# Properties

 Label 165.2.c.a.34.3 Level $165$ Weight $2$ Character 165.34 Analytic conductor $1.318$ Analytic rank $0$ Dimension $6$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$165 = 3 \cdot 5 \cdot 11$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 165.c (of order $$2$$, degree $$1$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$1.31753163335$$ Analytic rank: $$0$$ Dimension: $$6$$ Coefficient field: 6.0.350464.1 Defining polynomial: $$x^{6} - 2x^{5} + 2x^{4} + 2x^{3} + 4x^{2} - 4x + 2$$ x^6 - 2*x^5 + 2*x^4 + 2*x^3 + 4*x^2 - 4*x + 2 Coefficient ring: $$\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$2$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

## Embedding invariants

 Embedding label 34.3 Root $$1.45161 + 1.45161i$$ of defining polynomial Character $$\chi$$ $$=$$ 165.34 Dual form 165.2.c.a.34.4

## $q$-expansion

 $$f(q)$$ $$=$$ $$q-1.21432i q^{2} +1.00000i q^{3} +0.525428 q^{4} +(0.311108 + 2.21432i) q^{5} +1.21432 q^{6} +4.90321i q^{7} -3.06668i q^{8} -1.00000 q^{9} +O(q^{10})$$ $$q-1.21432i q^{2} +1.00000i q^{3} +0.525428 q^{4} +(0.311108 + 2.21432i) q^{5} +1.21432 q^{6} +4.90321i q^{7} -3.06668i q^{8} -1.00000 q^{9} +(2.68889 - 0.377784i) q^{10} -1.00000 q^{11} +0.525428i q^{12} -4.14764i q^{13} +5.95407 q^{14} +(-2.21432 + 0.311108i) q^{15} -2.67307 q^{16} -5.33185i q^{17} +1.21432i q^{18} +5.18421 q^{19} +(0.163465 + 1.16346i) q^{20} -4.90321 q^{21} +1.21432i q^{22} -4.00000i q^{23} +3.06668 q^{24} +(-4.80642 + 1.37778i) q^{25} -5.03657 q^{26} -1.00000i q^{27} +2.57628i q^{28} -1.80642 q^{29} +(0.377784 + 2.68889i) q^{30} +2.62222 q^{31} -2.88739i q^{32} -1.00000i q^{33} -6.47457 q^{34} +(-10.8573 + 1.52543i) q^{35} -0.525428 q^{36} +5.80642i q^{37} -6.29529i q^{38} +4.14764 q^{39} +(6.79060 - 0.954067i) q^{40} +1.80642 q^{41} +5.95407i q^{42} -4.90321i q^{43} -0.525428 q^{44} +(-0.311108 - 2.21432i) q^{45} -4.85728 q^{46} +7.05086i q^{47} -2.67307i q^{48} -17.0415 q^{49} +(1.67307 + 5.83654i) q^{50} +5.33185 q^{51} -2.17929i q^{52} +7.18421i q^{53} -1.21432 q^{54} +(-0.311108 - 2.21432i) q^{55} +15.0366 q^{56} +5.18421i q^{57} +2.19358i q^{58} -1.67307 q^{59} +(-1.16346 + 0.163465i) q^{60} +0.755569 q^{61} -3.18421i q^{62} -4.90321i q^{63} -8.85236 q^{64} +(9.18421 - 1.29036i) q^{65} -1.21432 q^{66} -4.85728i q^{67} -2.80150i q^{68} +4.00000 q^{69} +(1.85236 + 13.1842i) q^{70} +0.428639 q^{71} +3.06668i q^{72} -12.7096i q^{73} +7.05086 q^{74} +(-1.37778 - 4.80642i) q^{75} +2.72393 q^{76} -4.90321i q^{77} -5.03657i q^{78} +6.42864 q^{79} +(-0.831613 - 5.91903i) q^{80} +1.00000 q^{81} -2.19358i q^{82} +2.90321i q^{83} -2.57628 q^{84} +(11.8064 - 1.65878i) q^{85} -5.95407 q^{86} -1.80642i q^{87} +3.06668i q^{88} -0.622216 q^{89} +(-2.68889 + 0.377784i) q^{90} +20.3368 q^{91} -2.10171i q^{92} +2.62222i q^{93} +8.56199 q^{94} +(1.61285 + 11.4795i) q^{95} +2.88739 q^{96} -2.75557i q^{97} +20.6938i q^{98} +1.00000 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$6 q - 10 q^{4} + 2 q^{5} - 6 q^{6} - 6 q^{9}+O(q^{10})$$ 6 * q - 10 * q^4 + 2 * q^5 - 6 * q^6 - 6 * q^9 $$6 q - 10 q^{4} + 2 q^{5} - 6 q^{6} - 6 q^{9} + 16 q^{10} - 6 q^{11} - 4 q^{14} + 10 q^{16} + 4 q^{19} + 14 q^{20} - 16 q^{21} + 18 q^{24} - 2 q^{25} - 16 q^{26} + 16 q^{29} + 2 q^{30} + 16 q^{31} - 52 q^{34} - 12 q^{35} + 10 q^{36} + 12 q^{39} - 12 q^{40} - 16 q^{41} + 10 q^{44} - 2 q^{45} + 24 q^{46} - 22 q^{49} - 16 q^{50} - 8 q^{51} + 6 q^{54} - 2 q^{55} + 76 q^{56} + 16 q^{59} - 20 q^{60} + 4 q^{61} - 66 q^{64} + 28 q^{65} + 6 q^{66} + 24 q^{69} + 24 q^{70} - 24 q^{71} + 16 q^{74} - 8 q^{75} - 36 q^{76} + 12 q^{79} - 58 q^{80} + 6 q^{81} + 24 q^{84} + 44 q^{85} + 4 q^{86} - 4 q^{89} - 16 q^{90} + 16 q^{91} + 24 q^{94} - 44 q^{95} - 22 q^{96} + 6 q^{99}+O(q^{100})$$ 6 * q - 10 * q^4 + 2 * q^5 - 6 * q^6 - 6 * q^9 + 16 * q^10 - 6 * q^11 - 4 * q^14 + 10 * q^16 + 4 * q^19 + 14 * q^20 - 16 * q^21 + 18 * q^24 - 2 * q^25 - 16 * q^26 + 16 * q^29 + 2 * q^30 + 16 * q^31 - 52 * q^34 - 12 * q^35 + 10 * q^36 + 12 * q^39 - 12 * q^40 - 16 * q^41 + 10 * q^44 - 2 * q^45 + 24 * q^46 - 22 * q^49 - 16 * q^50 - 8 * q^51 + 6 * q^54 - 2 * q^55 + 76 * q^56 + 16 * q^59 - 20 * q^60 + 4 * q^61 - 66 * q^64 + 28 * q^65 + 6 * q^66 + 24 * q^69 + 24 * q^70 - 24 * q^71 + 16 * q^74 - 8 * q^75 - 36 * q^76 + 12 * q^79 - 58 * q^80 + 6 * q^81 + 24 * q^84 + 44 * q^85 + 4 * q^86 - 4 * q^89 - 16 * q^90 + 16 * q^91 + 24 * q^94 - 44 * q^95 - 22 * q^96 + 6 * q^99

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/165\mathbb{Z}\right)^\times$$.

 $$n$$ $$46$$ $$56$$ $$67$$ $$\chi(n)$$ $$1$$ $$1$$ $$-1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 1.21432i 0.858654i −0.903149 0.429327i $$-0.858751\pi$$
0.903149 0.429327i $$-0.141249\pi$$
$$3$$ 1.00000i 0.577350i
$$4$$ 0.525428 0.262714
$$5$$ 0.311108 + 2.21432i 0.139132 + 0.990274i
$$6$$ 1.21432 0.495744
$$7$$ 4.90321i 1.85324i 0.375999 + 0.926620i $$0.377300\pi$$
−0.375999 + 0.926620i $$0.622700\pi$$
$$8$$ 3.06668i 1.08423i
$$9$$ −1.00000 −0.333333
$$10$$ 2.68889 0.377784i 0.850302 0.119466i
$$11$$ −1.00000 −0.301511
$$12$$ 0.525428i 0.151678i
$$13$$ 4.14764i 1.15035i −0.818031 0.575175i $$-0.804934\pi$$
0.818031 0.575175i $$-0.195066\pi$$
$$14$$ 5.95407 1.59129
$$15$$ −2.21432 + 0.311108i −0.571735 + 0.0803277i
$$16$$ −2.67307 −0.668268
$$17$$ 5.33185i 1.29316i −0.762845 0.646582i $$-0.776198\pi$$
0.762845 0.646582i $$-0.223802\pi$$
$$18$$ 1.21432i 0.286218i
$$19$$ 5.18421 1.18934 0.594669 0.803970i $$-0.297283\pi$$
0.594669 + 0.803970i $$0.297283\pi$$
$$20$$ 0.163465 + 1.16346i 0.0365518 + 0.260159i
$$21$$ −4.90321 −1.06997
$$22$$ 1.21432i 0.258894i
$$23$$ 4.00000i 0.834058i −0.908893 0.417029i $$-0.863071\pi$$
0.908893 0.417029i $$-0.136929\pi$$
$$24$$ 3.06668 0.625983
$$25$$ −4.80642 + 1.37778i −0.961285 + 0.275557i
$$26$$ −5.03657 −0.987752
$$27$$ 1.00000i 0.192450i
$$28$$ 2.57628i 0.486872i
$$29$$ −1.80642 −0.335444 −0.167722 0.985834i $$-0.553641\pi$$
−0.167722 + 0.985834i $$0.553641\pi$$
$$30$$ 0.377784 + 2.68889i 0.0689737 + 0.490922i
$$31$$ 2.62222 0.470964 0.235482 0.971879i $$-0.424333\pi$$
0.235482 + 0.971879i $$0.424333\pi$$
$$32$$ 2.88739i 0.510423i
$$33$$ 1.00000i 0.174078i
$$34$$ −6.47457 −1.11038
$$35$$ −10.8573 + 1.52543i −1.83522 + 0.257844i
$$36$$ −0.525428 −0.0875713
$$37$$ 5.80642i 0.954570i 0.878749 + 0.477285i $$0.158379\pi$$
−0.878749 + 0.477285i $$0.841621\pi$$
$$38$$ 6.29529i 1.02123i
$$39$$ 4.14764 0.664154
$$40$$ 6.79060 0.954067i 1.07369 0.150851i
$$41$$ 1.80642 0.282116 0.141058 0.990001i $$-0.454950\pi$$
0.141058 + 0.990001i $$0.454950\pi$$
$$42$$ 5.95407i 0.918732i
$$43$$ 4.90321i 0.747733i −0.927483 0.373866i $$-0.878032\pi$$
0.927483 0.373866i $$-0.121968\pi$$
$$44$$ −0.525428 −0.0792112
$$45$$ −0.311108 2.21432i −0.0463772 0.330091i
$$46$$ −4.85728 −0.716167
$$47$$ 7.05086i 1.02847i 0.857648 + 0.514236i $$0.171925\pi$$
−0.857648 + 0.514236i $$0.828075\pi$$
$$48$$ 2.67307i 0.385825i
$$49$$ −17.0415 −2.43450
$$50$$ 1.67307 + 5.83654i 0.236608 + 0.825411i
$$51$$ 5.33185 0.746609
$$52$$ 2.17929i 0.302213i
$$53$$ 7.18421i 0.986827i 0.869795 + 0.493413i $$0.164251\pi$$
−0.869795 + 0.493413i $$0.835749\pi$$
$$54$$ −1.21432 −0.165248
$$55$$ −0.311108 2.21432i −0.0419498 0.298579i
$$56$$ 15.0366 2.00935
$$57$$ 5.18421i 0.686665i
$$58$$ 2.19358i 0.288031i
$$59$$ −1.67307 −0.217815 −0.108908 0.994052i $$-0.534735\pi$$
−0.108908 + 0.994052i $$0.534735\pi$$
$$60$$ −1.16346 + 0.163465i −0.150203 + 0.0211032i
$$61$$ 0.755569 0.0967407 0.0483703 0.998829i $$-0.484597\pi$$
0.0483703 + 0.998829i $$0.484597\pi$$
$$62$$ 3.18421i 0.404395i
$$63$$ 4.90321i 0.617747i
$$64$$ −8.85236 −1.10654
$$65$$ 9.18421 1.29036i 1.13916 0.160050i
$$66$$ −1.21432 −0.149472
$$67$$ 4.85728i 0.593411i −0.954969 0.296706i $$-0.904112\pi$$
0.954969 0.296706i $$-0.0958880\pi$$
$$68$$ 2.80150i 0.339732i
$$69$$ 4.00000 0.481543
$$70$$ 1.85236 + 13.1842i 0.221399 + 1.57581i
$$71$$ 0.428639 0.0508701 0.0254351 0.999676i $$-0.491903\pi$$
0.0254351 + 0.999676i $$0.491903\pi$$
$$72$$ 3.06668i 0.361411i
$$73$$ 12.7096i 1.48755i −0.668430 0.743775i $$-0.733033\pi$$
0.668430 0.743775i $$-0.266967\pi$$
$$74$$ 7.05086 0.819645
$$75$$ −1.37778 4.80642i −0.159093 0.554998i
$$76$$ 2.72393 0.312456
$$77$$ 4.90321i 0.558773i
$$78$$ 5.03657i 0.570279i
$$79$$ 6.42864 0.723278 0.361639 0.932318i $$-0.382217\pi$$
0.361639 + 0.932318i $$0.382217\pi$$
$$80$$ −0.831613 5.91903i −0.0929772 0.661768i
$$81$$ 1.00000 0.111111
$$82$$ 2.19358i 0.242240i
$$83$$ 2.90321i 0.318669i 0.987225 + 0.159334i $$0.0509348\pi$$
−0.987225 + 0.159334i $$0.949065\pi$$
$$84$$ −2.57628 −0.281095
$$85$$ 11.8064 1.65878i 1.28059 0.179920i
$$86$$ −5.95407 −0.642044
$$87$$ 1.80642i 0.193669i
$$88$$ 3.06668i 0.326909i
$$89$$ −0.622216 −0.0659547 −0.0329774 0.999456i $$-0.510499\pi$$
−0.0329774 + 0.999456i $$0.510499\pi$$
$$90$$ −2.68889 + 0.377784i −0.283434 + 0.0398220i
$$91$$ 20.3368 2.13187
$$92$$ 2.10171i 0.219118i
$$93$$ 2.62222i 0.271911i
$$94$$ 8.56199 0.883102
$$95$$ 1.61285 + 11.4795i 0.165475 + 1.17777i
$$96$$ 2.88739 0.294693
$$97$$ 2.75557i 0.279786i −0.990167 0.139893i $$-0.955324\pi$$
0.990167 0.139893i $$-0.0446758\pi$$
$$98$$ 20.6938i 2.09039i
$$99$$ 1.00000 0.100504
$$100$$ −2.52543 + 0.723926i −0.252543 + 0.0723926i
$$101$$ −17.8064 −1.77181 −0.885903 0.463871i $$-0.846460\pi$$
−0.885903 + 0.463871i $$0.846460\pi$$
$$102$$ 6.47457i 0.641078i
$$103$$ 4.94914i 0.487654i −0.969819 0.243827i $$-0.921597\pi$$
0.969819 0.243827i $$-0.0784029\pi$$
$$104$$ −12.7195 −1.24725
$$105$$ −1.52543 10.8573i −0.148866 1.05956i
$$106$$ 8.72393 0.847343
$$107$$ 11.1985i 1.08260i 0.840830 + 0.541300i $$0.182068\pi$$
−0.840830 + 0.541300i $$0.817932\pi$$
$$108$$ 0.525428i 0.0505593i
$$109$$ −15.7146 −1.50518 −0.752591 0.658488i $$-0.771196\pi$$
−0.752591 + 0.658488i $$0.771196\pi$$
$$110$$ −2.68889 + 0.377784i −0.256376 + 0.0360203i
$$111$$ −5.80642 −0.551121
$$112$$ 13.1066i 1.23846i
$$113$$ 1.76494i 0.166031i 0.996548 + 0.0830156i $$0.0264551\pi$$
−0.996548 + 0.0830156i $$0.973545\pi$$
$$114$$ 6.29529 0.589608
$$115$$ 8.85728 1.24443i 0.825946 0.116044i
$$116$$ −0.949145 −0.0881259
$$117$$ 4.14764i 0.383450i
$$118$$ 2.03164i 0.187028i
$$119$$ 26.1432 2.39654
$$120$$ 0.954067 + 6.79060i 0.0870940 + 0.619894i
$$121$$ 1.00000 0.0909091
$$122$$ 0.917502i 0.0830667i
$$123$$ 1.80642i 0.162880i
$$124$$ 1.37778 0.123729
$$125$$ −4.54617 10.2143i −0.406622 0.913597i
$$126$$ −5.95407 −0.530430
$$127$$ 18.7096i 1.66021i 0.557606 + 0.830106i $$0.311720\pi$$
−0.557606 + 0.830106i $$0.688280\pi$$
$$128$$ 4.97481i 0.439715i
$$129$$ 4.90321 0.431704
$$130$$ −1.56691 11.1526i −0.137428 0.978145i
$$131$$ −1.24443 −0.108726 −0.0543632 0.998521i $$-0.517313\pi$$
−0.0543632 + 0.998521i $$0.517313\pi$$
$$132$$ 0.525428i 0.0457326i
$$133$$ 25.4193i 2.20413i
$$134$$ −5.89829 −0.509535
$$135$$ 2.21432 0.311108i 0.190578 0.0267759i
$$136$$ −16.3511 −1.40209
$$137$$ 18.7971i 1.60594i 0.596019 + 0.802970i $$0.296748\pi$$
−0.596019 + 0.802970i $$0.703252\pi$$
$$138$$ 4.85728i 0.413479i
$$139$$ −14.0415 −1.19098 −0.595492 0.803361i $$-0.703043\pi$$
−0.595492 + 0.803361i $$0.703043\pi$$
$$140$$ −5.70471 + 0.801502i −0.482136 + 0.0677393i
$$141$$ −7.05086 −0.593789
$$142$$ 0.520505i 0.0436798i
$$143$$ 4.14764i 0.346843i
$$144$$ 2.67307 0.222756
$$145$$ −0.561993 4.00000i −0.0466709 0.332182i
$$146$$ −15.4336 −1.27729
$$147$$ 17.0415i 1.40556i
$$148$$ 3.05086i 0.250779i
$$149$$ 3.05086 0.249936 0.124968 0.992161i $$-0.460117\pi$$
0.124968 + 0.992161i $$0.460117\pi$$
$$150$$ −5.83654 + 1.67307i −0.476551 + 0.136606i
$$151$$ −0.326929 −0.0266051 −0.0133026 0.999912i $$-0.504234\pi$$
−0.0133026 + 0.999912i $$0.504234\pi$$
$$152$$ 15.8983i 1.28952i
$$153$$ 5.33185i 0.431055i
$$154$$ −5.95407 −0.479792
$$155$$ 0.815792 + 5.80642i 0.0655260 + 0.466383i
$$156$$ 2.17929 0.174483
$$157$$ 19.9081i 1.58884i −0.607367 0.794421i $$-0.707774\pi$$
0.607367 0.794421i $$-0.292226\pi$$
$$158$$ 7.80642i 0.621046i
$$159$$ −7.18421 −0.569745
$$160$$ 6.39361 0.898290i 0.505459 0.0710160i
$$161$$ 19.6128 1.54571
$$162$$ 1.21432i 0.0954060i
$$163$$ 12.1748i 0.953607i −0.879010 0.476804i $$-0.841795\pi$$
0.879010 0.476804i $$-0.158205\pi$$
$$164$$ 0.949145 0.0741158
$$165$$ 2.21432 0.311108i 0.172385 0.0242197i
$$166$$ 3.52543 0.273626
$$167$$ 13.0049i 1.00635i 0.864184 + 0.503176i $$0.167835\pi$$
−0.864184 + 0.503176i $$0.832165\pi$$
$$168$$ 15.0366i 1.16010i
$$169$$ −4.20294 −0.323303
$$170$$ −2.01429 14.3368i −0.154489 1.09958i
$$171$$ −5.18421 −0.396446
$$172$$ 2.57628i 0.196440i
$$173$$ 13.8938i 1.05633i −0.849142 0.528165i $$-0.822880\pi$$
0.849142 0.528165i $$-0.177120\pi$$
$$174$$ −2.19358 −0.166295
$$175$$ −6.75557 23.5669i −0.510673 1.78149i
$$176$$ 2.67307 0.201490
$$177$$ 1.67307i 0.125756i
$$178$$ 0.755569i 0.0566323i
$$179$$ −12.8573 −0.960998 −0.480499 0.876995i $$-0.659544\pi$$
−0.480499 + 0.876995i $$0.659544\pi$$
$$180$$ −0.163465 1.16346i −0.0121839 0.0867195i
$$181$$ 0.917502 0.0681974 0.0340987 0.999418i $$-0.489144\pi$$
0.0340987 + 0.999418i $$0.489144\pi$$
$$182$$ 24.6953i 1.83054i
$$183$$ 0.755569i 0.0558532i
$$184$$ −12.2667 −0.904314
$$185$$ −12.8573 + 1.80642i −0.945286 + 0.132811i
$$186$$ 3.18421 0.233477
$$187$$ 5.33185i 0.389904i
$$188$$ 3.70471i 0.270194i
$$189$$ 4.90321 0.356656
$$190$$ 13.9398 1.95851i 1.01130 0.142085i
$$191$$ 14.3684 1.03966 0.519831 0.854269i $$-0.325995\pi$$
0.519831 + 0.854269i $$0.325995\pi$$
$$192$$ 8.85236i 0.638864i
$$193$$ 11.7605i 0.846539i 0.906004 + 0.423269i $$0.139118\pi$$
−0.906004 + 0.423269i $$0.860882\pi$$
$$194$$ −3.34614 −0.240239
$$195$$ 1.29036 + 9.18421i 0.0924049 + 0.657695i
$$196$$ −8.95407 −0.639576
$$197$$ 3.82071i 0.272215i −0.990694 0.136107i $$-0.956541\pi$$
0.990694 0.136107i $$-0.0434592\pi$$
$$198$$ 1.21432i 0.0862979i
$$199$$ 13.7146 0.972199 0.486100 0.873903i $$-0.338419\pi$$
0.486100 + 0.873903i $$0.338419\pi$$
$$200$$ 4.22522 + 14.7397i 0.298768 + 1.04226i
$$201$$ 4.85728 0.342606
$$202$$ 21.6227i 1.52137i
$$203$$ 8.85728i 0.621659i
$$204$$ 2.80150 0.196144
$$205$$ 0.561993 + 4.00000i 0.0392513 + 0.279372i
$$206$$ −6.00984 −0.418726
$$207$$ 4.00000i 0.278019i
$$208$$ 11.0869i 0.768741i
$$209$$ −5.18421 −0.358599
$$210$$ −13.1842 + 1.85236i −0.909797 + 0.127825i
$$211$$ 1.95851 0.134830 0.0674148 0.997725i $$-0.478525\pi$$
0.0674148 + 0.997725i $$0.478525\pi$$
$$212$$ 3.77478i 0.259253i
$$213$$ 0.428639i 0.0293699i
$$214$$ 13.5986 0.929578
$$215$$ 10.8573 1.52543i 0.740460 0.104033i
$$216$$ −3.06668 −0.208661
$$217$$ 12.8573i 0.872809i
$$218$$ 19.0825i 1.29243i
$$219$$ 12.7096 0.858838
$$220$$ −0.163465 1.16346i −0.0110208 0.0784408i
$$221$$ −22.1146 −1.48759
$$222$$ 7.05086i 0.473222i
$$223$$ 26.0098i 1.74175i 0.491506 + 0.870874i $$0.336446\pi$$
−0.491506 + 0.870874i $$0.663554\pi$$
$$224$$ 14.1575 0.945937
$$225$$ 4.80642 1.37778i 0.320428 0.0918523i
$$226$$ 2.14320 0.142563
$$227$$ 6.34122i 0.420882i −0.977607 0.210441i $$-0.932510\pi$$
0.977607 0.210441i $$-0.0674899\pi$$
$$228$$ 2.72393i 0.180396i
$$229$$ 23.3274 1.54152 0.770759 0.637127i $$-0.219877\pi$$
0.770759 + 0.637127i $$0.219877\pi$$
$$230$$ −1.51114 10.7556i −0.0996415 0.709201i
$$231$$ 4.90321 0.322608
$$232$$ 5.53972i 0.363700i
$$233$$ 1.42372i 0.0932708i 0.998912 + 0.0466354i $$0.0148499\pi$$
−0.998912 + 0.0466354i $$0.985150\pi$$
$$234$$ 5.03657 0.329251
$$235$$ −15.6128 + 2.19358i −1.01847 + 0.143093i
$$236$$ −0.879077 −0.0572231
$$237$$ 6.42864i 0.417585i
$$238$$ 31.7462i 2.05780i
$$239$$ 18.9590 1.22636 0.613178 0.789945i $$-0.289891\pi$$
0.613178 + 0.789945i $$0.289891\pi$$
$$240$$ 5.91903 0.831613i 0.382072 0.0536804i
$$241$$ −1.34614 −0.0867126 −0.0433563 0.999060i $$-0.513805\pi$$
−0.0433563 + 0.999060i $$0.513805\pi$$
$$242$$ 1.21432i 0.0780594i
$$243$$ 1.00000i 0.0641500i
$$244$$ 0.396997 0.0254151
$$245$$ −5.30174 37.7353i −0.338716 2.41082i
$$246$$ 2.19358 0.139857
$$247$$ 21.5022i 1.36816i
$$248$$ 8.04149i 0.510635i
$$249$$ −2.90321 −0.183984
$$250$$ −12.4035 + 5.52051i −0.784463 + 0.349147i
$$251$$ 1.08250 0.0683267 0.0341633 0.999416i $$-0.489123\pi$$
0.0341633 + 0.999416i $$0.489123\pi$$
$$252$$ 2.57628i 0.162291i
$$253$$ 4.00000i 0.251478i
$$254$$ 22.7195 1.42555
$$255$$ 1.65878 + 11.8064i 0.103877 + 0.739347i
$$256$$ −11.6637 −0.728981
$$257$$ 0.133353i 0.00831834i −0.999991 0.00415917i $$-0.998676\pi$$
0.999991 0.00415917i $$-0.00132391\pi$$
$$258$$ 5.95407i 0.370684i
$$259$$ −28.4701 −1.76905
$$260$$ 4.82564 0.677993i 0.299273 0.0420473i
$$261$$ 1.80642 0.111815
$$262$$ 1.51114i 0.0933584i
$$263$$ 0.147643i 0.00910407i 0.999990 + 0.00455203i $$0.00144896\pi$$
−0.999990 + 0.00455203i $$0.998551\pi$$
$$264$$ −3.06668 −0.188741
$$265$$ −15.9081 + 2.23506i −0.977229 + 0.137299i
$$266$$ 30.8671 1.89258
$$267$$ 0.622216i 0.0380790i
$$268$$ 2.55215i 0.155897i
$$269$$ 26.8573 1.63752 0.818759 0.574138i $$-0.194663\pi$$
0.818759 + 0.574138i $$0.194663\pi$$
$$270$$ −0.377784 2.68889i −0.0229912 0.163641i
$$271$$ 3.08250 0.187248 0.0936242 0.995608i $$-0.470155\pi$$
0.0936242 + 0.995608i $$0.470155\pi$$
$$272$$ 14.2524i 0.864180i
$$273$$ 20.3368i 1.23084i
$$274$$ 22.8256 1.37895
$$275$$ 4.80642 1.37778i 0.289838 0.0830835i
$$276$$ 2.10171 0.126508
$$277$$ 8.70964i 0.523311i −0.965161 0.261656i $$-0.915732\pi$$
0.965161 0.261656i $$-0.0842685\pi$$
$$278$$ 17.0509i 1.02264i
$$279$$ −2.62222 −0.156988
$$280$$ 4.67799 + 33.2958i 0.279564 + 1.98980i
$$281$$ −20.3783 −1.21567 −0.607833 0.794065i $$-0.707961\pi$$
−0.607833 + 0.794065i $$0.707961\pi$$
$$282$$ 8.56199i 0.509859i
$$283$$ 6.32248i 0.375833i 0.982185 + 0.187916i $$0.0601734\pi$$
−0.982185 + 0.187916i $$0.939827\pi$$
$$284$$ 0.225219 0.0133643
$$285$$ −11.4795 + 1.61285i −0.679987 + 0.0955369i
$$286$$ 5.03657 0.297818
$$287$$ 8.85728i 0.522829i
$$288$$ 2.88739i 0.170141i
$$289$$ −11.4286 −0.672273
$$290$$ −4.85728 + 0.682439i −0.285229 + 0.0400742i
$$291$$ 2.75557 0.161534
$$292$$ 6.67799i 0.390800i
$$293$$ 16.6780i 0.974339i −0.873308 0.487169i $$-0.838029\pi$$
0.873308 0.487169i $$-0.161971\pi$$
$$294$$ −20.6938 −1.20689
$$295$$ −0.520505 3.70471i −0.0303050 0.215697i
$$296$$ 17.8064 1.03498
$$297$$ 1.00000i 0.0580259i
$$298$$ 3.70471i 0.214608i
$$299$$ −16.5906 −0.959458
$$300$$ −0.723926 2.52543i −0.0417959 0.145806i
$$301$$ 24.0415 1.38573
$$302$$ 0.396997i 0.0228446i
$$303$$ 17.8064i 1.02295i
$$304$$ −13.8578 −0.794797
$$305$$ 0.235063 + 1.67307i 0.0134597 + 0.0957998i
$$306$$ 6.47457 0.370127
$$307$$ 9.58565i 0.547082i −0.961860 0.273541i $$-0.911805\pi$$
0.961860 0.273541i $$-0.0881949\pi$$
$$308$$ 2.57628i 0.146797i
$$309$$ 4.94914 0.281547
$$310$$ 7.05086 0.990632i 0.400462 0.0562641i
$$311$$ 14.5303 0.823941 0.411970 0.911197i $$-0.364841\pi$$
0.411970 + 0.911197i $$0.364841\pi$$
$$312$$ 12.7195i 0.720099i
$$313$$ 21.0321i 1.18881i 0.804167 + 0.594403i $$0.202612\pi$$
−0.804167 + 0.594403i $$0.797388\pi$$
$$314$$ −24.1748 −1.36427
$$315$$ 10.8573 1.52543i 0.611738 0.0859481i
$$316$$ 3.37778 0.190015
$$317$$ 0.990632i 0.0556394i −0.999613 0.0278197i $$-0.991144\pi$$
0.999613 0.0278197i $$-0.00885643\pi$$
$$318$$ 8.72393i 0.489213i
$$319$$ 1.80642 0.101140
$$320$$ −2.75404 19.6019i −0.153955 1.09578i
$$321$$ −11.1985 −0.625039
$$322$$ 23.8163i 1.32723i
$$323$$ 27.6414i 1.53801i
$$324$$ 0.525428 0.0291904
$$325$$ 5.71456 + 19.9353i 0.316987 + 1.10581i
$$326$$ −14.7841 −0.818818
$$327$$ 15.7146i 0.869017i
$$328$$ 5.53972i 0.305880i
$$329$$ −34.5718 −1.90601
$$330$$ −0.377784 2.68889i −0.0207963 0.148019i
$$331$$ −17.5812 −0.966350 −0.483175 0.875524i $$-0.660517\pi$$
−0.483175 + 0.875524i $$0.660517\pi$$
$$332$$ 1.52543i 0.0837187i
$$333$$ 5.80642i 0.318190i
$$334$$ 15.7921 0.864107
$$335$$ 10.7556 1.51114i 0.587639 0.0825623i
$$336$$ 13.1066 0.715025
$$337$$ 3.16992i 0.172676i −0.996266 0.0863382i $$-0.972483\pi$$
0.996266 0.0863382i $$-0.0275166\pi$$
$$338$$ 5.10372i 0.277606i
$$339$$ −1.76494 −0.0958582
$$340$$ 6.20342 0.871569i 0.336428 0.0472675i
$$341$$ −2.62222 −0.142001
$$342$$ 6.29529i 0.340410i
$$343$$ 49.2355i 2.65847i
$$344$$ −15.0366 −0.810717
$$345$$ 1.24443 + 8.85728i 0.0669979 + 0.476860i
$$346$$ −16.8716 −0.907021
$$347$$ 4.97634i 0.267144i 0.991039 + 0.133572i $$0.0426447\pi$$
−0.991039 + 0.133572i $$0.957355\pi$$
$$348$$ 0.949145i 0.0508795i
$$349$$ −18.2034 −0.974407 −0.487203 0.873289i $$-0.661983\pi$$
−0.487203 + 0.873289i $$0.661983\pi$$
$$350$$ −28.6178 + 8.20342i −1.52968 + 0.438491i
$$351$$ −4.14764 −0.221385
$$352$$ 2.88739i 0.153898i
$$353$$ 22.4099i 1.19276i −0.802703 0.596379i $$-0.796605\pi$$
0.802703 0.596379i $$-0.203395\pi$$
$$354$$ −2.03164 −0.107981
$$355$$ 0.133353 + 0.949145i 0.00707765 + 0.0503754i
$$356$$ −0.326929 −0.0173272
$$357$$ 26.1432i 1.38364i
$$358$$ 15.6128i 0.825165i
$$359$$ −21.3274 −1.12562 −0.562809 0.826587i $$-0.690279\pi$$
−0.562809 + 0.826587i $$0.690279\pi$$
$$360$$ −6.79060 + 0.954067i −0.357896 + 0.0502837i
$$361$$ 7.87601 0.414527
$$362$$ 1.11414i 0.0585579i
$$363$$ 1.00000i 0.0524864i
$$364$$ 10.6855 0.560072
$$365$$ 28.1432 3.95407i 1.47308 0.206965i
$$366$$ 0.917502 0.0479586
$$367$$ 35.1338i 1.83397i 0.398921 + 0.916985i $$0.369385\pi$$
−0.398921 + 0.916985i $$0.630615\pi$$
$$368$$ 10.6923i 0.557374i
$$369$$ −1.80642 −0.0940387
$$370$$ 2.19358 + 15.6128i 0.114039 + 0.811673i
$$371$$ −35.2257 −1.82883
$$372$$ 1.37778i 0.0714348i
$$373$$ 17.0049i 0.880481i 0.897880 + 0.440241i $$0.145107\pi$$
−0.897880 + 0.440241i $$0.854893\pi$$
$$374$$ 6.47457 0.334792
$$375$$ 10.2143 4.54617i 0.527465 0.234763i
$$376$$ 21.6227 1.11511
$$377$$ 7.49240i 0.385878i
$$378$$ 5.95407i 0.306244i
$$379$$ −2.36842 −0.121657 −0.0608287 0.998148i $$-0.519374\pi$$
−0.0608287 + 0.998148i $$0.519374\pi$$
$$380$$ 0.847435 + 6.03164i 0.0434725 + 0.309417i
$$381$$ −18.7096 −0.958524
$$382$$ 17.4479i 0.892710i
$$383$$ 1.21585i 0.0621271i −0.999517 0.0310635i $$-0.990111\pi$$
0.999517 0.0310635i $$-0.00988942\pi$$
$$384$$ −4.97481 −0.253870
$$385$$ 10.8573 1.52543i 0.553338 0.0777430i
$$386$$ 14.2810 0.726884
$$387$$ 4.90321i 0.249244i
$$388$$ 1.44785i 0.0735035i
$$389$$ −2.26671 −0.114927 −0.0574633 0.998348i $$-0.518301\pi$$
−0.0574633 + 0.998348i $$0.518301\pi$$
$$390$$ 11.1526 1.56691i 0.564732 0.0793438i
$$391$$ −21.3274 −1.07857
$$392$$ 52.2607i 2.63957i
$$393$$ 1.24443i 0.0627733i
$$394$$ −4.63957 −0.233738
$$395$$ 2.00000 + 14.2351i 0.100631 + 0.716244i
$$396$$ 0.525428 0.0264037
$$397$$ 18.4889i 0.927929i −0.885854 0.463965i $$-0.846426\pi$$
0.885854 0.463965i $$-0.153574\pi$$
$$398$$ 16.6539i 0.834782i
$$399$$ −25.4193 −1.27256
$$400$$ 12.8479 3.68292i 0.642396 0.184146i
$$401$$ 17.5625 0.877028 0.438514 0.898724i $$-0.355505\pi$$
0.438514 + 0.898724i $$0.355505\pi$$
$$402$$ 5.89829i 0.294180i
$$403$$ 10.8760i 0.541773i
$$404$$ −9.35599 −0.465478
$$405$$ 0.311108 + 2.21432i 0.0154591 + 0.110030i
$$406$$ −10.7556 −0.533790
$$407$$ 5.80642i 0.287814i
$$408$$ 16.3511i 0.809498i
$$409$$ 21.3461 1.05550 0.527749 0.849400i $$-0.323036\pi$$
0.527749 + 0.849400i $$0.323036\pi$$
$$410$$ 4.85728 0.682439i 0.239884 0.0337032i
$$411$$ −18.7971 −0.927190
$$412$$ 2.60042i 0.128113i
$$413$$ 8.20342i 0.403664i
$$414$$ 4.85728 0.238722
$$415$$ −6.42864 + 0.903212i −0.315570 + 0.0443369i
$$416$$ −11.9759 −0.587165
$$417$$ 14.0415i 0.687615i
$$418$$ 6.29529i 0.307913i
$$419$$ −28.8573 −1.40977 −0.704885 0.709321i $$-0.749001\pi$$
−0.704885 + 0.709321i $$0.749001\pi$$
$$420$$ −0.801502 5.70471i −0.0391093 0.278362i
$$421$$ −35.4893 −1.72964 −0.864822 0.502078i $$-0.832569\pi$$
−0.864822 + 0.502078i $$0.832569\pi$$
$$422$$ 2.37826i 0.115772i
$$423$$ 7.05086i 0.342824i
$$424$$ 22.0316 1.06995
$$425$$ 7.34614 + 25.6271i 0.356340 + 1.24310i
$$426$$ 0.520505 0.0252186
$$427$$ 3.70471i 0.179284i
$$428$$ 5.88400i 0.284414i
$$429$$ −4.14764 −0.200250
$$430$$ −1.85236 13.1842i −0.0893286 0.635799i
$$431$$ 9.24443 0.445289 0.222644 0.974900i $$-0.428531\pi$$
0.222644 + 0.974900i $$0.428531\pi$$
$$432$$ 2.67307i 0.128608i
$$433$$ 6.28544i 0.302059i 0.988529 + 0.151030i $$0.0482589\pi$$
−0.988529 + 0.151030i $$0.951741\pi$$
$$434$$ 15.6128 0.749441
$$435$$ 4.00000 0.561993i 0.191785 0.0269455i
$$436$$ −8.25686 −0.395432
$$437$$ 20.7368i 0.991977i
$$438$$ 15.4336i 0.737444i
$$439$$ 36.5303 1.74350 0.871749 0.489952i $$-0.162986\pi$$
0.871749 + 0.489952i $$0.162986\pi$$
$$440$$ −6.79060 + 0.954067i −0.323729 + 0.0454834i
$$441$$ 17.0415 0.811499
$$442$$ 26.8542i 1.27732i
$$443$$ 38.2766i 1.81857i 0.416170 + 0.909287i $$0.363372\pi$$
−0.416170 + 0.909287i $$0.636628\pi$$
$$444$$ −3.05086 −0.144787
$$445$$ −0.193576 1.37778i −0.00917639 0.0653132i
$$446$$ 31.5843 1.49556
$$447$$ 3.05086i 0.144300i
$$448$$ 43.4050i 2.05069i
$$449$$ 31.8479 1.50300 0.751498 0.659735i $$-0.229332\pi$$
0.751498 + 0.659735i $$0.229332\pi$$
$$450$$ −1.67307 5.83654i −0.0788693 0.275137i
$$451$$ −1.80642 −0.0850612
$$452$$ 0.927346i 0.0436187i
$$453$$ 0.326929i 0.0153605i
$$454$$ −7.70027 −0.361391
$$455$$ 6.32693 + 45.0321i 0.296611 + 2.11114i
$$456$$ 15.8983 0.744506
$$457$$ 1.39207i 0.0651185i 0.999470 + 0.0325592i $$0.0103658\pi$$
−0.999470 + 0.0325592i $$0.989634\pi$$
$$458$$ 28.3269i 1.32363i
$$459$$ −5.33185 −0.248870
$$460$$ 4.65386 0.653858i 0.216987 0.0304863i
$$461$$ −7.70471 −0.358844 −0.179422 0.983772i $$-0.557423\pi$$
−0.179422 + 0.983772i $$0.557423\pi$$
$$462$$ 5.95407i 0.277008i
$$463$$ 4.68244i 0.217611i −0.994063 0.108806i $$-0.965297\pi$$
0.994063 0.108806i $$-0.0347026\pi$$
$$464$$ 4.82870 0.224167
$$465$$ −5.80642 + 0.815792i −0.269266 + 0.0378314i
$$466$$ 1.72885 0.0800873
$$467$$ 12.8573i 0.594964i 0.954727 + 0.297482i $$0.0961468\pi$$
−0.954727 + 0.297482i $$0.903853\pi$$
$$468$$ 2.17929i 0.100738i
$$469$$ 23.8163 1.09973
$$470$$ 2.66370 + 18.9590i 0.122867 + 0.874513i
$$471$$ 19.9081 0.917318
$$472$$ 5.13077i 0.236163i
$$473$$ 4.90321i 0.225450i
$$474$$ 7.80642 0.358561
$$475$$ −24.9175 + 7.14272i −1.14329 + 0.327731i
$$476$$ 13.7364 0.629605
$$477$$ 7.18421i 0.328942i
$$478$$ 23.0223i 1.05301i
$$479$$ −8.38715 −0.383219 −0.191609 0.981471i $$-0.561371\pi$$
−0.191609 + 0.981471i $$0.561371\pi$$
$$480$$ 0.898290 + 6.39361i 0.0410011 + 0.291827i
$$481$$ 24.0830 1.09809
$$482$$ 1.63465i 0.0744561i
$$483$$ 19.6128i 0.892415i
$$484$$ 0.525428 0.0238831
$$485$$ 6.10171 0.857279i 0.277064 0.0389270i
$$486$$ 1.21432 0.0550827
$$487$$ 9.83500i 0.445667i 0.974857 + 0.222833i $$0.0715306\pi$$
−0.974857 + 0.222833i $$0.928469\pi$$
$$488$$ 2.31708i 0.104890i
$$489$$ 12.1748 0.550565
$$490$$ −45.8227 + 6.43801i −2.07006 + 0.290840i
$$491$$ −32.9403 −1.48657 −0.743286 0.668973i $$-0.766734\pi$$
−0.743286 + 0.668973i $$0.766734\pi$$
$$492$$ 0.949145i 0.0427908i
$$493$$ 9.63158i 0.433785i
$$494$$ −26.1106 −1.17477
$$495$$ 0.311108 + 2.21432i 0.0139833 + 0.0995263i
$$496$$ −7.00937 −0.314730
$$497$$ 2.10171i 0.0942746i
$$498$$ 3.52543i 0.157978i
$$499$$ 1.63158 0.0730397 0.0365199 0.999333i $$-0.488373\pi$$
0.0365199 + 0.999333i $$0.488373\pi$$
$$500$$ −2.38868 5.36689i −0.106825 0.240014i
$$501$$ −13.0049 −0.581017
$$502$$ 1.31450i 0.0586689i
$$503$$ 41.8622i 1.86654i −0.359171 0.933272i $$-0.616941\pi$$
0.359171 0.933272i $$-0.383059\pi$$
$$504$$ −15.0366 −0.669782
$$505$$ −5.53972 39.4291i −0.246514 1.75457i
$$506$$ 4.85728 0.215932
$$507$$ 4.20294i 0.186659i
$$508$$ 9.83056i 0.436160i
$$509$$ 38.8573 1.72232 0.861159 0.508335i $$-0.169739\pi$$
0.861159 + 0.508335i $$0.169739\pi$$
$$510$$ 14.3368 2.01429i 0.634843 0.0891943i
$$511$$ 62.3180 2.75679
$$512$$ 24.1131i 1.06566i
$$513$$ 5.18421i 0.228888i
$$514$$ −0.161933 −0.00714257
$$515$$ 10.9590 1.53972i 0.482911 0.0678481i
$$516$$ 2.57628 0.113415
$$517$$ 7.05086i 0.310096i
$$518$$ 34.5718i 1.51900i
$$519$$ 13.8938 0.609872
$$520$$ −3.95713 28.1650i −0.173532 1.23512i
$$521$$ 11.1111 0.486785 0.243393 0.969928i $$-0.421740\pi$$
0.243393 + 0.969928i $$0.421740\pi$$
$$522$$ 2.19358i 0.0960102i
$$523$$ 27.3002i 1.19375i −0.802332 0.596877i $$-0.796408\pi$$
0.802332 0.596877i $$-0.203592\pi$$
$$524$$ −0.653858 −0.0285639
$$525$$ 23.5669 6.75557i 1.02854 0.294837i
$$526$$ 0.179286 0.00781724
$$527$$ 13.9813i 0.609033i
$$528$$ 2.67307i 0.116330i
$$529$$ 7.00000 0.304348
$$530$$ 2.71408 + 19.3176i 0.117892 + 0.839101i
$$531$$ 1.67307 0.0726051
$$532$$ 13.3560i 0.579055i
$$533$$ 7.49240i 0.324532i
$$534$$ −0.755569 −0.0326967
$$535$$ −24.7971 + 3.48394i −1.07207 + 0.150624i
$$536$$ −14.8957 −0.643396
$$537$$ 12.8573i 0.554833i
$$538$$ 32.6133i 1.40606i
$$539$$ 17.0415 0.734029
$$540$$ 1.16346 0.163465i 0.0500675 0.00703440i
$$541$$ −16.1017 −0.692267 −0.346133 0.938185i $$-0.612506\pi$$
−0.346133 + 0.938185i $$0.612506\pi$$
$$542$$ 3.74314i 0.160782i
$$543$$ 0.917502i 0.0393738i
$$544$$ −15.3951 −0.660061
$$545$$ −4.88892 34.7971i −0.209418 1.49054i
$$546$$ 24.6953 1.05686
$$547$$ 40.0370i 1.71186i 0.517091 + 0.855930i $$0.327015\pi$$
−0.517091 + 0.855930i $$0.672985\pi$$
$$548$$ 9.87649i 0.421903i
$$549$$ −0.755569 −0.0322469
$$550$$ −1.67307 5.83654i −0.0713400 0.248871i
$$551$$ −9.36488 −0.398957
$$552$$ 12.2667i 0.522106i
$$553$$ 31.5210i 1.34041i
$$554$$ −10.5763 −0.449343
$$555$$ −1.80642 12.8573i −0.0766784 0.545761i
$$556$$ −7.37778 −0.312888
$$557$$ 28.2908i 1.19872i −0.800479 0.599361i $$-0.795422\pi$$
0.800479 0.599361i $$-0.204578\pi$$
$$558$$ 3.18421i 0.134798i
$$559$$ −20.3368 −0.860154
$$560$$ 29.0223 4.07758i 1.22641 0.172309i
$$561$$ −5.33185 −0.225111
$$562$$ 24.7457i 1.04384i
$$563$$ 32.7926i 1.38204i 0.722834 + 0.691022i $$0.242839\pi$$
−0.722834 + 0.691022i $$0.757161\pi$$
$$564$$ −3.70471 −0.155997
$$565$$ −3.90813 + 0.549086i −0.164416 + 0.0231002i
$$566$$ 7.67752 0.322710
$$567$$ 4.90321i 0.205916i
$$568$$ 1.31450i 0.0551551i
$$569$$ 8.88586 0.372515 0.186257 0.982501i $$-0.440364\pi$$
0.186257 + 0.982501i $$0.440364\pi$$
$$570$$ 1.95851 + 13.9398i 0.0820331 + 0.583873i
$$571$$ −10.6953 −0.447586 −0.223793 0.974637i $$-0.571844\pi$$
−0.223793 + 0.974637i $$0.571844\pi$$
$$572$$ 2.17929i 0.0911205i
$$573$$ 14.3684i 0.600249i
$$574$$ 10.7556 0.448929
$$575$$ 5.51114 + 19.2257i 0.229830 + 0.801767i
$$576$$ 8.85236 0.368848
$$577$$ 27.1338i 1.12960i −0.825229 0.564798i $$-0.808954\pi$$
0.825229 0.564798i $$-0.191046\pi$$
$$578$$ 13.8780i 0.577250i
$$579$$ −11.7605 −0.488749
$$580$$ −0.295286 2.10171i −0.0122611 0.0872688i
$$581$$ −14.2351 −0.590570
$$582$$ 3.34614i 0.138702i
$$583$$ 7.18421i 0.297540i
$$584$$ −38.9763 −1.61285
$$585$$ −9.18421 + 1.29036i −0.379720 + 0.0533500i
$$586$$ −20.2524 −0.836620
$$587$$ 10.9590i 0.452326i −0.974089 0.226163i $$-0.927382\pi$$
0.974089 0.226163i $$-0.0726182\pi$$
$$588$$ 8.95407i 0.369260i
$$589$$ 13.5941 0.560136
$$590$$ −4.49871 + 0.632060i −0.185209 + 0.0260215i
$$591$$ 3.82071 0.157163
$$592$$ 15.5210i 0.637908i
$$593$$ 23.7003i 0.973253i 0.873610 + 0.486627i $$0.161773\pi$$
−0.873610 + 0.486627i $$0.838227\pi$$
$$594$$ 1.21432 0.0498241
$$595$$ 8.13335 + 57.8894i 0.333435 + 2.37323i
$$596$$ 1.60300 0.0656616
$$597$$ 13.7146i 0.561299i
$$598$$ 20.1463i 0.823842i
$$599$$ −41.7146 −1.70441 −0.852205 0.523208i $$-0.824735\pi$$
−0.852205 + 0.523208i $$0.824735\pi$$
$$600$$ −14.7397 + 4.22522i −0.601748 + 0.172494i
$$601$$ 14.5906 0.595162 0.297581 0.954697i $$-0.403820\pi$$
0.297581 + 0.954697i $$0.403820\pi$$
$$602$$ 29.1941i 1.18986i
$$603$$ 4.85728i 0.197804i
$$604$$ −0.171778 −0.00698953
$$605$$ 0.311108 + 2.21432i 0.0126483 + 0.0900249i
$$606$$ −21.6227 −0.878362
$$607$$ 19.9826i 0.811071i −0.914079 0.405535i $$-0.867085\pi$$
0.914079 0.405535i $$-0.132915\pi$$
$$608$$ 14.9688i 0.607066i
$$609$$ 8.85728 0.358915
$$610$$ 2.03164 0.285442i 0.0822588 0.0115572i
$$611$$ 29.2444 1.18310
$$612$$ 2.80150i 0.113244i
$$613$$ 19.0781i 0.770555i −0.922801 0.385278i $$-0.874106\pi$$
0.922801 0.385278i $$-0.125894\pi$$
$$614$$ −11.6400 −0.469754
$$615$$ −4.00000 + 0.561993i −0.161296 + 0.0226617i
$$616$$ −15.0366 −0.605840
$$617$$ 39.3590i 1.58454i −0.610174 0.792268i $$-0.708900\pi$$
0.610174 0.792268i $$-0.291100\pi$$
$$618$$ 6.00984i 0.241751i
$$619$$ 23.0923 0.928160 0.464080 0.885793i $$-0.346385\pi$$
0.464080 + 0.885793i $$0.346385\pi$$
$$620$$ 0.428639 + 3.05086i 0.0172146 + 0.122525i
$$621$$ −4.00000 −0.160514
$$622$$ 17.6445i 0.707480i
$$623$$ 3.05086i 0.122230i
$$624$$ −11.0869 −0.443833
$$625$$ 21.2034 13.2444i 0.848137 0.529777i
$$626$$ 25.5397 1.02077
$$627$$ 5.18421i 0.207037i
$$628$$ 10.4603i 0.417411i
$$629$$ 30.9590 1.23442
$$630$$ −1.85236 13.1842i −0.0737997 0.525271i
$$631$$ −25.5111 −1.01558 −0.507791 0.861480i $$-0.669538\pi$$
−0.507791 + 0.861480i $$0.669538\pi$$
$$632$$ 19.7146i 0.784203i
$$633$$ 1.95851i 0.0778439i
$$634$$ −1.20294 −0.0477750
$$635$$ −41.4291 + 5.82071i −1.64406 + 0.230988i
$$636$$ −3.77478 −0.149680
$$637$$ 70.6820i 2.80052i
$$638$$ 2.19358i 0.0868445i
$$639$$ −0.428639 −0.0169567
$$640$$ −11.0158 + 1.54770i −0.435439 + 0.0611783i
$$641$$ −6.25380 −0.247010 −0.123505 0.992344i $$-0.539414\pi$$
−0.123505 + 0.992344i $$0.539414\pi$$
$$642$$ 13.5986i 0.536692i
$$643$$ 6.84743i 0.270036i −0.990843 0.135018i $$-0.956891\pi$$
0.990843 0.135018i $$-0.0431093\pi$$
$$644$$ 10.3051 0.406079
$$645$$ 1.52543 + 10.8573i 0.0600637 + 0.427505i
$$646$$ −33.5655 −1.32062
$$647$$ 20.2953i 0.797890i 0.916975 + 0.398945i $$0.130624\pi$$
−0.916975 + 0.398945i $$0.869376\pi$$
$$648$$ 3.06668i 0.120470i
$$649$$ 1.67307 0.0656738
$$650$$ 24.2079 6.93930i 0.949511 0.272182i
$$651$$ −12.8573 −0.503916
$$652$$ 6.39700i 0.250526i
$$653$$ 10.6222i 0.415679i 0.978163 + 0.207840i $$0.0666432\pi$$
−0.978163 + 0.207840i $$0.933357\pi$$
$$654$$ −19.0825 −0.746185
$$655$$ −0.387152 2.75557i −0.0151273 0.107669i
$$656$$ −4.82870 −0.188529
$$657$$ 12.7096i 0.495850i
$$658$$ 41.9813i 1.63660i
$$659$$ −10.1017 −0.393507 −0.196753 0.980453i $$-0.563040\pi$$
−0.196753 + 0.980453i $$0.563040\pi$$
$$660$$ 1.16346 0.163465i 0.0452878 0.00636285i
$$661$$ 21.6128 0.840642 0.420321 0.907375i $$-0.361917\pi$$
0.420321 + 0.907375i $$0.361917\pi$$
$$662$$ 21.3492i 0.829760i
$$663$$ 22.1146i 0.858861i
$$664$$ 8.90321 0.345512
$$665$$ −56.2864 + 7.90813i −2.18269 + 0.306664i
$$666$$ −7.05086 −0.273215
$$667$$ 7.22570i 0.279780i
$$668$$ 6.83314i 0.264382i
$$669$$ −26.0098 −1.00560
$$670$$ −1.83500 13.0607i −0.0708924 0.504579i
$$671$$ −0.755569 −0.0291684
$$672$$ 14.1575i 0.546137i
$$673$$ 10.2208i 0.393982i −0.980405 0.196991i $$-0.936883\pi$$
0.980405 0.196991i $$-0.0631170\pi$$
$$674$$ −3.84929 −0.148269
$$675$$ 1.37778 + 4.80642i 0.0530309 + 0.184999i
$$676$$ −2.20834 −0.0849363
$$677$$ 13.9224i 0.535082i 0.963546 + 0.267541i $$0.0862111\pi$$
−0.963546 + 0.267541i $$0.913789\pi$$
$$678$$ 2.14320i 0.0823090i
$$679$$ 13.5111 0.518510
$$680$$ −5.08694 36.2065i −0.195075 1.38846i
$$681$$ 6.34122 0.242996
$$682$$ 3.18421i 0.121930i
$$683$$ 10.3970i 0.397830i 0.980017 + 0.198915i $$0.0637418\pi$$
−0.980017 + 0.198915i $$0.936258\pi$$
$$684$$ −2.72393 −0.104152
$$685$$ −41.6227 + 5.84791i −1.59032 + 0.223437i
$$686$$ −59.7877 −2.28270
$$687$$ 23.3274i 0.889996i
$$688$$ 13.1066i 0.499686i
$$689$$ 29.7975 1.13520
$$690$$ 10.7556 1.51114i 0.409458 0.0575280i
$$691$$ −0.977725 −0.0371944 −0.0185972 0.999827i $$-0.505920\pi$$
−0.0185972 + 0.999827i $$0.505920\pi$$
$$692$$ 7.30021i 0.277512i
$$693$$ 4.90321i 0.186258i
$$694$$ 6.04287 0.229384
$$695$$ −4.36842 31.0923i −0.165703 1.17940i
$$696$$ −5.53972 −0.209982
$$697$$ 9.63158i 0.364822i
$$698$$ 22.1048i 0.836678i
$$699$$ −1.42372 −0.0538499
$$700$$ −3.54956 12.3827i −0.134161 0.468022i
$$701$$ 48.9688 1.84953 0.924764 0.380542i $$-0.124263\pi$$
0.924764 + 0.380542i $$0.124263\pi$$
$$702$$ 5.03657i 0.190093i
$$703$$ 30.1017i 1.13531i
$$704$$ 8.85236 0.333636
$$705$$ −2.19358 15.6128i −0.0826149 0.588014i
$$706$$ −27.2128 −1.02417
$$707$$ 87.3087i 3.28358i
$$708$$ 0.879077i 0.0330378i
$$709$$ 37.2672 1.39960 0.699799 0.714340i $$-0.253273\pi$$
0.699799 + 0.714340i $$0.253273\pi$$
$$710$$ 1.15257 0.161933i 0.0432550 0.00607725i
$$711$$ −6.42864 −0.241093
$$712$$ 1.90813i 0.0715103i
$$713$$ 10.4889i 0.392811i
$$714$$ 31.7462 1.18807
$$715$$ −9.18421 + 1.29036i −0.343470 + 0.0482569i
$$716$$ −6.75557 −0.252467
$$717$$ 18.9590i 0.708036i
$$718$$ 25.8983i 0.966516i
$$719$$ −5.83500 −0.217609 −0.108804 0.994063i $$-0.534702\pi$$
−0.108804 + 0.994063i $$0.534702\pi$$
$$720$$ 0.831613 + 5.91903i 0.0309924 + 0.220589i
$$721$$ 24.2667 0.903739
$$722$$ 9.56400i 0.355935i
$$723$$ 1.34614i 0.0500635i
$$724$$ 0.482081 0.0179164
$$725$$ 8.68244 2.48886i 0.322458 0.0924340i
$$726$$ 1.21432 0.0450676
$$727$$ 46.8385i 1.73715i −0.495562 0.868573i $$-0.665038\pi$$
0.495562 0.868573i $$-0.334962\pi$$
$$728$$ 62.3663i 2.31145i
$$729$$ −1.00000 −0.0370370
$$730$$ −4.80150 34.1748i −0.177712 1.26487i
$$731$$ −26.1432 −0.966941
$$732$$ 0.396997i 0.0146734i
$$733$$ 45.2083i 1.66981i 0.550395 + 0.834904i $$0.314477\pi$$
−0.550395 + 0.834904i $$0.685523\pi$$
$$734$$ 42.6637 1.57475
$$735$$ 37.7353 5.30174i 1.39189 0.195558i
$$736$$ −11.5496 −0.425723
$$737$$ 4.85728i 0.178920i
$$738$$ 2.19358i 0.0807467i
$$739$$ −5.65433 −0.207998 −0.103999 0.994577i $$-0.533164\pi$$
−0.103999 + 0.994577i $$0.533164\pi$$
$$740$$ −6.75557 + 0.949145i −0.248340 + 0.0348913i
$$741$$ 21.5022 0.789905
$$742$$ 42.7753i 1.57033i
$$743$$ 4.50622i 0.165317i −0.996578 0.0826585i $$-0.973659\pi$$
0.996578 0.0826585i $$-0.0263411\pi$$
$$744$$ 8.04149 0.294815
$$745$$ 0.949145 + 6.75557i 0.0347740 + 0.247505i
$$746$$ 20.6494 0.756029
$$747$$ 2.90321i 0.106223i
$$748$$ 2.80150i 0.102433i
$$749$$ −54.9086 −2.00632
$$750$$ −5.52051 12.4035i −0.201580 0.452910i
$$751$$ 47.5121 1.73374 0.866870 0.498534i $$-0.166128\pi$$
0.866870 + 0.498534i $$0.166128\pi$$
$$752$$ 18.8474i 0.687295i
$$753$$ 1.08250i 0.0394484i
$$754$$ 9.09817 0.331336
$$755$$ −0.101710 0.723926i −0.00370161 0.0263464i
$$756$$ 2.57628 0.0936985
$$757$$ 46.6637i 1.69602i −0.529979 0.848011i $$-0.677800\pi$$
0.529979 0.848011i $$-0.322200\pi$$
$$758$$ 2.87601i 0.104462i
$$759$$ −4.00000 −0.145191
$$760$$ 35.2039 4.94608i 1.27698 0.179413i
$$761$$ 14.9304 0.541227 0.270613 0.962688i $$-0.412773\pi$$
0.270613 + 0.962688i $$0.412773\pi$$
$$762$$ 22.7195i 0.823040i
$$763$$ 77.0518i 2.78946i
$$764$$ 7.54956 0.273134
$$765$$ −11.8064 + 1.65878i −0.426862 + 0.0599733i
$$766$$ −1.47643 −0.0533457
$$767$$ 6.93930i 0.250564i
$$768$$ 11.6637i 0.420878i
$$769$$ −38.8573 −1.40123 −0.700615 0.713540i $$-0.747091\pi$$
−0.700615 + 0.713540i $$0.747091\pi$$
$$770$$ −1.85236 13.1842i −0.0667543 0.475126i
$$771$$ 0.133353 0.00480259
$$772$$ 6.17929i 0.222397i
$$773$$ 36.3368i 1.30694i 0.756951 + 0.653471i $$0.226688\pi$$
−0.756951 + 0.653471i $$0.773312\pi$$
$$774$$ 5.95407 0.214015
$$775$$ −12.6035 + 3.61285i −0.452730 + 0.129777i
$$776$$ −8.45044 −0.303353
$$777$$ 28.4701i 1.02136i
$$778$$ 2.75251i 0.0986821i
$$779$$ 9.36488 0.335532
$$780$$ 0.677993 + 4.82564i 0.0242760 + 0.172785i
$$781$$ −0.428639 −0.0153379
$$782$$ 25.8983i 0.926121i
$$783$$ 1.80642i 0.0645563i
$$784$$ 45.5531 1.62690
$$785$$ 44.0830 6.19358i 1.57339 0.221058i