# Properties

 Label 128.3.h.a.47.3 Level $128$ Weight $3$ Character 128.47 Analytic conductor $3.488$ Analytic rank $0$ Dimension $28$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$128 = 2^{7}$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 128.h (of order $$8$$, degree $$4$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$3.48774738381$$ Analytic rank: $$0$$ Dimension: $$28$$ Relative dimension: $$7$$ over $$\Q(\zeta_{8})$$ Twist minimal: no (minimal twist has level 32) Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

## Embedding invariants

 Embedding label 47.3 Character $$\chi$$ $$=$$ 128.47 Dual form 128.3.h.a.79.3

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-0.527719 + 1.27403i) q^{3} +(-0.642823 - 1.55191i) q^{5} +(4.95044 + 4.95044i) q^{7} +(5.01930 + 5.01930i) q^{9} +O(q^{10})$$ $$q+(-0.527719 + 1.27403i) q^{3} +(-0.642823 - 1.55191i) q^{5} +(4.95044 + 4.95044i) q^{7} +(5.01930 + 5.01930i) q^{9} +(4.27221 + 10.3140i) q^{11} +(1.68327 - 4.06379i) q^{13} +2.31641 q^{15} +28.6469i q^{17} +(-17.5460 - 7.26778i) q^{19} +(-8.91944 + 3.69455i) q^{21} +(24.3334 - 24.3334i) q^{23} +(15.6825 - 15.6825i) q^{25} +(-20.5098 + 8.49542i) q^{27} +(8.57286 + 3.55100i) q^{29} -5.73273i q^{31} -15.3949 q^{33} +(4.50039 - 10.8649i) q^{35} +(-26.1364 - 63.0989i) q^{37} +(4.28908 + 4.28908i) q^{39} +(-14.2561 - 14.2561i) q^{41} +(10.1365 + 24.4717i) q^{43} +(4.56299 - 11.0160i) q^{45} -57.9804 q^{47} +0.0137567i q^{49} +(-36.4969 - 15.1175i) q^{51} +(-46.3830 + 19.2124i) q^{53} +(13.2602 - 13.2602i) q^{55} +(18.5187 - 18.5187i) q^{57} +(27.6347 - 11.4467i) q^{59} +(76.3985 + 31.6453i) q^{61} +49.6955i q^{63} -7.38868 q^{65} +(36.1949 - 87.3821i) q^{67} +(18.1602 + 43.8425i) q^{69} +(5.39666 + 5.39666i) q^{71} +(-25.4031 - 25.4031i) q^{73} +(11.7039 + 28.2558i) q^{75} +(-29.9097 + 72.2084i) q^{77} -50.1674 q^{79} +33.2721i q^{81} +(100.805 + 41.7550i) q^{83} +(44.4574 - 18.4149i) q^{85} +(-9.04814 + 9.04814i) q^{87} +(10.6266 - 10.6266i) q^{89} +(28.4505 - 11.7846i) q^{91} +(7.30366 + 3.02527i) q^{93} +31.9017i q^{95} -14.3055 q^{97} +(-30.3257 + 73.2128i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$28q + 4q^{3} - 4q^{5} + 4q^{7} - 4q^{9} + O(q^{10})$$ $$28q + 4q^{3} - 4q^{5} + 4q^{7} - 4q^{9} + 4q^{11} - 4q^{13} + 8q^{15} + 4q^{19} - 4q^{21} + 68q^{23} - 4q^{25} + 100q^{27} - 4q^{29} - 8q^{33} - 92q^{35} - 4q^{37} - 188q^{39} - 4q^{41} - 92q^{43} - 40q^{45} + 8q^{47} - 224q^{51} - 164q^{53} - 252q^{55} - 4q^{57} - 124q^{59} - 68q^{61} - 8q^{65} + 164q^{67} + 188q^{69} + 260q^{71} - 4q^{73} + 488q^{75} + 220q^{77} + 520q^{79} + 484q^{83} + 96q^{85} + 452q^{87} - 4q^{89} + 196q^{91} + 32q^{93} - 8q^{97} - 216q^{99} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/128\mathbb{Z}\right)^\times$$.

 $$n$$ $$5$$ $$127$$ $$\chi(n)$$ $$e\left(\frac{3}{8}\right)$$ $$-1$$

## 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
$$3$$ −0.527719 + 1.27403i −0.175906 + 0.424676i −0.987101 0.160101i $$-0.948818\pi$$
0.811194 + 0.584777i $$0.198818\pi$$
$$4$$ 0 0
$$5$$ −0.642823 1.55191i −0.128565 0.310382i 0.846470 0.532437i $$-0.178724\pi$$
−0.975034 + 0.222055i $$0.928724\pi$$
$$6$$ 0 0
$$7$$ 4.95044 + 4.95044i 0.707206 + 0.707206i 0.965947 0.258741i $$-0.0833075\pi$$
−0.258741 + 0.965947i $$0.583308\pi$$
$$8$$ 0 0
$$9$$ 5.01930 + 5.01930i 0.557700 + 0.557700i
$$10$$ 0 0
$$11$$ 4.27221 + 10.3140i 0.388383 + 0.937640i 0.990283 + 0.139068i $$0.0444106\pi$$
−0.601900 + 0.798572i $$0.705589\pi$$
$$12$$ 0 0
$$13$$ 1.68327 4.06379i 0.129483 0.312599i −0.845821 0.533467i $$-0.820889\pi$$
0.975304 + 0.220868i $$0.0708890\pi$$
$$14$$ 0 0
$$15$$ 2.31641 0.154427
$$16$$ 0 0
$$17$$ 28.6469i 1.68511i 0.538609 + 0.842556i $$0.318950\pi$$
−0.538609 + 0.842556i $$0.681050\pi$$
$$18$$ 0 0
$$19$$ −17.5460 7.26778i −0.923473 0.382515i −0.130274 0.991478i $$-0.541586\pi$$
−0.793199 + 0.608963i $$0.791586\pi$$
$$20$$ 0 0
$$21$$ −8.91944 + 3.69455i −0.424735 + 0.175931i
$$22$$ 0 0
$$23$$ 24.3334 24.3334i 1.05797 1.05797i 0.0597590 0.998213i $$-0.480967\pi$$
0.998213 0.0597590i $$-0.0190332\pi$$
$$24$$ 0 0
$$25$$ 15.6825 15.6825i 0.627298 0.627298i
$$26$$ 0 0
$$27$$ −20.5098 + 8.49542i −0.759621 + 0.314645i
$$28$$ 0 0
$$29$$ 8.57286 + 3.55100i 0.295616 + 0.122448i 0.525562 0.850755i $$-0.323855\pi$$
−0.229946 + 0.973203i $$0.573855\pi$$
$$30$$ 0 0
$$31$$ 5.73273i 0.184927i −0.995716 0.0924634i $$-0.970526\pi$$
0.995716 0.0924634i $$-0.0294741\pi$$
$$32$$ 0 0
$$33$$ −15.3949 −0.466512
$$34$$ 0 0
$$35$$ 4.50039 10.8649i 0.128583 0.310426i
$$36$$ 0 0
$$37$$ −26.1364 63.0989i −0.706390 1.70538i −0.708831 0.705379i $$-0.750777\pi$$
0.00244114 0.999997i $$-0.499223\pi$$
$$38$$ 0 0
$$39$$ 4.28908 + 4.28908i 0.109976 + 0.109976i
$$40$$ 0 0
$$41$$ −14.2561 14.2561i −0.347711 0.347711i 0.511545 0.859256i $$-0.329073\pi$$
−0.859256 + 0.511545i $$0.829073\pi$$
$$42$$ 0 0
$$43$$ 10.1365 + 24.4717i 0.235733 + 0.569109i 0.996833 0.0795253i $$-0.0253404\pi$$
−0.761100 + 0.648634i $$0.775340\pi$$
$$44$$ 0 0
$$45$$ 4.56299 11.0160i 0.101400 0.244801i
$$46$$ 0 0
$$47$$ −57.9804 −1.23363 −0.616813 0.787110i $$-0.711576\pi$$
−0.616813 + 0.787110i $$0.711576\pi$$
$$48$$ 0 0
$$49$$ 0.0137567i 0.000280749i
$$50$$ 0 0
$$51$$ −36.4969 15.1175i −0.715626 0.296422i
$$52$$ 0 0
$$53$$ −46.3830 + 19.2124i −0.875150 + 0.362499i −0.774614 0.632434i $$-0.782056\pi$$
−0.100536 + 0.994933i $$0.532056\pi$$
$$54$$ 0 0
$$55$$ 13.2602 13.2602i 0.241094 0.241094i
$$56$$ 0 0
$$57$$ 18.5187 18.5187i 0.324890 0.324890i
$$58$$ 0 0
$$59$$ 27.6347 11.4467i 0.468384 0.194011i −0.135992 0.990710i $$-0.543422\pi$$
0.604377 + 0.796699i $$0.293422\pi$$
$$60$$ 0 0
$$61$$ 76.3985 + 31.6453i 1.25243 + 0.518775i 0.907579 0.419881i $$-0.137928\pi$$
0.344855 + 0.938656i $$0.387928\pi$$
$$62$$ 0 0
$$63$$ 49.6955i 0.788818i
$$64$$ 0 0
$$65$$ −7.38868 −0.113672
$$66$$ 0 0
$$67$$ 36.1949 87.3821i 0.540222 1.30421i −0.384345 0.923190i $$-0.625573\pi$$
0.924566 0.381021i $$-0.124427\pi$$
$$68$$ 0 0
$$69$$ 18.1602 + 43.8425i 0.263191 + 0.635399i
$$70$$ 0 0
$$71$$ 5.39666 + 5.39666i 0.0760092 + 0.0760092i 0.744089 0.668080i $$-0.232884\pi$$
−0.668080 + 0.744089i $$0.732884\pi$$
$$72$$ 0 0
$$73$$ −25.4031 25.4031i −0.347988 0.347988i 0.511372 0.859360i $$-0.329137\pi$$
−0.859360 + 0.511372i $$0.829137\pi$$
$$74$$ 0 0
$$75$$ 11.7039 + 28.2558i 0.156053 + 0.376744i
$$76$$ 0 0
$$77$$ −29.9097 + 72.2084i −0.388438 + 0.937771i
$$78$$ 0 0
$$79$$ −50.1674 −0.635030 −0.317515 0.948253i $$-0.602848\pi$$
−0.317515 + 0.948253i $$0.602848\pi$$
$$80$$ 0 0
$$81$$ 33.2721i 0.410767i
$$82$$ 0 0
$$83$$ 100.805 + 41.7550i 1.21452 + 0.503072i 0.895665 0.444730i $$-0.146700\pi$$
0.318859 + 0.947802i $$0.396700\pi$$
$$84$$ 0 0
$$85$$ 44.4574 18.4149i 0.523029 0.216646i
$$86$$ 0 0
$$87$$ −9.04814 + 9.04814i −0.104002 + 0.104002i
$$88$$ 0 0
$$89$$ 10.6266 10.6266i 0.119400 0.119400i −0.644882 0.764282i $$-0.723094\pi$$
0.764282 + 0.644882i $$0.223094\pi$$
$$90$$ 0 0
$$91$$ 28.4505 11.7846i 0.312643 0.129501i
$$92$$ 0 0
$$93$$ 7.30366 + 3.02527i 0.0785339 + 0.0325298i
$$94$$ 0 0
$$95$$ 31.9017i 0.335807i
$$96$$ 0 0
$$97$$ −14.3055 −0.147479 −0.0737395 0.997278i $$-0.523493\pi$$
−0.0737395 + 0.997278i $$0.523493\pi$$
$$98$$ 0 0
$$99$$ −30.3257 + 73.2128i −0.306321 + 0.739523i
$$100$$ 0 0
$$101$$ 51.6638 + 124.728i 0.511523 + 1.23493i 0.942997 + 0.332801i $$0.107994\pi$$
−0.431474 + 0.902125i $$0.642006\pi$$
$$102$$ 0 0
$$103$$ −4.87593 4.87593i −0.0473392 0.0473392i 0.683041 0.730380i $$-0.260657\pi$$
−0.730380 + 0.683041i $$0.760657\pi$$
$$104$$ 0 0
$$105$$ 11.4672 + 11.4672i 0.109212 + 0.109212i
$$106$$ 0 0
$$107$$ 4.55603 + 10.9992i 0.0425797 + 0.102797i 0.943739 0.330692i $$-0.107282\pi$$
−0.901159 + 0.433489i $$0.857282\pi$$
$$108$$ 0 0
$$109$$ 11.0098 26.5800i 0.101007 0.243853i −0.865295 0.501263i $$-0.832869\pi$$
0.966302 + 0.257410i $$0.0828690\pi$$
$$110$$ 0 0
$$111$$ 94.1824 0.848490
$$112$$ 0 0
$$113$$ 120.275i 1.06438i −0.846624 0.532191i $$-0.821369\pi$$
0.846624 0.532191i $$-0.178631\pi$$
$$114$$ 0 0
$$115$$ −53.4052 22.1212i −0.464393 0.192358i
$$116$$ 0 0
$$117$$ 28.8462 11.9485i 0.246549 0.102124i
$$118$$ 0 0
$$119$$ −141.815 + 141.815i −1.19172 + 1.19172i
$$120$$ 0 0
$$121$$ −2.56759 + 2.56759i −0.0212197 + 0.0212197i
$$122$$ 0 0
$$123$$ 25.6860 10.6395i 0.208829 0.0864998i
$$124$$ 0 0
$$125$$ −73.2166 30.3273i −0.585733 0.242619i
$$126$$ 0 0
$$127$$ 128.040i 1.00819i −0.863648 0.504095i $$-0.831826\pi$$
0.863648 0.504095i $$-0.168174\pi$$
$$128$$ 0 0
$$129$$ −36.5268 −0.283154
$$130$$ 0 0
$$131$$ −20.1358 + 48.6121i −0.153708 + 0.371084i −0.981911 0.189345i $$-0.939364\pi$$
0.828203 + 0.560429i $$0.189364\pi$$
$$132$$ 0 0
$$133$$ −50.8816 122.839i −0.382569 0.923602i
$$134$$ 0 0
$$135$$ 26.3683 + 26.3683i 0.195321 + 0.195321i
$$136$$ 0 0
$$137$$ −1.66083 1.66083i −0.0121228 0.0121228i 0.701019 0.713142i $$-0.252729\pi$$
−0.713142 + 0.701019i $$0.752729\pi$$
$$138$$ 0 0
$$139$$ −75.6997 182.755i −0.544602 1.31479i −0.921445 0.388508i $$-0.872991\pi$$
0.376843 0.926277i $$-0.377009\pi$$
$$140$$ 0 0
$$141$$ 30.5974 73.8686i 0.217003 0.523891i
$$142$$ 0 0
$$143$$ 49.1053 0.343394
$$144$$ 0 0
$$145$$ 15.5870i 0.107496i
$$146$$ 0 0
$$147$$ −0.0175264 0.00725967i −0.000119227 4.93855e-5i
$$148$$ 0 0
$$149$$ −16.1203 + 6.67724i −0.108190 + 0.0448137i −0.436122 0.899888i $$-0.643648\pi$$
0.327932 + 0.944701i $$0.393648\pi$$
$$150$$ 0 0
$$151$$ 127.344 127.344i 0.843335 0.843335i −0.145956 0.989291i $$-0.546626\pi$$
0.989291 + 0.145956i $$0.0466258\pi$$
$$152$$ 0 0
$$153$$ −143.787 + 143.787i −0.939787 + 0.939787i
$$154$$ 0 0
$$155$$ −8.89669 + 3.68513i −0.0573980 + 0.0237750i
$$156$$ 0 0
$$157$$ −236.255 97.8598i −1.50481 0.623311i −0.530328 0.847793i $$-0.677931\pi$$
−0.974478 + 0.224482i $$0.927931\pi$$
$$158$$ 0 0
$$159$$ 69.2319i 0.435421i
$$160$$ 0 0
$$161$$ 240.922 1.49641
$$162$$ 0 0
$$163$$ −38.0947 + 91.9687i −0.233710 + 0.564225i −0.996608 0.0822932i $$-0.973776\pi$$
0.762898 + 0.646518i $$0.223776\pi$$
$$164$$ 0 0
$$165$$ 9.89619 + 23.8915i 0.0599769 + 0.144797i
$$166$$ 0 0
$$167$$ −223.831 223.831i −1.34031 1.34031i −0.895750 0.444558i $$-0.853361\pi$$
−0.444558 0.895750i $$-0.646639\pi$$
$$168$$ 0 0
$$169$$ 105.820 + 105.820i 0.626154 + 0.626154i
$$170$$ 0 0
$$171$$ −51.5894 124.548i −0.301692 0.728350i
$$172$$ 0 0
$$173$$ 13.2654 32.0254i 0.0766784 0.185118i −0.880892 0.473317i $$-0.843056\pi$$
0.957571 + 0.288199i $$0.0930565\pi$$
$$174$$ 0 0
$$175$$ 155.270 0.887259
$$176$$ 0 0
$$177$$ 41.2480i 0.233039i
$$178$$ 0 0
$$179$$ 13.8305 + 5.72877i 0.0772652 + 0.0320043i 0.420981 0.907069i $$-0.361686\pi$$
−0.343716 + 0.939074i $$0.611686\pi$$
$$180$$ 0 0
$$181$$ 153.596 63.6217i 0.848599 0.351501i 0.0843605 0.996435i $$-0.473115\pi$$
0.764238 + 0.644934i $$0.223115\pi$$
$$182$$ 0 0
$$183$$ −80.6339 + 80.6339i −0.440623 + 0.440623i
$$184$$ 0 0
$$185$$ −81.1228 + 81.1228i −0.438502 + 0.438502i
$$186$$ 0 0
$$187$$ −295.465 + 122.386i −1.58003 + 0.654469i
$$188$$ 0 0
$$189$$ −143.588 59.4763i −0.759727 0.314689i
$$190$$ 0 0
$$191$$ 2.00135i 0.0104783i 0.999986 + 0.00523914i $$0.00166768\pi$$
−0.999986 + 0.00523914i $$0.998332\pi$$
$$192$$ 0 0
$$193$$ −107.502 −0.557003 −0.278502 0.960436i $$-0.589838\pi$$
−0.278502 + 0.960436i $$0.589838\pi$$
$$194$$ 0 0
$$195$$ 3.89915 9.41338i 0.0199956 0.0482738i
$$196$$ 0 0
$$197$$ 35.9828 + 86.8701i 0.182654 + 0.440965i 0.988512 0.151144i $$-0.0482956\pi$$
−0.805858 + 0.592109i $$0.798296\pi$$
$$198$$ 0 0
$$199$$ 228.742 + 228.742i 1.14946 + 1.14946i 0.986659 + 0.162799i $$0.0520521\pi$$
0.162799 + 0.986659i $$0.447948\pi$$
$$200$$ 0 0
$$201$$ 92.2265 + 92.2265i 0.458838 + 0.458838i
$$202$$ 0 0
$$203$$ 24.8605 + 60.0185i 0.122465 + 0.295658i
$$204$$ 0 0
$$205$$ −12.9601 + 31.2885i −0.0632200 + 0.152627i
$$206$$ 0 0
$$207$$ 244.273 1.18006
$$208$$ 0 0
$$209$$ 212.019i 1.01445i
$$210$$ 0 0
$$211$$ 244.800 + 101.400i 1.16019 + 0.480567i 0.877938 0.478773i $$-0.158918\pi$$
0.282252 + 0.959340i $$0.408918\pi$$
$$212$$ 0 0
$$213$$ −9.72341 + 4.02757i −0.0456498 + 0.0189088i
$$214$$ 0 0
$$215$$ 31.4619 31.4619i 0.146335 0.146335i
$$216$$ 0 0
$$217$$ 28.3796 28.3796i 0.130781 0.130781i
$$218$$ 0 0
$$219$$ 45.7700 18.9585i 0.208995 0.0865687i
$$220$$ 0 0
$$221$$ 116.415 + 48.2206i 0.526764 + 0.218193i
$$222$$ 0 0
$$223$$ 110.575i 0.495853i 0.968779 + 0.247927i $$0.0797492\pi$$
−0.968779 + 0.247927i $$0.920251\pi$$
$$224$$ 0 0
$$225$$ 157.430 0.699689
$$226$$ 0 0
$$227$$ −153.333 + 370.178i −0.675475 + 1.63074i 0.0966861 + 0.995315i $$0.469176\pi$$
−0.772161 + 0.635427i $$0.780824\pi$$
$$228$$ 0 0
$$229$$ −24.0559 58.0760i −0.105047 0.253607i 0.862612 0.505865i $$-0.168827\pi$$
−0.967660 + 0.252258i $$0.918827\pi$$
$$230$$ 0 0
$$231$$ −76.2115 76.2115i −0.329920 0.329920i
$$232$$ 0 0
$$233$$ −104.978 104.978i −0.450547 0.450547i 0.444989 0.895536i $$-0.353208\pi$$
−0.895536 + 0.444989i $$0.853208\pi$$
$$234$$ 0 0
$$235$$ 37.2711 + 89.9804i 0.158600 + 0.382895i
$$236$$ 0 0
$$237$$ 26.4743 63.9146i 0.111706 0.269682i
$$238$$ 0 0
$$239$$ −122.643 −0.513151 −0.256576 0.966524i $$-0.582594\pi$$
−0.256576 + 0.966524i $$0.582594\pi$$
$$240$$ 0 0
$$241$$ 188.784i 0.783335i 0.920107 + 0.391668i $$0.128102\pi$$
−0.920107 + 0.391668i $$0.871898\pi$$
$$242$$ 0 0
$$243$$ −226.977 94.0171i −0.934063 0.386902i
$$244$$ 0 0
$$245$$ 0.0213492 0.00884311i 8.71395e−5 3.60943e-5i
$$246$$ 0 0
$$247$$ −59.0694 + 59.0694i −0.239147 + 0.239147i
$$248$$ 0 0
$$249$$ −106.394 + 106.394i −0.427285 + 0.427285i
$$250$$ 0 0
$$251$$ 355.365 147.197i 1.41580 0.586443i 0.461997 0.886881i $$-0.347133\pi$$
0.953801 + 0.300439i $$0.0971330\pi$$
$$252$$ 0 0
$$253$$ 354.932 + 147.018i 1.40289 + 0.581098i
$$254$$ 0 0
$$255$$ 66.3579i 0.260227i
$$256$$ 0 0
$$257$$ 84.4316 0.328528 0.164264 0.986416i $$-0.447475\pi$$
0.164264 + 0.986416i $$0.447475\pi$$
$$258$$ 0 0
$$259$$ 182.981 441.754i 0.706489 1.70561i
$$260$$ 0 0
$$261$$ 25.2063 + 60.8533i 0.0965758 + 0.233155i
$$262$$ 0 0
$$263$$ 37.2079 + 37.2079i 0.141475 + 0.141475i 0.774297 0.632822i $$-0.218104\pi$$
−0.632822 + 0.774297i $$0.718104\pi$$
$$264$$ 0 0
$$265$$ 59.6320 + 59.6320i 0.225027 + 0.225027i
$$266$$ 0 0
$$267$$ 7.93072 + 19.1464i 0.0297031 + 0.0717095i
$$268$$ 0 0
$$269$$ −90.5201 + 218.535i −0.336506 + 0.812398i 0.661540 + 0.749910i $$0.269903\pi$$
−0.998046 + 0.0624874i $$0.980097\pi$$
$$270$$ 0 0
$$271$$ −312.612 −1.15355 −0.576775 0.816903i $$-0.695689\pi$$
−0.576775 + 0.816903i $$0.695689\pi$$
$$272$$ 0 0
$$273$$ 42.4657i 0.155552i
$$274$$ 0 0
$$275$$ 228.748 + 94.7506i 0.831812 + 0.344548i
$$276$$ 0 0
$$277$$ −199.434 + 82.6083i −0.719978 + 0.298225i −0.712426 0.701747i $$-0.752404\pi$$
−0.00755172 + 0.999971i $$0.502404\pi$$
$$278$$ 0 0
$$279$$ 28.7743 28.7743i 0.103134 0.103134i
$$280$$ 0 0
$$281$$ 237.700 237.700i 0.845909 0.845909i −0.143711 0.989620i $$-0.545904\pi$$
0.989620 + 0.143711i $$0.0459036\pi$$
$$282$$ 0 0
$$283$$ −58.7408 + 24.3312i −0.207565 + 0.0859761i −0.484044 0.875044i $$-0.660832\pi$$
0.276479 + 0.961020i $$0.410832\pi$$
$$284$$ 0 0
$$285$$ −40.6436 16.8351i −0.142609 0.0590707i
$$286$$ 0 0
$$287$$ 141.148i 0.491807i
$$288$$ 0 0
$$289$$ −531.645 −1.83960
$$290$$ 0 0
$$291$$ 7.54927 18.2256i 0.0259425 0.0626308i
$$292$$ 0 0
$$293$$ 47.5607 + 114.822i 0.162323 + 0.391883i 0.984024 0.178036i $$-0.0569745\pi$$
−0.821701 + 0.569919i $$0.806974\pi$$
$$294$$ 0 0
$$295$$ −35.5284 35.5284i −0.120435 0.120435i
$$296$$ 0 0
$$297$$ −175.244 175.244i −0.590048 0.590048i
$$298$$ 0 0
$$299$$ −57.9258 139.845i −0.193732 0.467710i
$$300$$ 0 0
$$301$$ −70.9655 + 171.326i −0.235766 + 0.569189i
$$302$$ 0 0
$$303$$ −186.170 −0.614423
$$304$$ 0 0
$$305$$ 138.906i 0.455429i
$$306$$ 0 0
$$307$$ −407.254 168.690i −1.32656 0.549480i −0.396889 0.917867i $$-0.629910\pi$$
−0.929673 + 0.368387i $$0.879910\pi$$
$$308$$ 0 0
$$309$$ 8.78520 3.63895i 0.0284311 0.0117765i
$$310$$ 0 0
$$311$$ −149.458 + 149.458i −0.480572 + 0.480572i −0.905314 0.424742i $$-0.860365\pi$$
0.424742 + 0.905314i $$0.360365\pi$$
$$312$$ 0 0
$$313$$ 295.452 295.452i 0.943937 0.943937i −0.0545726 0.998510i $$-0.517380\pi$$
0.998510 + 0.0545726i $$0.0173796\pi$$
$$314$$ 0 0
$$315$$ 77.1231 31.9454i 0.244835 0.101414i
$$316$$ 0 0
$$317$$ −222.852 92.3084i −0.703004 0.291194i 0.00240221 0.999997i $$-0.499235\pi$$
−0.705406 + 0.708803i $$0.749235\pi$$
$$318$$ 0 0
$$319$$ 103.591i 0.324738i
$$320$$ 0 0
$$321$$ −16.4176 −0.0511453
$$322$$ 0 0
$$323$$ 208.199 502.638i 0.644580 1.55615i
$$324$$ 0 0
$$325$$ −37.3323 90.1281i −0.114868 0.277317i
$$326$$ 0 0
$$327$$ 28.0535 + 28.0535i 0.0857906 + 0.0857906i
$$328$$ 0 0
$$329$$ −287.029 287.029i −0.872427 0.872427i
$$330$$ 0 0
$$331$$ 200.624 + 484.350i 0.606115 + 1.46329i 0.867192 + 0.497974i $$0.165923\pi$$
−0.261076 + 0.965318i $$0.584077\pi$$
$$332$$ 0 0
$$333$$ 185.526 447.899i 0.557135 1.34504i
$$334$$ 0 0
$$335$$ −158.876 −0.474257
$$336$$ 0 0
$$337$$ 248.089i 0.736169i 0.929792 + 0.368085i $$0.119986\pi$$
−0.929792 + 0.368085i $$0.880014\pi$$
$$338$$ 0 0
$$339$$ 153.234 + 63.4715i 0.452017 + 0.187232i
$$340$$ 0 0
$$341$$ 59.1276 24.4914i 0.173395 0.0718224i
$$342$$ 0 0
$$343$$ 242.504 242.504i 0.707007 0.707007i
$$344$$ 0 0
$$345$$ 56.3660 56.3660i 0.163380 0.163380i
$$346$$ 0 0
$$347$$ 101.462 42.0270i 0.292398 0.121115i −0.231662 0.972796i $$-0.574416\pi$$
0.524061 + 0.851681i $$0.324416\pi$$
$$348$$ 0 0
$$349$$ 489.895 + 202.921i 1.40371 + 0.581436i 0.950712 0.310076i $$-0.100354\pi$$
0.452998 + 0.891512i $$0.350354\pi$$
$$350$$ 0 0
$$351$$ 97.6474i 0.278198i
$$352$$ 0 0
$$353$$ −185.627 −0.525856 −0.262928 0.964815i $$-0.584688\pi$$
−0.262928 + 0.964815i $$0.584688\pi$$
$$354$$ 0 0
$$355$$ 4.90604 11.8442i 0.0138198 0.0333640i
$$356$$ 0 0
$$357$$ −105.838 255.514i −0.296464 0.715727i
$$358$$ 0 0
$$359$$ −222.847 222.847i −0.620743 0.620743i 0.324978 0.945722i $$-0.394643\pi$$
−0.945722 + 0.324978i $$0.894643\pi$$
$$360$$ 0 0
$$361$$ −0.224842 0.224842i −0.000622830 0.000622830i
$$362$$ 0 0
$$363$$ −1.91621 4.62614i −0.00527882 0.0127442i
$$364$$ 0 0
$$365$$ −23.0937 + 55.7530i −0.0632703 + 0.152748i
$$366$$ 0 0
$$367$$ −532.771 −1.45169 −0.725846 0.687857i $$-0.758552\pi$$
−0.725846 + 0.687857i $$0.758552\pi$$
$$368$$ 0 0
$$369$$ 143.112i 0.387837i
$$370$$ 0 0
$$371$$ −324.726 134.506i −0.875273 0.362550i
$$372$$ 0 0
$$373$$ −277.629 + 114.998i −0.744313 + 0.308305i −0.722419 0.691456i $$-0.756970\pi$$
−0.0218944 + 0.999760i $$0.506970\pi$$
$$374$$ 0 0
$$375$$ 77.2757 77.2757i 0.206068 0.206068i
$$376$$ 0 0
$$377$$ 28.8610 28.8610i 0.0765543 0.0765543i
$$378$$ 0 0
$$379$$ −306.344 + 126.892i −0.808296 + 0.334807i −0.748274 0.663390i $$-0.769117\pi$$
−0.0600223 + 0.998197i $$0.519117\pi$$
$$380$$ 0 0
$$381$$ 163.127 + 67.5692i 0.428154 + 0.177347i
$$382$$ 0 0
$$383$$ 163.336i 0.426465i 0.977001 + 0.213233i $$0.0683992\pi$$
−0.977001 + 0.213233i $$0.931601\pi$$
$$384$$ 0 0
$$385$$ 131.288 0.341007
$$386$$ 0 0
$$387$$ −71.9526 + 173.709i −0.185924 + 0.448861i
$$388$$ 0 0
$$389$$ −27.0717 65.3568i −0.0695930 0.168012i 0.885256 0.465104i $$-0.153983\pi$$
−0.954849 + 0.297092i $$0.903983\pi$$
$$390$$ 0 0
$$391$$ 697.075 + 697.075i 1.78280 + 1.78280i
$$392$$ 0 0
$$393$$ −51.3071 51.3071i −0.130552 0.130552i
$$394$$ 0 0
$$395$$ 32.2487 + 77.8553i 0.0816423 + 0.197102i
$$396$$ 0 0
$$397$$ −153.949 + 371.666i −0.387781 + 0.936187i 0.602628 + 0.798022i $$0.294120\pi$$
−0.990409 + 0.138165i $$0.955880\pi$$
$$398$$ 0 0
$$399$$ 183.352 0.459528
$$400$$ 0 0
$$401$$ 287.838i 0.717801i 0.933376 + 0.358900i $$0.116848\pi$$
−0.933376 + 0.358900i $$0.883152\pi$$
$$402$$ 0 0
$$403$$ −23.2966 9.64976i −0.0578079 0.0239448i
$$404$$ 0 0
$$405$$ 51.6353 21.3881i 0.127495 0.0528100i
$$406$$ 0 0
$$407$$ 539.144 539.144i 1.32468 1.32468i
$$408$$ 0 0
$$409$$ −134.641 + 134.641i −0.329195 + 0.329195i −0.852280 0.523085i $$-0.824781\pi$$
0.523085 + 0.852280i $$0.324781\pi$$
$$410$$ 0 0
$$411$$ 2.99239 1.23949i 0.00728076 0.00301579i
$$412$$ 0 0
$$413$$ 193.470 + 80.1378i 0.468450 + 0.194038i
$$414$$ 0 0
$$415$$ 183.282i 0.441644i
$$416$$ 0 0
$$417$$ 272.783 0.654156
$$418$$ 0 0
$$419$$ −94.1979 + 227.414i −0.224816 + 0.542754i −0.995532 0.0944249i $$-0.969899\pi$$
0.770716 + 0.637179i $$0.219899\pi$$
$$420$$ 0 0
$$421$$ −151.850 366.598i −0.360689 0.870779i −0.995200 0.0978656i $$-0.968798\pi$$
0.634511 0.772914i $$-0.281202\pi$$
$$422$$ 0 0
$$423$$ −291.021 291.021i −0.687993 0.687993i
$$424$$ 0 0
$$425$$ 449.254 + 449.254i 1.05707 + 1.05707i
$$426$$ 0 0
$$427$$ 221.548 + 534.864i 0.518848 + 1.25261i
$$428$$ 0 0
$$429$$ −25.9138 + 62.5615i −0.0604052 + 0.145831i
$$430$$ 0 0
$$431$$ 691.406 1.60419 0.802095 0.597196i $$-0.203719\pi$$
0.802095 + 0.597196i $$0.203719\pi$$
$$432$$ 0 0
$$433$$ 580.011i 1.33952i 0.742579 + 0.669758i $$0.233602\pi$$
−0.742579 + 0.669758i $$0.766398\pi$$
$$434$$ 0 0
$$435$$ 19.8582 + 8.22556i 0.0456511 + 0.0189093i
$$436$$ 0 0
$$437$$ −603.802 + 250.103i −1.38170 + 0.572318i
$$438$$ 0 0
$$439$$ −411.067 + 411.067i −0.936371 + 0.936371i −0.998093 0.0617227i $$-0.980341\pi$$
0.0617227 + 0.998093i $$0.480341\pi$$
$$440$$ 0 0
$$441$$ −0.0690490 + 0.0690490i −0.000156574 + 0.000156574i
$$442$$ 0 0
$$443$$ 34.4767 14.2807i 0.0778256 0.0322364i −0.343431 0.939178i $$-0.611589\pi$$
0.421257 + 0.906941i $$0.361589\pi$$
$$444$$ 0 0
$$445$$ −23.3226 9.66052i −0.0524102 0.0217090i
$$446$$ 0 0
$$447$$ 24.0614i 0.0538286i
$$448$$ 0 0
$$449$$ 185.456 0.413043 0.206521 0.978442i $$-0.433786\pi$$
0.206521 + 0.978442i $$0.433786\pi$$
$$450$$ 0 0
$$451$$ 86.1331 207.944i 0.190982 0.461073i
$$452$$ 0 0
$$453$$ 95.0375 + 229.441i 0.209796 + 0.506492i
$$454$$ 0 0
$$455$$ −36.5772 36.5772i −0.0803895 0.0803895i
$$456$$ 0 0
$$457$$ 386.211 + 386.211i 0.845100 + 0.845100i 0.989517 0.144417i $$-0.0461306\pi$$
−0.144417 + 0.989517i $$0.546131\pi$$
$$458$$ 0 0
$$459$$ −243.367 587.541i −0.530212 1.28005i
$$460$$ 0 0
$$461$$ 268.824 648.999i 0.583133 1.40781i −0.306826 0.951766i $$-0.599267\pi$$
0.889958 0.456042i $$-0.150733\pi$$
$$462$$ 0 0
$$463$$ −49.4705 −0.106848 −0.0534238 0.998572i $$-0.517013\pi$$
−0.0534238 + 0.998572i $$0.517013\pi$$
$$464$$ 0 0
$$465$$ 13.2793i 0.0285577i
$$466$$ 0 0
$$467$$ 192.753 + 79.8411i 0.412748 + 0.170966i 0.579388 0.815052i $$-0.303292\pi$$
−0.166640 + 0.986018i $$0.553292\pi$$
$$468$$ 0 0
$$469$$ 611.761 253.400i 1.30439 0.540297i
$$470$$ 0 0
$$471$$ 249.352 249.352i 0.529410 0.529410i
$$472$$ 0 0
$$473$$ −209.097 + 209.097i −0.442065 + 0.442065i
$$474$$ 0 0
$$475$$ −389.141 + 161.187i −0.819244 + 0.339342i
$$476$$ 0 0
$$477$$ −329.243 136.377i −0.690237 0.285906i
$$478$$ 0 0
$$479$$ 256.988i 0.536509i 0.963348 + 0.268254i $$0.0864468\pi$$
−0.963348 + 0.268254i $$0.913553\pi$$
$$480$$ 0 0
$$481$$ −300.415 −0.624564
$$482$$ 0 0
$$483$$ −127.139 + 306.941i −0.263228 + 0.635488i
$$484$$ 0 0
$$485$$ 9.19588 + 22.2008i 0.0189606 + 0.0457749i
$$486$$ 0 0
$$487$$ 10.7898 + 10.7898i 0.0221557 + 0.0221557i 0.718098 0.695942i $$-0.245013\pi$$
−0.695942 + 0.718098i $$0.745013\pi$$
$$488$$ 0 0
$$489$$ −97.0673 97.0673i −0.198502 0.198502i
$$490$$ 0 0
$$491$$ −58.0314 140.100i −0.118190 0.285336i 0.853702 0.520761i $$-0.174352\pi$$
−0.971893 + 0.235425i $$0.924352\pi$$
$$492$$ 0 0
$$493$$ −101.725 + 245.586i −0.206339 + 0.498146i
$$494$$ 0 0
$$495$$ 133.114 0.268917
$$496$$ 0 0
$$497$$ 53.4317i 0.107508i
$$498$$ 0 0
$$499$$ 72.1133 + 29.8703i 0.144516 + 0.0598603i 0.453769 0.891119i $$-0.350079\pi$$
−0.309253 + 0.950980i $$0.600079\pi$$
$$500$$ 0 0
$$501$$ 403.288 167.047i 0.804965 0.333428i
$$502$$ 0 0
$$503$$ −151.600 + 151.600i −0.301393 + 0.301393i −0.841559 0.540166i $$-0.818361\pi$$
0.540166 + 0.841559i $$0.318361\pi$$
$$504$$ 0 0
$$505$$ 160.355 160.355i 0.317535 0.317535i
$$506$$ 0 0
$$507$$ −190.661 + 78.9744i −0.376057 + 0.155768i
$$508$$ 0 0
$$509$$ −562.711 233.082i −1.10552 0.457922i −0.246128 0.969237i $$-0.579158\pi$$
−0.859393 + 0.511315i $$0.829158\pi$$
$$510$$ 0 0
$$511$$ 251.513i 0.492198i
$$512$$ 0 0
$$513$$ 421.607 0.821845
$$514$$ 0 0
$$515$$ −4.43266 + 10.7014i −0.00860710 + 0.0207794i
$$516$$ 0 0
$$517$$ −247.705 598.012i −0.479119 1.15670i
$$518$$ 0 0
$$519$$ 33.8009 + 33.8009i 0.0651270 + 0.0651270i
$$520$$ 0 0
$$521$$ −224.985 224.985i −0.431833 0.431833i 0.457418 0.889252i $$-0.348774\pi$$
−0.889252 + 0.457418i $$0.848774\pi$$
$$522$$ 0 0
$$523$$ 9.30771 + 22.4708i 0.0177968 + 0.0429652i 0.932528 0.361097i $$-0.117598\pi$$
−0.914731 + 0.404063i $$0.867598\pi$$
$$524$$ 0 0
$$525$$ −81.9391 + 197.819i −0.156075 + 0.376797i
$$526$$ 0 0
$$527$$ 164.225 0.311622
$$528$$ 0 0
$$529$$ 655.224i 1.23861i
$$530$$ 0 0
$$531$$ 196.161 + 81.2525i 0.369418 + 0.153018i
$$532$$ 0 0
$$533$$ −81.9309 + 33.9369i −0.153717 + 0.0636715i
$$534$$ 0 0
$$535$$ 14.1411 14.1411i 0.0264320 0.0264320i
$$536$$ 0 0
$$537$$ −14.5972 + 14.5972i −0.0271829 + 0.0271829i
$$538$$ 0 0
$$539$$ −0.141887 + 0.0587715i −0.000263241 + 0.000109038i
$$540$$ 0 0
$$541$$ −357.866 148.233i −0.661490 0.273998i 0.0265752 0.999647i $$-0.491540\pi$$
−0.688066 + 0.725649i $$0.741540\pi$$
$$542$$ 0 0
$$543$$ 229.260i 0.422211i
$$544$$ 0 0
$$545$$ −48.3271 −0.0886735
$$546$$ 0 0
$$547$$ −187.175 + 451.879i −0.342184 + 0.826105i 0.655311 + 0.755360i $$0.272538\pi$$
−0.997494 + 0.0707454i $$0.977462\pi$$
$$548$$ 0 0
$$549$$ 224.630 + 542.304i 0.409162 + 0.987804i
$$550$$ 0 0
$$551$$ −124.611 124.611i −0.226155 0.226155i
$$552$$ 0 0
$$553$$ −248.351 248.351i −0.449097 0.449097i
$$554$$ 0 0
$$555$$ −60.5426 146.163i −0.109086 0.263356i
$$556$$ 0 0
$$557$$ 307.716 742.891i 0.552452 1.33374i −0.363181 0.931719i $$-0.618309\pi$$
0.915632 0.402017i $$-0.131691\pi$$
$$558$$ 0 0
$$559$$ 116.510 0.208426
$$560$$ 0 0
$$561$$ 441.016i 0.786125i
$$562$$ 0 0
$$563$$ −706.303 292.560i −1.25454 0.519646i −0.346307 0.938121i $$-0.612565\pi$$
−0.908228 + 0.418476i $$0.862565\pi$$
$$564$$ 0 0
$$565$$ −186.656 + 77.3156i −0.330365 + 0.136842i
$$566$$ 0 0
$$567$$ −164.712 + 164.712i −0.290497 + 0.290497i
$$568$$ 0 0
$$569$$ −552.550 + 552.550i −0.971089 + 0.971089i −0.999594 0.0285048i $$-0.990925\pi$$
0.0285048 + 0.999594i $$0.490925\pi$$
$$570$$ 0 0
$$571$$ 476.739 197.472i 0.834919 0.345835i 0.0760707 0.997102i $$-0.475763\pi$$
0.758848 + 0.651268i $$0.225763\pi$$
$$572$$ 0 0
$$573$$ −2.54978 1.05615i −0.00444988 0.00184320i
$$574$$ 0 0
$$575$$ 763.214i 1.32733i
$$576$$ 0 0
$$577$$ −188.090 −0.325980 −0.162990 0.986628i $$-0.552114\pi$$
−0.162990 + 0.986628i $$0.552114\pi$$
$$578$$ 0 0
$$579$$ 56.7307 136.960i 0.0979805 0.236546i
$$580$$ 0 0
$$581$$ 292.326 + 705.737i 0.503143 + 1.21469i
$$582$$ 0 0
$$583$$ −396.316 396.316i −0.679787 0.679787i
$$584$$ 0 0
$$585$$ −37.0860 37.0860i −0.0633949 0.0633949i
$$586$$ 0 0
$$587$$ −229.302 553.585i −0.390634 0.943075i −0.989802 0.142451i $$-0.954502\pi$$
0.599167 0.800624i $$-0.295498\pi$$
$$588$$ 0 0
$$589$$ −41.6642 + 100.586i −0.0707372 + 0.170775i
$$590$$ 0 0
$$591$$ −129.664 −0.219397
$$592$$ 0 0
$$593$$ 378.708i 0.638630i −0.947649 0.319315i $$-0.896547\pi$$
0.947649 0.319315i $$-0.103453\pi$$
$$594$$ 0 0
$$595$$ 311.246 + 128.922i 0.523102 + 0.216676i
$$596$$ 0 0
$$597$$ −412.135 + 170.712i −0.690344 + 0.285950i
$$598$$ 0 0
$$599$$ −745.316 + 745.316i −1.24427 + 1.24427i −0.286055 + 0.958213i $$0.592344\pi$$
−0.958213 + 0.286055i $$0.907656\pi$$
$$600$$ 0 0
$$601$$ 130.996 130.996i 0.217963 0.217963i −0.589676 0.807640i $$-0.700745\pi$$
0.807640 + 0.589676i $$0.200745\pi$$
$$602$$ 0 0
$$603$$ 620.270 256.924i 1.02864 0.426077i
$$604$$ 0 0
$$605$$ 5.63517 + 2.33416i 0.00931433 + 0.00385812i
$$606$$ 0 0
$$607$$ 732.344i 1.20650i −0.797553 0.603249i $$-0.793873\pi$$
0.797553 0.603249i $$-0.206127\pi$$
$$608$$ 0 0
$$609$$ −89.5845 −0.147101
$$610$$ 0 0
$$611$$ −97.5969 + 235.620i −0.159733 + 0.385630i
$$612$$ 0 0
$$613$$ 208.204 + 502.648i 0.339647 + 0.819981i 0.997749 + 0.0670521i $$0.0213594\pi$$
−0.658102 + 0.752928i $$0.728641\pi$$
$$614$$ 0 0
$$615$$ −33.0230 33.0230i −0.0536960 0.0536960i
$$616$$ 0 0
$$617$$ 209.834 + 209.834i 0.340087 + 0.340087i 0.856400 0.516313i $$-0.172696\pi$$
−0.516313 + 0.856400i $$0.672696\pi$$
$$618$$ 0 0
$$619$$ −175.433 423.533i −0.283414 0.684222i 0.716497 0.697590i $$-0.245744\pi$$
−0.999911 + 0.0133688i $$0.995744\pi$$
$$620$$ 0 0
$$621$$ −292.349 + 705.793i −0.470772 + 1.13654i
$$622$$ 0 0
$$623$$ 105.213 0.168881
$$624$$ 0 0
$$625$$ 421.338i 0.674141i
$$626$$ 0 0
$$627$$ 270.118 + 111.887i 0.430811 + 0.178448i
$$628$$ 0 0
$$629$$ 1807.59 748.727i 2.87375 1.19035i
$$630$$ 0 0
$$631$$ −232.756 + 232.756i −0.368868 + 0.368868i −0.867064 0.498196i $$-0.833996\pi$$
0.498196 + 0.867064i $$0.333996\pi$$
$$632$$ 0 0
$$633$$ −258.372 + 258.372i −0.408170 + 0.408170i
$$634$$ 0 0
$$635$$ −198.707 + 82.3071i −0.312924 + 0.129617i
$$636$$ 0 0
$$637$$ 0.0559042 + 0.0231563i 8.77618e−5 + 3.63521e-5i
$$638$$ 0 0
$$639$$ 54.1749i 0.0847807i
$$640$$ 0 0
$$641$$ −123.632 −0.192873 −0.0964366 0.995339i $$-0.530744\pi$$
−0.0964366 + 0.995339i $$0.530744\pi$$
$$642$$ 0 0
$$643$$ 351.513 848.628i 0.546677 1.31979i −0.373260 0.927727i $$-0.621760\pi$$
0.919936 0.392068i $$-0.128240\pi$$
$$644$$ 0 0
$$645$$ 23.4803 + 56.6864i 0.0364035 + 0.0878859i
$$646$$ 0 0
$$647$$ 191.561 + 191.561i 0.296076 + 0.296076i 0.839475 0.543399i $$-0.182863\pi$$
−0.543399 + 0.839475i $$0.682863\pi$$
$$648$$ 0 0
$$649$$ 236.122 + 236.122i 0.363825 + 0.363825i
$$650$$ 0 0
$$651$$ 21.1799 + 51.1328i 0.0325344 + 0.0785450i
$$652$$ 0 0
$$653$$ −89.1964 + 215.339i −0.136595 + 0.329769i −0.977344 0.211655i $$-0.932115\pi$$
0.840750 + 0.541424i $$0.182115\pi$$
$$654$$ 0 0
$$655$$ 88.3853 0.134939
$$656$$ 0 0
$$657$$ 255.012i 0.388146i
$$658$$ 0 0
$$659$$ 911.099 + 377.389i 1.38255 + 0.572670i 0.945161 0.326604i $$-0.105904\pi$$
0.437386 + 0.899274i $$0.355904\pi$$
$$660$$ 0 0
$$661$$ −496.993 + 205.861i −0.751880 + 0.311439i −0.725509 0.688213i $$-0.758395\pi$$
−0.0263718 + 0.999652i $$0.508395\pi$$
$$662$$ 0 0
$$663$$ −122.869 + 122.869i −0.185322 + 0.185322i
$$664$$ 0 0
$$665$$ −157.928 + 157.928i −0.237485 + 0.237485i
$$666$$ 0 0
$$667$$ 295.014 122.199i 0.442300 0.183207i
$$668$$ 0 0
$$669$$ −140.876 58.3527i −0.210577 0.0872238i
$$670$$ 0 0
$$671$$ 923.172i 1.37582i
$$672$$ 0 0
$$673$$ 374.150 0.555944 0.277972 0.960589i $$-0.410338\pi$$
0.277972 + 0.960589i $$0.410338\pi$$
$$674$$ 0 0
$$675$$ −188.414 + 454.873i −0.279132 + 0.673885i
$$676$$ 0 0
$$677$$ 12.3571 + 29.8326i 0.0182527 + 0.0440659i 0.932743 0.360542i $$-0.117408\pi$$
−0.914490 + 0.404608i $$0.867408\pi$$
$$678$$ 0 0
$$679$$ −70.8184 70.8184i −0.104298 0.104298i
$$680$$ 0 0
$$681$$ −390.701 390.701i −0.573716 0.573716i
$$682$$ 0 0
$$683$$ −22.0894 53.3285i −0.0323417 0.0780799i 0.906883 0.421382i $$-0.138455\pi$$
−0.939225 + 0.343302i $$0.888455\pi$$
$$684$$ 0 0
$$685$$ −1.50984 + 3.64508i −0.00220415 + 0.00532128i
$$686$$ 0 0
$$687$$ 86.6852 0.126179
$$688$$ 0 0
$$689$$ 220.830i 0.320508i
$$690$$ 0 0
$$691$$ 622.510 + 257.852i 0.900883 + 0.373158i 0.784560 0.620053i $$-0.212889\pi$$
0.116323 + 0.993211i $$0.462889\pi$$
$$692$$ 0 0
$$693$$ −512.562 + 212.310i −0.739627 + 0.306364i
$$694$$ 0 0
$$695$$ −234.958 + 234.958i −0.338069 + 0.338069i
$$696$$ 0 0
$$697$$ 408.394 408.394i 0.585932 0.585932i
$$698$$ 0 0
$$699$$ 189.143 78.3456i 0.270591 0.112082i
$$700$$ 0 0
$$701$$ −34.0835 14.1179i −0.0486213 0.0201396i 0.358240 0.933629i $$-0.383377\pi$$
−0.406862 + 0.913490i $$0.633377\pi$$
$$702$$ 0 0
$$703$$ 1297.09i 1.84507i
$$704$$ 0 0
$$705$$ −134.306 −0.190505
$$706$$ 0 0
$$707$$ −361.698 + 873.215i −0.511595 + 1.23510i
$$708$$ 0 0
$$709$$ 285.114 + 688.325i 0.402135 + 0.970840i 0.987147 + 0.159815i $$0.0510898\pi$$
−0.585012 + 0.811025i $$0.698910\pi$$
$$710$$ 0 0
$$711$$ −251.805 251.805i −0.354156 0.354156i
$$712$$ 0 0
$$713$$ −139.497 139.497i −0.195647 0.195647i
$$714$$ 0 0
$$715$$ −31.5660 76.2071i −0.0441483 0.106583i
$$716$$ 0 0
$$717$$ 64.7212 156.251i 0.0902666 0.217923i
$$718$$ 0 0
$$719$$ 478.037 0.664863 0.332432 0.943127i $$-0.392131\pi$$
0.332432 + 0.943127i $$0.392131\pi$$
$$720$$ 0 0
$$721$$ 48.2761i 0.0669571i
$$722$$ 0 0
$$723$$ −240.516 99.6249i −0.332664 0.137794i
$$724$$ 0 0
$$725$$ 190.132 78.7553i 0.262251 0.108628i
$$726$$ 0 0
$$727$$ 408.395 408.395i 0.561753 0.561753i −0.368052 0.929805i $$-0.619975\pi$$
0.929805 + 0.368052i $$0.119975\pi$$
$$728$$ 0 0
$$729$$ 27.8184 27.8184i 0.0381597 0.0381597i
$$730$$ 0 0
$$731$$ −701.038 + 290.379i −0.959012 + 0.397236i
$$732$$ 0 0
$$733$$ 747.573 + 309.655i 1.01988 + 0.422449i 0.829050 0.559174i $$-0.188882\pi$$
0.190831 + 0.981623i $$0.438882\pi$$
$$734$$ 0 0
$$735$$ 0.0318661i 4.33552e-5i
$$736$$ 0 0
$$737$$ 1055.89 1.43269
$$738$$ 0 0
$$739$$ 348.876 842.261i 0.472092 1.13973i −0.491145 0.871078i $$-0.663421\pi$$
0.963237 0.268653i $$-0.0865786\pi$$
$$740$$ 0 0
$$741$$ −44.0840 106.428i −0.0594925 0.143628i
$$742$$ 0 0
$$743$$ 345.072 + 345.072i 0.464430 + 0.464430i 0.900104 0.435674i $$-0.143490\pi$$
−0.435674 + 0.900104i $$0.643490\pi$$
$$744$$ 0 0
$$745$$ 20.7250 + 20.7250i 0.0278187 + 0.0278187i
$$746$$ 0 0
$$747$$ 296.392 + 715.554i 0.396777 + 0.957903i
$$748$$ 0 0
$$749$$ −31.8967 + 77.0054i −0.0425857 + 0.102811i
$$750$$ 0 0
$$751$$ −642.659 −0.855737 −0.427869 0.903841i $$-0.640735\pi$$
−0.427869 + 0.903841i $$0.640735\pi$$
$$752$$ 0 0
$$753$$ 530.424i 0.704414i
$$754$$ 0 0
$$755$$ −279.485 115.767i −0.370179 0.153333i
$$756$$ 0 0
$$757$$ 241.802 100.158i 0.319422 0.132309i −0.217211 0.976125i $$-0.569696\pi$$
0.536633 + 0.843816i $$0.319696\pi$$
$$758$$ 0 0
$$759$$ −374.609 + 374.609i −0.493556 + 0.493556i
$$760$$ 0 0
$$761$$ −253.025 + 253.025i −0.332490 + 0.332490i −0.853531 0.521042i $$-0.825544\pi$$
0.521042 + 0.853531i $$0.325544\pi$$
$$762$$ 0 0
$$763$$ 186.086 77.0793i 0.243887 0.101021i
$$764$$ 0 0
$$765$$ 315.575 + 130.716i 0.412517 + 0.170870i
$$766$$ 0 0
$$767$$ 131.569i 0.171537i
$$768$$ 0 0
$$769$$ −1066.22 −1.38650 −0.693248 0.720699i $$-0.743821\pi$$
−0.693248 + 0.720699i $$0.743821\pi$$
$$770$$ 0 0
$$771$$ −44.5562 + 107.568i −0.0577902 + 0.139518i
$$772$$ 0 0
$$773$$ −497.702 1201.56i −0.643857 1.55441i −0.821435 0.570302i $$-0.806826\pi$$
0.177578 0.984107i $$-0.443174\pi$$
$$774$$ 0 0
$$775$$ −89.9033 89.9033i −0.116004 0.116004i
$$776$$ 0 0
$$777$$ 466.245 + 466.245i 0.600057 + 0.600057i
$$778$$ 0 0
$$779$$ 146.527 + 353.749i 0.188097 + 0.454106i
$$780$$ 0 0
$$781$$ −32.6056 + 78.7170i −0.0417486 + 0.100790i
$$782$$ 0 0
$$783$$ −205.995 −0.263084
$$784$$ 0 0
$$785$$ 429.553i 0.547201i
$$786$$ 0 0
$$787$$ −307.578 127.403i −0.390823 0.161884i 0.178614 0.983919i $$-0.442839\pi$$
−0.569437 + 0.822035i $$0.692839\pi$$
$$788$$ 0 0