0.188243i −0.0118582 0.0118582i
$$253$$ 28.4074i 1.78596i
$$254$$ −13.9019 + 13.9019i −0.872280 + 0.872280i
$$255$$ 32.8951 + 2.43718i 2.05997 + 0.152622i
$$256$$ 1.00000 0.0625000
$$257$$ 15.1135i 0.942757i 0.881931 + 0.471378i $$0.156243\pi$$
−0.881931 + 0.471378i $$0.843757\pi$$
$$258$$ −14.0741 + 14.0741i −0.876213 + 0.876213i
$$259$$ −4.93540 + 0.722344i −0.306671 + 0.0448842i
$$260$$ 5.26221 4.53625i 0.326348 0.281326i
$$261$$ −0.446297 0.446297i −0.0276251 0.0276251i
$$262$$ −2.71250 2.71250i −0.167579 0.167579i
$$263$$ 9.74250 9.74250i 0.600749 0.600749i −0.339763 0.940511i $$-0.610347\pi$$
0.940511 + 0.339763i $$0.110347\pi$$
$$264$$ 4.70126 + 4.70126i 0.289342 + 0.289342i
$$265$$ 1.40827 + 0.104338i 0.0865094 + 0.00640942i
$$266$$ 3.53975 0.217036
$$267$$ 14.9564i 0.915319i
$$268$$ −2.01024 2.01024i −0.122795 0.122795i
$$269$$ 6.43418i 0.392299i −0.980574 0.196150i $$-0.937156\pi$$
0.980574 0.196150i $$-0.0628438\pi$$
$$270$$ −10.8780 0.805947i −0.662016 0.0490483i
$$271$$ −25.6662 −1.55911 −0.779556 0.626332i $$-0.784555\pi$$
−0.779556 + 0.626332i $$0.784555\pi$$
$$272$$ 8.09027i 0.490544i
$$273$$ 4.64561i 0.281165i
$$274$$ 11.4519 11.4519i 0.691837 0.691837i
$$275$$ −18.0326 2.68680i −1.08741 0.162020i
$$276$$ −10.0446 + 10.0446i −0.604614 + 0.604614i
$$277$$ −17.2625 −1.03720 −0.518602 0.855016i $$-0.673548\pi$$
−0.518602 + 0.855016i $$0.673548\pi$$
$$278$$ 2.41427 0.144798
$$279$$ 1.05154 1.05154i 0.0629541 0.0629541i
$$280$$ −0.135480 + 1.82861i −0.00809650 + 0.109280i
$$281$$ −3.84098 + 3.84098i −0.229134 + 0.229134i −0.812331 0.583197i $$-0.801802\pi$$
0.583197 + 0.812331i $$0.301802\pi$$
$$282$$ 10.6186i 0.632329i
$$283$$ 20.5564i 1.22195i 0.791650 + 0.610975i $$0.209222\pi$$
−0.791650 + 0.610975i $$0.790778\pi$$
$$284$$ 0.00151598 8.99567e−5
$$285$$ −13.3304 + 11.4914i −0.789624 + 0.680689i
$$286$$ 11.3293i 0.669915i
$$287$$ −5.39894 5.39894i −0.318689 0.318689i
$$288$$ 0.324646i 0.0191299i
$$289$$ −48.4524 −2.85014
$$290$$ −0.321204 + 4.33536i −0.0188618 + 0.254581i
$$291$$ 18.8504 + 18.8504i 1.10503 + 1.10503i
$$292$$ −9.32759 + 9.32759i −0.545856 + 0.545856i
$$293$$ −11.2671 11.2671i −0.658232 0.658232i 0.296729 0.954962i $$-0.404104\pi$$
−0.954962 + 0.296729i $$0.904104\pi$$
$$294$$ −8.15820 8.15820i −0.475796 0.475796i
$$295$$ −19.4386 1.44019i −1.13176 0.0838514i
$$296$$ 4.87870 + 3.63294i 0.283569 + 0.211160i
$$297$$ 12.5775 12.5775i 0.729822 0.729822i
$$298$$ 4.02923i 0.233407i
$$299$$ −24.2059 −1.39986
$$300$$ −5.42614 7.32620i −0.313278 0.422978i
$$301$$ 6.32952 6.32952i 0.364828 0.364828i
$$302$$ 8.86568i 0.510163i
$$303$$ −4.75588 4.75588i −0.273218 0.273218i
$$304$$ −3.05234 3.05234i −0.175064 0.175064i
$$305$$ 27.4802 + 2.03599i 1.57351 + 0.116581i
$$306$$ −2.62647 −0.150145
$$307$$ 9.43686 + 9.43686i 0.538590 + 0.538590i 0.923115 0.384525i $$-0.125635\pi$$
−0.384525 + 0.923115i $$0.625635\pi$$
$$308$$ −2.11429 2.11429i −0.120473 0.120473i
$$309$$ 14.3814 + 14.3814i 0.818131 + 0.818131i
$$310$$ −10.2148 0.756805i −0.580159 0.0429836i
$$311$$ 6.70368 + 6.70368i 0.380131 + 0.380131i 0.871149 0.491019i $$-0.163375\pi$$
−0.491019 + 0.871149i $$0.663375\pi$$
$$312$$ −4.00594 + 4.00594i −0.226791 + 0.226791i
$$313$$ −23.2157 −1.31223 −0.656114 0.754662i $$-0.727801\pi$$
−0.656114 + 0.754662i $$0.727801\pi$$
$$314$$ −6.87897 + 6.87897i −0.388203 + 0.388203i
$$315$$ −0.593650 0.0439832i −0.0334484 0.00247817i
$$316$$ 0.760897 + 0.760897i 0.0428038 + 0.0428038i
$$317$$ −15.3696 15.3696i −0.863245 0.863245i 0.128469 0.991714i $$-0.458994\pi$$
−0.991714 + 0.128469i $$0.958994\pi$$
$$318$$ −1.15150 −0.0645727
$$319$$ −5.01268 5.01268i −0.280656 0.280656i
$$320$$ 1.69364 1.45999i 0.0946775 0.0816160i
$$321$$ 10.0131i 0.558875i
$$322$$ 4.51735 4.51735i 0.251742 0.251742i
$$323$$ 24.6943 24.6943i 1.37403 1.37403i
$$324$$ 9.86854 0.548252
$$325$$ 2.28942 15.3656i 0.126994 0.852328i
$$326$$ 10.6733i 0.591137i
$$327$$ 5.19806 0.287454
$$328$$ 9.31106i 0.514117i
$$329$$ 4.77550i 0.263282i
$$330$$ 14.8260 + 1.09845i 0.816147 + 0.0604678i
$$331$$ −5.72839 + 5.72839i −0.314861 + 0.314861i −0.846789 0.531929i $$-0.821467\pi$$
0.531929 + 0.846789i $$0.321467\pi$$
$$332$$ 3.16981 + 3.16981i 0.173966 + 0.173966i
$$333$$ −1.17942 + 1.58385i −0.0646318 + 0.0867945i
$$334$$ 0.864796i 0.0473195i
$$335$$ −6.33957 0.469695i −0.346368 0.0256622i
$$336$$ 1.49519i 0.0815694i
$$337$$ 5.31333 + 5.31333i 0.289436 + 0.289436i 0.836857 0.547421i $$-0.184391\pi$$
−0.547421 + 0.836857i $$0.684391\pi$$
$$338$$ 3.34633 0.182016
$$339$$ 15.3288 + 15.3288i 0.832549 + 0.832549i
$$340$$ 11.8117 + 13.7020i 0.640580 + 0.743096i
$$341$$ 11.8106 11.8106i 0.639581 0.639581i
$$342$$ 0.990930 0.990930i 0.0535834 0.0535834i
$$343$$ 7.72788 + 7.72788i 0.417266 + 0.417266i
$$344$$ −10.9160 −0.588549
$$345$$ −2.34693 + 31.6770i −0.126354 + 1.70543i
$$346$$ 2.14973 2.14973i 0.115570 0.115570i
$$347$$ 32.7620 1.75876 0.879379 0.476123i $$-0.157958\pi$$
0.879379 + 0.476123i $$0.157958\pi$$
$$348$$ 3.54488i 0.190026i
$$349$$ 14.0604i 0.752637i 0.926490 + 0.376318i $$0.122810\pi$$
−0.926490 + 0.376318i $$0.877190\pi$$
$$350$$ 2.44030 + 3.29481i 0.130439 + 0.176115i
$$351$$ 10.7173 + 10.7173i 0.572047 + 0.572047i
$$352$$ 3.64633i 0.194350i
$$353$$ 6.79098i 0.361447i 0.983534 + 0.180724i $$0.0578440\pi$$
−0.983534 + 0.180724i $$0.942156\pi$$
$$354$$ 15.8943 0.844773
$$355$$ 0.00256752 0.00221331i 0.000136270 0.000117471i
$$356$$ −5.80016 + 5.80016i −0.307408 + 0.307408i
$$357$$ 12.0965 0.640215
$$358$$ 0.313292 0.313292i 0.0165580 0.0165580i
$$359$$ 4.91904i 0.259617i −0.991539 0.129808i $$-0.958564\pi$$
0.991539 0.129808i $$-0.0414362\pi$$
$$360$$ 0.473980 + 0.549834i 0.0249810 + 0.0289788i
$$361$$ 0.366413i 0.0192849i
$$362$$ −16.2161 −0.852300
$$363$$ −2.95992 + 2.95992i −0.155356 + 0.155356i
$$364$$ 1.80159 1.80159i 0.0944289 0.0944289i
$$365$$ −2.17940 + 29.4158i −0.114075 + 1.53969i
$$366$$ −22.4697 −1.17451
$$367$$ 21.4924 21.4924i 1.12189 1.12189i 0.130436 0.991457i $$-0.458362\pi$$
0.991457 0.130436i $$-0.0416378\pi$$
$$368$$ −7.79067 −0.406117
$$369$$ −3.02280 −0.157361
$$370$$ 13.5668 0.969960i 0.705306 0.0504258i
$$371$$ 0.517862 0.0268860
$$372$$ 8.35226 0.433045
$$373$$ 19.5734 19.5734i 1.01347 1.01347i 0.0135632 0.999908i $$-0.495683\pi$$
0.999908 0.0135632i $$-0.00431743\pi$$
$$374$$ −29.4998 −1.52540
$$375$$ −19.8861 4.48584i −1.02692 0.231648i
$$376$$ 4.11794 4.11794i 0.212367 0.212367i
$$377$$ 4.27130 4.27130i 0.219983 0.219983i
$$378$$ −4.00017 −0.205746
$$379$$ 1.90775i 0.0979943i −0.998799 0.0489972i $$-0.984397\pi$$
0.998799 0.0489972i $$-0.0156025\pi$$
$$380$$ −9.62597 0.713182i −0.493802 0.0365855i
$$381$$ 35.8476i 1.83653i
$$382$$ −0.276686 + 0.276686i −0.0141565 + 0.0141565i
$$383$$ 12.0669 0.616591 0.308295 0.951291i $$-0.400241\pi$$
0.308295 + 0.951291i $$0.400241\pi$$
$$384$$ −1.28931 + 1.28931i −0.0657949 + 0.0657949i
$$385$$ −6.66771 0.494007i −0.339818 0.0251769i
$$386$$ −8.78779 −0.447287
$$387$$ 3.54382i 0.180142i
$$388$$ 14.6206i 0.742246i
$$389$$ −16.8015 16.8015i −0.851868 0.851868i 0.138495 0.990363i $$-0.455773\pi$$
−0.990363 + 0.138495i $$0.955773\pi$$
$$390$$ −0.935990 + 12.6333i −0.0473957 + 0.639710i
$$391$$ 63.0286i 3.18749i
$$392$$ 6.32757i 0.319590i
$$393$$ 6.99450 0.352826
$$394$$ −8.41487 + 8.41487i −0.423935 + 0.423935i
$$395$$ 2.39959 + 0.177784i 0.120737 + 0.00894529i
$$396$$ −1.18377 −0.0594865
$$397$$ −6.99419 6.99419i −0.351028 0.351028i 0.509464 0.860492i $$-0.329844\pi$$
−0.860492 + 0.509464i $$0.829844\pi$$
$$398$$ −4.20114 + 4.20114i −0.210584 + 0.210584i
$$399$$ −4.56384 + 4.56384i −0.228478 + 0.228478i
$$400$$ 0.736849 4.94541i 0.0368425 0.247270i
$$401$$ 0.759591 + 0.759591i 0.0379322 + 0.0379322i 0.725818 0.687886i $$-0.241461\pi$$
−0.687886 + 0.725818i $$0.741461\pi$$
$$402$$ 5.18365 0.258537
$$403$$ 10.0638 + 10.0638i 0.501315 + 0.501315i
$$404$$ 3.68870i 0.183520i
$$405$$ 16.7138 14.4080i 0.830515 0.715939i
$$406$$ 1.59424i 0.0791207i
$$407$$ −13.2469 + 17.7894i −0.656625 + 0.881786i
$$408$$ −10.4309 10.4309i −0.516405 0.516405i
$$409$$ 22.0320 22.0320i 1.08941 1.08941i 0.0938237 0.995589i $$-0.470091\pi$$
0.995589 0.0938237i $$-0.0299090\pi$$
$$410$$ 13.5941 + 15.7696i 0.671363 + 0.778805i
$$411$$ 29.5302i 1.45662i
$$412$$ 11.1543i 0.549535i
$$413$$ −7.14814 −0.351737
$$414$$ 2.52921i 0.124304i
$$415$$ 9.99642 + 0.740629i 0.490705 + 0.0363560i
$$416$$ −3.10704 −0.152335
$$417$$ −3.11274 + 3.11274i −0.152432 + 0.152432i
$$418$$ 11.1299 11.1299i 0.544379 0.544379i
$$419$$ 13.7527i 0.671863i −0.941886 0.335931i $$-0.890949\pi$$
0.941886 0.335931i $$-0.109051\pi$$
$$420$$ −2.18297 2.53232i −0.106518 0.123565i
$$421$$ 4.62725 + 4.62725i 0.225519 + 0.225519i 0.810818 0.585299i $$-0.199023\pi$$
−0.585299 + 0.810818i $$0.699023\pi$$
$$422$$ 27.4901 1.33820
$$423$$ 1.33687 + 1.33687i 0.0650010 + 0.0650010i
$$424$$ −0.446555 0.446555i −0.0216866 0.0216866i
$$425$$ 40.0097 + 5.96131i 1.94075 + 0.289166i
$$426$$ −0.00195457 + 0.00195457i −9.46990e−5 + 9.46990e-5i
$$427$$ 10.1053 0.489028
$$428$$ −3.88311 + 3.88311i −0.187697 + 0.187697i
$$429$$ −14.6070 14.6070i −0.705231 0.705231i
$$430$$ −18.4877 + 15.9372i −0.891557 + 0.768560i
$$431$$ 2.01292 + 2.01292i 0.0969591 + 0.0969591i 0.753922 0.656963i $$-0.228159\pi$$
−0.656963 + 0.753922i $$0.728159\pi$$
$$432$$ 3.44936 + 3.44936i 0.165958 + 0.165958i
$$433$$ −23.2986 23.2986i −1.11966 1.11966i −0.991791 0.127870i $$-0.959186\pi$$
−0.127870 0.991791i $$-0.540814\pi$$
$$434$$ −3.75626 −0.180306
$$435$$ −5.17549 6.00376i −0.248146 0.287858i
$$436$$ 2.01583 + 2.01583i 0.0965407 + 0.0965407i
$$437$$ 23.7798 + 23.7798i 1.13754 + 1.13754i
$$438$$ 24.0523i 1.14927i
$$439$$ −6.59762 + 6.59762i −0.314887 + 0.314887i −0.846800 0.531912i $$-0.821474\pi$$
0.531912 + 0.846800i $$0.321474\pi$$
$$440$$ 5.32361 + 6.17558i 0.253793 + 0.294409i
$$441$$ 2.05422 0.0978199
$$442$$ 25.1367i 1.19563i
$$443$$ −28.2758 + 28.2758i −1.34343 + 1.34343i −0.450801 + 0.892625i $$0.648862\pi$$
−0.892625 + 0.450801i $$0.851138\pi$$
$$444$$ −10.9742 + 1.60617i −0.520810 + 0.0762256i
$$445$$ −1.35521 + 18.2916i −0.0642432 + 0.867105i
$$446$$ 9.42660 + 9.42660i 0.446363 + 0.446363i
$$447$$ −5.19493 5.19493i −0.245712 0.245712i
$$448$$ 0.579841 0.579841i 0.0273949 0.0273949i
$$449$$ 11.7576 + 11.7576i 0.554876 + 0.554876i 0.927844 0.372968i $$-0.121660\pi$$
−0.372968 + 0.927844i $$0.621660\pi$$
$$450$$ 1.60551 + 0.239215i 0.0756843 + 0.0112767i
$$451$$ −33.9512 −1.59870
$$452$$ 11.8892i 0.559220i
$$453$$ −11.4306 11.4306i −0.537057 0.537057i
$$454$$ 17.9587i 0.842844i
$$455$$ 0.420942 5.68155i 0.0197341 0.266355i
$$456$$ 7.87084 0.368586
$$457$$ 31.9954i 1.49668i −0.663314 0.748341i $$-0.730851\pi$$
0.663314 0.748341i $$-0.269149\pi$$
$$458$$ 18.1673i 0.848901i
$$459$$ −27.9063 + 27.9063i −1.30255 + 1.30255i
$$460$$ −13.1946 + 11.3743i −0.615202 + 0.530330i
$$461$$ −17.2203 + 17.2203i −0.802031 + 0.802031i −0.983413 0.181382i $$-0.941943\pi$$
0.181382 + 0.983413i $$0.441943\pi$$
$$462$$ 5.45197 0.253648
$$463$$ −13.3316 −0.619570 −0.309785 0.950807i $$-0.600257\pi$$
−0.309785 + 0.950807i $$0.600257\pi$$
$$464$$ 1.37472 1.37472i 0.0638197 0.0638197i
$$465$$ 14.1457 12.1942i 0.655993 0.565494i
$$466$$ −2.23686 + 2.23686i −0.103620 + 0.103620i
$$467$$ 32.1997i 1.49003i −0.667050 0.745013i $$-0.732443\pi$$
0.667050 0.745013i $$-0.267557\pi$$
$$468$$ 1.00869i 0.0466265i
$$469$$ −2.33124 −0.107647
$$470$$ 0.962160 12.9865i 0.0443811 0.599022i
$$471$$ 17.7383i 0.817336i
$$472$$ 6.16388 + 6.16388i 0.283715 + 0.283715i
$$473$$ 39.8032i 1.83015i
$$474$$ −1.96207 −0.0901207
$$475$$ −17.3442 + 12.8460i −0.795806 + 0.589413i
$$476$$ 4.69107 + 4.69107i 0.215015 + 0.215015i
$$477$$ 0.144972 0.144972i 0.00663782 0.00663782i
$$478$$ −4.53542 4.53542i −0.207445 0.207445i
$$479$$ 10.6512 + 10.6512i 0.486664 + 0.486664i 0.907252 0.420588i $$-0.138176\pi$$
−0.420588 + 0.907252i $$0.638176\pi$$
$$480$$ −0.301249 + 4.06602i −0.0137501 + 0.185587i
$$481$$ −15.1583 11.2877i −0.691159 0.514674i
$$482$$ −2.95256 + 2.95256i −0.134486 + 0.134486i
$$483$$ 11.6485i 0.530027i
$$484$$ −2.29574 −0.104352
$$485$$ 21.3459 + 24.7620i 0.969267 + 1.12438i
$$486$$ −2.37553 + 2.37553i −0.107756 + 0.107756i
$$487$$ 17.1695i 0.778022i −0.921233 0.389011i $$-0.872817\pi$$
0.921233 0.389011i $$-0.127183\pi$$
$$488$$ −8.71382 8.71382i −0.394456 0.394456i
$$489$$ −13.7612 13.7612i −0.622301 0.622301i
$$490$$ −9.23820 10.7166i −0.417339 0.484128i
$$491$$ −9.04897 −0.408374 −0.204187 0.978932i $$-0.565455\pi$$
−0.204187 + 0.978932i $$0.565455\pi$$
$$492$$ −12.0049 12.0049i −0.541221 0.541221i
$$493$$ 11.1218 + 11.1218i 0.500902 + 0.500902i
$$494$$ 9.48374 + 9.48374i 0.426694 + 0.426694i
$$495$$ −2.00488 + 1.72829i −0.0901125 + 0.0776808i
$$496$$ 3.23904 + 3.23904i 0.145437 + 0.145437i
$$497$$ 0.000879026 0 0.000879026i 3.94297e−5 0 3.94297e-5i
$$498$$ −8.17374 −0.366274
$$499$$ −8.81194 + 8.81194i −0.394477 + 0.394477i −0.876280 0.481803i $$-0.839982\pi$$
0.481803 + 0.876280i $$0.339982\pi$$
$$500$$ −5.97229 9.45154i −0.267089 0.422686i
$$501$$ 1.11499 + 1.11499i 0.0498141 + 0.0498141i
$$502$$ 9.93109 + 9.93109i 0.443246 + 0.443246i
$$503$$ 13.2027 0.588678 0.294339 0.955701i $$-0.404900\pi$$
0.294339 + 0.955701i $$0.404900\pi$$
$$504$$ 0.188243 + 0.188243i 0.00838501 + 0.00838501i
$$505$$ −5.38547 6.24734i −0.239650 0.278003i
$$506$$ 28.4074i 1.26286i
$$507$$ −4.31446 + 4.31446i −0.191612 + 0.191612i
$$508$$ 13.9019 13.9019i 0.616795 0.616795i
$$509$$ 25.2057 1.11722 0.558612 0.829429i $$-0.311334\pi$$
0.558612 + 0.829429i $$0.311334\pi$$
$$510$$ −32.8951 2.43718i −1.45662 0.107920i
$$511$$ 10.8170i 0.478518i
$$512$$ −1.00000 −0.0441942
$$513$$ 21.0573i 0.929701i
$$514$$ 15.1135i 0.666630i
$$515$$ 16.2853 + 18.8915i 0.717614 + 0.832458i
$$516$$ 14.0741 14.0741i 0.619576 0.619576i
$$517$$ 15.0154 + 15.0154i 0.660376 + 0.660376i
$$518$$ 4.93540 0.722344i 0.216849 0.0317380i
$$519$$ 5.54335i 0.243326i
$$520$$ −5.26221 + 4.53625i −0.230763 + 0.198928i
$$521$$ 8.65279i 0.379086i 0.981872 + 0.189543i $$0.0607006\pi$$
−0.981872 + 0.189543i $$0.939299\pi$$
$$522$$ 0.446297 + 0.446297i 0.0195339 + 0.0195339i
$$523$$ −28.4569 −1.24433 −0.622167 0.782884i $$-0.713748\pi$$
−0.622167 + 0.782884i $$0.713748\pi$$
$$524$$ 2.71250 + 2.71250i 0.118496 + 0.118496i
$$525$$ −7.39433 1.10173i −0.322715 0.0480835i
$$526$$ −9.74250 + 9.74250i −0.424793 + 0.424793i
$$527$$ −26.2047 + 26.2047i −1.14149 + 1.14149i
$$528$$ −4.70126 4.70126i −0.204596 0.204596i
$$529$$ 37.6945 1.63889
$$530$$ −1.40827 0.104338i −0.0611713 0.00453215i
$$531$$ −2.00108 + 2.00108i −0.0868393 + 0.0868393i
$$532$$ −3.53975 −0.153468
$$533$$ 28.9298i 1.25309i
$$534$$ 14.9564i 0.647228i
$$535$$ −0.907292 + 12.2459i −0.0392256 + 0.529437i
$$536$$ 2.01024 + 2.01024i 0.0868292 + 0.0868292i
$$537$$ 0.807861i 0.0348618i
$$538$$ 6.43418i 0.277397i
$$539$$ 23.0724 0.993799
$$540$$ 10.8780 + 0.805947i 0.468116 + 0.0346824i
$$541$$ 22.0757 22.0757i 0.949106 0.949106i −0.0496598 0.998766i $$-0.515814\pi$$
0.998766 + 0.0496598i $$0.0158137\pi$$
$$542$$ 25.6662 1.10246
$$543$$ 20.9076 20.9076i 0.897231 0.897231i
$$544$$ 8.09027i 0.346867i
$$545$$ 6.35719 + 0.471000i 0.272312 + 0.0201754i
$$546$$ 4.64561i 0.198814i
$$547$$ −24.7795 −1.05949 −0.529747 0.848155i $$-0.677713\pi$$
−0.529747 + 0.848155i $$0.677713\pi$$
$$548$$ −11.4519 + 11.4519i −0.489203 + 0.489203i
$$549$$ 2.82891 2.82891i 0.120735 0.120735i
$$550$$ 18.0326 + 2.68680i 0.768913 + 0.114565i
$$551$$ −8.39222 −0.357521
$$552$$ 10.0446 10.0446i 0.427526 0.427526i
$$553$$ 0.882399 0.0375234
$$554$$ 17.2625 0.733415
$$555$$ −16.2413 + 18.7425i −0.689405 + 0.795573i
$$556$$ −2.41427 −0.102388
$$557$$ −28.3582 −1.20157 −0.600787 0.799409i $$-0.705146\pi$$
−0.600787 + 0.799409i $$0.705146\pi$$
$$558$$ −1.05154 + 1.05154i −0.0445153 + 0.0445153i
$$559$$ 33.9163 1.43451
$$560$$ 0.135480 1.82861i 0.00572509 0.0772728i
$$561$$ 38.0344 38.0344i 1.60581 1.60581i
$$562$$ 3.84098 3.84098i 0.162022 0.162022i
$$563$$ −16.8486 −0.710085 −0.355043 0.934850i $$-0.615534\pi$$
−0.355043 + 0.934850i $$0.615534\pi$$
$$564$$ 10.6186i 0.447124i
$$565$$ 17.3581 + 20.1360i 0.730261 + 0.847128i
$$566$$ 20.5564i 0.864049i
$$567$$ 5.72219 5.72219i 0.240309 0.240309i
$$568$$ −0.00151598 −6.36090e−5
$$569$$ 4.89447 4.89447i 0.205187 0.205187i −0.597031 0.802218i $$-0.703653\pi$$
0.802218 + 0.597031i $$0.203653\pi$$
$$570$$ 13.3304 11.4914i 0.558348 0.481320i
$$571$$ −38.8520 −1.62590 −0.812952 0.582330i $$-0.802141\pi$$
−0.812952 + 0.582330i $$0.802141\pi$$
$$572$$ 11.3293i 0.473701i
$$573$$ 0.713470i 0.0298056i
$$574$$ 5.39894 + 5.39894i 0.225347 + 0.225347i
$$575$$ −5.74055 + 38.5280i −0.239397 + 1.60673i
$$576$$ 0.324646i 0.0135269i
$$577$$ 18.6556i 0.776642i 0.921524 + 0.388321i $$0.126945\pi$$
−0.921524 + 0.388321i $$0.873055\pi$$
$$578$$ 48.4524 2.01535
$$579$$ 11.3302 11.3302i 0.470867 0.470867i
$$580$$ 0.321204 4.33536i 0.0133373 0.180016i
$$581$$ 3.67597 0.152505
$$582$$ −18.8504 18.8504i −0.781376 0.781376i
$$583$$ 1.62829 1.62829i 0.0674368 0.0674368i
$$584$$ 9.32759 9.32759i 0.385979 0.385979i
$$585$$ −1.47267 1.70835i −0.0608876 0.0706317i
$$586$$ 11.2671 + 11.2671i 0.465441 + 0.465441i
$$587$$ −5.75904 −0.237701 −0.118851 0.992912i $$-0.537921\pi$$
−0.118851 + 0.992912i $$0.537921\pi$$
$$588$$ 8.15820 + 8.15820i 0.336439 + 0.336439i
$$589$$ 19.7733i 0.814746i
$$590$$ 19.4386 + 1.44019i 0.800275 + 0.0592919i
$$591$$ 21.6988i 0.892568i
$$592$$ −4.87870 3.63294i −0.200513 0.149313i
$$593$$ −16.3572 16.3572i −0.671709 0.671709i 0.286401 0.958110i $$-0.407541\pi$$
−0.958110 + 0.286401i $$0.907541\pi$$
$$594$$ −12.5775 + 12.5775i −0.516062 + 0.516062i
$$595$$ 14.7939 + 1.09607i 0.606492 + 0.0449346i
$$596$$ 4.02923i 0.165044i
$$597$$ 10.8332i 0.443372i
$$598$$ 24.2059 0.989852
$$599$$ 23.6157i 0.964910i 0.875921 + 0.482455i $$0.160255\pi$$
−0.875921 + 0.482455i $$0.839745\pi$$
$$600$$ 5.42614 + 7.32620i 0.221521 + 0.299091i
$$601$$ 30.4617 1.24256 0.621279 0.783589i $$-0.286613\pi$$
0.621279 + 0.783589i $$0.286613\pi$$
$$602$$ −6.32952 + 6.32952i −0.257972 + 0.257972i
$$603$$ −0.652617 + 0.652617i −0.0265766 + 0.0265766i
$$604$$ 8.86568i 0.360739i
$$605$$ −3.88816 + 3.35176i −0.158076 + 0.136268i
$$606$$ 4.75588 + 4.75588i 0.193195 + 0.193195i
$$607$$ −17.6781 −0.717530 −0.358765 0.933428i $$-0.616802\pi$$
−0.358765 + 0.933428i $$0.616802\pi$$
$$608$$ 3.05234 + 3.05234i 0.123789 + 0.123789i
$$609$$ −2.05547 2.05547i −0.0832918 0.0832918i
$$610$$ −27.4802 2.03599i −1.11264 0.0824349i
$$611$$ −12.7946 + 12.7946i −0.517614 + 0.517614i
$$612$$ 2.62647 0.106169
$$613$$ −24.9613 + 24.9613i −1.00818 + 1.00818i −0.00821132 + 0.999966i $$0.502614\pi$$
−0.999966 + 0.00821132i $$0.997386\pi$$
$$614$$ −9.43686 9.43686i −0.380841 0.380841i
$$615$$ −37.8589 2.80494i −1.52662 0.113106i
$$616$$ 2.11429 + 2.11429i 0.0851873 + 0.0851873i
$$617$$ −6.37297 6.37297i −0.256566 0.256566i 0.567090 0.823656i $$-0.308069\pi$$
−0.823656 + 0.567090i $$0.808069\pi$$
$$618$$ −14.3814 14.3814i −0.578506 0.578506i
$$619$$ −2.43520 −0.0978789 −0.0489394 0.998802i $$-0.515584\pi$$
−0.0489394 + 0.998802i $$0.515584\pi$$
$$620$$ 10.2148 + 0.756805i 0.410234 + 0.0303940i
$$621$$ −26.8729 26.8729i −1.07837 1.07837i
$$622$$ −6.70368 6.70368i −0.268793 0.268793i
$$623$$ 6.72635i 0.269485i
$$624$$ 4.00594 4.00594i 0.160366 0.160366i
$$625$$ −23.9141 7.28804i −0.956564 0.291522i
$$626$$ 23.2157 0.927885
$$627$$ 28.6997i 1.14616i
$$628$$ 6.87897 6.87897i 0.274501 0.274501i
$$629$$ 29.3915 39.4700i 1.17191 1.57377i
$$630$$ 0.593650 + 0.0439832i 0.0236516 + 0.00175233i
$$631$$ 8.01035 + 8.01035i 0.318887 + 0.318887i 0.848340 0.529453i $$-0.177603\pi$$
−0.529453 + 0.848340i $$0.677603\pi$$
$$632$$ −0.760897 0.760897i −0.0302669 0.0302669i
$$633$$ −35.4433 + 35.4433i −1.40874 + 1.40874i
$$634$$ 15.3696 + 15.3696i 0.610406 + 0.610406i
$$635$$ 3.24818 43.8414i 0.128900 1.73979i
$$636$$ 1.15150 0.0456598
$$637$$ 19.6600i 0.778957i
$$638$$ 5.01268 + 5.01268i 0.198454 + 0.198454i
$$639$$ 0 0.000492156i 0 1.94694e-5i
$$640$$ −1.69364 + 1.45999i −0.0669471 + 0.0577112i
$$641$$ 20.0552 0.792134 0.396067 0.918222i $$-0.370375\pi$$
0.396067 + 0.918222i $$0.370375\pi$$
$$642$$ 10.0131i 0.395184i
$$643$$ 2.02458i 0.0798417i −0.999203 0.0399208i $$-0.987289\pi$$
0.999203 0.0399208i $$-0.0127106\pi$$
$$644$$ −4.51735 + 4.51735i −0.178009 + 0.178009i
$$645$$ 3.28842 44.3844i 0.129481 1.74764i
$$646$$ −24.6943 + 24.6943i −0.971583 + 0.971583i
$$647$$ 37.8245 1.48703 0.743517 0.668717i $$-0.233156\pi$$
0.743517 + 0.668717i $$0.233156\pi$$
$$648$$ −9.86854 −0.387673
$$649$$ −22.4755 + 22.4755i −0.882242 + 0.882242i
$$650$$ −2.28942 + 15.3656i −0.0897983 + 0.602687i
$$651$$ 4.84299 4.84299i 0.189812 0.189812i
$$652$$ 10.6733i 0.417997i
$$653$$ 24.2252i 0.948006i 0.880523 + 0.474003i $$0.157192\pi$$
−0.880523 + 0.474003i $$0.842808\pi$$
$$654$$ −5.19806 −0.203260
$$655$$ 8.55422 + 0.633777i 0.334241 + 0.0247637i
$$656$$ 9.31106i 0.363536i
$$657$$ 3.02816 + 3.02816i 0.118140 + 0.118140i
$$658$$ 4.77550i 0.186169i
$$659$$ 16.7841 0.653814 0.326907 0.945056i $$-0.393994\pi$$
0.326907 + 0.945056i $$0.393994\pi$$
$$660$$ −14.8260 1.09845i −0.577103 0.0427572i
$$661$$ 2.96671 + 2.96671i 0.115392 + 0.115392i 0.762445 0.647053i $$-0.223999\pi$$
−0.647053 + 0.762445i $$0.723999\pi$$
$$662$$ 5.72839 5.72839i 0.222640 0.222640i
$$663$$ 32.4091 + 32.4091i 1.25866 + 1.25866i
$$664$$ −3.16981 3.16981i −0.123012 0.123012i
$$665$$ −5.99507 + 5.16800i −0.232479 + 0.200407i
$$666$$ 1.17942 1.58385i 0.0457016 0.0613730i
$$667$$ −10.7100 + 10.7100i −0.414692 + 0.414692i
$$668$$ 0.864796i 0.0334600i
$$669$$ −24.3077 −0.939788
$$670$$ 6.33957 + 0.469695i 0.244919 + 0.0181459i
$$671$$ 31.7735 31.7735i 1.22660 1.22660i
$$672$$ 1.49519i 0.0576783i
$$673$$ 23.2071 + 23.2071i 0.894567 + 0.894567i 0.994949 0.100382i $$-0.0320066\pi$$
−0.100382 + 0.994949i $$0.532007\pi$$
$$674$$ −5.31333 5.31333i −0.204662 0.204662i
$$675$$ 19.6002 14.5168i 0.754411 0.558754i
$$676$$ −3.34633 −0.128705
$$677$$ 4.70869 + 4.70869i 0.180970 + 0.180970i 0.791778 0.610809i $$-0.209156\pi$$
−0.610809 + 0.791778i $$0.709156\pi$$
$$678$$ −15.3288 15.3288i −0.588701 0.588701i
$$679$$ 8.47761 + 8.47761i 0.325341 + 0.325341i
$$680$$ −11.8117 13.7020i −0.452959 0.525448i
$$681$$ −23.1544 23.1544i −0.887277 0.887277i
$$682$$ −11.8106 + 11.8106i −0.452252 + 0.452252i
$$683$$ −46.0160 −1.76075 −0.880376 0.474277i $$-0.842710\pi$$
−0.880376 + 0.474277i $$0.842710\pi$$
$$684$$ −0.990930 + 0.990930i −0.0378892 + 0.0378892i
$$685$$ −2.67576 + 36.1152i −0.102235 + 1.37989i
$$686$$ −7.72788 7.72788i −0.295052 0.295052i
$$687$$ −23.4233 23.4233i −0.893653 0.893653i
$$688$$ 10.9160 0.416167
$$689$$ 1.38746 + 1.38746i 0.0528581 + 0.0528581i
$$690$$ 2.34693 31.6770i 0.0893460 1.20592i
$$691$$ 37.9434i 1.44344i 0.692187 + 0.721718i $$0.256647\pi$$
−0.692187 + 0.721718i $$0.743353\pi$$
$$692$$ −2.14973 + 2.14973i −0.0817206 + 0.0817206i
$$693$$ −0.686397 + 0.686397i −0.0260741 + 0.0260741i
$$694$$ −32.7620 −1.24363
$$695$$ −4.08890 + 3.52481i −0.155101 + 0.133704i
$$696$$ 3.54488i 0.134368i
$$697$$ 75.3290 2.85329
$$698$$ 14.0604i 0.532194i
$$699$$ 5.76801i 0.218166i
$$700$$ −2.44030 3.29481i −0.0922345 0.124532i
$$701$$ 11.9143 11.9143i 0.449995 0.449995i −0.445358 0.895353i $$-0.646923\pi$$
0.895353 + 0.445358i $$0.146923\pi$$
$$702$$ −10.7173 10.7173i −0.404498 0.404498i
$$703$$ 3.80249 + 25.9805i 0.143414 + 0.979871i
$$704$$ 3.64633i 0.137426i
$$705$$ 15.5031 + 17.9841i 0.583880 + 0.677322i
$$706$$ 6.79098i 0.255582i
$$707$$ −2.13886 2.13886i −0.0804402 0.0804402i
$$708$$ −15.8943 −0.597345
$$709$$ −13.4491 13.4491i −0.505093 0.505093i 0.407923 0.913016i $$-0.366253\pi$$
−0.913016 + 0.407923i $$0.866253\pi$$
$$710$$ −0.00256752 + 0.00221331i −9.63574e−5 + 8.30642e-5i
$$711$$ 0.247022 0.247022i 0.00926405 0.00926405i
$$712$$ 5.80016 5.80016i 0.217370 0.217370i
$$713$$ −25.2343 25.2343i −0.945032 0.945032i
$$714$$ −12.0965 −0.452700
$$715$$ −16.5407 19.1878i −0.618586 0.717582i
$$716$$ −0.313292 + 0.313292i −0.0117083 + 0.0117083i
$$717$$ 11.6951 0.436763
$$718$$ 4.91904i 0.183577i
$$719$$ 15.0482i 0.561204i −0.959824 0.280602i $$-0.909466\pi$$
0.959824 0.280602i $$-0.0905342\pi$$
$$720$$ −0.473980 0.549834i −0.0176642 0.0204911i
$$721$$ 6.46775 + 6.46775i 0.240872 + 0.240872i
$$722$$ 0.366413i 0.0136365i
$$723$$ 7.61354i 0.283151i
$$724$$ 16.2161 0.602667
$$725$$ −5.78558 7.81150i −0.214871 0.290112i
$$726$$ 2.95992 2.95992i 0.109853 0.109853i
$$727$$ −48.0498 −1.78207 −0.891033 0.453938i $$-0.850019\pi$$
−0.891033 + 0.453938i $$0.850019\pi$$
$$728$$ −1.80159 + 1.80159i −0.0667713 + 0.0667713i
$$729$$ 23.4800i 0.869631i
$$730$$ 2.17940 29.4158i 0.0806632 1.08873i
$$731$$ 88.3130i 3.26637i
$$732$$ 22.4697 0.830502
$$733$$ 17.9391 17.9391i 0.662596 0.662596i −0.293395 0.955991i $$-0.594785\pi$$
0.955991 + 0.293395i $$0.0947851\pi$$
$$734$$ −21.4924 + 21.4924i −0.793298 + 0.793298i
$$735$$ 25.7280 + 1.90617i 0.948991 + 0.0703102i
$$736$$ 7.79067 0.287168
$$737$$ −7.33001 + 7.33001i −0.270004 + 0.270004i
$$738$$ 3.02280 0.111271
$$739$$ 27.0049 0.993391 0.496696 0.867925i $$-0.334547\pi$$
0.496696 + 0.867925i $$0.334547\pi$$
$$740$$ −13.5668 + 0.969960i −0.498727 + 0.0356564i
$$741$$ −24.4550 −0.898376
$$742$$ −0.517862 −0.0190113
$$743$$ 21.8683 21.8683i 0.802270 0.802270i −0.181180 0.983450i $$-0.557992\pi$$
0.983450 + 0.181180i $$0.0579917\pi$$
$$744$$ −8.35226 −0.306209
$$745$$ −5.88265 6.82408i −0.215523 0.250015i
$$746$$ −19.5734 + 19.5734i −0.716632 + 0.716632i
$$747$$ 1.02907 1.02907i 0.0376515 0.0376515i
$$748$$ 29.4998 1.07862
$$749$$ 4.50318i 0.164542i
$$750$$ 19.8861 + 4.48584i 0.726139 + 0.163800i
$$751$$ 17.0169i 0.620957i −0.950580 0.310479i $$-0.899511\pi$$
0.950580 0.310479i $$-0.100489\pi$$
$$752$$ −4.11794 + 4.11794i −0.150166 + 0.150166i
$$753$$ −25.6085 −0.933227
$$754$$ −4.27130 + 4.27130i −0.155552 + 0.155552i
$$755$$ −12.9438 15.0153i −0.471074 0.546462i
$$756$$ 4.00017 0.145485
$$757$$ 31.0722i 1.12934i −0.825317 0.564669i $$-0.809004\pi$$
0.825317 0.564669i $$-0.190996\pi$$
$$758$$ 1.90775i 0.0692925i
$$759$$ 36.6259 + 36.6259i 1.32944 + 1.32944i
$$760$$ 9.62597 + 0.713182i 0.349171 + 0.0258698i
$$761$$ 14.8739i 0.539180i 0.962975 + 0.269590i $$0.0868882\pi$$
−0.962975 + 0.269590i $$0.913112\pi$$
$$762$$ 35.8476i 1.29862i
$$763$$ 2.33772 0.0846312
$$764$$ 0.276686 0.276686i 0.0100102 0.0100102i
$$765$$ 4.44830 3.83463i 0.160829 0.138641i
$$766$$ −12.0669 −0.435996
$$767$$ −19.1514 19.1514i −0.691516 0.691516i
$$768$$ 1.28931 1.28931i 0.0465240 0.0465240i
$$769$$ 21.6211 21.6211i 0.779677 0.779677i −0.200099 0.979776i $$-0.564126\pi$$
0.979776 + 0.200099i $$0.0641264\pi$$
$$770$$ 6.66771 + 0.494007i 0.240288 + 0.0178028i
$$771$$ 19.4861 + 19.4861i 0.701773 + 0.701773i
$$772$$ 8.78779 0.316279
$$773$$ 8.11195 + 8.11195i 0.291766 + 0.291766i 0.837778 0.546011i $$-0.183854\pi$$
−0.546011 + 0.837778i $$0.683854\pi$$
$$774$$ 3.54382i 0.127380i
$$775$$ 18.4051 13.6317i 0.661129 0.489665i
$$776$$ 14.6206i 0.524847i
$$777$$ −5.43194 + 7.29460i −0.194870 + 0.261692i