# Properties

 Label 1183.2.e.d.170.2 Level $1183$ Weight $2$ Character 1183.170 Analytic conductor $9.446$ Analytic rank $0$ Dimension $4$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$1183 = 7 \cdot 13^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1183.e (of order $$3$$, degree $$2$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$9.44630255912$$ Analytic rank: $$0$$ Dimension: $$4$$ Relative dimension: $$2$$ over $$\Q(\zeta_{3})$$ Coefficient field: $$\Q(\sqrt{-3}, \sqrt{5})$$ Defining polynomial: $$x^{4} - x^{3} + 2 x^{2} + x + 1$$ Coefficient ring: $$\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 91) Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 170.2 Root $$-0.309017 + 0.535233i$$ of defining polynomial Character $$\chi$$ $$=$$ 1183.170 Dual form 1183.2.e.d.508.2

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-0.190983 + 0.330792i) q^{2} +(-1.11803 - 1.93649i) q^{3} +(0.927051 + 1.60570i) q^{4} +(-1.11803 + 1.93649i) q^{5} +0.854102 q^{6} +(2.00000 + 1.73205i) q^{7} -1.47214 q^{8} +(-1.00000 + 1.73205i) q^{9} +O(q^{10})$$ $$q+(-0.190983 + 0.330792i) q^{2} +(-1.11803 - 1.93649i) q^{3} +(0.927051 + 1.60570i) q^{4} +(-1.11803 + 1.93649i) q^{5} +0.854102 q^{6} +(2.00000 + 1.73205i) q^{7} -1.47214 q^{8} +(-1.00000 + 1.73205i) q^{9} +(-0.427051 - 0.739674i) q^{10} +(-1.50000 - 2.59808i) q^{11} +(2.07295 - 3.59045i) q^{12} +(-0.954915 + 0.330792i) q^{14} +5.00000 q^{15} +(-1.57295 + 2.72443i) q^{16} +(3.73607 + 6.47106i) q^{17} +(-0.381966 - 0.661585i) q^{18} +(1.50000 - 2.59808i) q^{19} -4.14590 q^{20} +(1.11803 - 5.80948i) q^{21} +1.14590 q^{22} +(1.88197 - 3.25966i) q^{23} +(1.64590 + 2.85078i) q^{24} -2.23607 q^{27} +(-0.927051 + 4.81710i) q^{28} -4.47214 q^{29} +(-0.954915 + 1.65396i) q^{30} +(2.50000 + 4.33013i) q^{31} +(-2.07295 - 3.59045i) q^{32} +(-3.35410 + 5.80948i) q^{33} -2.85410 q^{34} +(-5.59017 + 1.93649i) q^{35} -3.70820 q^{36} +(-4.35410 + 7.54153i) q^{37} +(0.572949 + 0.992377i) q^{38} +(1.64590 - 2.85078i) q^{40} -4.47214 q^{41} +(1.70820 + 1.47935i) q^{42} -8.00000 q^{43} +(2.78115 - 4.81710i) q^{44} +(-2.23607 - 3.87298i) q^{45} +(0.718847 + 1.24508i) q^{46} +(0.736068 - 1.27491i) q^{47} +7.03444 q^{48} +(1.00000 + 6.92820i) q^{49} +(8.35410 - 14.4697i) q^{51} +(-0.736068 - 1.27491i) q^{53} +(0.427051 - 0.739674i) q^{54} +6.70820 q^{55} +(-2.94427 - 2.54981i) q^{56} -6.70820 q^{57} +(0.854102 - 1.47935i) q^{58} +(3.73607 + 6.47106i) q^{59} +(4.63525 + 8.02850i) q^{60} +(-1.50000 + 2.59808i) q^{61} -1.90983 q^{62} +(-5.00000 + 1.73205i) q^{63} -4.70820 q^{64} +(-1.28115 - 2.21902i) q^{66} +(-1.50000 - 2.59808i) q^{67} +(-6.92705 + 11.9980i) q^{68} -8.41641 q^{69} +(0.427051 - 2.21902i) q^{70} -8.94427 q^{71} +(1.47214 - 2.54981i) q^{72} +(5.35410 + 9.27358i) q^{73} +(-1.66312 - 2.88061i) q^{74} +5.56231 q^{76} +(1.50000 - 7.79423i) q^{77} +(-5.35410 + 9.27358i) q^{79} +(-3.51722 - 6.09201i) q^{80} +(5.50000 + 9.52628i) q^{81} +(0.854102 - 1.47935i) q^{82} +(10.3647 - 3.59045i) q^{84} -16.7082 q^{85} +(1.52786 - 2.64634i) q^{86} +(5.00000 + 8.66025i) q^{87} +(2.20820 + 3.82472i) q^{88} +(-1.11803 + 1.93649i) q^{89} +1.70820 q^{90} +6.97871 q^{92} +(5.59017 - 9.68246i) q^{93} +(0.281153 + 0.486971i) q^{94} +(3.35410 + 5.80948i) q^{95} +(-4.63525 + 8.02850i) q^{96} +17.4164 q^{97} +(-2.48278 - 0.992377i) q^{98} +6.00000 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4 q - 3 q^{2} - 3 q^{4} - 10 q^{6} + 8 q^{7} + 12 q^{8} - 4 q^{9} + O(q^{10})$$ $$4 q - 3 q^{2} - 3 q^{4} - 10 q^{6} + 8 q^{7} + 12 q^{8} - 4 q^{9} + 5 q^{10} - 6 q^{11} + 15 q^{12} - 15 q^{14} + 20 q^{15} - 13 q^{16} + 6 q^{17} - 6 q^{18} + 6 q^{19} - 30 q^{20} + 18 q^{22} + 12 q^{23} + 20 q^{24} + 3 q^{28} - 15 q^{30} + 10 q^{31} - 15 q^{32} + 2 q^{34} + 12 q^{36} - 4 q^{37} + 9 q^{38} + 20 q^{40} - 20 q^{42} - 32 q^{43} - 9 q^{44} + 23 q^{46} - 6 q^{47} - 30 q^{48} + 4 q^{49} + 20 q^{51} + 6 q^{53} - 5 q^{54} + 24 q^{56} - 10 q^{58} + 6 q^{59} - 15 q^{60} - 6 q^{61} - 30 q^{62} - 20 q^{63} + 8 q^{64} + 15 q^{66} - 6 q^{67} - 21 q^{68} + 20 q^{69} - 5 q^{70} - 12 q^{72} + 8 q^{73} + 9 q^{74} - 18 q^{76} + 6 q^{77} - 8 q^{79} + 15 q^{80} + 22 q^{81} - 10 q^{82} + 75 q^{84} - 40 q^{85} + 24 q^{86} + 20 q^{87} - 18 q^{88} - 20 q^{90} - 66 q^{92} - 19 q^{94} + 15 q^{96} + 16 q^{97} - 39 q^{98} + 24 q^{99} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1183\mathbb{Z}\right)^\times$$.

 $$n$$ $$339$$ $$1016$$ $$\chi(n)$$ $$e\left(\frac{1}{3}\right)$$ $$1$$

## Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −0.190983 + 0.330792i −0.135045 + 0.233905i −0.925615 0.378467i $$-0.876451\pi$$
0.790569 + 0.612372i $$0.209785\pi$$
$$3$$ −1.11803 1.93649i −0.645497 1.11803i −0.984186 0.177136i $$-0.943317\pi$$
0.338689 0.940898i $$-0.390016\pi$$
$$4$$ 0.927051 + 1.60570i 0.463525 + 0.802850i
$$5$$ −1.11803 + 1.93649i −0.500000 + 0.866025i 0.500000 + 0.866025i $$0.333333\pi$$
−1.00000 $$\pi$$
$$6$$ 0.854102 0.348686
$$7$$ 2.00000 + 1.73205i 0.755929 + 0.654654i
$$8$$ −1.47214 −0.520479
$$9$$ −1.00000 + 1.73205i −0.333333 + 0.577350i
$$10$$ −0.427051 0.739674i −0.135045 0.233905i
$$11$$ −1.50000 2.59808i −0.452267 0.783349i 0.546259 0.837616i $$-0.316051\pi$$
−0.998526 + 0.0542666i $$0.982718\pi$$
$$12$$ 2.07295 3.59045i 0.598409 1.03647i
$$13$$ 0 0
$$14$$ −0.954915 + 0.330792i −0.255212 + 0.0884080i
$$15$$ 5.00000 1.29099
$$16$$ −1.57295 + 2.72443i −0.393237 + 0.681107i
$$17$$ 3.73607 + 6.47106i 0.906130 + 1.56946i 0.819394 + 0.573231i $$0.194310\pi$$
0.0867359 + 0.996231i $$0.472356\pi$$
$$18$$ −0.381966 0.661585i −0.0900303 0.155937i
$$19$$ 1.50000 2.59808i 0.344124 0.596040i −0.641071 0.767482i $$-0.721509\pi$$
0.985194 + 0.171442i $$0.0548427\pi$$
$$20$$ −4.14590 −0.927051
$$21$$ 1.11803 5.80948i 0.243975 1.26773i
$$22$$ 1.14590 0.244306
$$23$$ 1.88197 3.25966i 0.392417 0.679686i −0.600351 0.799737i $$-0.704972\pi$$
0.992768 + 0.120051i $$0.0383057\pi$$
$$24$$ 1.64590 + 2.85078i 0.335968 + 0.581913i
$$25$$ 0 0
$$26$$ 0 0
$$27$$ −2.23607 −0.430331
$$28$$ −0.927051 + 4.81710i −0.175196 + 0.910346i
$$29$$ −4.47214 −0.830455 −0.415227 0.909718i $$-0.636298\pi$$
−0.415227 + 0.909718i $$0.636298\pi$$
$$30$$ −0.954915 + 1.65396i −0.174343 + 0.301971i
$$31$$ 2.50000 + 4.33013i 0.449013 + 0.777714i 0.998322 0.0579057i $$-0.0184423\pi$$
−0.549309 + 0.835619i $$0.685109\pi$$
$$32$$ −2.07295 3.59045i −0.366449 0.634708i
$$33$$ −3.35410 + 5.80948i −0.583874 + 1.01130i
$$34$$ −2.85410 −0.489474
$$35$$ −5.59017 + 1.93649i −0.944911 + 0.327327i
$$36$$ −3.70820 −0.618034
$$37$$ −4.35410 + 7.54153i −0.715810 + 1.23982i 0.246836 + 0.969057i $$0.420609\pi$$
−0.962646 + 0.270762i $$0.912724\pi$$
$$38$$ 0.572949 + 0.992377i 0.0929446 + 0.160985i
$$39$$ 0 0
$$40$$ 1.64590 2.85078i 0.260239 0.450748i
$$41$$ −4.47214 −0.698430 −0.349215 0.937043i $$-0.613552\pi$$
−0.349215 + 0.937043i $$0.613552\pi$$
$$42$$ 1.70820 + 1.47935i 0.263582 + 0.228268i
$$43$$ −8.00000 −1.21999 −0.609994 0.792406i $$-0.708828\pi$$
−0.609994 + 0.792406i $$0.708828\pi$$
$$44$$ 2.78115 4.81710i 0.419275 0.726205i
$$45$$ −2.23607 3.87298i −0.333333 0.577350i
$$46$$ 0.718847 + 1.24508i 0.105988 + 0.183577i
$$47$$ 0.736068 1.27491i 0.107367 0.185964i −0.807336 0.590092i $$-0.799091\pi$$
0.914703 + 0.404128i $$0.132425\pi$$
$$48$$ 7.03444 1.01533
$$49$$ 1.00000 + 6.92820i 0.142857 + 0.989743i
$$50$$ 0 0
$$51$$ 8.35410 14.4697i 1.16981 2.02617i
$$52$$ 0 0
$$53$$ −0.736068 1.27491i −0.101107 0.175122i 0.811034 0.584999i $$-0.198905\pi$$
−0.912141 + 0.409877i $$0.865572\pi$$
$$54$$ 0.427051 0.739674i 0.0581143 0.100657i
$$55$$ 6.70820 0.904534
$$56$$ −2.94427 2.54981i −0.393445 0.340733i
$$57$$ −6.70820 −0.888523
$$58$$ 0.854102 1.47935i 0.112149 0.194248i
$$59$$ 3.73607 + 6.47106i 0.486395 + 0.842460i 0.999878 0.0156395i $$-0.00497842\pi$$
−0.513483 + 0.858100i $$0.671645\pi$$
$$60$$ 4.63525 + 8.02850i 0.598409 + 1.03647i
$$61$$ −1.50000 + 2.59808i −0.192055 + 0.332650i −0.945931 0.324367i $$-0.894849\pi$$
0.753876 + 0.657017i $$0.228182\pi$$
$$62$$ −1.90983 −0.242549
$$63$$ −5.00000 + 1.73205i −0.629941 + 0.218218i
$$64$$ −4.70820 −0.588525
$$65$$ 0 0
$$66$$ −1.28115 2.21902i −0.157699 0.273143i
$$67$$ −1.50000 2.59808i −0.183254 0.317406i 0.759733 0.650236i $$-0.225330\pi$$
−0.942987 + 0.332830i $$0.891996\pi$$
$$68$$ −6.92705 + 11.9980i −0.840028 + 1.45497i
$$69$$ −8.41641 −1.01322
$$70$$ 0.427051 2.21902i 0.0510424 0.265224i
$$71$$ −8.94427 −1.06149 −0.530745 0.847532i $$-0.678088\pi$$
−0.530745 + 0.847532i $$0.678088\pi$$
$$72$$ 1.47214 2.54981i 0.173493 0.300498i
$$73$$ 5.35410 + 9.27358i 0.626650 + 1.08539i 0.988219 + 0.153045i $$0.0489079\pi$$
−0.361569 + 0.932345i $$0.617759\pi$$
$$74$$ −1.66312 2.88061i −0.193334 0.334864i
$$75$$ 0 0
$$76$$ 5.56231 0.638040
$$77$$ 1.50000 7.79423i 0.170941 0.888235i
$$78$$ 0 0
$$79$$ −5.35410 + 9.27358i −0.602384 + 1.04336i 0.390076 + 0.920783i $$0.372449\pi$$
−0.992459 + 0.122576i $$0.960884\pi$$
$$80$$ −3.51722 6.09201i −0.393237 0.681107i
$$81$$ 5.50000 + 9.52628i 0.611111 + 1.05848i
$$82$$ 0.854102 1.47935i 0.0943198 0.163367i
$$83$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$84$$ 10.3647 3.59045i 1.13089 0.391751i
$$85$$ −16.7082 −1.81226
$$86$$ 1.52786 2.64634i 0.164754 0.285362i
$$87$$ 5.00000 + 8.66025i 0.536056 + 0.928477i
$$88$$ 2.20820 + 3.82472i 0.235395 + 0.407717i
$$89$$ −1.11803 + 1.93649i −0.118511 + 0.205268i −0.919178 0.393842i $$-0.871146\pi$$
0.800667 + 0.599110i $$0.204479\pi$$
$$90$$ 1.70820 0.180061
$$91$$ 0 0
$$92$$ 6.97871 0.727581
$$93$$ 5.59017 9.68246i 0.579674 1.00402i
$$94$$ 0.281153 + 0.486971i 0.0289987 + 0.0502272i
$$95$$ 3.35410 + 5.80948i 0.344124 + 0.596040i
$$96$$ −4.63525 + 8.02850i −0.473084 + 0.819405i
$$97$$ 17.4164 1.76837 0.884184 0.467139i $$-0.154715\pi$$
0.884184 + 0.467139i $$0.154715\pi$$
$$98$$ −2.48278 0.992377i −0.250799 0.100245i
$$99$$ 6.00000 0.603023
$$100$$ 0 0
$$101$$ 4.50000 + 7.79423i 0.447767 + 0.775555i 0.998240 0.0592978i $$-0.0188862\pi$$
−0.550474 + 0.834853i $$0.685553\pi$$
$$102$$ 3.19098 + 5.52694i 0.315954 + 0.547249i
$$103$$ −5.35410 + 9.27358i −0.527555 + 0.913753i 0.471929 + 0.881637i $$0.343558\pi$$
−0.999484 + 0.0321160i $$0.989775\pi$$
$$104$$ 0 0
$$105$$ 10.0000 + 8.66025i 0.975900 + 0.845154i
$$106$$ 0.562306 0.0546160
$$107$$ 7.11803 12.3288i 0.688126 1.19187i −0.284317 0.958730i $$-0.591767\pi$$
0.972443 0.233139i $$-0.0748999\pi$$
$$108$$ −2.07295 3.59045i −0.199470 0.345492i
$$109$$ 5.35410 + 9.27358i 0.512830 + 0.888248i 0.999889 + 0.0148787i $$0.00473620\pi$$
−0.487059 + 0.873369i $$0.661930\pi$$
$$110$$ −1.28115 + 2.21902i −0.122153 + 0.211575i
$$111$$ 19.4721 1.84821
$$112$$ −7.86475 + 2.72443i −0.743149 + 0.257434i
$$113$$ −14.9443 −1.40584 −0.702919 0.711269i $$-0.748121\pi$$
−0.702919 + 0.711269i $$0.748121\pi$$
$$114$$ 1.28115 2.21902i 0.119991 0.207830i
$$115$$ 4.20820 + 7.28882i 0.392417 + 0.679686i
$$116$$ −4.14590 7.18091i −0.384937 0.666730i
$$117$$ 0 0
$$118$$ −2.85410 −0.262741
$$119$$ −3.73607 + 19.4132i −0.342485 + 1.77960i
$$120$$ −7.36068 −0.671935
$$121$$ 1.00000 1.73205i 0.0909091 0.157459i
$$122$$ −0.572949 0.992377i −0.0518724 0.0898456i
$$123$$ 5.00000 + 8.66025i 0.450835 + 0.780869i
$$124$$ −4.63525 + 8.02850i −0.416258 + 0.720980i
$$125$$ −11.1803 −1.00000
$$126$$ 0.381966 1.98475i 0.0340282 0.176816i
$$127$$ 15.4164 1.36798 0.683992 0.729489i $$-0.260242\pi$$
0.683992 + 0.729489i $$0.260242\pi$$
$$128$$ 5.04508 8.73834i 0.445927 0.772368i
$$129$$ 8.94427 + 15.4919i 0.787499 + 1.36399i
$$130$$ 0 0
$$131$$ 1.88197 3.25966i 0.164428 0.284798i −0.772024 0.635593i $$-0.780755\pi$$
0.936452 + 0.350796i $$0.114089\pi$$
$$132$$ −12.4377 −1.08256
$$133$$ 7.50000 2.59808i 0.650332 0.225282i
$$134$$ 1.14590 0.0989905
$$135$$ 2.50000 4.33013i 0.215166 0.372678i
$$136$$ −5.50000 9.52628i −0.471621 0.816872i
$$137$$ −1.88197 3.25966i −0.160787 0.278492i 0.774364 0.632740i $$-0.218070\pi$$
−0.935151 + 0.354249i $$0.884737\pi$$
$$138$$ 1.60739 2.78408i 0.136830 0.236997i
$$139$$ 3.41641 0.289776 0.144888 0.989448i $$-0.453718\pi$$
0.144888 + 0.989448i $$0.453718\pi$$
$$140$$ −8.29180 7.18091i −0.700785 0.606897i
$$141$$ −3.29180 −0.277219
$$142$$ 1.70820 2.95870i 0.143349 0.248288i
$$143$$ 0 0
$$144$$ −3.14590 5.44886i −0.262158 0.454071i
$$145$$ 5.00000 8.66025i 0.415227 0.719195i
$$146$$ −4.09017 −0.338505
$$147$$ 12.2984 9.68246i 1.01435 0.798596i
$$148$$ −16.1459 −1.32718
$$149$$ −6.35410 + 11.0056i −0.520548 + 0.901616i 0.479166 + 0.877724i $$0.340939\pi$$
−0.999715 + 0.0238920i $$0.992394\pi$$
$$150$$ 0 0
$$151$$ −3.20820 5.55677i −0.261080 0.452204i 0.705449 0.708760i $$-0.250745\pi$$
−0.966529 + 0.256557i $$0.917412\pi$$
$$152$$ −2.20820 + 3.82472i −0.179109 + 0.310226i
$$153$$ −14.9443 −1.20817
$$154$$ 2.29180 + 1.98475i 0.184678 + 0.159936i
$$155$$ −11.1803 −0.898027
$$156$$ 0 0
$$157$$ −3.50000 6.06218i −0.279330 0.483814i 0.691888 0.722005i $$-0.256779\pi$$
−0.971219 + 0.238190i $$0.923446\pi$$
$$158$$ −2.04508 3.54219i −0.162698 0.281802i
$$159$$ −1.64590 + 2.85078i −0.130528 + 0.226081i
$$160$$ 9.27051 0.732898
$$161$$ 9.40983 3.25966i 0.741598 0.256897i
$$162$$ −4.20163 −0.330111
$$163$$ 5.20820 9.02087i 0.407938 0.706569i −0.586721 0.809789i $$-0.699581\pi$$
0.994659 + 0.103220i $$0.0329146\pi$$
$$164$$ −4.14590 7.18091i −0.323740 0.560735i
$$165$$ −7.50000 12.9904i −0.583874 1.01130i
$$166$$ 0 0
$$167$$ −13.5279 −1.04682 −0.523409 0.852082i $$-0.675340\pi$$
−0.523409 + 0.852082i $$0.675340\pi$$
$$168$$ −1.64590 + 8.55234i −0.126984 + 0.659827i
$$169$$ 0 0
$$170$$ 3.19098 5.52694i 0.244737 0.423897i
$$171$$ 3.00000 + 5.19615i 0.229416 + 0.397360i
$$172$$ −7.41641 12.8456i −0.565496 0.979467i
$$173$$ −5.20820 + 9.02087i −0.395972 + 0.685844i −0.993225 0.116209i $$-0.962926\pi$$
0.597252 + 0.802053i $$0.296259\pi$$
$$174$$ −3.81966 −0.289568
$$175$$ 0 0
$$176$$ 9.43769 0.711393
$$177$$ 8.35410 14.4697i 0.627933 1.08761i
$$178$$ −0.427051 0.739674i −0.0320088 0.0554409i
$$179$$ −10.0623 17.4284i −0.752092 1.30266i −0.946807 0.321802i $$-0.895712\pi$$
0.194715 0.980860i $$-0.437622\pi$$
$$180$$ 4.14590 7.18091i 0.309017 0.535233i
$$181$$ 1.41641 0.105281 0.0526404 0.998614i $$-0.483236\pi$$
0.0526404 + 0.998614i $$0.483236\pi$$
$$182$$ 0 0
$$183$$ 6.70820 0.495885
$$184$$ −2.77051 + 4.79866i −0.204245 + 0.353762i
$$185$$ −9.73607 16.8634i −0.715810 1.23982i
$$186$$ 2.13525 + 3.69837i 0.156564 + 0.271178i
$$187$$ 11.2082 19.4132i 0.819625 1.41963i
$$188$$ 2.72949 0.199069
$$189$$ −4.47214 3.87298i −0.325300 0.281718i
$$190$$ −2.56231 −0.185889
$$191$$ 5.59017 9.68246i 0.404491 0.700598i −0.589772 0.807570i $$-0.700782\pi$$
0.994262 + 0.106972i $$0.0341155\pi$$
$$192$$ 5.26393 + 9.11740i 0.379892 + 0.657992i
$$193$$ −6.35410 11.0056i −0.457378 0.792202i 0.541443 0.840737i $$-0.317878\pi$$
−0.998821 + 0.0485349i $$0.984545\pi$$
$$194$$ −3.32624 + 5.76121i −0.238810 + 0.413631i
$$195$$ 0 0
$$196$$ −10.1976 + 8.02850i −0.728397 + 0.573464i
$$197$$ 26.9443 1.91970 0.959850 0.280514i $$-0.0905049\pi$$
0.959850 + 0.280514i $$0.0905049\pi$$
$$198$$ −1.14590 + 1.98475i −0.0814354 + 0.141050i
$$199$$ 3.64590 + 6.31488i 0.258451 + 0.447650i 0.965827 0.259187i $$-0.0834547\pi$$
−0.707376 + 0.706837i $$0.750121\pi$$
$$200$$ 0 0
$$201$$ −3.35410 + 5.80948i −0.236580 + 0.409769i
$$202$$ −3.43769 −0.241875
$$203$$ −8.94427 7.74597i −0.627765 0.543660i
$$204$$ 30.9787 2.16894
$$205$$ 5.00000 8.66025i 0.349215 0.604858i
$$206$$ −2.04508 3.54219i −0.142488 0.246796i
$$207$$ 3.76393 + 6.51932i 0.261611 + 0.453124i
$$208$$ 0 0
$$209$$ −9.00000 −0.622543
$$210$$ −4.77458 + 1.65396i −0.329477 + 0.114134i
$$211$$ 4.00000 0.275371 0.137686 0.990476i $$-0.456034\pi$$
0.137686 + 0.990476i $$0.456034\pi$$
$$212$$ 1.36475 2.36381i 0.0937311 0.162347i
$$213$$ 10.0000 + 17.3205i 0.685189 + 1.18678i
$$214$$ 2.71885 + 4.70918i 0.185857 + 0.321913i
$$215$$ 8.94427 15.4919i 0.609994 1.05654i
$$216$$ 3.29180 0.223978
$$217$$ −2.50000 + 12.9904i −0.169711 + 0.881845i
$$218$$ −4.09017 −0.277021
$$219$$ 11.9721 20.7363i 0.809002 1.40123i
$$220$$ 6.21885 + 10.7714i 0.419275 + 0.726205i
$$221$$ 0 0
$$222$$ −3.71885 + 6.44123i −0.249593 + 0.432307i
$$223$$ 4.00000 0.267860 0.133930 0.990991i $$-0.457240\pi$$
0.133930 + 0.990991i $$0.457240\pi$$
$$224$$ 2.07295 10.7714i 0.138505 0.719692i
$$225$$ 0 0
$$226$$ 2.85410 4.94345i 0.189852 0.328833i
$$227$$ −5.97214 10.3440i −0.396385 0.686558i 0.596892 0.802321i $$-0.296402\pi$$
−0.993277 + 0.115763i $$0.963069\pi$$
$$228$$ −6.21885 10.7714i −0.411853 0.713351i
$$229$$ −8.06231 + 13.9643i −0.532772 + 0.922788i 0.466495 + 0.884524i $$0.345516\pi$$
−0.999268 + 0.0382649i $$0.987817\pi$$
$$230$$ −3.21478 −0.211976
$$231$$ −16.7705 + 5.80948i −1.10342 + 0.382235i
$$232$$ 6.58359 0.432234
$$233$$ 2.97214 5.14789i 0.194711 0.337250i −0.752095 0.659055i $$-0.770956\pi$$
0.946806 + 0.321806i $$0.104290\pi$$
$$234$$ 0 0
$$235$$ 1.64590 + 2.85078i 0.107367 + 0.185964i
$$236$$ −6.92705 + 11.9980i −0.450913 + 0.781004i
$$237$$ 23.9443 1.55535
$$238$$ −5.70820 4.94345i −0.370008 0.320436i
$$239$$ 7.41641 0.479728 0.239864 0.970807i $$-0.422897\pi$$
0.239864 + 0.970807i $$0.422897\pi$$
$$240$$ −7.86475 + 13.6221i −0.507667 + 0.879305i
$$241$$ −4.35410 7.54153i −0.280472 0.485792i 0.691029 0.722827i $$-0.257158\pi$$
−0.971501 + 0.237035i $$0.923824\pi$$
$$242$$ 0.381966 + 0.661585i 0.0245537 + 0.0425283i
$$243$$ 8.94427 15.4919i 0.573775 0.993808i
$$244$$ −5.56231 −0.356090
$$245$$ −14.5344 5.80948i −0.928571 0.371154i
$$246$$ −3.81966 −0.243533
$$247$$ 0 0
$$248$$ −3.68034 6.37454i −0.233702 0.404783i
$$249$$ 0 0
$$250$$ 2.13525 3.69837i 0.135045 0.233905i
$$251$$ 10.4721 0.660995 0.330498 0.943807i $$-0.392783\pi$$
0.330498 + 0.943807i $$0.392783\pi$$
$$252$$ −7.41641 6.42280i −0.467190 0.404598i
$$253$$ −11.2918 −0.709909
$$254$$ −2.94427 + 5.09963i −0.184740 + 0.319979i
$$255$$ 18.6803 + 32.3553i 1.16981 + 2.02617i
$$256$$ −2.78115 4.81710i −0.173822 0.301069i
$$257$$ 8.97214 15.5402i 0.559666 0.969371i −0.437858 0.899044i $$-0.644263\pi$$
0.997524 0.0703264i $$-0.0224041\pi$$
$$258$$ −6.83282 −0.425393
$$259$$ −21.7705 + 7.54153i −1.35275 + 0.468608i
$$260$$ 0 0
$$261$$ 4.47214 7.74597i 0.276818 0.479463i
$$262$$ 0.718847 + 1.24508i 0.0444105 + 0.0769213i
$$263$$ 7.06231 + 12.2323i 0.435480 + 0.754274i 0.997335 0.0729620i $$-0.0232452\pi$$
−0.561854 + 0.827236i $$0.689912\pi$$
$$264$$ 4.93769 8.55234i 0.303894 0.526360i
$$265$$ 3.29180 0.202213
$$266$$ −0.572949 + 2.97713i −0.0351298 + 0.182540i
$$267$$ 5.00000 0.305995
$$268$$ 2.78115 4.81710i 0.169886 0.294251i
$$269$$ −2.26393 3.92125i −0.138034 0.239083i 0.788718 0.614755i $$-0.210745\pi$$
−0.926753 + 0.375672i $$0.877412\pi$$
$$270$$ 0.954915 + 1.65396i 0.0581143 + 0.100657i
$$271$$ 3.20820 5.55677i 0.194885 0.337550i −0.751978 0.659188i $$-0.770900\pi$$
0.946863 + 0.321638i $$0.104233\pi$$
$$272$$ −23.5066 −1.42530
$$273$$ 0 0
$$274$$ 1.43769 0.0868543
$$275$$ 0 0
$$276$$ −7.80244 13.5142i −0.469652 0.813461i
$$277$$ −13.2082 22.8773i −0.793604 1.37456i −0.923722 0.383064i $$-0.874869\pi$$
0.130118 0.991499i $$-0.458464\pi$$
$$278$$ −0.652476 + 1.13012i −0.0391329 + 0.0677802i
$$279$$ −10.0000 −0.598684
$$280$$ 8.22949 2.85078i 0.491806 0.170367i
$$281$$ −9.05573 −0.540219 −0.270110 0.962830i $$-0.587060\pi$$
−0.270110 + 0.962830i $$0.587060\pi$$
$$282$$ 0.628677 1.08890i 0.0374372 0.0648431i
$$283$$ 7.06231 + 12.2323i 0.419811 + 0.727133i 0.995920 0.0902393i $$-0.0287632\pi$$
−0.576110 + 0.817372i $$0.695430\pi$$
$$284$$ −8.29180 14.3618i −0.492028 0.852217i
$$285$$ 7.50000 12.9904i 0.444262 0.769484i
$$286$$ 0 0
$$287$$ −8.94427 7.74597i −0.527964 0.457230i
$$288$$ 8.29180 0.488599
$$289$$ −19.4164 + 33.6302i −1.14214 + 1.97825i
$$290$$ 1.90983 + 3.30792i 0.112149 + 0.194248i
$$291$$ −19.4721 33.7267i −1.14148 1.97710i
$$292$$ −9.92705 + 17.1942i −0.580937 + 1.00621i
$$293$$ −2.94427 −0.172006 −0.0860031 0.996295i $$-0.527409\pi$$
−0.0860031 + 0.996295i $$0.527409\pi$$
$$294$$ 0.854102 + 5.91739i 0.0498122 + 0.345109i
$$295$$ −16.7082 −0.972789
$$296$$ 6.40983 11.1022i 0.372564 0.645299i
$$297$$ 3.35410 + 5.80948i 0.194625 + 0.337100i
$$298$$ −2.42705 4.20378i −0.140595 0.243518i
$$299$$ 0 0
$$300$$ 0 0
$$301$$ −16.0000 13.8564i −0.922225 0.798670i
$$302$$ 2.45085 0.141031
$$303$$ 10.0623 17.4284i 0.578064 1.00124i
$$304$$ 4.71885 + 8.17328i 0.270644 + 0.468770i
$$305$$ −3.35410 5.80948i −0.192055 0.332650i
$$306$$ 2.85410 4.94345i 0.163158 0.282598i
$$307$$ 7.41641 0.423277 0.211638 0.977348i $$-0.432120\pi$$
0.211638 + 0.977348i $$0.432120\pi$$
$$308$$ 13.9058 4.81710i 0.792354 0.274480i
$$309$$ 23.9443 1.36214
$$310$$ 2.13525 3.69837i 0.121274 0.210053i
$$311$$ 16.1180 + 27.9173i 0.913970 + 1.58304i 0.808403 + 0.588630i $$0.200333\pi$$
0.105567 + 0.994412i $$0.466334\pi$$
$$312$$ 0 0
$$313$$ 16.2082 28.0734i 0.916142 1.58680i 0.110921 0.993829i $$-0.464620\pi$$
0.805221 0.592975i $$-0.202047\pi$$
$$314$$ 2.67376 0.150889
$$315$$ 2.23607 11.6190i 0.125988 0.654654i
$$316$$ −19.8541 −1.11688
$$317$$ −1.88197 + 3.25966i −0.105702 + 0.183081i −0.914025 0.405659i $$-0.867042\pi$$
0.808323 + 0.588739i $$0.200376\pi$$
$$318$$ −0.628677 1.08890i −0.0352545 0.0610625i
$$319$$ 6.70820 + 11.6190i 0.375587 + 0.650536i
$$320$$ 5.26393 9.11740i 0.294263 0.509678i
$$321$$ −31.8328 −1.77673
$$322$$ −0.718847 + 3.73524i −0.0400598 + 0.208157i
$$323$$ 22.4164 1.24728
$$324$$ −10.1976 + 17.6627i −0.566531 + 0.981261i
$$325$$ 0 0
$$326$$ 1.98936 + 3.44567i 0.110180 + 0.190838i
$$327$$ 11.9721 20.7363i 0.662061 1.14672i
$$328$$ 6.58359 0.363518
$$329$$ 3.68034 1.27491i 0.202904 0.0702879i
$$330$$ 5.72949 0.315398
$$331$$ −14.2082 + 24.6093i −0.780954 + 1.35265i 0.150433 + 0.988620i $$0.451933\pi$$
−0.931387 + 0.364031i $$0.881400\pi$$
$$332$$ 0 0
$$333$$ −8.70820 15.0831i −0.477207 0.826546i
$$334$$ 2.58359 4.47491i 0.141368 0.244856i
$$335$$ 6.70820 0.366508
$$336$$ 14.0689 + 12.1840i 0.767521 + 0.664692i
$$337$$ 18.0000 0.980522 0.490261 0.871576i $$-0.336901\pi$$
0.490261 + 0.871576i $$0.336901\pi$$
$$338$$ 0 0
$$339$$ 16.7082 + 28.9395i 0.907465 + 1.57178i
$$340$$ −15.4894 26.8284i −0.840028 1.45497i
$$341$$ 7.50000 12.9904i 0.406148 0.703469i
$$342$$ −2.29180 −0.123926
$$343$$ −10.0000 + 15.5885i −0.539949 + 0.841698i
$$344$$ 11.7771 0.634978
$$345$$ 9.40983 16.2983i 0.506608 0.877471i
$$346$$ −1.98936 3.44567i −0.106948 0.185240i
$$347$$ 17.5344 + 30.3705i 0.941298 + 1.63038i 0.762999 + 0.646400i $$0.223726\pi$$
0.178299 + 0.983976i $$0.442940\pi$$
$$348$$ −9.27051 + 16.0570i −0.496951 + 0.860745i
$$349$$ 2.58359 0.138297 0.0691483 0.997606i $$-0.477972\pi$$
0.0691483 + 0.997606i $$0.477972\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ −6.21885 + 10.7714i −0.331466 + 0.574115i
$$353$$ 15.3541 + 26.5941i 0.817216 + 1.41546i 0.907725 + 0.419565i $$0.137817\pi$$
−0.0905091 + 0.995896i $$0.528849\pi$$
$$354$$ 3.19098 + 5.52694i 0.169599 + 0.293754i
$$355$$ 10.0000 17.3205i 0.530745 0.919277i
$$356$$ −4.14590 −0.219732
$$357$$ 41.7705 14.4697i 2.21073 0.765819i
$$358$$ 7.68692 0.406266
$$359$$ −2.97214 + 5.14789i −0.156863 + 0.271695i −0.933736 0.357963i $$-0.883472\pi$$
0.776873 + 0.629658i $$0.216805\pi$$
$$360$$ 3.29180 + 5.70156i 0.173493 + 0.300498i
$$361$$ 5.00000 + 8.66025i 0.263158 + 0.455803i
$$362$$ −0.270510 + 0.468537i −0.0142177 + 0.0246257i
$$363$$ −4.47214 −0.234726
$$364$$ 0 0
$$365$$ −23.9443 −1.25330
$$366$$ −1.28115 + 2.21902i −0.0669669 + 0.115990i
$$367$$ −0.354102 0.613323i −0.0184840 0.0320152i 0.856635 0.515922i $$-0.172551\pi$$
−0.875119 + 0.483907i $$0.839217\pi$$
$$368$$ 5.92047 + 10.2546i 0.308626 + 0.534556i
$$369$$ 4.47214 7.74597i 0.232810 0.403239i
$$370$$ 7.43769 0.386667
$$371$$ 0.736068 3.82472i 0.0382147 0.198570i
$$372$$ 20.7295 1.07477
$$373$$ 14.2082 24.6093i 0.735673 1.27422i −0.218755 0.975780i $$-0.570199\pi$$
0.954427 0.298443i $$-0.0964673\pi$$
$$374$$ 4.28115 + 7.41517i 0.221373 + 0.383430i
$$375$$ 12.5000 + 21.6506i 0.645497 + 1.11803i
$$376$$ −1.08359 + 1.87684i −0.0558820 + 0.0967905i
$$377$$ 0 0
$$378$$ 2.13525 0.739674i 0.109826 0.0380447i
$$379$$ −11.4164 −0.586421 −0.293211 0.956048i $$-0.594724\pi$$
−0.293211 + 0.956048i $$0.594724\pi$$
$$380$$ −6.21885 + 10.7714i −0.319020 + 0.552559i
$$381$$ −17.2361 29.8537i −0.883031 1.52945i
$$382$$ 2.13525 + 3.69837i 0.109249 + 0.189225i
$$383$$ 7.50000 12.9904i 0.383232 0.663777i −0.608290 0.793715i $$-0.708144\pi$$
0.991522 + 0.129937i $$0.0414776\pi$$
$$384$$ −22.5623 −1.15138
$$385$$ 13.4164 + 11.6190i 0.683763 + 0.592157i
$$386$$ 4.85410 0.247067
$$387$$ 8.00000 13.8564i 0.406663 0.704361i
$$388$$ 16.1459 + 27.9655i 0.819684 + 1.41973i
$$389$$ 3.73607 + 6.47106i 0.189426 + 0.328096i 0.945059 0.326900i $$-0.106004\pi$$
−0.755633 + 0.654995i $$0.772671\pi$$
$$390$$ 0 0
$$391$$ 28.1246 1.42232
$$392$$ −1.47214 10.1993i −0.0743541 0.515140i
$$393$$ −8.41641 −0.424552
$$394$$ −5.14590 + 8.91296i −0.259247 + 0.449028i
$$395$$ −11.9721 20.7363i −0.602384 1.04336i
$$396$$ 5.56231 + 9.63420i 0.279516 + 0.484137i
$$397$$ 7.06231 12.2323i 0.354447 0.613920i −0.632576 0.774498i $$-0.718002\pi$$
0.987023 + 0.160578i $$0.0513358\pi$$
$$398$$ −2.78522 −0.139610
$$399$$ −13.4164 11.6190i −0.671660 0.581675i
$$400$$ 0 0
$$401$$ 4.88197 8.45581i 0.243794 0.422263i −0.717998 0.696045i $$-0.754941\pi$$
0.961792 + 0.273782i $$0.0882747\pi$$
$$402$$ −1.28115 2.21902i −0.0638981 0.110675i
$$403$$ 0 0
$$404$$ −8.34346 + 14.4513i −0.415103 + 0.718979i
$$405$$ −24.5967 −1.22222
$$406$$ 4.27051 1.47935i 0.211942 0.0734188i
$$407$$ 26.1246 1.29495
$$408$$ −12.2984 + 21.3014i −0.608860 + 1.05458i
$$409$$ −2.35410 4.07742i −0.116403 0.201616i 0.801937 0.597409i $$-0.203803\pi$$
−0.918340 + 0.395793i $$0.870470\pi$$
$$410$$ 1.90983 + 3.30792i 0.0943198 + 0.163367i
$$411$$ −4.20820 + 7.28882i −0.207575 + 0.359531i
$$412$$ −19.8541 −0.978141
$$413$$ −3.73607 + 19.4132i −0.183840 + 0.955260i
$$414$$ −2.87539 −0.141318
$$415$$ 0 0
$$416$$ 0 0
$$417$$ −3.81966 6.61585i −0.187050 0.323979i
$$418$$ 1.71885 2.97713i 0.0840716 0.145616i
$$419$$ 15.0557 0.735520 0.367760 0.929921i $$-0.380125\pi$$
0.367760 + 0.929921i $$0.380125\pi$$
$$420$$ −4.63525 + 24.0855i −0.226177 + 1.17525i
$$421$$ 13.4164 0.653876 0.326938 0.945046i $$-0.393983\pi$$
0.326938 + 0.945046i $$0.393983\pi$$
$$422$$ −0.763932 + 1.32317i −0.0371876 + 0.0644109i
$$423$$ 1.47214 + 2.54981i 0.0715777 + 0.123976i
$$424$$ 1.08359 + 1.87684i 0.0526239 + 0.0911472i
$$425$$ 0 0
$$426$$ −7.63932 −0.370126
$$427$$ −7.50000 + 2.59808i −0.362950 + 0.125730i
$$428$$ 26.3951 1.27586
$$429$$ 0 0
$$430$$ 3.41641 + 5.91739i 0.164754 + 0.285362i
$$431$$ 6.68034 + 11.5707i 0.321781 + 0.557340i 0.980856 0.194737i $$-0.0623853\pi$$
−0.659075 + 0.752077i $$0.729052\pi$$
$$432$$ 3.51722 6.09201i 0.169222 0.293102i
$$433$$ 2.58359 0.124160 0.0620798 0.998071i $$-0.480227\pi$$
0.0620798 + 0.998071i $$0.480227\pi$$
$$434$$ −3.81966 3.30792i −0.183350 0.158785i
$$435$$ −22.3607 −1.07211
$$436$$ −9.92705 + 17.1942i −0.475420 + 0.823451i
$$437$$ −5.64590 9.77898i −0.270080 0.467792i
$$438$$ 4.57295 + 7.92058i 0.218504 + 0.378460i
$$439$$ 8.06231 13.9643i 0.384793 0.666481i −0.606948 0.794742i $$-0.707606\pi$$
0.991740 + 0.128261i $$0.0409395\pi$$
$$440$$ −9.87539 −0.470791
$$441$$ −13.0000 5.19615i −0.619048 0.247436i
$$442$$ 0 0
$$443$$ 1.11803 1.93649i 0.0531194 0.0920055i −0.838243 0.545297i $$-0.816417\pi$$
0.891362 + 0.453291i $$0.149750\pi$$
$$444$$ 18.0517 + 31.2664i 0.856694 + 1.48384i
$$445$$ −2.50000 4.33013i −0.118511 0.205268i
$$446$$ −0.763932 + 1.32317i −0.0361732 + 0.0626539i
$$447$$ 28.4164 1.34405
$$448$$ −9.41641 8.15485i −0.444883 0.385280i
$$449$$ −10.3607 −0.488951 −0.244475 0.969656i $$-0.578616\pi$$
−0.244475 + 0.969656i $$0.578616\pi$$
$$450$$ 0 0
$$451$$ 6.70820 + 11.6190i 0.315877 + 0.547115i
$$452$$ −13.8541 23.9960i −0.651642 1.12868i
$$453$$ −7.17376 + 12.4253i −0.337053 + 0.583792i
$$454$$ 4.56231 0.214120
$$455$$ 0 0
$$456$$ 9.87539 0.462457
$$457$$ 17.0623 29.5528i 0.798141 1.38242i −0.122684 0.992446i $$-0.539150\pi$$
0.920825 0.389975i $$-0.127516\pi$$
$$458$$ −3.07953 5.33390i −0.143897 0.249237i
$$459$$ −8.35410 14.4697i −0.389936 0.675389i
$$460$$ −7.80244 + 13.5142i −0.363791 + 0.630104i
$$461$$ 10.3607 0.482545 0.241272 0.970457i $$-0.422435\pi$$
0.241272 + 0.970457i $$0.422435\pi$$
$$462$$ 1.28115 6.65707i 0.0596046 0.309715i
$$463$$ 24.0000 1.11537 0.557687 0.830051i $$-0.311689\pi$$
0.557687 + 0.830051i $$0.311689\pi$$
$$464$$ 7.03444 12.1840i 0.326566 0.565628i
$$465$$ 12.5000 + 21.6506i 0.579674 + 1.00402i
$$466$$ 1.13525 + 1.96632i 0.0525897 + 0.0910880i
$$467$$ 10.8262 18.7516i 0.500979 0.867720i −0.499021 0.866590i $$-0.666307\pi$$
0.999999 0.00113029i $$-0.000359784\pi$$
$$468$$ 0 0
$$469$$ 1.50000 7.79423i 0.0692636 0.359904i
$$470$$ −1.25735 −0.0579974
$$471$$ −7.82624 + 13.5554i −0.360614 + 0.624602i
$$472$$ −5.50000 9.52628i −0.253158 0.438483i
$$473$$ 12.0000 + 20.7846i 0.551761 + 0.955677i
$$474$$ −4.57295 + 7.92058i −0.210043 + 0.363804i
$$475$$ 0 0
$$476$$ −34.6353 + 11.9980i −1.58750 + 0.549928i
$$477$$ 2.94427 0.134809
$$478$$ −1.41641 + 2.45329i −0.0647850 + 0.112211i
$$479$$ −14.9164 25.8360i −0.681548 1.18048i −0.974508 0.224351i $$-0.927974\pi$$
0.292960 0.956125i $$-0.405360\pi$$
$$480$$ −10.3647 17.9523i −0.473084 0.819405i
$$481$$ 0 0
$$482$$ 3.32624 0.151506
$$483$$ −16.8328 14.5776i −0.765920 0.663306i
$$484$$ 3.70820 0.168555
$$485$$ −19.4721 + 33.7267i −0.884184 + 1.53145i
$$486$$ 3.41641 + 5.91739i 0.154971 + 0.268418i
$$487$$ 15.9164 + 27.5680i 0.721241 + 1.24923i 0.960503 + 0.278271i $$0.0897614\pi$$
−0.239261 + 0.970955i $$0.576905\pi$$
$$488$$ 2.20820 3.82472i 0.0999607 0.173137i
$$489$$ −23.2918 −1.05329
$$490$$ 4.69756 3.69837i 0.212214 0.167075i
$$491$$ −34.4721 −1.55571 −0.777853 0.628446i $$-0.783691\pi$$
−0.777853 + 0.628446i $$0.783691\pi$$
$$492$$ −9.27051 + 16.0570i −0.417947 + 0.723905i
$$493$$ −16.7082 28.9395i −0.752500 1.30337i
$$494$$ 0 0
$$495$$ −6.70820 + 11.6190i −0.301511 + 0.522233i
$$496$$ −15.7295 −0.706275
$$497$$ −17.8885 15.4919i −0.802411 0.694908i
$$498$$ 0 0
$$499$$ −0.208204 + 0.360620i −0.00932049 + 0.0161436i −0.870648 0.491907i $$-0.836300\pi$$
0.861328 + 0.508050i $$0.169634\pi$$
$$500$$ −10.3647 17.9523i −0.463525 0.802850i
$$501$$ 15.1246 + 26.1966i 0.675718 + 1.17038i
$$502$$ −2.00000 + 3.46410i −0.0892644 + 0.154610i
$$503$$ 3.05573 0.136248 0.0681241 0.997677i $$-0.478299\pi$$
0.0681241 + 0.997677i $$0.478299\pi$$
$$504$$ 7.36068 2.54981i 0.327871 0.113578i
$$505$$ −20.1246 −0.895533
$$506$$ 2.15654 3.73524i 0.0958699 0.166052i
$$507$$ 0 0
$$508$$ 14.2918 + 24.7541i 0.634096 + 1.09829i
$$509$$ −7.88197 + 13.6520i −0.349362 + 0.605113i −0.986136 0.165938i $$-0.946935\pi$$
0.636774 + 0.771050i $$0.280268\pi$$
$$510$$ −14.2705 −0.631909
$$511$$ −5.35410 + 27.8207i −0.236852 + 1.23072i
$$512$$ 22.3050 0.985749
$$513$$ −3.35410 + 5.80948i −0.148087 + 0.256495i
$$514$$ 3.42705 + 5.93583i 0.151161 + 0.261818i
$$515$$ −11.9721 20.7363i −0.527555 0.913753i
$$516$$ −16.5836 + 28.7236i −0.730052 + 1.26449i
$$517$$ −4.41641 −0.194233
$$518$$ 1.66312 8.64182i 0.0730733 0.379700i
$$519$$ 23.2918 1.02240
$$520$$ 0 0
$$521$$ 0.0278640 + 0.0482619i 0.00122075 + 0.00211439i 0.866635 0.498942i $$-0.166278\pi$$
−0.865414 + 0.501057i $$0.832945\pi$$
$$522$$ 1.70820 + 2.95870i 0.0747661 + 0.129499i
$$523$$ −9.64590 + 16.7072i −0.421786 + 0.730554i −0.996114 0.0880707i $$-0.971930\pi$$
0.574329 + 0.818625i $$0.305263\pi$$
$$524$$ 6.97871 0.304867
$$525$$ 0 0
$$526$$ −5.39512 −0.235238
$$527$$ −18.6803 + 32.3553i −0.813728 + 1.40942i
$$528$$ −10.5517 18.2760i −0.459202 0.795362i
$$529$$ 4.41641 + 7.64944i 0.192018 + 0.332584i
$$530$$ −0.628677 + 1.08890i −0.0273080 + 0.0472988i
$$531$$ −14.9443 −0.648526
$$532$$ 11.1246 + 9.63420i 0.482313 + 0.417695i
$$533$$ 0 0
$$534$$ −0.954915 + 1.65396i −0.0413232 + 0.0715739i
$$535$$ 15.9164 + 27.5680i 0.688126 + 1.19187i
$$536$$ 2.20820 + 3.82472i 0.0953799 + 0.165203i
$$537$$ −22.5000 + 38.9711i −0.970947 + 1.68173i
$$538$$ 1.72949 0.0745636
$$539$$ 16.5000 12.9904i 0.710705 0.559535i
$$540$$ 9.27051 0.398939
$$541$$ 7.35410 12.7377i 0.316178 0.547636i −0.663510 0.748168i $$-0.730934\pi$$
0.979687 + 0.200532i $$0.0642671\pi$$
$$542$$ 1.22542 + 2.12250i 0.0526365 + 0.0911691i
$$543$$ −1.58359 2.74286i −0.0679584 0.117707i
$$544$$ 15.4894 26.8284i 0.664101 1.15026i
$$545$$ −23.9443 −1.02566
$$546$$ 0 0
$$547$$ −31.4164 −1.34327 −0.671634 0.740883i $$-0.734407\pi$$
−0.671634 + 0.740883i $$0.734407\pi$$
$$548$$ 3.48936 6.04374i 0.149058 0.258176i
$$549$$ −3.00000 5.19615i −0.128037 0.221766i
$$550$$ 0 0
$$551$$ −6.70820 + 11.6190i −0.285779 + 0.494984i
$$552$$ 12.3901 0.527358
$$553$$ −26.7705 + 9.27358i −1.13840 + 0.394353i
$$554$$ 10.0902 0.428690
$$555$$ −21.7705 + 37.7076i −0.924107 + 1.60060i
$$556$$ 3.16718 + 5.48572i 0.134319 + 0.232647i
$$557$$ −2.64590 4.58283i −0.112110 0.194181i 0.804511 0.593938i $$-0.202428\pi$$
−0.916621 + 0.399758i $$0.869094\pi$$
$$558$$ 1.90983 3.30792i 0.0808496 0.140036i
$$559$$ 0 0
$$560$$ 3.51722 18.2760i 0.148630 0.772303i
$$561$$ −50.1246 −2.11626
$$562$$ 1.72949 2.99556i 0.0729541 0.126360i
$$563$$ 18.2984 + 31.6937i 0.771185 + 1.33573i 0.936914 + 0.349560i $$0.113669\pi$$
−0.165730 + 0.986171i $$0.552998\pi$$
$$564$$ −3.05166 5.28563i −0.128498 0.222565i
$$565$$ 16.7082 28.9395i 0.702919 1.21749i
$$566$$ −5.39512 −0.226774
$$567$$ −5.50000 + 28.5788i −0.230978 + 1.20020i
$$568$$ 13.1672 0.552483
$$569$$ −8.26393 + 14.3136i −0.346442 + 0.600055i −0.985615 0.169008i $$-0.945944\pi$$
0.639173 + 0.769063i $$0.279277\pi$$
$$570$$ 2.86475 + 4.96188i 0.119991 + 0.207830i
$$571$$ −2.06231 3.57202i −0.0863048 0.149484i 0.819642 0.572877i $$-0.194173\pi$$
−0.905946 + 0.423392i $$0.860839\pi$$
$$572$$ 0 0
$$573$$ −25.0000 −1.04439
$$574$$ 4.27051 1.47935i 0.178248 0.0617468i
$$575$$ 0 0
$$576$$ 4.70820 8.15485i 0.196175 0.339785i
$$577$$ −16.3541 28.3261i −0.680830 1.17923i −0.974728 0.223396i $$-0.928286\pi$$
0.293898 0.955837i $$-0.405047\pi$$
$$578$$ −7.41641 12.8456i −0.308482 0.534306i
$$579$$ −14.2082 + 24.6093i −0.590473 + 1.02273i
$$580$$ 18.5410 0.769874
$$581$$ 0 0
$$582$$ 14.8754 0.616605
$$583$$ −2.20820 + 3.82472i −0.0914545 + 0.158404i
$$584$$ −7.88197 13.6520i −0.326158 0.564922i
$$585$$ 0 0
$$586$$ 0.562306 0.973942i 0.0232286 0.0402332i
$$587$$ 41.8885 1.72893 0.864463 0.502697i $$-0.167659\pi$$
0.864463 + 0.502697i $$0.167659\pi$$
$$588$$ 26.9483 + 10.7714i 1.11133 + 0.444203i
$$589$$ 15.0000 0.618064
$$590$$ 3.19098 5.52694i 0.131371 0.227541i
$$591$$ −30.1246 52.1774i −1.23916 2.14629i
$$592$$ −13.6976 23.7249i −0.562966 0.975086i
$$593$$ 16.1180 27.9173i 0.661888 1.14642i −0.318231 0.948013i $$-0.603089\pi$$
0.980119 0.198411i $$-0.0635780\pi$$
$$594$$ −2.56231 −0.105133
$$595$$ −33.4164 28.9395i −1.36994 1.18640i
$$596$$ −23.5623 −0.965150
$$597$$ 8.15248 14.1205i 0.333659 0.577914i
$$598$$ 0 0
$$599$$ −20.5344 35.5667i −0.839015 1.45322i −0.890719 0.454553i $$-0.849799\pi$$
0.0517049 0.998662i $$-0.483534\pi$$
$$600$$ 0 0
$$601$$ −22.0000 −0.897399 −0.448699 0.893683i $$-0.648113\pi$$
−0.448699 + 0.893683i $$0.648113\pi$$
$$602$$ 7.63932 2.64634i 0.311355 0.107857i
$$603$$ 6.00000 0.244339
$$604$$ 5.94834 10.3028i 0.242034 0.419216i
$$605$$ 2.23607 + 3.87298i 0.0909091 + 0.157459i
$$606$$ 3.84346 + 6.65707i 0.156130 + 0.270425i
$$607$$ 8.06231 13.9643i 0.327239 0.566794i −0.654724 0.755868i $$-0.727215\pi$$
0.981963 + 0.189074i $$0.0605485\pi$$
$$608$$ −12.4377 −0.504415
$$609$$ −5.00000 + 25.9808i −0.202610 + 1.05279i
$$610$$ 2.56231 0.103745
$$611$$ 0 0
$$612$$ −13.8541 23.9960i −0.560019 0.969981i
$$613$$ 11.0623 + 19.1605i 0.446802 + 0.773884i 0.998176 0.0603742i $$-0.0192294\pi$$
−0.551373 + 0.834259i $$0.685896\pi$$
$$614$$ −1.41641 + 2.45329i −0.0571616 + 0.0990067i
$$615$$ −22.3607 −0.901670
$$616$$ −2.20820 + 11.4742i −0.0889711 + 0.462307i
$$617$$ −4.47214 −0.180041 −0.0900207 0.995940i $$-0.528693\pi$$
−0.0900207 + 0.995940i $$0.528693\pi$$
$$618$$ −4.57295 + 7.92058i −0.183951 + 0.318612i
$$619$$ 8.50000 + 14.7224i 0.341644 + 0.591744i 0.984738 0.174042i $$-0.0556830\pi$$
−0.643094 + 0.765787i $$0.722350\pi$$
$$620$$ −10.3647 17.9523i −0.416258 0.720980i
$$621$$ −4.20820 + 7.28882i −0.168869 + 0.292490i
$$622$$ −12.3131 −0.493710
$$623$$ −5.59017 + 1.93649i −0.223965 + 0.0775839i
$$624$$ 0 0
$$625$$ 12.5000 21.6506i 0.500000 0.866025i
$$626$$ 6.19098 + 10.7231i 0.247441 + 0.428581i
$$627$$ 10.0623 + 17.4284i 0.401850 + 0.696024i
$$628$$ 6.48936 11.2399i 0.258954 0.448521i
$$629$$ −65.0689 −2.59447
$$630$$ 3.41641 + 2.95870i 0.136113 + 0.117877i
$$631$$ 30.8328 1.22744 0.613718 0.789526i $$-0.289673\pi$$
0.613718 + 0.789526i $$0.289673\pi$$
$$632$$ 7.88197 13.6520i 0.313528 0.543046i
$$633$$ −4.47214 7.74597i −0.177751 0.307875i
$$634$$ −0.718847 1.24508i −0.0285491 0.0494484i
$$635$$ −17.2361 + 29.8537i −0.683992 + 1.18471i
$$636$$ −6.10333 −0.242013
$$637$$ 0 0
$$638$$ −5.12461 −0.202885
$$639$$ 8.94427 15.4919i 0.353830 0.612851i
$$640$$ 11.2812 + 19.5395i 0.445927 + 0.772368i
$$641$$ 2.97214 + 5.14789i 0.117392 + 0.203329i 0.918734 0.394878i $$-0.129213\pi$$
−0.801341 + 0.598208i $$0.795880\pi$$
$$642$$ 6.07953 10.5300i 0.239940 0.415588i
$$643$$ 18.8328 0.742694 0.371347 0.928494i $$-0.378896\pi$$
0.371347 + 0.928494i $$0.378896\pi$$
$$644$$ 13.9574 + 12.0875i 0.550000 + 0.476314i
$$645$$ −40.0000 −1.57500
$$646$$ −4.28115 + 7.41517i −0.168440 + 0.291746i
$$647$$ −7.88197 13.6520i −0.309872 0.536714i 0.668462 0.743746i $$-0.266953\pi$$
−0.978334 + 0.207032i $$0.933620\pi$$
$$648$$ −8.09675 14.0240i −0.318070 0.550914i
$$649$$ 11.2082 19.4132i 0.439960 0.762034i
$$650$$ 0 0
$$651$$ 27.9508 9.68246i 1.09548 0.379485i
$$652$$ 19.3131 0.756359
$$653$$ −6.73607 + 11.6672i −0.263603 + 0.456573i −0.967197 0.254029i $$-0.918244\pi$$
0.703594 + 0.710602i $$0.251577\pi$$
$$654$$ 4.57295 + 7.92058i 0.178816 + 0.309719i
$$655$$ 4.20820 + 7.28882i 0.164428 + 0.284798i
$$656$$ 7.03444 12.1840i 0.274649 0.475706i
$$657$$ −21.4164 −0.835534
$$658$$ −0.281153 + 1.46091i −0.0109605 + 0.0569523i
$$659$$ 8.94427 0.348419 0.174210 0.984709i $$-0.444263\pi$$
0.174210 + 0.984709i $$0.444263\pi$$
$$660$$ 13.9058 24.0855i 0.541281 0.937526i
$$661$$ 3.35410 + 5.80948i 0.130459 + 0.225962i 0.923854 0.382746i $$-0.125021\pi$$
−0.793394 + 0.608708i $$0.791688\pi$$
$$662$$ −5.42705 9.39993i −0.210928 0.365339i
$$663$$ 0 0
$$664$$ 0 0
$$665$$ −3.35410 + 17.4284i −0.130066 + 0.675845i
$$666$$ 6.65248 0.257778
$$667$$ −8.41641 + 14.5776i −0.325885 + 0.564449i
$$668$$ −12.5410 21.7217i −0.485227 0.840437i
$$669$$ −4.47214 7.74597i −0.172903 0.299476i
$$670$$ −1.28115 + 2.21902i −0.0494953 + 0.0857283i
$$671$$ 9.00000 0.347441
$$672$$ −23.1763 + 8.02850i −0.894044 + 0.309706i
$$673$$ 17.4164 0.671353 0.335677 0.941977i $$-0.391035\pi$$
0.335677 + 0.941977i $$0.391035\pi$$
$$674$$ −3.43769 + 5.95426i −0.132415 + 0.229350i
$$675$$ 0 0
$$676$$ 0 0
$$677$$ −16.4443 + 28.4823i −0.632005 + 1.09466i 0.355137 + 0.934814i $$0.384434\pi$$
−0.987141 + 0.159850i $$0.948899\pi$$
$$678$$ −12.7639 −0.490196
$$679$$ 34.8328 + 30.1661i 1.33676 + 1.15767i
$$680$$ 24.5967 0.943242
$$681$$ −13.3541 + 23.1300i −0.511730 + 0.886343i
$$682$$ 2.86475 + 4.96188i 0.109697 + 0.190000i
$$683$$ −2.26393 3.92125i −0.0866270 0.150042i 0.819456 0.573142i $$-0.194275\pi$$
−0.906083 + 0.423099i $$0.860942\pi$$
$$684$$ −5.56231 + 9.63420i −0.212680 + 0.368373i
$$685$$ 8.41641 0.321574
$$686$$ −3.24671 6.28505i −0.123960 0.239964i
$$687$$ 36.0557 1.37561
$$688$$ 12.5836 21.7954i 0.479745 0.830943i
$$689$$ 0 0
$$690$$ 3.59424 + 6.22540i 0.136830 + 0.236997i
$$691$$ 0.916408 1.58726i 0.0348618 0.0603824i −0.848068 0.529887i $$-0.822234\pi$$
0.882930 + 0.469505i $$0.155568\pi$$
$$692$$ −19.3131 −0.734173
$$693$$ 12.0000 + 10.3923i 0.455842 + 0.394771i
$$694$$ −13.3951 −0.508472
$$695$$ −3.81966 + 6.61585i −0.144888 + 0.250953i
$$696$$ −7.36068 12.7491i −0.279006 0.483252i
$$697$$ −16.7082 28.9395i −0.632868 1.09616i
$$698$$ −0.493422 + 0.854632i −0.0186763 + 0.0323483i
$$699$$ −13.2918 −0.502742
$$700$$ 0 0
$$701$$ 22.3607 0.844551 0.422276 0.906467i $$-0.361231\pi$$
0.422276 + 0.906467i $$0.361231\pi$$
$$702$$ 0 0
$$703$$ 13.0623 + 22.6246i 0.492654 + 0.853302i
$$704$$ 7.06231 + 12.2323i 0.266171 + 0.461021i
$$705$$ 3.68034 6.37454i 0.138610 0.240079i
$$706$$ −11.7295 −0.441445
$$707$$ −4.50000 + 23.3827i −0.169240 + 0.879396i
$$708$$ 30.9787 1.16425
$$709$$ −4.93769 + 8.55234i −0.185439 + 0.321190i −0.943724 0.330733i $$-0.892704\pi$$
0.758285 + 0.651923i $$0.226037\pi$$
$$710$$ 3.81966 + 6.61585i 0.143349 + 0.248288i
$$711$$ −10.7082 18.5472i −0.401589 0.695573i
$$712$$ 1.64590 2.85078i 0.0616826 0.106837i
$$713$$ 18.8197 0.704802
$$714$$ −3.19098 + 16.5808i −0.119420 + 0.620522i
$$715$$ 0 0
$$716$$ 18.6565 32.3141i 0.697228 1.20763i
$$717$$ −8.29180 14.3618i −0.309663 0.536352i
$$718$$ −1.13525 1.96632i −0.0423673 0.0733824i
$$719$$ −5.64590 + 9.77898i −0.210556 + 0.364694i −0.951889 0.306444i $$-0.900861\pi$$
0.741332 + 0.671138i $$0.234194\pi$$
$$720$$ 14.0689 0.524316
$$721$$ −26.7705 + 9.27358i −0.996986 + 0.345366i
$$722$$ −3.81966 −0.142153
$$723$$ −9.73607 + 16.8634i −0.362088 + 0.627155i
$$724$$ 1.31308 + 2.27433i 0.0488003 + 0.0845246i
$$725$$ 0 0
$$726$$ 0.854102 1.47935i 0.0316987 0.0549038i
$$727$$ 14.8328 0.550119 0.275059 0.961427i $$-0.411302\pi$$
0.275059 + 0.961427i $$0.411302\pi$$
$$728$$ 0 0
$$729$$ −7.00000 −0.259259
$$730$$ 4.57295 7.92058i 0.169252 0.293154i
$$731$$ −29.8885 51.7685i −1.10547 1.91473i
$$732$$ 6.21885 + 10.7714i 0.229855 + 0.398121i
$$733$$ 7.64590 13.2431i 0.282408 0.489144i −0.689570 0.724219i $$-0.742200\pi$$
0.971977 + 0.235075i $$0.0755336\pi$$
$$734$$ 0.270510 0.00998470
$$735$$ 5.00000 + 34.6410i 0.184428 + 1.27775i
$$736$$ −15.6049 −0.575203
$$737$$ −4.50000 + 7.79423i −0.165760 + 0.287104i
$$738$$ 1.70820 + 2.95870i 0.0628799 + 0.108911i
$$739$$ 17.9164 + 31.0321i 0.659066 + 1.14154i 0.980858 + 0.194725i $$0.0623814\pi$$
−0.321792 + 0.946810i $$0.604285\pi$$
$$740$$ 18.0517 31.2664i 0.663592 1.14938i
$$741$$ 0 0
$$742$$ 1.12461 + 0.973942i 0.0412858 + 0.0357545i
$$743$$ −15.0557 −0.552341 −0.276171 0.961109i $$-0.589065\pi$$
−0.276171 + 0.961109i $$0.589065\pi$$
$$744$$ −8.22949 + 14.2539i −0.301708 + 0.522573i
$$745$$ −14.2082 24.6093i −0.520548 0.901616i
$$746$$ 5.42705 + 9.39993i 0.198698 + 0.344156i
$$747$$ 0 0
$$748$$ 41.5623 1.51967
$$749$$ 35.5902 12.3288i 1.30044 0.450484i
$$750$$ −9.54915 −0.348686
$$751$$ −15.0623 + 26.0887i −0.549631 + 0.951989i 0.448668 + 0.893698i $$0.351898\pi$$
−0.998300 + 0.0582911i $$0.981435\pi$$
$$752$$ 2.31559 + 4.01073i 0.0844411 + 0.146256i
$$753$$ −11.7082 20.2792i −0.426671 0.739015i
$$754$$ 0 0
$$755$$ 14.3475 0.522160
$$756$$ 2.07295 10.7714i 0.0753924 0.391751i
$$757$$ 0.832816 0.0302692 0.0151346 0.999885i $$-0.495182\pi$$
0.0151346 + 0.999885i $$0.495182\pi$$
$$758$$ 2.18034 3.77646i 0.0791935 0.137167i
$$759$$ 12.6246 + 21.8665i 0.458244 + 0.793703i
$$760$$ −4.93769 8.55234i −0.179109 0.310226i
$$761$$ 16.7705 29.0474i 0.607931 1.05297i −0.383650 0.923478i $$-0.625333\pi$$
0.991581 0.129488i $$-0.0413334\pi$$
$$762$$ 13.1672 0.476997
$$763$$ −5.35410 + 27.8207i −0.193832 + 1.00718i
$$764$$ 20.7295 0.749967
$$765$$ 16.7082 28.9395i 0.604086 1.04631i
$$766$$ 2.86475 + 4.96188i 0.103507 + 0.179280i
$$767$$ 0 0
$$768$$ −6.21885 + 10.7714i −0.224403 + 0.388678i
$$769$$ −46.0000 −1.65880 −0.829401 0.558653i $$-0.811318\pi$$
−0.829401 + 0.558653i $$0.811318\pi$$
$$770$$ −6.40576 + 2.21902i −0.230848 + 0.0799680i
$$771$$ −40.1246 −1.44505
$$772$$ 11.7812 20.4056i 0.424013 0.734412i
$$773$$ 5.53444 + 9.58593i 0.199060 + 0.344782i 0.948224 0.317603i $$-0.102878\pi$$
−0.749164 + 0.662385i $$0.769544\pi$$
$$774$$ 3.05573 + 5.29268i 0.109836 + 0.190241i
$$775$$ 0 0
$$776$$ −25.6393 −0.920398
$$777$$ 38.9443 + 33.7267i 1.39712 + 1.20994i
$$778$$ −2.85410 −0.102325
$$779$$ −6.70820 + 11.6190i −0.240346 + 0.416292i
$$780$$