# Properties

 Label 384.3.i.c.353.6 Level $384$ Weight $3$ Character 384.353 Analytic conductor $10.463$ Analytic rank $0$ Dimension $20$ CM no Inner twists $4$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$384 = 2^{7} \cdot 3$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 384.i (of order $$4$$, degree $$2$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$10.4632421514$$ Analytic rank: $$0$$ Dimension: $$20$$ Relative dimension: $$10$$ over $$\Q(i)$$ Coefficient field: $$\mathbb{Q}[x]/(x^{20} - \cdots)$$ Defining polynomial: $$x^{20} - 2 x^{18} + 6 x^{16} - 24 x^{14} - 24 x^{12} + 1216 x^{10} - 384 x^{8} - 6144 x^{6} + 24576 x^{4} - 131072 x^{2} + 1048576$$ x^20 - 2*x^18 + 6*x^16 - 24*x^14 - 24*x^12 + 1216*x^10 - 384*x^8 - 6144*x^6 + 24576*x^4 - 131072*x^2 + 1048576 Coefficient ring: $$\Z[a_1, \ldots, a_{11}]$$ Coefficient ring index: $$2^{23}$$ Twist minimal: no (minimal twist has level 48) Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

## Embedding invariants

 Embedding label 353.6 Root $$1.96139 + 0.391068i$$ of defining polynomial Character $$\chi$$ $$=$$ 384.353 Dual form 384.3.i.c.161.6

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-0.164573 + 2.99548i) q^{3} +(3.61305 - 3.61305i) q^{5} +12.2792i q^{7} +(-8.94583 - 0.985948i) q^{9} +O(q^{10})$$ $$q+(-0.164573 + 2.99548i) q^{3} +(3.61305 - 3.61305i) q^{5} +12.2792i q^{7} +(-8.94583 - 0.985948i) q^{9} +(1.76932 - 1.76932i) q^{11} +(2.38826 - 2.38826i) q^{13} +(10.2282 + 11.4174i) q^{15} +20.0754i q^{17} +(-8.77090 + 8.77090i) q^{19} +(-36.7820 - 2.02081i) q^{21} +13.1821 q^{23} -1.10820i q^{25} +(4.42563 - 26.6348i) q^{27} +(6.51544 + 6.51544i) q^{29} -37.5922 q^{31} +(5.00877 + 5.59113i) q^{33} +(44.3652 + 44.3652i) q^{35} +(-10.0057 - 10.0057i) q^{37} +(6.76096 + 7.54704i) q^{39} -4.57407 q^{41} +(21.2835 + 21.2835i) q^{43} +(-35.8840 + 28.7594i) q^{45} +54.8366i q^{47} -101.778 q^{49} +(-60.1356 - 3.30386i) q^{51} +(-21.5215 + 21.5215i) q^{53} -12.7852i q^{55} +(-24.8296 - 27.7165i) q^{57} +(-53.6617 + 53.6617i) q^{59} +(19.2186 - 19.2186i) q^{61} +(12.1066 - 109.847i) q^{63} -17.2578i q^{65} +(31.5603 - 31.5603i) q^{67} +(-2.16941 + 39.4867i) q^{69} +65.1220 q^{71} -50.2451i q^{73} +(3.31960 + 0.182380i) q^{75} +(21.7257 + 21.7257i) q^{77} -20.9299 q^{79} +(79.0558 + 17.6403i) q^{81} +(-6.35791 - 6.35791i) q^{83} +(72.5334 + 72.5334i) q^{85} +(-20.5891 + 18.4446i) q^{87} +166.399 q^{89} +(29.3259 + 29.3259i) q^{91} +(6.18664 - 112.607i) q^{93} +63.3793i q^{95} +139.213 q^{97} +(-17.5725 + 14.0835i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$20 q - 6 q^{3}+O(q^{10})$$ 20 * q - 6 * q^3 $$20 q - 6 q^{3} - 92 q^{13} + 116 q^{15} - 52 q^{19} - 48 q^{21} + 18 q^{27} + 80 q^{31} + 60 q^{33} + 116 q^{37} + 172 q^{43} - 60 q^{45} - 364 q^{49} + 128 q^{51} + 244 q^{61} - 296 q^{63} + 356 q^{67} + 20 q^{69} - 146 q^{75} - 384 q^{79} - 188 q^{81} - 48 q^{85} + 136 q^{91} + 132 q^{93} + 472 q^{97} - 452 q^{99}+O(q^{100})$$ 20 * q - 6 * q^3 - 92 * q^13 + 116 * q^15 - 52 * q^19 - 48 * q^21 + 18 * q^27 + 80 * q^31 + 60 * q^33 + 116 * q^37 + 172 * q^43 - 60 * q^45 - 364 * q^49 + 128 * q^51 + 244 * q^61 - 296 * q^63 + 356 * q^67 + 20 * q^69 - 146 * q^75 - 384 * q^79 - 188 * q^81 - 48 * q^85 + 136 * q^91 + 132 * q^93 + 472 * q^97 - 452 * q^99

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/384\mathbb{Z}\right)^\times$$.

 $$n$$ $$127$$ $$133$$ $$257$$ $$\chi(n)$$ $$1$$ $$e\left(\frac{1}{4}\right)$$ $$-1$$

## 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 0
$$3$$ −0.164573 + 2.99548i −0.0548575 + 0.998494i
$$4$$ 0 0
$$5$$ 3.61305 3.61305i 0.722609 0.722609i −0.246527 0.969136i $$-0.579289\pi$$
0.969136 + 0.246527i $$0.0792893\pi$$
$$6$$ 0 0
$$7$$ 12.2792i 1.75417i 0.480338 + 0.877083i $$0.340514\pi$$
−0.480338 + 0.877083i $$0.659486\pi$$
$$8$$ 0 0
$$9$$ −8.94583 0.985948i −0.993981 0.109550i
$$10$$ 0 0
$$11$$ 1.76932 1.76932i 0.160847 0.160847i −0.622095 0.782942i $$-0.713718\pi$$
0.782942 + 0.622095i $$0.213718\pi$$
$$12$$ 0 0
$$13$$ 2.38826 2.38826i 0.183713 0.183713i −0.609259 0.792971i $$-0.708533\pi$$
0.792971 + 0.609259i $$0.208533\pi$$
$$14$$ 0 0
$$15$$ 10.2282 + 11.4174i 0.681881 + 0.761162i
$$16$$ 0 0
$$17$$ 20.0754i 1.18091i 0.807072 + 0.590453i $$0.201051\pi$$
−0.807072 + 0.590453i $$0.798949\pi$$
$$18$$ 0 0
$$19$$ −8.77090 + 8.77090i −0.461626 + 0.461626i −0.899188 0.437562i $$-0.855842\pi$$
0.437562 + 0.899188i $$0.355842\pi$$
$$20$$ 0 0
$$21$$ −36.7820 2.02081i −1.75153 0.0962292i
$$22$$ 0 0
$$23$$ 13.1821 0.573134 0.286567 0.958060i $$-0.407486\pi$$
0.286567 + 0.958060i $$0.407486\pi$$
$$24$$ 0 0
$$25$$ 1.10820i 0.0443281i
$$26$$ 0 0
$$27$$ 4.42563 26.6348i 0.163912 0.986475i
$$28$$ 0 0
$$29$$ 6.51544 + 6.51544i 0.224670 + 0.224670i 0.810462 0.585792i $$-0.199216\pi$$
−0.585792 + 0.810462i $$0.699216\pi$$
$$30$$ 0 0
$$31$$ −37.5922 −1.21265 −0.606326 0.795216i $$-0.707357\pi$$
−0.606326 + 0.795216i $$0.707357\pi$$
$$32$$ 0 0
$$33$$ 5.00877 + 5.59113i 0.151781 + 0.169428i
$$34$$ 0 0
$$35$$ 44.3652 + 44.3652i 1.26758 + 1.26758i
$$36$$ 0 0
$$37$$ −10.0057 10.0057i −0.270423 0.270423i 0.558847 0.829271i $$-0.311244\pi$$
−0.829271 + 0.558847i $$0.811244\pi$$
$$38$$ 0 0
$$39$$ 6.76096 + 7.54704i 0.173358 + 0.193514i
$$40$$ 0 0
$$41$$ −4.57407 −0.111563 −0.0557814 0.998443i $$-0.517765\pi$$
−0.0557814 + 0.998443i $$0.517765\pi$$
$$42$$ 0 0
$$43$$ 21.2835 + 21.2835i 0.494966 + 0.494966i 0.909867 0.414901i $$-0.136184\pi$$
−0.414901 + 0.909867i $$0.636184\pi$$
$$44$$ 0 0
$$45$$ −35.8840 + 28.7594i −0.797422 + 0.639098i
$$46$$ 0 0
$$47$$ 54.8366i 1.16674i 0.812208 + 0.583368i $$0.198266\pi$$
−0.812208 + 0.583368i $$0.801734\pi$$
$$48$$ 0 0
$$49$$ −101.778 −2.07710
$$50$$ 0 0
$$51$$ −60.1356 3.30386i −1.17913 0.0647816i
$$52$$ 0 0
$$53$$ −21.5215 + 21.5215i −0.406065 + 0.406065i −0.880364 0.474299i $$-0.842702\pi$$
0.474299 + 0.880364i $$0.342702\pi$$
$$54$$ 0 0
$$55$$ 12.7852i 0.232459i
$$56$$ 0 0
$$57$$ −24.8296 27.7165i −0.435607 0.486255i
$$58$$ 0 0
$$59$$ −53.6617 + 53.6617i −0.909520 + 0.909520i −0.996233 0.0867132i $$-0.972364\pi$$
0.0867132 + 0.996233i $$0.472364\pi$$
$$60$$ 0 0
$$61$$ 19.2186 19.2186i 0.315059 0.315059i −0.531807 0.846866i $$-0.678487\pi$$
0.846866 + 0.531807i $$0.178487\pi$$
$$62$$ 0 0
$$63$$ 12.1066 109.847i 0.192169 1.74361i
$$64$$ 0 0
$$65$$ 17.2578i 0.265505i
$$66$$ 0 0
$$67$$ 31.5603 31.5603i 0.471049 0.471049i −0.431205 0.902254i $$-0.641911\pi$$
0.902254 + 0.431205i $$0.141911\pi$$
$$68$$ 0 0
$$69$$ −2.16941 + 39.4867i −0.0314407 + 0.572271i
$$70$$ 0 0
$$71$$ 65.1220 0.917211 0.458606 0.888640i $$-0.348349\pi$$
0.458606 + 0.888640i $$0.348349\pi$$
$$72$$ 0 0
$$73$$ 50.2451i 0.688290i −0.938917 0.344145i $$-0.888169\pi$$
0.938917 0.344145i $$-0.111831\pi$$
$$74$$ 0 0
$$75$$ 3.31960 + 0.182380i 0.0442614 + 0.00243173i
$$76$$ 0 0
$$77$$ 21.7257 + 21.7257i 0.282152 + 0.282152i
$$78$$ 0 0
$$79$$ −20.9299 −0.264935 −0.132468 0.991187i $$-0.542290\pi$$
−0.132468 + 0.991187i $$0.542290\pi$$
$$80$$ 0 0
$$81$$ 79.0558 + 17.6403i 0.975998 + 0.217781i
$$82$$ 0 0
$$83$$ −6.35791 6.35791i −0.0766013 0.0766013i 0.667768 0.744369i $$-0.267250\pi$$
−0.744369 + 0.667768i $$0.767250\pi$$
$$84$$ 0 0
$$85$$ 72.5334 + 72.5334i 0.853334 + 0.853334i
$$86$$ 0 0
$$87$$ −20.5891 + 18.4446i −0.236657 + 0.212007i
$$88$$ 0 0
$$89$$ 166.399 1.86966 0.934828 0.355102i $$-0.115554\pi$$
0.934828 + 0.355102i $$0.115554\pi$$
$$90$$ 0 0
$$91$$ 29.3259 + 29.3259i 0.322262 + 0.322262i
$$92$$ 0 0
$$93$$ 6.18664 112.607i 0.0665231 1.21083i
$$94$$ 0 0
$$95$$ 63.3793i 0.667151i
$$96$$ 0 0
$$97$$ 139.213 1.43519 0.717593 0.696463i $$-0.245244\pi$$
0.717593 + 0.696463i $$0.245244\pi$$
$$98$$ 0 0
$$99$$ −17.5725 + 14.0835i −0.177500 + 0.142258i
$$100$$ 0 0
$$101$$ 125.879 125.879i 1.24632 1.24632i 0.288994 0.957331i $$-0.406679\pi$$
0.957331 0.288994i $$-0.0933207\pi$$
$$102$$ 0 0
$$103$$ 26.3937i 0.256250i −0.991758 0.128125i $$-0.959104\pi$$
0.991758 0.128125i $$-0.0408958\pi$$
$$104$$ 0 0
$$105$$ −140.196 + 125.594i −1.33520 + 1.19613i
$$106$$ 0 0
$$107$$ 83.9534 83.9534i 0.784611 0.784611i −0.195994 0.980605i $$-0.562793\pi$$
0.980605 + 0.195994i $$0.0627933\pi$$
$$108$$ 0 0
$$109$$ −2.29518 + 2.29518i −0.0210567 + 0.0210567i −0.717557 0.696500i $$-0.754740\pi$$
0.696500 + 0.717557i $$0.254740\pi$$
$$110$$ 0 0
$$111$$ 31.6184 28.3251i 0.284851 0.255181i
$$112$$ 0 0
$$113$$ 177.630i 1.57195i −0.618260 0.785974i $$-0.712162\pi$$
0.618260 0.785974i $$-0.287838\pi$$
$$114$$ 0 0
$$115$$ 47.6275 47.6275i 0.414152 0.414152i
$$116$$ 0 0
$$117$$ −23.7197 + 19.0103i −0.202733 + 0.162481i
$$118$$ 0 0
$$119$$ −246.509 −2.07151
$$120$$ 0 0
$$121$$ 114.739i 0.948257i
$$122$$ 0 0
$$123$$ 0.752766 13.7016i 0.00612005 0.111395i
$$124$$ 0 0
$$125$$ 86.3222 + 86.3222i 0.690577 + 0.690577i
$$126$$ 0 0
$$127$$ 152.167 1.19816 0.599082 0.800687i $$-0.295532\pi$$
0.599082 + 0.800687i $$0.295532\pi$$
$$128$$ 0 0
$$129$$ −67.2571 + 60.2517i −0.521373 + 0.467068i
$$130$$ 0 0
$$131$$ −65.6955 65.6955i −0.501492 0.501492i 0.410409 0.911901i $$-0.365386\pi$$
−0.911901 + 0.410409i $$0.865386\pi$$
$$132$$ 0 0
$$133$$ −107.699 107.699i −0.809769 0.809769i
$$134$$ 0 0
$$135$$ −80.2428 112.223i −0.594391 0.831280i
$$136$$ 0 0
$$137$$ 53.1509 0.387963 0.193982 0.981005i $$-0.437860\pi$$
0.193982 + 0.981005i $$0.437860\pi$$
$$138$$ 0 0
$$139$$ −161.324 161.324i −1.16060 1.16060i −0.984343 0.176261i $$-0.943600\pi$$
−0.176261 0.984343i $$-0.556400\pi$$
$$140$$ 0 0
$$141$$ −164.262 9.02460i −1.16498 0.0640043i
$$142$$ 0 0
$$143$$ 8.45118i 0.0590992i
$$144$$ 0 0
$$145$$ 47.0811 0.324698
$$146$$ 0 0
$$147$$ 16.7498 304.874i 0.113945 2.07397i
$$148$$ 0 0
$$149$$ 116.911 116.911i 0.784638 0.784638i −0.195971 0.980610i $$-0.562786\pi$$
0.980610 + 0.195971i $$0.0627859\pi$$
$$150$$ 0 0
$$151$$ 10.9723i 0.0726643i −0.999340 0.0363321i $$-0.988433\pi$$
0.999340 0.0363321i $$-0.0115674\pi$$
$$152$$ 0 0
$$153$$ 19.7933 179.591i 0.129368 1.17380i
$$154$$ 0 0
$$155$$ −135.822 + 135.822i −0.876273 + 0.876273i
$$156$$ 0 0
$$157$$ −49.8246 + 49.8246i −0.317354 + 0.317354i −0.847750 0.530396i $$-0.822043\pi$$
0.530396 + 0.847750i $$0.322043\pi$$
$$158$$ 0 0
$$159$$ −60.9253 68.0090i −0.383178 0.427730i
$$160$$ 0 0
$$161$$ 161.865i 1.00537i
$$162$$ 0 0
$$163$$ −66.4240 + 66.4240i −0.407509 + 0.407509i −0.880869 0.473360i $$-0.843041\pi$$
0.473360 + 0.880869i $$0.343041\pi$$
$$164$$ 0 0
$$165$$ 38.2980 + 2.10410i 0.232109 + 0.0127521i
$$166$$ 0 0
$$167$$ 182.851 1.09492 0.547459 0.836832i $$-0.315595\pi$$
0.547459 + 0.836832i $$0.315595\pi$$
$$168$$ 0 0
$$169$$ 157.592i 0.932499i
$$170$$ 0 0
$$171$$ 87.1106 69.8153i 0.509419 0.408277i
$$172$$ 0 0
$$173$$ −123.809 123.809i −0.715661 0.715661i 0.252052 0.967714i $$-0.418894\pi$$
−0.967714 + 0.252052i $$0.918894\pi$$
$$174$$ 0 0
$$175$$ 13.6078 0.0777589
$$176$$ 0 0
$$177$$ −151.911 169.574i −0.858257 0.958045i
$$178$$ 0 0
$$179$$ 168.642 + 168.642i 0.942134 + 0.942134i 0.998415 0.0562807i $$-0.0179242\pi$$
−0.0562807 + 0.998415i $$0.517924\pi$$
$$180$$ 0 0
$$181$$ 162.162 + 162.162i 0.895920 + 0.895920i 0.995072 0.0991520i $$-0.0316130\pi$$
−0.0991520 + 0.995072i $$0.531613\pi$$
$$182$$ 0 0
$$183$$ 54.4061 + 60.7318i 0.297301 + 0.331868i
$$184$$ 0 0
$$185$$ −72.3018 −0.390821
$$186$$ 0 0
$$187$$ 35.5198 + 35.5198i 0.189945 + 0.189945i
$$188$$ 0 0
$$189$$ 327.053 + 54.3430i 1.73044 + 0.287529i
$$190$$ 0 0
$$191$$ 60.8777i 0.318731i 0.987220 + 0.159366i $$0.0509449\pi$$
−0.987220 + 0.159366i $$0.949055\pi$$
$$192$$ 0 0
$$193$$ 177.871 0.921611 0.460806 0.887501i $$-0.347561\pi$$
0.460806 + 0.887501i $$0.347561\pi$$
$$194$$ 0 0
$$195$$ 51.6955 + 2.84016i 0.265105 + 0.0145649i
$$196$$ 0 0
$$197$$ −66.9411 + 66.9411i −0.339803 + 0.339803i −0.856293 0.516490i $$-0.827238\pi$$
0.516490 + 0.856293i $$0.327238\pi$$
$$198$$ 0 0
$$199$$ 0.826328i 0.00415240i −0.999998 0.00207620i $$-0.999339\pi$$
0.999998 0.00207620i $$-0.000660875\pi$$
$$200$$ 0 0
$$201$$ 89.3443 + 99.7322i 0.444499 + 0.496180i
$$202$$ 0 0
$$203$$ −80.0041 + 80.0041i −0.394109 + 0.394109i
$$204$$ 0 0
$$205$$ −16.5263 + 16.5263i −0.0806162 + 0.0806162i
$$206$$ 0 0
$$207$$ −117.925 12.9969i −0.569685 0.0627868i
$$208$$ 0 0
$$209$$ 31.0370i 0.148502i
$$210$$ 0 0
$$211$$ −181.344 + 181.344i −0.859448 + 0.859448i −0.991273 0.131825i $$-0.957916\pi$$
0.131825 + 0.991273i $$0.457916\pi$$
$$212$$ 0 0
$$213$$ −10.7173 + 195.072i −0.0503159 + 0.915830i
$$214$$ 0 0
$$215$$ 153.797 0.715333
$$216$$ 0 0
$$217$$ 461.601i 2.12719i
$$218$$ 0 0
$$219$$ 150.508 + 8.26897i 0.687253 + 0.0377579i
$$220$$ 0 0
$$221$$ 47.9454 + 47.9454i 0.216947 + 0.216947i
$$222$$ 0 0
$$223$$ 17.7339 0.0795241 0.0397621 0.999209i $$-0.487340\pi$$
0.0397621 + 0.999209i $$0.487340\pi$$
$$224$$ 0 0
$$225$$ −1.09263 + 9.91380i −0.00485614 + 0.0440613i
$$226$$ 0 0
$$227$$ 7.53766 + 7.53766i 0.0332055 + 0.0332055i 0.723515 0.690309i $$-0.242525\pi$$
−0.690309 + 0.723515i $$0.742525\pi$$
$$228$$ 0 0
$$229$$ −223.748 223.748i −0.977063 0.977063i 0.0226794 0.999743i $$-0.492780\pi$$
−0.999743 + 0.0226794i $$0.992780\pi$$
$$230$$ 0 0
$$231$$ −68.6545 + 61.5036i −0.297205 + 0.266249i
$$232$$ 0 0
$$233$$ −123.585 −0.530406 −0.265203 0.964193i $$-0.585439\pi$$
−0.265203 + 0.964193i $$0.585439\pi$$
$$234$$ 0 0
$$235$$ 198.127 + 198.127i 0.843095 + 0.843095i
$$236$$ 0 0
$$237$$ 3.44448 62.6951i 0.0145337 0.264536i
$$238$$ 0 0
$$239$$ 118.501i 0.495820i −0.968783 0.247910i $$-0.920256\pi$$
0.968783 0.247910i $$-0.0797437\pi$$
$$240$$ 0 0
$$241$$ −264.162 −1.09611 −0.548053 0.836443i $$-0.684631\pi$$
−0.548053 + 0.836443i $$0.684631\pi$$
$$242$$ 0 0
$$243$$ −65.8515 + 233.907i −0.270994 + 0.962581i
$$244$$ 0 0
$$245$$ −367.728 + 367.728i −1.50093 + 1.50093i
$$246$$ 0 0
$$247$$ 41.8944i 0.169613i
$$248$$ 0 0
$$249$$ 20.0913 17.9987i 0.0806881 0.0722838i
$$250$$ 0 0
$$251$$ 152.477 152.477i 0.607478 0.607478i −0.334808 0.942286i $$-0.608672\pi$$
0.942286 + 0.334808i $$0.108672\pi$$
$$252$$ 0 0
$$253$$ 23.3233 23.3233i 0.0921869 0.0921869i
$$254$$ 0 0
$$255$$ −229.210 + 205.336i −0.898861 + 0.805238i
$$256$$ 0 0
$$257$$ 113.118i 0.440147i 0.975483 + 0.220074i $$0.0706298\pi$$
−0.975483 + 0.220074i $$0.929370\pi$$
$$258$$ 0 0
$$259$$ 122.861 122.861i 0.474367 0.474367i
$$260$$ 0 0
$$261$$ −51.8621 64.7099i −0.198705 0.247931i
$$262$$ 0 0
$$263$$ −129.324 −0.491727 −0.245864 0.969304i $$-0.579072\pi$$
−0.245864 + 0.969304i $$0.579072\pi$$
$$264$$ 0 0
$$265$$ 155.516i 0.586853i
$$266$$ 0 0
$$267$$ −27.3848 + 498.446i −0.102565 + 1.86684i
$$268$$ 0 0
$$269$$ −129.457 129.457i −0.481253 0.481253i 0.424278 0.905532i $$-0.360528\pi$$
−0.905532 + 0.424278i $$0.860528\pi$$
$$270$$ 0 0
$$271$$ −170.727 −0.629990 −0.314995 0.949093i $$-0.602003\pi$$
−0.314995 + 0.949093i $$0.602003\pi$$
$$272$$ 0 0
$$273$$ −92.6714 + 83.0189i −0.339456 + 0.304099i
$$274$$ 0 0
$$275$$ −1.96076 1.96076i −0.00713004 0.00713004i
$$276$$ 0 0
$$277$$ −114.051 114.051i −0.411737 0.411737i 0.470606 0.882343i $$-0.344035\pi$$
−0.882343 + 0.470606i $$0.844035\pi$$
$$278$$ 0 0
$$279$$ 336.294 + 37.0640i 1.20535 + 0.132846i
$$280$$ 0 0
$$281$$ 136.468 0.485650 0.242825 0.970070i $$-0.421926\pi$$
0.242825 + 0.970070i $$0.421926\pi$$
$$282$$ 0 0
$$283$$ −132.657 132.657i −0.468752 0.468752i 0.432758 0.901510i $$-0.357540\pi$$
−0.901510 + 0.432758i $$0.857540\pi$$
$$284$$ 0 0
$$285$$ −189.852 10.4305i −0.666146 0.0365982i
$$286$$ 0 0
$$287$$ 56.1658i 0.195700i
$$288$$ 0 0
$$289$$ −114.022 −0.394541
$$290$$ 0 0
$$291$$ −22.9106 + 417.010i −0.0787307 + 1.43303i
$$292$$ 0 0
$$293$$ 143.968 143.968i 0.491360 0.491360i −0.417375 0.908735i $$-0.637050\pi$$
0.908735 + 0.417375i $$0.137050\pi$$
$$294$$ 0 0
$$295$$ 387.764i 1.31446i
$$296$$ 0 0
$$297$$ −39.2951 54.9557i −0.132307 0.185036i
$$298$$ 0 0
$$299$$ 31.4823 31.4823i 0.105292 0.105292i
$$300$$ 0 0
$$301$$ −261.344 + 261.344i −0.868252 + 0.868252i
$$302$$ 0 0
$$303$$ 356.352 + 397.784i 1.17608 + 1.31282i
$$304$$ 0 0
$$305$$ 138.875i 0.455328i
$$306$$ 0 0
$$307$$ −89.3258 + 89.3258i −0.290964 + 0.290964i −0.837461 0.546497i $$-0.815961\pi$$
0.546497 + 0.837461i $$0.315961\pi$$
$$308$$ 0 0
$$309$$ 79.0619 + 4.34368i 0.255864 + 0.0140572i
$$310$$ 0 0
$$311$$ 314.507 1.01128 0.505638 0.862746i $$-0.331257\pi$$
0.505638 + 0.862746i $$0.331257\pi$$
$$312$$ 0 0
$$313$$ 103.874i 0.331867i −0.986137 0.165934i $$-0.946936\pi$$
0.986137 0.165934i $$-0.0530638\pi$$
$$314$$ 0 0
$$315$$ −353.142 440.625i −1.12108 1.39881i
$$316$$ 0 0
$$317$$ 321.109 + 321.109i 1.01296 + 1.01296i 0.999915 + 0.0130482i $$0.00415349\pi$$
0.0130482 + 0.999915i $$0.495847\pi$$
$$318$$ 0 0
$$319$$ 23.0557 0.0722750
$$320$$ 0 0
$$321$$ 237.665 + 265.297i 0.740388 + 0.826472i
$$322$$ 0 0
$$323$$ −176.079 176.079i −0.545138 0.545138i
$$324$$ 0 0
$$325$$ −2.64668 2.64668i −0.00814363 0.00814363i
$$326$$ 0 0
$$327$$ −6.49746 7.25291i −0.0198699 0.0221801i
$$328$$ 0 0
$$329$$ −673.348 −2.04665
$$330$$ 0 0
$$331$$ −313.858 313.858i −0.948213 0.948213i 0.0505107 0.998724i $$-0.483915\pi$$
−0.998724 + 0.0505107i $$0.983915\pi$$
$$332$$ 0 0
$$333$$ 79.6439 + 99.3740i 0.239171 + 0.298420i
$$334$$ 0 0
$$335$$ 228.057i 0.680768i
$$336$$ 0 0
$$337$$ −236.028 −0.700380 −0.350190 0.936679i $$-0.613883\pi$$
−0.350190 + 0.936679i $$0.613883\pi$$
$$338$$ 0 0
$$339$$ 532.088 + 29.2330i 1.56958 + 0.0862331i
$$340$$ 0 0
$$341$$ −66.5125 + 66.5125i −0.195051 + 0.195051i
$$342$$ 0 0
$$343$$ 648.069i 1.88941i
$$344$$ 0 0
$$345$$ 134.829 + 150.506i 0.390809 + 0.436248i
$$346$$ 0 0
$$347$$ 441.946 441.946i 1.27362 1.27362i 0.329445 0.944175i $$-0.393138\pi$$
0.944175 0.329445i $$-0.106862\pi$$
$$348$$ 0 0
$$349$$ 476.643 476.643i 1.36574 1.36574i 0.499321 0.866417i $$-0.333583\pi$$
0.866417 0.499321i $$-0.166417\pi$$
$$350$$ 0 0
$$351$$ −53.0414 74.1805i −0.151115 0.211341i
$$352$$ 0 0
$$353$$ 452.246i 1.28115i 0.767895 + 0.640575i $$0.221304\pi$$
−0.767895 + 0.640575i $$0.778696\pi$$
$$354$$ 0 0
$$355$$ 235.289 235.289i 0.662785 0.662785i
$$356$$ 0 0
$$357$$ 40.5687 738.415i 0.113638 2.06839i
$$358$$ 0 0
$$359$$ −617.295 −1.71948 −0.859742 0.510728i $$-0.829376\pi$$
−0.859742 + 0.510728i $$0.829376\pi$$
$$360$$ 0 0
$$361$$ 207.143i 0.573803i
$$362$$ 0 0
$$363$$ −343.699 18.8829i −0.946829 0.0520190i
$$364$$ 0 0
$$365$$ −181.538 181.538i −0.497364 0.497364i
$$366$$ 0 0
$$367$$ 11.3588 0.0309505 0.0154753 0.999880i $$-0.495074\pi$$
0.0154753 + 0.999880i $$0.495074\pi$$
$$368$$ 0 0
$$369$$ 40.9189 + 4.50980i 0.110891 + 0.0122217i
$$370$$ 0 0
$$371$$ −264.266 264.266i −0.712306 0.712306i
$$372$$ 0 0
$$373$$ 59.4092 + 59.4092i 0.159274 + 0.159274i 0.782245 0.622971i $$-0.214075\pi$$
−0.622971 + 0.782245i $$0.714075\pi$$
$$374$$ 0 0
$$375$$ −272.783 + 244.370i −0.727421 + 0.651654i
$$376$$ 0 0
$$377$$ 31.1212 0.0825495
$$378$$ 0 0
$$379$$ 435.432 + 435.432i 1.14890 + 1.14890i 0.986770 + 0.162129i $$0.0518359\pi$$
0.162129 + 0.986770i $$0.448164\pi$$
$$380$$ 0 0
$$381$$ −25.0425 + 455.813i −0.0657283 + 1.19636i
$$382$$ 0 0
$$383$$ 272.117i 0.710488i 0.934774 + 0.355244i $$0.115602\pi$$
−0.934774 + 0.355244i $$0.884398\pi$$
$$384$$ 0 0
$$385$$ 156.992 0.407772
$$386$$ 0 0
$$387$$ −169.414 211.383i −0.437763 0.546210i
$$388$$ 0 0
$$389$$ −260.985 + 260.985i −0.670913 + 0.670913i −0.957927 0.287013i $$-0.907338\pi$$
0.287013 + 0.957927i $$0.407338\pi$$
$$390$$ 0 0
$$391$$ 264.636i 0.676818i
$$392$$ 0 0
$$393$$ 207.601 185.978i 0.528248 0.473226i
$$394$$ 0 0
$$395$$ −75.6206 + 75.6206i −0.191445 + 0.191445i
$$396$$ 0 0
$$397$$ −258.248 + 258.248i −0.650500 + 0.650500i −0.953113 0.302614i $$-0.902141\pi$$
0.302614 + 0.953113i $$0.402141\pi$$
$$398$$ 0 0
$$399$$ 340.336 304.887i 0.852972 0.764128i
$$400$$ 0 0
$$401$$ 430.073i 1.07250i −0.844059 0.536250i $$-0.819840\pi$$
0.844059 0.536250i $$-0.180160\pi$$
$$402$$ 0 0
$$403$$ −89.7801 + 89.7801i −0.222779 + 0.222779i
$$404$$ 0 0
$$405$$ 349.367 221.897i 0.862635 0.547894i
$$406$$ 0 0
$$407$$ −35.4063 −0.0869935
$$408$$ 0 0
$$409$$ 207.501i 0.507337i 0.967291 + 0.253668i $$0.0816372\pi$$
−0.967291 + 0.253668i $$0.918363\pi$$
$$410$$ 0 0
$$411$$ −8.74718 + 159.213i −0.0212827 + 0.387379i
$$412$$ 0 0
$$413$$ −658.921 658.921i −1.59545 1.59545i
$$414$$ 0 0
$$415$$ −45.9428 −0.110706
$$416$$ 0 0
$$417$$ 509.793 456.694i 1.22253 1.09519i
$$418$$ 0 0
$$419$$ −108.717 108.717i −0.259467 0.259467i 0.565370 0.824837i $$-0.308733\pi$$
−0.824837 + 0.565370i $$0.808733\pi$$
$$420$$ 0 0
$$421$$ 484.985 + 484.985i 1.15198 + 1.15198i 0.986155 + 0.165829i $$0.0530300\pi$$
0.165829 + 0.986155i $$0.446970\pi$$
$$422$$ 0 0
$$423$$ 54.0661 490.559i 0.127816 1.15971i
$$424$$ 0 0
$$425$$ 22.2476 0.0523474
$$426$$ 0 0
$$427$$ 235.988 + 235.988i 0.552665 + 0.552665i
$$428$$ 0 0
$$429$$ 25.3154 + 1.39083i 0.0590102 + 0.00324203i
$$430$$ 0 0
$$431$$ 213.570i 0.495522i −0.968821 0.247761i $$-0.920305\pi$$
0.968821 0.247761i $$-0.0796947\pi$$
$$432$$ 0 0
$$433$$ 440.669 1.01771 0.508856 0.860852i $$-0.330069\pi$$
0.508856 + 0.860852i $$0.330069\pi$$
$$434$$ 0 0
$$435$$ −7.74826 + 141.031i −0.0178121 + 0.324209i
$$436$$ 0 0
$$437$$ −115.619 + 115.619i −0.264574 + 0.264574i
$$438$$ 0 0
$$439$$ 400.367i 0.911998i 0.889980 + 0.455999i $$0.150718\pi$$
−0.889980 + 0.455999i $$0.849282\pi$$
$$440$$ 0 0
$$441$$ 910.488 + 100.348i 2.06460 + 0.227546i
$$442$$ 0 0
$$443$$ −324.076 + 324.076i −0.731549 + 0.731549i −0.970926 0.239378i $$-0.923057\pi$$
0.239378 + 0.970926i $$0.423057\pi$$
$$444$$ 0 0
$$445$$ 601.208 601.208i 1.35103 1.35103i
$$446$$ 0 0
$$447$$ 330.965 + 369.446i 0.740414 + 0.826500i
$$448$$ 0 0
$$449$$ 691.918i 1.54102i −0.637427 0.770510i $$-0.720001\pi$$
0.637427 0.770510i $$-0.279999\pi$$
$$450$$ 0 0
$$451$$ −8.09298 + 8.09298i −0.0179445 + 0.0179445i
$$452$$ 0 0
$$453$$ 32.8674 + 1.80574i 0.0725549 + 0.00398618i
$$454$$ 0 0
$$455$$ 211.912 0.465740
$$456$$ 0 0
$$457$$ 385.436i 0.843404i 0.906734 + 0.421702i $$0.138567\pi$$
−0.906734 + 0.421702i $$0.861433\pi$$
$$458$$ 0 0
$$459$$ 534.705 + 88.8463i 1.16494 + 0.193565i
$$460$$ 0 0
$$461$$ 312.070 + 312.070i 0.676942 + 0.676942i 0.959307 0.282365i $$-0.0911190\pi$$
−0.282365 + 0.959307i $$0.591119\pi$$
$$462$$ 0 0
$$463$$ −718.961 −1.55283 −0.776416 0.630220i $$-0.782965\pi$$
−0.776416 + 0.630220i $$0.782965\pi$$
$$464$$ 0 0
$$465$$ −384.501 429.206i −0.826884 0.923024i
$$466$$ 0 0
$$467$$ −82.7894 82.7894i −0.177279 0.177279i 0.612889 0.790169i $$-0.290007\pi$$
−0.790169 + 0.612889i $$0.790007\pi$$
$$468$$ 0 0
$$469$$ 387.534 + 387.534i 0.826298 + 0.826298i
$$470$$ 0 0
$$471$$ −141.049 157.448i −0.299467 0.334285i
$$472$$ 0 0
$$473$$ 75.3145 0.159227
$$474$$ 0 0
$$475$$ 9.71993 + 9.71993i 0.0204630 + 0.0204630i
$$476$$ 0 0
$$477$$ 213.746 171.308i 0.448106 0.359137i
$$478$$ 0 0
$$479$$ 749.099i 1.56388i −0.623353 0.781941i $$-0.714230\pi$$
0.623353 0.781941i $$-0.285770\pi$$
$$480$$ 0 0
$$481$$ −47.7923 −0.0993603
$$482$$ 0 0
$$483$$ −484.864 26.6385i −1.00386 0.0551523i
$$484$$ 0 0
$$485$$ 502.983 502.983i 1.03708 1.03708i
$$486$$ 0 0
$$487$$ 533.210i 1.09489i −0.836843 0.547443i $$-0.815601\pi$$
0.836843 0.547443i $$-0.184399\pi$$
$$488$$ 0 0
$$489$$ −188.040 209.904i −0.384541 0.429251i
$$490$$ 0 0
$$491$$ −6.75013 + 6.75013i −0.0137477 + 0.0137477i −0.713947 0.700200i $$-0.753094\pi$$
0.700200 + 0.713947i $$0.253094\pi$$
$$492$$ 0 0
$$493$$ −130.800 + 130.800i −0.265315 + 0.265315i
$$494$$ 0 0
$$495$$ −12.6056 + 114.375i −0.0254658 + 0.231060i
$$496$$ 0 0
$$497$$ 799.644i 1.60894i
$$498$$ 0 0
$$499$$ 556.347 556.347i 1.11492 1.11492i 0.122448 0.992475i $$-0.460925\pi$$
0.992475 0.122448i $$-0.0390746\pi$$
$$500$$ 0 0
$$501$$ −30.0923 + 547.728i −0.0600645 + 1.09327i
$$502$$ 0 0
$$503$$ −304.892 −0.606147 −0.303074 0.952967i $$-0.598013\pi$$
−0.303074 + 0.952967i $$0.598013\pi$$
$$504$$ 0 0
$$505$$ 909.612i 1.80121i
$$506$$ 0 0
$$507$$ −472.065 25.9354i −0.931095 0.0511546i
$$508$$ 0 0
$$509$$ 118.591 + 118.591i 0.232988 + 0.232988i 0.813939 0.580951i $$-0.197319\pi$$
−0.580951 + 0.813939i $$0.697319\pi$$
$$510$$ 0 0
$$511$$ 616.968 1.20737
$$512$$ 0 0
$$513$$ 194.795 + 272.428i 0.379716 + 0.531049i
$$514$$ 0 0
$$515$$ −95.3617 95.3617i −0.185168 0.185168i
$$516$$ 0 0
$$517$$ 97.0233 + 97.0233i 0.187666 + 0.187666i
$$518$$ 0 0
$$519$$ 391.244 350.493i 0.753843 0.675324i
$$520$$ 0 0
$$521$$ −105.077 −0.201683 −0.100842 0.994902i $$-0.532154\pi$$
−0.100842 + 0.994902i $$0.532154\pi$$
$$522$$ 0 0
$$523$$ −479.455 479.455i −0.916740 0.916740i 0.0800507 0.996791i $$-0.474492\pi$$
−0.996791 + 0.0800507i $$0.974492\pi$$
$$524$$ 0 0
$$525$$ −2.23947 + 40.7619i −0.00426566 + 0.0776418i
$$526$$ 0 0
$$527$$ 754.679i 1.43203i
$$528$$ 0 0
$$529$$ −355.232 −0.671517
$$530$$ 0 0
$$531$$ 532.956 427.141i 1.00368 0.804408i
$$532$$ 0 0
$$533$$ −10.9241 + 10.9241i −0.0204955 + 0.0204955i
$$534$$ 0 0
$$535$$ 606.655i 1.13393i
$$536$$ 0 0
$$537$$ −532.918 + 477.410i −0.992399 + 0.889032i
$$538$$ 0 0
$$539$$ −180.077 + 180.077i −0.334095 + 0.334095i
$$540$$ 0 0
$$541$$ −726.230 + 726.230i −1.34238 + 1.34238i −0.448704 + 0.893680i $$0.648114\pi$$
−0.893680 + 0.448704i $$0.851886\pi$$
$$542$$ 0 0
$$543$$ −512.439 + 459.065i −0.943719 + 0.845423i
$$544$$ 0 0
$$545$$ 16.5852i 0.0304316i
$$546$$ 0 0
$$547$$ 314.507 314.507i 0.574966 0.574966i −0.358546 0.933512i $$-0.616727\pi$$
0.933512 + 0.358546i $$0.116727\pi$$
$$548$$ 0 0
$$549$$ −190.875 + 152.978i −0.347677 + 0.278648i
$$550$$ 0 0
$$551$$ −114.292 −0.207427
$$552$$ 0 0
$$553$$ 257.002i 0.464741i
$$554$$ 0 0
$$555$$ 11.8989 216.579i 0.0214394 0.390232i
$$556$$ 0 0
$$557$$ −134.274 134.274i −0.241066 0.241066i 0.576225 0.817291i $$-0.304525\pi$$
−0.817291 + 0.576225i $$0.804525\pi$$
$$558$$ 0 0
$$559$$ 101.661 0.181863
$$560$$ 0 0
$$561$$ −112.244 + 100.553i −0.200079 + 0.179239i
$$562$$ 0 0
$$563$$ 102.810 + 102.810i 0.182612 + 0.182612i 0.792493 0.609881i $$-0.208783\pi$$
−0.609881 + 0.792493i $$0.708783\pi$$
$$564$$ 0 0
$$565$$ −641.785 641.785i −1.13590 1.13590i
$$566$$ 0 0
$$567$$ −216.608 + 970.739i −0.382024 + 1.71206i
$$568$$ 0 0
$$569$$ 78.4572 0.137886 0.0689430 0.997621i $$-0.478037\pi$$
0.0689430 + 0.997621i $$0.478037\pi$$
$$570$$ 0 0
$$571$$ 363.164 + 363.164i 0.636013 + 0.636013i 0.949570 0.313556i $$-0.101520\pi$$
−0.313556 + 0.949570i $$0.601520\pi$$
$$572$$ 0 0
$$573$$ −182.358 10.0188i −0.318251 0.0174848i
$$574$$ 0 0
$$575$$ 14.6084i 0.0254060i
$$576$$ 0 0
$$577$$ −566.880 −0.982460 −0.491230 0.871030i $$-0.663453\pi$$
−0.491230 + 0.871030i $$0.663453\pi$$
$$578$$ 0 0
$$579$$ −29.2727 + 532.809i −0.0505573 + 0.920223i
$$580$$ 0 0
$$581$$ 78.0698 78.0698i 0.134371 0.134371i
$$582$$ 0 0
$$583$$ 76.1565i 0.130629i
$$584$$ 0 0
$$585$$ −17.0153 + 154.385i −0.0290860 + 0.263907i
$$586$$ 0 0
$$587$$ 73.3693 73.3693i 0.124990 0.124990i −0.641845 0.766835i $$-0.721831\pi$$
0.766835 + 0.641845i $$0.221831\pi$$
$$588$$ 0 0
$$589$$ 329.717 329.717i 0.559792 0.559792i
$$590$$ 0 0
$$591$$ −189.504 211.538i −0.320650 0.357932i
$$592$$ 0 0
$$593$$ 458.708i 0.773538i −0.922177 0.386769i $$-0.873591\pi$$
0.922177 0.386769i $$-0.126409\pi$$
$$594$$ 0 0
$$595$$ −890.650 + 890.650i −1.49689 + 1.49689i
$$596$$ 0 0
$$597$$ 2.47525 + 0.135991i 0.00414615 + 0.000227790i
$$598$$ 0 0
$$599$$ 423.611 0.707197 0.353599 0.935397i $$-0.384958\pi$$
0.353599 + 0.935397i $$0.384958\pi$$
$$600$$ 0 0
$$601$$ 795.376i 1.32342i 0.749759 + 0.661711i $$0.230169\pi$$
−0.749759 + 0.661711i $$0.769831\pi$$
$$602$$ 0 0
$$603$$ −313.450 + 251.216i −0.519817 + 0.416610i
$$604$$ 0 0
$$605$$ 414.557 + 414.557i 0.685219 + 0.685219i
$$606$$ 0 0
$$607$$ 631.699 1.04069 0.520345 0.853956i $$-0.325803\pi$$
0.520345 + 0.853956i $$0.325803\pi$$
$$608$$ 0 0
$$609$$ −226.484 252.817i −0.371896 0.415135i
$$610$$ 0 0
$$611$$ 130.964 + 130.964i 0.214344 + 0.214344i
$$612$$ 0 0
$$613$$ −385.264 385.264i −0.628490 0.628490i 0.319198 0.947688i $$-0.396586\pi$$
−0.947688 + 0.319198i $$0.896586\pi$$
$$614$$ 0 0
$$615$$ −46.7846 52.2241i −0.0760724 0.0849173i
$$616$$ 0 0
$$617$$ 953.333 1.54511 0.772555 0.634947i $$-0.218978\pi$$
0.772555 + 0.634947i $$0.218978\pi$$
$$618$$ 0 0
$$619$$ −574.046 574.046i −0.927377 0.927377i 0.0701591 0.997536i $$-0.477649\pi$$
−0.997536 + 0.0701591i $$0.977649\pi$$
$$620$$ 0 0
$$621$$ 58.3390 351.103i 0.0939437 0.565383i
$$622$$ 0 0
$$623$$ 2043.24i 3.27969i
$$624$$ 0 0
$$625$$ 651.477 1.04236
$$626$$ 0 0
$$627$$ −92.9707 5.10783i −0.148279 0.00814646i
$$628$$ 0 0
$$629$$ 200.868 200.868i 0.319345 0.319345i
$$630$$ 0 0
$$631$$ 138.048i 0.218777i 0.993999 + 0.109389i $$0.0348893\pi$$
−0.993999 + 0.109389i $$0.965111\pi$$
$$632$$ 0 0
$$633$$ −513.367 573.056i −0.811007 0.905301i
$$634$$ 0 0
$$635$$ 549.786 549.786i 0.865805 0.865805i
$$636$$ 0 0
$$637$$ −243.072 + 243.072i −0.381589 + 0.381589i
$$638$$ 0 0
$$639$$ −582.570 64.2069i −0.911691 0.100480i
$$640$$ 0 0
$$641$$ 784.889i 1.22448i 0.790673 + 0.612238i $$0.209731\pi$$
−0.790673 + 0.612238i $$0.790269\pi$$
$$642$$ 0 0
$$643$$ −238.456 + 238.456i −0.370850 + 0.370850i −0.867787 0.496937i $$-0.834458\pi$$
0.496937 + 0.867787i $$0.334458\pi$$
$$644$$ 0 0
$$645$$ −25.3107 + 460.695i −0.0392414 + 0.714256i
$$646$$ 0 0
$$647$$ 681.751 1.05371 0.526855 0.849955i $$-0.323371\pi$$
0.526855 + 0.849955i $$0.323371\pi$$
$$648$$ 0 0
$$649$$ 189.889i 0.292587i
$$650$$ 0 0
$$651$$ 1382.72 + 75.9668i 2.12399 + 0.116693i
$$652$$ 0 0
$$653$$ −636.071 636.071i −0.974075 0.974075i 0.0255977 0.999672i $$-0.491851\pi$$
−0.999672 + 0.0255977i $$0.991851\pi$$
$$654$$ 0 0
$$655$$ −474.721 −0.724766
$$656$$ 0 0
$$657$$ −49.5391 + 449.485i −0.0754020 + 0.684147i
$$658$$ 0 0
$$659$$ −91.6052 91.6052i −0.139006 0.139006i 0.634179 0.773186i $$-0.281338\pi$$
−0.773186 + 0.634179i $$0.781338\pi$$
$$660$$ 0 0
$$661$$ −721.715 721.715i −1.09185 1.09185i −0.995331 0.0965216i $$-0.969228\pi$$
−0.0965216 0.995331i $$-0.530772\pi$$
$$662$$ 0 0
$$663$$ −151.510 + 135.729i −0.228522 + 0.204720i
$$664$$ 0 0
$$665$$ −778.245 −1.17029
$$666$$ 0 0
$$667$$ 85.8871 + 85.8871i 0.128766 + 0.128766i
$$668$$ 0 0
$$669$$ −2.91851 + 53.1215i −0.00436250 + 0.0794044i
$$670$$ 0 0
$$671$$ 68.0074i 0.101352i
$$672$$ 0 0
$$673$$ 417.305 0.620067 0.310033 0.950726i $$-0.399660\pi$$
0.310033 + 0.950726i $$0.399660\pi$$
$$674$$ 0 0
$$675$$ −29.5168 4.90449i −0.0437286 0.00726592i
$$676$$ 0 0
$$677$$ −585.326 + 585.326i −0.864587 + 0.864587i −0.991867 0.127280i $$-0.959375\pi$$
0.127280 + 0.991867i $$0.459375\pi$$
$$678$$ 0 0
$$679$$ 1709.42i 2.51756i
$$680$$ 0 0
$$681$$ −23.8194 + 21.3384i −0.0349771 + 0.0313340i
$$682$$ 0 0
$$683$$ −104.261 + 104.261i −0.152651 + 0.152651i −0.779301 0.626650i $$-0.784426\pi$$
0.626650 + 0.779301i $$0.284426\pi$$
$$684$$ 0 0
$$685$$ 192.037 192.037i 0.280346 0.280346i
$$686$$ 0 0
$$687$$ 707.054 633.409i 1.02919 0.921993i
$$688$$ 0 0
$$689$$ 102.798i 0.149199i
$$690$$ 0 0
$$691$$ −335.701 + 335.701i −0.485818 + 0.485818i −0.906984 0.421165i $$-0.861621\pi$$
0.421165 + 0.906984i $$0.361621\pi$$
$$692$$ 0 0
$$693$$ −172.934 215.775i −0.249544 0.311364i
$$694$$ 0 0
$$695$$ −1165.74 −1.67733
$$696$$ 0 0
$$697$$ 91.8264i 0.131745i
$$698$$ 0 0
$$699$$ 20.3386 370.196i 0.0290968 0.529608i
$$700$$ 0 0
$$701$$ 490.458 + 490.458i 0.699655 + 0.699655i 0.964336 0.264681i $$-0.0852666\pi$$
−0.264681 + 0.964336i $$0.585267\pi$$
$$702$$ 0 0
$$703$$ 175.517 0.249669
$$704$$ 0 0
$$705$$ −626.093 + 560.881i −0.888075 + 0.795575i
$$706$$ 0 0
$$707$$ 1545.69 + 1545.69i 2.18626 + 2.18626i
$$708$$ 0 0
$$709$$ −435.817 435.817i −0.614692 0.614692i 0.329473 0.944165i $$-0.393129\pi$$
−0.944165 + 0.329473i $$0.893129\pi$$
$$710$$ 0 0
$$711$$ 187.235 + 20.6358i 0.263341 + 0.0290236i
$$712$$ 0 0
$$713$$ −495.544 −0.695012
$$714$$ 0 0
$$715$$ −30.5345 30.5345i −0.0427056 0.0427056i
$$716$$ 0 0
$$717$$ 354.968 + 19.5020i 0.495073 + 0.0271994i
$$718$$ 0 0
$$719$$ 1083.05i 1.50633i 0.657831 + 0.753166i $$0.271474\pi$$
−0.657831 + 0.753166i $$0.728526\pi$$
$$720$$ 0 0
$$721$$ 324.093 0.449505
$$722$$ 0 0
$$723$$ 43.4738 791.292i 0.0601297 1.09446i
$$724$$ 0 0
$$725$$ 7.22042 7.22042i 0.00995921 0.00995921i
$$726$$ 0 0
$$727$$ 513.215i 0.705935i −0.935636 0.352968i $$-0.885173\pi$$
0.935636 0.352968i $$-0.114827\pi$$
$$728$$ 0 0
$$729$$ −689.828 235.752i −0.946266 0.323390i
$$730$$ 0 0
$$731$$ −427.276 + 427.276i −0.584508 + 0.584508i
$$732$$ 0 0
$$733$$ −73.6001 + 73.6001i −0.100409 + 0.100409i −0.755527 0.655118i $$-0.772619\pi$$
0.655118 + 0.755527i $$0.272619\pi$$
$$734$$ 0 0
$$735$$ −1041.01 1162.04i −1.41633 1.58101i
$$736$$ 0 0
$$737$$ 111.680i 0.151533i
$$738$$ 0 0
$$739$$ 152.386 152.386i 0.206206 0.206206i −0.596447 0.802653i $$-0.703421\pi$$
0.802653 + 0.596447i $$0.203421\pi$$
$$740$$ 0 0
$$741$$ −125.494 6.89467i −0.169358 0.00930455i
$$742$$ 0 0
$$743$$ 574.044 0.772603 0.386302 0.922373i $$-0.373752\pi$$
0.386302 + 0.922373i $$0.373752\pi$$
$$744$$ 0 0
$$745$$ 844.811i 1.13397i
$$746$$ 0 0
$$747$$ 50.6082 + 63.1454i 0.0677486 + 0.0845319i
$$748$$ 0 0
$$749$$ 1030.88 + 1030.88i 1.37634 + 1.37634i
$$750$$ 0 0
$$751$$ 1014.28 1.35058 0.675289 0.737553i $$-0.264019\pi$$
0.675289 + 0.737553i $$0.264019\pi$$
$$752$$ 0 0
$$753$$ 431.649 + 481.836i 0.573239 + 0.639888i
$$754$$ 0 0
$$755$$ −39.6435 39.6435i −0.0525079 0.0525079i
$$756$$ 0 0
$$757$$ 1003.73 + 1003.73i 1.32594 + 1.32594i 0.908880 + 0.417057i $$0.136938\pi$$
0.417057 + 0.908880i $$0.363062\pi$$
$$758$$ 0 0
$$759$$ 66.0261 + 73.7028i 0.0869909 + 0.0971052i
$$760$$ 0 0
$$761$$ 54.1069 0.0710997 0.0355499 0.999368i $$-0.488682\pi$$
0.0355499 + 0.999368i $$0.488682\pi$$
$$762$$ 0 0
$$763$$ −28.1829 28.1829i −0.0369370 0.0369370i
$$764$$ 0 0
$$765$$ −577.358 720.386i −0.754716 0.941681i
$$766$$ 0 0
$$767$$ 256.316i 0.334181i
$$768$$ 0 0
$$769$$ 143.904 0.187132 0.0935659 0.995613i $$-0.470173\pi$$
0.0935659 + 0.995613i $$0.470173\pi$$
$$770$$ 0 0
$$771$$ −338.843 18.6161i −0.439485 0.0241454i
$$772$$ 0 0
$$773$$ −339.143 + 339.143i −0.438736 + 0.438736i −0.891586 0.452850i $$-0.850407\pi$$
0.452850 + 0.891586i $$0.350407\pi$$
$$774$$ 0 0
$$775$$ 41.6598i 0.0537546i
$$776$$ 0 0
$$777$$ 347.809 + 388.248i 0.447630 + 0.499676i
$$778$$ 0 0
$$779$$ 40.1187 40.1187i 0.0515003 0.0515003i
$$780$$ 0 0
$$781$$ 115.221 115.221i 0.147531 0.147531i
$$782$$ 0 0
$$783$$ 202.372 144.703i 0.258458 0.184805i
$$784$$ 0 0
$$785$$ 360.037i 0.458646i
$$786$$ 0 0
$$787$$ −924.878 + 924.878i −1.17519 + 1.17519i −0.194241 + 0.980954i $$0.562224\pi$$
−0.980954 + 0.194241i $$0.937776\pi$$
$$788$$ 0 0
$$789$$ 21.2832 387.389i 0.0269749 0.490987i
$$790$$ 0 0
$$791$$ 2181.15 2.75746
$$792$$ 0 0
$$793$$