# Properties

 Label 384.3.i.b.353.2 Level $384$ Weight $3$ Character 384.353 Analytic conductor $10.463$ Analytic rank $0$ Dimension $8$ 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: $$8$$ Relative dimension: $$4$$ over $$\Q(i)$$ Coefficient field: 8.0.629407744.1 Defining polynomial: $$x^{8} - 2x^{6} + 2x^{4} - 8x^{2} + 16$$ x^8 - 2*x^6 + 2*x^4 - 8*x^2 + 16 Coefficient ring: $$\Z[a_1, \ldots, a_{7}]$$ Coefficient ring index: $$2^{4}$$ Twist minimal: no (minimal twist has level 48) Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

## Embedding invariants

 Embedding label 353.2 Root $$1.38255 - 0.297594i$$ of defining polynomial Character $$\chi$$ $$=$$ 384.353 Dual form 384.3.i.b.161.2

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(0.737922 - 2.90783i) q^{3} +(1.57472 - 1.57472i) q^{5} +3.64575i q^{7} +(-7.91094 - 4.29150i) q^{9} +O(q^{10})$$ $$q+(0.737922 - 2.90783i) q^{3} +(1.57472 - 1.57472i) q^{5} +3.64575i q^{7} +(-7.91094 - 4.29150i) q^{9} +(-1.19038 + 1.19038i) q^{11} +(14.6458 - 14.6458i) q^{13} +(-3.41699 - 5.74103i) q^{15} -28.0726i q^{17} +(12.5830 - 12.5830i) q^{19} +(10.6012 + 2.69028i) q^{21} -29.2630 q^{23} +20.0405i q^{25} +(-18.3166 + 19.8369i) q^{27} +(-19.3557 - 19.3557i) q^{29} -11.6458 q^{31} +(2.58301 + 4.33981i) q^{33} +(5.74103 + 5.74103i) q^{35} +(-0.771243 - 0.771243i) q^{37} +(-31.7799 - 53.3948i) q^{39} +25.6919 q^{41} +(-40.5830 - 40.5830i) q^{43} +(-19.2154 + 5.69960i) q^{45} +50.2681i q^{47} +35.7085 q^{49} +(-81.6304 - 20.7154i) q^{51} +(46.2379 - 46.2379i) q^{53} +3.74902i q^{55} +(-27.3040 - 45.8745i) q^{57} +(-22.7533 + 22.7533i) q^{59} +(-12.7712 + 12.7712i) q^{61} +(15.6458 - 28.8413i) q^{63} -46.1259i q^{65} +(10.6863 - 10.6863i) q^{67} +(-21.5938 + 85.0919i) q^{69} +122.086 q^{71} -15.0405i q^{73} +(58.2744 + 14.7883i) q^{75} +(-4.33981 - 4.33981i) q^{77} +51.3948 q^{79} +(44.1660 + 67.8997i) q^{81} +(37.8680 + 37.8680i) q^{83} +(-44.2065 - 44.2065i) q^{85} +(-70.5659 + 42.0000i) q^{87} -5.45550 q^{89} +(53.3948 + 53.3948i) q^{91} +(-8.59366 + 33.8639i) q^{93} -39.6294i q^{95} -81.1660 q^{97} +(14.5255 - 4.30849i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$8 q + 4 q^{3}+O(q^{10})$$ 8 * q + 4 * q^3 $$8 q + 4 q^{3} + 96 q^{13} - 112 q^{15} + 16 q^{19} + 32 q^{21} - 68 q^{27} - 72 q^{31} - 64 q^{33} - 112 q^{37} - 240 q^{43} + 112 q^{45} + 328 q^{49} - 32 q^{51} - 208 q^{61} + 104 q^{63} - 232 q^{67} + 324 q^{75} + 136 q^{79} + 184 q^{81} + 112 q^{85} + 152 q^{91} - 64 q^{93} - 480 q^{97} + 160 q^{99}+O(q^{100})$$ 8 * q + 4 * q^3 + 96 * q^13 - 112 * q^15 + 16 * q^19 + 32 * q^21 - 68 * q^27 - 72 * q^31 - 64 * q^33 - 112 * q^37 - 240 * q^43 + 112 * q^45 + 328 * q^49 - 32 * q^51 - 208 * q^61 + 104 * q^63 - 232 * q^67 + 324 * q^75 + 136 * q^79 + 184 * q^81 + 112 * q^85 + 152 * q^91 - 64 * q^93 - 480 * q^97 + 160 * 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
$$3$$ 0.737922 2.90783i 0.245974 0.969276i
$$4$$ 0 0
$$5$$ 1.57472 1.57472i 0.314944 0.314944i −0.531877 0.846821i $$-0.678513\pi$$
0.846821 + 0.531877i $$0.178513\pi$$
$$6$$ 0 0
$$7$$ 3.64575i 0.520822i 0.965498 + 0.260411i $$0.0838580\pi$$
−0.965498 + 0.260411i $$0.916142\pi$$
$$8$$ 0 0
$$9$$ −7.91094 4.29150i −0.878994 0.476834i
$$10$$ 0 0
$$11$$ −1.19038 + 1.19038i −0.108216 + 0.108216i −0.759142 0.650926i $$-0.774381\pi$$
0.650926 + 0.759142i $$0.274381\pi$$
$$12$$ 0 0
$$13$$ 14.6458 14.6458i 1.12660 1.12660i 0.135870 0.990727i $$-0.456617\pi$$
0.990727 0.135870i $$-0.0433828\pi$$
$$14$$ 0 0
$$15$$ −3.41699 5.74103i −0.227800 0.382736i
$$16$$ 0 0
$$17$$ 28.0726i 1.65133i −0.564159 0.825666i $$-0.690800\pi$$
0.564159 0.825666i $$-0.309200\pi$$
$$18$$ 0 0
$$19$$ 12.5830 12.5830i 0.662263 0.662263i −0.293650 0.955913i $$-0.594870\pi$$
0.955913 + 0.293650i $$0.0948699\pi$$
$$20$$ 0 0
$$21$$ 10.6012 + 2.69028i 0.504820 + 0.128109i
$$22$$ 0 0
$$23$$ −29.2630 −1.27231 −0.636153 0.771563i $$-0.719475\pi$$
−0.636153 + 0.771563i $$0.719475\pi$$
$$24$$ 0 0
$$25$$ 20.0405i 0.801621i
$$26$$ 0 0
$$27$$ −18.3166 + 19.8369i −0.678393 + 0.734699i
$$28$$ 0 0
$$29$$ −19.3557 19.3557i −0.667437 0.667437i 0.289685 0.957122i $$-0.406449\pi$$
−0.957122 + 0.289685i $$0.906449\pi$$
$$30$$ 0 0
$$31$$ −11.6458 −0.375669 −0.187835 0.982201i $$-0.560147\pi$$
−0.187835 + 0.982201i $$0.560147\pi$$
$$32$$ 0 0
$$33$$ 2.58301 + 4.33981i 0.0782729 + 0.131510i
$$34$$ 0 0
$$35$$ 5.74103 + 5.74103i 0.164030 + 0.164030i
$$36$$ 0 0
$$37$$ −0.771243 0.771243i −0.0208444 0.0208444i 0.696608 0.717452i $$-0.254692\pi$$
−0.717452 + 0.696608i $$0.754692\pi$$
$$38$$ 0 0
$$39$$ −31.7799 53.3948i −0.814870 1.36910i
$$40$$ 0 0
$$41$$ 25.6919 0.626631 0.313316 0.949649i $$-0.398560\pi$$
0.313316 + 0.949649i $$0.398560\pi$$
$$42$$ 0 0
$$43$$ −40.5830 40.5830i −0.943791 0.943791i 0.0547114 0.998502i $$-0.482576\pi$$
−0.998502 + 0.0547114i $$0.982576\pi$$
$$44$$ 0 0
$$45$$ −19.2154 + 5.69960i −0.427009 + 0.126658i
$$46$$ 0 0
$$47$$ 50.2681i 1.06953i 0.845000 + 0.534767i $$0.179601\pi$$
−0.845000 + 0.534767i $$0.820399\pi$$
$$48$$ 0 0
$$49$$ 35.7085 0.728745
$$50$$ 0 0
$$51$$ −81.6304 20.7154i −1.60060 0.406185i
$$52$$ 0 0
$$53$$ 46.2379 46.2379i 0.872414 0.872414i −0.120321 0.992735i $$-0.538392\pi$$
0.992735 + 0.120321i $$0.0383925\pi$$
$$54$$ 0 0
$$55$$ 3.74902i 0.0681639i
$$56$$ 0 0
$$57$$ −27.3040 45.8745i −0.479017 0.804816i
$$58$$ 0 0
$$59$$ −22.7533 + 22.7533i −0.385649 + 0.385649i −0.873132 0.487483i $$-0.837915\pi$$
0.487483 + 0.873132i $$0.337915\pi$$
$$60$$ 0 0
$$61$$ −12.7712 + 12.7712i −0.209365 + 0.209365i −0.803997 0.594633i $$-0.797297\pi$$
0.594633 + 0.803997i $$0.297297\pi$$
$$62$$ 0 0
$$63$$ 15.6458 28.8413i 0.248345 0.457799i
$$64$$ 0 0
$$65$$ 46.1259i 0.709629i
$$66$$ 0 0
$$67$$ 10.6863 10.6863i 0.159497 0.159497i −0.622847 0.782344i $$-0.714024\pi$$
0.782344 + 0.622847i $$0.214024\pi$$
$$68$$ 0 0
$$69$$ −21.5938 + 85.0919i −0.312954 + 1.23322i
$$70$$ 0 0
$$71$$ 122.086 1.71952 0.859760 0.510699i $$-0.170613\pi$$
0.859760 + 0.510699i $$0.170613\pi$$
$$72$$ 0 0
$$73$$ 15.0405i 0.206034i −0.994680 0.103017i $$-0.967150\pi$$
0.994680 0.103017i $$-0.0328497\pi$$
$$74$$ 0 0
$$75$$ 58.2744 + 14.7883i 0.776992 + 0.197178i
$$76$$ 0 0
$$77$$ −4.33981 4.33981i −0.0563612 0.0563612i
$$78$$ 0 0
$$79$$ 51.3948 0.650567 0.325283 0.945617i $$-0.394540\pi$$
0.325283 + 0.945617i $$0.394540\pi$$
$$80$$ 0 0
$$81$$ 44.1660 + 67.8997i 0.545259 + 0.838267i
$$82$$ 0 0
$$83$$ 37.8680 + 37.8680i 0.456240 + 0.456240i 0.897419 0.441179i $$-0.145440\pi$$
−0.441179 + 0.897419i $$0.645440\pi$$
$$84$$ 0 0
$$85$$ −44.2065 44.2065i −0.520077 0.520077i
$$86$$ 0 0
$$87$$ −70.5659 + 42.0000i −0.811103 + 0.482759i
$$88$$ 0 0
$$89$$ −5.45550 −0.0612977 −0.0306489 0.999530i $$-0.509757\pi$$
−0.0306489 + 0.999530i $$0.509757\pi$$
$$90$$ 0 0
$$91$$ 53.3948 + 53.3948i 0.586756 + 0.586756i
$$92$$ 0 0
$$93$$ −8.59366 + 33.8639i −0.0924049 + 0.364127i
$$94$$ 0 0
$$95$$ 39.6294i 0.417152i
$$96$$ 0 0
$$97$$ −81.1660 −0.836763 −0.418381 0.908271i $$-0.637402\pi$$
−0.418381 + 0.908271i $$0.637402\pi$$
$$98$$ 0 0
$$99$$ 14.5255 4.30849i 0.146722 0.0435201i
$$100$$ 0 0
$$101$$ 32.4498 32.4498i 0.321285 0.321285i −0.527975 0.849260i $$-0.677048\pi$$
0.849260 + 0.527975i $$0.177048\pi$$
$$102$$ 0 0
$$103$$ 51.1882i 0.496973i 0.968635 + 0.248487i $$0.0799332\pi$$
−0.968635 + 0.248487i $$0.920067\pi$$
$$104$$ 0 0
$$105$$ 20.9304 12.4575i 0.199337 0.118643i
$$106$$ 0 0
$$107$$ 85.4698 85.4698i 0.798783 0.798783i −0.184121 0.982904i $$-0.558944\pi$$
0.982904 + 0.184121i $$0.0589438\pi$$
$$108$$ 0 0
$$109$$ 52.8523 52.8523i 0.484883 0.484883i −0.421804 0.906687i $$-0.638603\pi$$
0.906687 + 0.421804i $$0.138603\pi$$
$$110$$ 0 0
$$111$$ −2.81176 + 1.67353i −0.0253312 + 0.0150768i
$$112$$ 0 0
$$113$$ 73.5045i 0.650483i 0.945631 + 0.325241i $$0.105446\pi$$
−0.945631 + 0.325241i $$0.894554\pi$$
$$114$$ 0 0
$$115$$ −46.0810 + 46.0810i −0.400705 + 0.400705i
$$116$$ 0 0
$$117$$ −178.714 + 53.0094i −1.52747 + 0.453072i
$$118$$ 0 0
$$119$$ 102.346 0.860049
$$120$$ 0 0
$$121$$ 118.166i 0.976579i
$$122$$ 0 0
$$123$$ 18.9586 74.7076i 0.154135 0.607379i
$$124$$ 0 0
$$125$$ 70.9262 + 70.9262i 0.567409 + 0.567409i
$$126$$ 0 0
$$127$$ −73.9333 −0.582152 −0.291076 0.956700i $$-0.594013\pi$$
−0.291076 + 0.956700i $$0.594013\pi$$
$$128$$ 0 0
$$129$$ −147.956 + 88.0614i −1.14694 + 0.682646i
$$130$$ 0 0
$$131$$ 158.430 + 158.430i 1.20939 + 1.20939i 0.971226 + 0.238161i $$0.0765447\pi$$
0.238161 + 0.971226i $$0.423455\pi$$
$$132$$ 0 0
$$133$$ 45.8745 + 45.8745i 0.344921 + 0.344921i
$$134$$ 0 0
$$135$$ 2.39398 + 60.0810i 0.0177332 + 0.445045i
$$136$$ 0 0
$$137$$ 100.734 0.735283 0.367642 0.929968i $$-0.380165\pi$$
0.367642 + 0.929968i $$0.380165\pi$$
$$138$$ 0 0
$$139$$ 18.2732 + 18.2732i 0.131462 + 0.131462i 0.769776 0.638314i $$-0.220368\pi$$
−0.638314 + 0.769776i $$0.720368\pi$$
$$140$$ 0 0
$$141$$ 146.171 + 37.0939i 1.03667 + 0.263078i
$$142$$ 0 0
$$143$$ 34.8679i 0.243831i
$$144$$ 0 0
$$145$$ −60.9595 −0.420410
$$146$$ 0 0
$$147$$ 26.3501 103.834i 0.179252 0.706355i
$$148$$ 0 0
$$149$$ 44.9729 44.9729i 0.301831 0.301831i −0.539899 0.841730i $$-0.681537\pi$$
0.841730 + 0.539899i $$0.181537\pi$$
$$150$$ 0 0
$$151$$ 28.1033i 0.186114i 0.995661 + 0.0930572i $$0.0296639\pi$$
−0.995661 + 0.0930572i $$0.970336\pi$$
$$152$$ 0 0
$$153$$ −120.474 + 222.081i −0.787411 + 1.45151i
$$154$$ 0 0
$$155$$ −18.3388 + 18.3388i −0.118315 + 0.118315i
$$156$$ 0 0
$$157$$ −173.265 + 173.265i −1.10360 + 1.10360i −0.109628 + 0.993973i $$0.534966\pi$$
−0.993973 + 0.109628i $$0.965034\pi$$
$$158$$ 0 0
$$159$$ −100.332 168.572i −0.631019 1.06020i
$$160$$ 0 0
$$161$$ 106.686i 0.662644i
$$162$$ 0 0
$$163$$ 51.9190 51.9190i 0.318521 0.318521i −0.529678 0.848199i $$-0.677687\pi$$
0.848199 + 0.529678i $$0.177687\pi$$
$$164$$ 0 0
$$165$$ 10.9015 + 2.76648i 0.0660697 + 0.0167666i
$$166$$ 0 0
$$167$$ 57.5333 0.344511 0.172255 0.985052i $$-0.444895\pi$$
0.172255 + 0.985052i $$0.444895\pi$$
$$168$$ 0 0
$$169$$ 259.996i 1.53844i
$$170$$ 0 0
$$171$$ −153.543 + 45.5434i −0.897915 + 0.266336i
$$172$$ 0 0
$$173$$ 112.600 + 112.600i 0.650868 + 0.650868i 0.953202 0.302334i $$-0.0977657\pi$$
−0.302334 + 0.953202i $$0.597766\pi$$
$$174$$ 0 0
$$175$$ −73.0627 −0.417501
$$176$$ 0 0
$$177$$ 49.3725 + 82.9529i 0.278941 + 0.468660i
$$178$$ 0 0
$$179$$ −22.4810 22.4810i −0.125592 0.125592i 0.641517 0.767109i $$-0.278305\pi$$
−0.767109 + 0.641517i $$0.778305\pi$$
$$180$$ 0 0
$$181$$ 18.6013 + 18.6013i 0.102770 + 0.102770i 0.756622 0.653852i $$-0.226848\pi$$
−0.653852 + 0.756622i $$0.726848\pi$$
$$182$$ 0 0
$$183$$ 27.7124 + 46.5608i 0.151434 + 0.254430i
$$184$$ 0 0
$$185$$ −2.42898 −0.0131296
$$186$$ 0 0
$$187$$ 33.4170 + 33.4170i 0.178701 + 0.178701i
$$188$$ 0 0
$$189$$ −72.3203 66.7778i −0.382647 0.353322i
$$190$$ 0 0
$$191$$ 191.672i 1.00352i 0.865007 + 0.501760i $$0.167314\pi$$
−0.865007 + 0.501760i $$0.832686\pi$$
$$192$$ 0 0
$$193$$ 48.6275 0.251956 0.125978 0.992033i $$-0.459793\pi$$
0.125978 + 0.992033i $$0.459793\pi$$
$$194$$ 0 0
$$195$$ −134.126 34.0373i −0.687827 0.174550i
$$196$$ 0 0
$$197$$ −136.258 + 136.258i −0.691667 + 0.691667i −0.962599 0.270932i $$-0.912668\pi$$
0.270932 + 0.962599i $$0.412668\pi$$
$$198$$ 0 0
$$199$$ 144.767i 0.727474i −0.931502 0.363737i $$-0.881501\pi$$
0.931502 0.363737i $$-0.118499\pi$$
$$200$$ 0 0
$$201$$ −23.1882 38.9595i −0.115364 0.193828i
$$202$$ 0 0
$$203$$ 70.5659 70.5659i 0.347615 0.347615i
$$204$$ 0 0
$$205$$ 40.4575 40.4575i 0.197354 0.197354i
$$206$$ 0 0
$$207$$ 231.498 + 125.582i 1.11835 + 0.606678i
$$208$$ 0 0
$$209$$ 29.9570i 0.143335i
$$210$$ 0 0
$$211$$ −196.354 + 196.354i −0.930589 + 0.930589i −0.997743 0.0671538i $$-0.978608\pi$$
0.0671538 + 0.997743i $$0.478608\pi$$
$$212$$ 0 0
$$213$$ 90.0899 355.005i 0.422957 1.66669i
$$214$$ 0 0
$$215$$ −127.814 −0.594482
$$216$$ 0 0
$$217$$ 42.4575i 0.195657i
$$218$$ 0 0
$$219$$ −43.7353 11.0987i −0.199704 0.0506791i
$$220$$ 0 0
$$221$$ −411.145 411.145i −1.86038 1.86038i
$$222$$ 0 0
$$223$$ 375.261 1.68279 0.841393 0.540423i $$-0.181736\pi$$
0.841393 + 0.540423i $$0.181736\pi$$
$$224$$ 0 0
$$225$$ 86.0039 158.539i 0.382240 0.704619i
$$226$$ 0 0
$$227$$ −181.108 181.108i −0.797834 0.797834i 0.184920 0.982754i $$-0.440797\pi$$
−0.982754 + 0.184920i $$0.940797\pi$$
$$228$$ 0 0
$$229$$ 153.937 + 153.937i 0.672215 + 0.672215i 0.958226 0.286011i $$-0.0923295\pi$$
−0.286011 + 0.958226i $$0.592329\pi$$
$$230$$ 0 0
$$231$$ −15.8219 + 9.41699i −0.0684930 + 0.0407662i
$$232$$ 0 0
$$233$$ 51.7790 0.222228 0.111114 0.993808i $$-0.464558\pi$$
0.111114 + 0.993808i $$0.464558\pi$$
$$234$$ 0 0
$$235$$ 79.1581 + 79.1581i 0.336843 + 0.336843i
$$236$$ 0 0
$$237$$ 37.9253 149.447i 0.160022 0.630579i
$$238$$ 0 0
$$239$$ 249.900i 1.04560i −0.852454 0.522802i $$-0.824887\pi$$
0.852454 0.522802i $$-0.175113\pi$$
$$240$$ 0 0
$$241$$ 442.531 1.83623 0.918113 0.396318i $$-0.129712\pi$$
0.918113 + 0.396318i $$0.129712\pi$$
$$242$$ 0 0
$$243$$ 230.032 78.3226i 0.946632 0.322315i
$$244$$ 0 0
$$245$$ 56.2309 56.2309i 0.229514 0.229514i
$$246$$ 0 0
$$247$$ 368.575i 1.49221i
$$248$$ 0 0
$$249$$ 138.057 82.1699i 0.554446 0.330000i
$$250$$ 0 0
$$251$$ −43.3235 + 43.3235i −0.172603 + 0.172603i −0.788122 0.615519i $$-0.788947\pi$$
0.615519 + 0.788122i $$0.288947\pi$$
$$252$$ 0 0
$$253$$ 34.8340 34.8340i 0.137684 0.137684i
$$254$$ 0 0
$$255$$ −161.166 + 95.9241i −0.632024 + 0.376173i
$$256$$ 0 0
$$257$$ 179.197i 0.697266i −0.937259 0.348633i $$-0.886646\pi$$
0.937259 0.348633i $$-0.113354\pi$$
$$258$$ 0 0
$$259$$ 2.81176 2.81176i 0.0108562 0.0108562i
$$260$$ 0 0
$$261$$ 70.0567 + 236.186i 0.268416 + 0.904929i
$$262$$ 0 0
$$263$$ −419.478 −1.59497 −0.797486 0.603338i $$-0.793837\pi$$
−0.797486 + 0.603338i $$0.793837\pi$$
$$264$$ 0 0
$$265$$ 145.624i 0.549523i
$$266$$ 0 0
$$267$$ −4.02573 + 15.8637i −0.0150777 + 0.0594145i
$$268$$ 0 0
$$269$$ 33.7631 + 33.7631i 0.125513 + 0.125513i 0.767073 0.641560i $$-0.221712\pi$$
−0.641560 + 0.767073i $$0.721712\pi$$
$$270$$ 0 0
$$271$$ −329.269 −1.21502 −0.607508 0.794314i $$-0.707831\pi$$
−0.607508 + 0.794314i $$0.707831\pi$$
$$272$$ 0 0
$$273$$ 194.664 115.862i 0.713055 0.424402i
$$274$$ 0 0
$$275$$ −23.8557 23.8557i −0.0867482 0.0867482i
$$276$$ 0 0
$$277$$ −251.265 251.265i −0.907095 0.907095i 0.0889417 0.996037i $$-0.471652\pi$$
−0.996037 + 0.0889417i $$0.971652\pi$$
$$278$$ 0 0
$$279$$ 92.1289 + 49.9778i 0.330211 + 0.179132i
$$280$$ 0 0
$$281$$ −171.809 −0.611421 −0.305711 0.952124i $$-0.598894\pi$$
−0.305711 + 0.952124i $$0.598894\pi$$
$$282$$ 0 0
$$283$$ −193.476 193.476i −0.683660 0.683660i 0.277163 0.960823i $$-0.410606\pi$$
−0.960823 + 0.277163i $$0.910606\pi$$
$$284$$ 0 0
$$285$$ −115.236 29.2434i −0.404335 0.102608i
$$286$$ 0 0
$$287$$ 93.6662i 0.326363i
$$288$$ 0 0
$$289$$ −499.073 −1.72690
$$290$$ 0 0
$$291$$ −59.8942 + 236.017i −0.205822 + 0.811055i
$$292$$ 0 0
$$293$$ 73.4937 73.4937i 0.250832 0.250832i −0.570480 0.821312i $$-0.693243\pi$$
0.821312 + 0.570480i $$0.193243\pi$$
$$294$$ 0 0
$$295$$ 71.6601i 0.242916i
$$296$$ 0 0
$$297$$ −1.80968 45.4170i −0.00609320 0.152919i
$$298$$ 0 0
$$299$$ −428.579 + 428.579i −1.43337 + 1.43337i
$$300$$ 0 0
$$301$$ 147.956 147.956i 0.491547 0.491547i
$$302$$ 0 0
$$303$$ −70.4131 118.304i −0.232386 0.390442i
$$304$$ 0 0
$$305$$ 40.2222i 0.131876i
$$306$$ 0 0
$$307$$ 283.055 283.055i 0.922003 0.922003i −0.0751680 0.997171i $$-0.523949\pi$$
0.997171 + 0.0751680i $$0.0239493\pi$$
$$308$$ 0 0
$$309$$ 148.847 + 37.7729i 0.481704 + 0.122242i
$$310$$ 0 0
$$311$$ −54.0368 −0.173752 −0.0868759 0.996219i $$-0.527688\pi$$
−0.0868759 + 0.996219i $$0.527688\pi$$
$$312$$ 0 0
$$313$$ 490.280i 1.56639i 0.621777 + 0.783194i $$0.286411\pi$$
−0.621777 + 0.783194i $$0.713589\pi$$
$$314$$ 0 0
$$315$$ −20.7793 70.0547i −0.0659661 0.222396i
$$316$$ 0 0
$$317$$ 319.550 + 319.550i 1.00804 + 1.00804i 0.999967 + 0.00807607i $$0.00257072\pi$$
0.00807607 + 0.999967i $$0.497429\pi$$
$$318$$ 0 0
$$319$$ 46.0810 0.144455
$$320$$ 0 0
$$321$$ −185.461 311.601i −0.577762 0.970721i
$$322$$ 0 0
$$323$$ −353.238 353.238i −1.09362 1.09362i
$$324$$ 0 0
$$325$$ 293.508 + 293.508i 0.903103 + 0.903103i
$$326$$ 0 0
$$327$$ −114.685 192.686i −0.350717 0.589255i
$$328$$ 0 0
$$329$$ −183.265 −0.557036
$$330$$ 0 0
$$331$$ −269.431 269.431i −0.813992 0.813992i 0.171238 0.985230i $$-0.445223\pi$$
−0.985230 + 0.171238i $$0.945223\pi$$
$$332$$ 0 0
$$333$$ 2.79147 + 9.41106i 0.00838279 + 0.0282614i
$$334$$ 0 0
$$335$$ 33.6557i 0.100465i
$$336$$ 0 0
$$337$$ 143.041 0.424453 0.212226 0.977221i $$-0.431929\pi$$
0.212226 + 0.977221i $$0.431929\pi$$
$$338$$ 0 0
$$339$$ 213.739 + 54.2406i 0.630497 + 0.160002i
$$340$$ 0 0
$$341$$ 13.8628 13.8628i 0.0406534 0.0406534i
$$342$$ 0 0
$$343$$ 308.826i 0.900368i
$$344$$ 0 0
$$345$$ 99.9916 + 168.000i 0.289831 + 0.486957i
$$346$$ 0 0
$$347$$ 126.922 126.922i 0.365770 0.365770i −0.500162 0.865932i $$-0.666726\pi$$
0.865932 + 0.500162i $$0.166726\pi$$
$$348$$ 0 0
$$349$$ −195.893 + 195.893i −0.561297 + 0.561297i −0.929676 0.368378i $$-0.879913\pi$$
0.368378 + 0.929676i $$0.379913\pi$$
$$350$$ 0 0
$$351$$ 22.2653 + 558.787i 0.0634340 + 1.59198i
$$352$$ 0 0
$$353$$ 291.488i 0.825745i 0.910789 + 0.412873i $$0.135475\pi$$
−0.910789 + 0.412873i $$0.864525\pi$$
$$354$$ 0 0
$$355$$ 192.251 192.251i 0.541552 0.541552i
$$356$$ 0 0
$$357$$ 75.5233 297.604i 0.211550 0.833626i
$$358$$ 0 0
$$359$$ 40.3499 0.112395 0.0561976 0.998420i $$-0.482102\pi$$
0.0561976 + 0.998420i $$0.482102\pi$$
$$360$$ 0 0
$$361$$ 44.3360i 0.122814i
$$362$$ 0 0
$$363$$ 343.607 + 87.1973i 0.946575 + 0.240213i
$$364$$ 0 0
$$365$$ −23.6846 23.6846i −0.0648893 0.0648893i
$$366$$ 0 0
$$367$$ −340.678 −0.928279 −0.464140 0.885762i $$-0.653636\pi$$
−0.464140 + 0.885762i $$0.653636\pi$$
$$368$$ 0 0
$$369$$ −203.247 110.257i −0.550805 0.298799i
$$370$$ 0 0
$$371$$ 168.572 + 168.572i 0.454372 + 0.454372i
$$372$$ 0 0
$$373$$ −237.678 237.678i −0.637207 0.637207i 0.312658 0.949866i $$-0.398781\pi$$
−0.949866 + 0.312658i $$0.898781\pi$$
$$374$$ 0 0
$$375$$ 258.579 153.903i 0.689544 0.410409i
$$376$$ 0 0
$$377$$ −566.957 −1.50386
$$378$$ 0 0
$$379$$ 320.332 + 320.332i 0.845203 + 0.845203i 0.989530 0.144327i $$-0.0461017\pi$$
−0.144327 + 0.989530i $$0.546102\pi$$
$$380$$ 0 0
$$381$$ −54.5570 + 214.985i −0.143194 + 0.564266i
$$382$$ 0 0
$$383$$ 632.700i 1.65196i −0.563702 0.825978i $$-0.690623\pi$$
0.563702 0.825978i $$-0.309377\pi$$
$$384$$ 0 0
$$385$$ −13.6680 −0.0355012
$$386$$ 0 0
$$387$$ 146.888 + 495.212i 0.379555 + 1.27962i
$$388$$ 0 0
$$389$$ −424.351 + 424.351i −1.09088 + 1.09088i −0.0954418 + 0.995435i $$0.530426\pi$$
−0.995435 + 0.0954418i $$0.969574\pi$$
$$390$$ 0 0
$$391$$ 821.490i 2.10100i
$$392$$ 0 0
$$393$$ 577.595 343.778i 1.46971 0.874752i
$$394$$ 0 0
$$395$$ 80.9323 80.9323i 0.204892 0.204892i
$$396$$ 0 0
$$397$$ 445.678 445.678i 1.12262 1.12262i 0.131269 0.991347i $$-0.458095\pi$$
0.991347 0.131269i $$-0.0419051\pi$$
$$398$$ 0 0
$$399$$ 167.247 99.5434i 0.419166 0.249482i
$$400$$ 0 0
$$401$$ 555.896i 1.38627i 0.720806 + 0.693137i $$0.243772\pi$$
−0.720806 + 0.693137i $$0.756228\pi$$
$$402$$ 0 0
$$403$$ −170.561 + 170.561i −0.423228 + 0.423228i
$$404$$ 0 0
$$405$$ 176.472 + 37.3738i 0.435733 + 0.0922811i
$$406$$ 0 0
$$407$$ 1.83614 0.00451140
$$408$$ 0 0
$$409$$ 44.8261i 0.109599i 0.998497 + 0.0547997i $$0.0174520\pi$$
−0.998497 + 0.0547997i $$0.982548\pi$$
$$410$$ 0 0
$$411$$ 74.3337 292.917i 0.180861 0.712693i
$$412$$ 0 0
$$413$$ −82.9529 82.9529i −0.200854 0.200854i
$$414$$ 0 0
$$415$$ 119.263 0.287380
$$416$$ 0 0
$$417$$ 66.6196 39.6512i 0.159759 0.0950868i
$$418$$ 0 0
$$419$$ −15.2026 15.2026i −0.0362830 0.0362830i 0.688733 0.725016i $$-0.258167\pi$$
−0.725016 + 0.688733i $$0.758167\pi$$
$$420$$ 0 0
$$421$$ −262.889 262.889i −0.624439 0.624439i 0.322224 0.946663i $$-0.395569\pi$$
−0.946663 + 0.322224i $$0.895569\pi$$
$$422$$ 0 0
$$423$$ 215.726 397.668i 0.509990 0.940113i
$$424$$ 0 0
$$425$$ 562.590 1.32374
$$426$$ 0 0
$$427$$ −46.5608 46.5608i −0.109042 0.109042i
$$428$$ 0 0
$$429$$ 101.390 + 25.7298i 0.236340 + 0.0599762i
$$430$$ 0 0
$$431$$ 163.103i 0.378430i −0.981936 0.189215i $$-0.939406\pi$$
0.981936 0.189215i $$-0.0605943\pi$$
$$432$$ 0 0
$$433$$ −140.737 −0.325028 −0.162514 0.986706i $$-0.551960\pi$$
−0.162514 + 0.986706i $$0.551960\pi$$
$$434$$ 0 0
$$435$$ −44.9833 + 177.260i −0.103410 + 0.407494i
$$436$$ 0 0
$$437$$ −368.217 + 368.217i −0.842601 + 0.842601i
$$438$$ 0 0
$$439$$ 434.893i 0.990644i −0.868709 0.495322i $$-0.835050\pi$$
0.868709 0.495322i $$-0.164950\pi$$
$$440$$ 0 0
$$441$$ −282.488 153.243i −0.640562 0.347490i
$$442$$ 0 0
$$443$$ 260.367 260.367i 0.587736 0.587736i −0.349282 0.937018i $$-0.613574\pi$$
0.937018 + 0.349282i $$0.113574\pi$$
$$444$$ 0 0
$$445$$ −8.59088 + 8.59088i −0.0193053 + 0.0193053i
$$446$$ 0 0
$$447$$ −97.5869 163.960i −0.218315 0.366801i
$$448$$ 0 0
$$449$$ 98.9506i 0.220380i 0.993911 + 0.110190i $$0.0351459\pi$$
−0.993911 + 0.110190i $$0.964854\pi$$
$$450$$ 0 0
$$451$$ −30.5830 + 30.5830i −0.0678115 + 0.0678115i
$$452$$ 0 0
$$453$$ 81.7195 + 20.7380i 0.180396 + 0.0457793i
$$454$$ 0 0
$$455$$ 168.164 0.369590
$$456$$ 0 0
$$457$$ 14.4209i 0.0315556i 0.999876 + 0.0157778i $$0.00502245\pi$$
−0.999876 + 0.0157778i $$0.994978\pi$$
$$458$$ 0 0
$$459$$ 556.873 + 514.196i 1.21323 + 1.12025i
$$460$$ 0 0
$$461$$ 328.278 + 328.278i 0.712099 + 0.712099i 0.966974 0.254875i $$-0.0820343\pi$$
−0.254875 + 0.966974i $$0.582034\pi$$
$$462$$ 0 0
$$463$$ 848.427 1.83246 0.916228 0.400657i $$-0.131218\pi$$
0.916228 + 0.400657i $$0.131218\pi$$
$$464$$ 0 0
$$465$$ 39.7935 + 66.8587i 0.0855774 + 0.143782i
$$466$$ 0 0
$$467$$ −56.0706 56.0706i −0.120066 0.120066i 0.644521 0.764587i $$-0.277057\pi$$
−0.764587 + 0.644521i $$0.777057\pi$$
$$468$$ 0 0
$$469$$ 38.9595 + 38.9595i 0.0830693 + 0.0830693i
$$470$$ 0 0
$$471$$ 375.970 + 631.682i 0.798237 + 1.34115i
$$472$$ 0 0
$$473$$ 96.6181 0.204267
$$474$$ 0 0
$$475$$ 252.170 + 252.170i 0.530884 + 0.530884i
$$476$$ 0 0
$$477$$ −564.216 + 167.355i −1.18284 + 0.350850i
$$478$$ 0 0
$$479$$ 648.794i 1.35448i 0.735764 + 0.677238i $$0.236823\pi$$
−0.735764 + 0.677238i $$0.763177\pi$$
$$480$$ 0 0
$$481$$ −22.5909 −0.0469665
$$482$$ 0 0
$$483$$ −310.224 78.7257i −0.642285 0.162993i
$$484$$ 0 0
$$485$$ −127.814 + 127.814i −0.263533 + 0.263533i
$$486$$ 0 0
$$487$$ 176.783i 0.363004i 0.983391 + 0.181502i $$0.0580959\pi$$
−0.983391 + 0.181502i $$0.941904\pi$$
$$488$$ 0 0
$$489$$ −112.659 189.284i −0.230387 0.387083i
$$490$$ 0 0
$$491$$ 317.369 317.369i 0.646373 0.646373i −0.305742 0.952114i $$-0.598904\pi$$
0.952114 + 0.305742i $$0.0989044\pi$$
$$492$$ 0 0
$$493$$ −543.365 + 543.365i −1.10216 + 1.10216i
$$494$$ 0 0
$$495$$ 16.0889 29.6582i 0.0325029 0.0599156i
$$496$$ 0 0
$$497$$ 445.095i 0.895563i
$$498$$ 0 0
$$499$$ −374.391 + 374.391i −0.750282 + 0.750282i −0.974532 0.224250i $$-0.928007\pi$$
0.224250 + 0.974532i $$0.428007\pi$$
$$500$$ 0 0
$$501$$ 42.4551 167.297i 0.0847407 0.333926i
$$502$$ 0 0
$$503$$ 386.094 0.767583 0.383791 0.923420i $$-0.374618\pi$$
0.383791 + 0.923420i $$0.374618\pi$$
$$504$$ 0 0
$$505$$ 102.199i 0.202374i
$$506$$ 0 0
$$507$$ −756.024 191.857i −1.49117 0.378416i
$$508$$ 0 0
$$509$$ 41.6258 + 41.6258i 0.0817796 + 0.0817796i 0.746813 0.665034i $$-0.231583\pi$$
−0.665034 + 0.746813i $$0.731583\pi$$
$$510$$ 0 0
$$511$$ 54.8340 0.107307
$$512$$ 0 0
$$513$$ 19.1294 + 480.086i 0.0372893 + 0.935839i
$$514$$ 0 0
$$515$$ 80.6071 + 80.6071i 0.156519 + 0.156519i
$$516$$ 0 0
$$517$$ −59.8379 59.8379i −0.115741 0.115741i
$$518$$ 0 0
$$519$$ 410.512 244.332i 0.790968 0.470775i
$$520$$ 0 0
$$521$$ −233.704 −0.448569 −0.224284 0.974524i $$-0.572004\pi$$
−0.224284 + 0.974524i $$0.572004\pi$$
$$522$$ 0 0
$$523$$ −219.506 219.506i −0.419705 0.419705i 0.465397 0.885102i $$-0.345912\pi$$
−0.885102 + 0.465397i $$0.845912\pi$$
$$524$$ 0 0
$$525$$ −53.9146 + 212.454i −0.102694 + 0.404674i
$$526$$ 0 0
$$527$$ 326.927i 0.620355i
$$528$$ 0 0
$$529$$ 327.324 0.618760
$$530$$ 0 0
$$531$$ 277.646 82.3542i 0.522873 0.155093i
$$532$$ 0 0
$$533$$ 376.277 376.277i 0.705961 0.705961i
$$534$$ 0 0
$$535$$ 269.182i 0.503143i
$$536$$ 0 0
$$537$$ −81.9601 + 48.7817i −0.152626 + 0.0908411i
$$538$$ 0 0
$$539$$ −42.5065 + 42.5065i −0.0788618 + 0.0788618i
$$540$$ 0 0
$$541$$ −80.5203 + 80.5203i −0.148836 + 0.148836i −0.777598 0.628762i $$-0.783562\pi$$
0.628762 + 0.777598i $$0.283562\pi$$
$$542$$ 0 0
$$543$$ 67.8157 40.3631i 0.124891 0.0743335i
$$544$$ 0 0
$$545$$ 166.455i 0.305422i
$$546$$ 0 0
$$547$$ 1.49803 1.49803i 0.00273863 0.00273863i −0.705736 0.708475i $$-0.749384\pi$$
0.708475 + 0.705736i $$0.249384\pi$$
$$548$$ 0 0
$$549$$ 155.840 46.2247i 0.283862 0.0841981i
$$550$$ 0 0
$$551$$ −487.105 −0.884038
$$552$$ 0 0
$$553$$ 187.373i 0.338829i
$$554$$ 0 0
$$555$$ −1.79240 + 7.06307i −0.00322955 + 0.0127263i
$$556$$ 0 0
$$557$$ −322.326 322.326i −0.578682 0.578682i 0.355858 0.934540i $$-0.384189\pi$$
−0.934540 + 0.355858i $$0.884189\pi$$
$$558$$ 0 0
$$559$$ −1188.74 −2.12654
$$560$$ 0 0
$$561$$ 121.830 72.5118i 0.217166 0.129255i
$$562$$ 0 0
$$563$$ −523.954 523.954i −0.930646 0.930646i 0.0671003 0.997746i $$-0.478625\pi$$
−0.997746 + 0.0671003i $$0.978625\pi$$
$$564$$ 0 0
$$565$$ 115.749 + 115.749i 0.204866 + 0.204866i
$$566$$ 0 0
$$567$$ −247.545 + 161.018i −0.436588 + 0.283983i
$$568$$ 0 0
$$569$$ 767.880 1.34952 0.674762 0.738035i $$-0.264246\pi$$
0.674762 + 0.738035i $$0.264246\pi$$
$$570$$ 0 0
$$571$$ −3.43922 3.43922i −0.00602316 0.00602316i 0.704089 0.710112i $$-0.251356\pi$$
−0.710112 + 0.704089i $$0.751356\pi$$
$$572$$ 0 0
$$573$$ 557.350 + 141.439i 0.972688 + 0.246840i
$$574$$ 0 0
$$575$$ 586.446i 1.01991i
$$576$$ 0 0
$$577$$ −572.442 −0.992100 −0.496050 0.868294i $$-0.665217\pi$$
−0.496050 + 0.868294i $$0.665217\pi$$
$$578$$ 0 0
$$579$$ 35.8833 141.400i 0.0619746 0.244215i
$$580$$ 0 0
$$581$$ −138.057 + 138.057i −0.237620 + 0.237620i
$$582$$ 0 0
$$583$$ 110.081i 0.188818i
$$584$$ 0 0
$$585$$ −197.949 + 364.899i −0.338375 + 0.623759i
$$586$$ 0 0
$$587$$ −446.694 + 446.694i −0.760977 + 0.760977i −0.976499 0.215522i $$-0.930855\pi$$
0.215522 + 0.976499i $$0.430855\pi$$
$$588$$ 0 0
$$589$$ −146.539 + 146.539i −0.248792 + 0.248792i
$$590$$ 0 0
$$591$$ 295.668 + 496.764i 0.500284 + 0.840548i
$$592$$ 0 0
$$593$$ 838.112i 1.41334i −0.707542 0.706671i $$-0.750196\pi$$
0.707542 0.706671i $$-0.249804\pi$$
$$594$$ 0 0
$$595$$ 161.166 161.166i 0.270867 0.270867i
$$596$$ 0 0
$$597$$ −420.959 106.827i −0.705123 0.178940i
$$598$$ 0 0
$$599$$ −414.241 −0.691555 −0.345777 0.938317i $$-0.612385\pi$$
−0.345777 + 0.938317i $$0.612385\pi$$
$$600$$ 0 0
$$601$$ 305.786i 0.508795i −0.967100 0.254397i $$-0.918123\pi$$
0.967100 0.254397i $$-0.0818771\pi$$
$$602$$ 0 0
$$603$$ −130.399 + 38.6783i −0.216250 + 0.0641431i
$$604$$ 0 0
$$605$$ 186.078 + 186.078i 0.307567 + 0.307567i
$$606$$ 0 0
$$607$$ 103.217 0.170044 0.0850222 0.996379i $$-0.472904\pi$$
0.0850222 + 0.996379i $$0.472904\pi$$
$$608$$ 0 0
$$609$$ −153.122 257.266i −0.251431 0.422440i
$$610$$ 0 0
$$611$$ 736.214 + 736.214i 1.20493 + 1.20493i
$$612$$ 0 0
$$613$$ 391.273 + 391.273i 0.638292 + 0.638292i 0.950134 0.311842i $$-0.100946\pi$$
−0.311842 + 0.950134i $$0.600946\pi$$
$$614$$ 0 0
$$615$$ −87.7891 147.498i −0.142746 0.239834i
$$616$$ 0 0
$$617$$ −713.373 −1.15620 −0.578098 0.815967i $$-0.696205\pi$$
−0.578098 + 0.815967i $$0.696205\pi$$
$$618$$ 0 0
$$619$$ −399.763 399.763i −0.645821 0.645821i 0.306159 0.951980i $$-0.400956\pi$$
−0.951980 + 0.306159i $$0.900956\pi$$
$$620$$ 0 0
$$621$$ 535.999 580.487i 0.863123 0.934761i
$$622$$ 0 0
$$623$$ 19.8894i 0.0319252i
$$624$$ 0 0
$$625$$ −277.635 −0.444217
$$626$$ 0 0
$$627$$ 87.1099 + 22.1059i 0.138931 + 0.0352567i
$$628$$ 0 0
$$629$$ −21.6508 + 21.6508i −0.0344210 + 0.0344210i
$$630$$ 0 0
$$631$$ 934.242i 1.48057i −0.672291 0.740287i $$-0.734690\pi$$
0.672291 0.740287i $$-0.265310\pi$$
$$632$$ 0 0
$$633$$ 426.071 + 715.859i 0.673097 + 1.13090i
$$634$$ 0 0
$$635$$ −116.424 + 116.424i −0.183345 + 0.183345i
$$636$$ 0 0
$$637$$ 522.978 522.978i 0.821001 0.821001i
$$638$$ 0 0
$$639$$ −965.814 523.932i −1.51145 0.819925i
$$640$$ 0 0
$$641$$ 26.1836i 0.0408480i −0.999791 0.0204240i $$-0.993498\pi$$
0.999791 0.0204240i $$-0.00650162\pi$$
$$642$$ 0 0
$$643$$ 625.336 625.336i 0.972529 0.972529i −0.0271039 0.999633i $$-0.508629\pi$$
0.999633 + 0.0271039i $$0.00862850\pi$$
$$644$$ 0 0
$$645$$ −94.3165 + 371.660i −0.146227 + 0.576218i
$$646$$ 0 0
$$647$$ −97.2591 −0.150323 −0.0751616 0.997171i $$-0.523947\pi$$
−0.0751616 + 0.997171i $$0.523947\pi$$
$$648$$ 0 0
$$649$$ 54.1699i 0.0834668i
$$650$$ 0 0
$$651$$ −123.459 31.3303i −0.189645 0.0481265i
$$652$$ 0 0
$$653$$ −129.213 129.213i −0.197875 0.197875i 0.601213 0.799089i $$-0.294684\pi$$
−0.799089 + 0.601213i $$0.794684\pi$$
$$654$$ 0 0
$$655$$ 498.965 0.761778
$$656$$ 0 0
$$657$$ −64.5464 + 118.985i −0.0982442 + 0.181103i
$$658$$ 0 0
$$659$$ 3.10975 + 3.10975i 0.00471889 + 0.00471889i 0.709462 0.704743i $$-0.248938\pi$$
−0.704743 + 0.709462i $$0.748938\pi$$
$$660$$ 0 0
$$661$$ 22.3424 + 22.3424i 0.0338010 + 0.0338010i 0.723805 0.690004i $$-0.242391\pi$$
−0.690004 + 0.723805i $$0.742391\pi$$
$$662$$ 0 0
$$663$$ −1498.93 + 892.146i −2.26083 + 1.34562i
$$664$$ 0 0
$$665$$ 144.479 0.217262
$$666$$ 0 0
$$667$$ 566.405 + 566.405i 0.849183 + 0.849183i
$$668$$ 0 0
$$669$$ 276.914 1091.20i 0.413922 1.63109i
$$670$$ 0 0
$$671$$ 30.4052i 0.0453132i
$$672$$ 0 0
$$673$$ 1085.74 1.61329 0.806643 0.591039i $$-0.201282\pi$$
0.806643 + 0.591039i $$0.201282\pi$$
$$674$$ 0 0
$$675$$ −397.541 367.074i −0.588950 0.543814i
$$676$$ 0 0
$$677$$ 813.520 813.520i 1.20165 1.20165i 0.227991 0.973663i $$-0.426784\pi$$
0.973663 0.227991i $$-0.0732157\pi$$
$$678$$ 0 0
$$679$$ 295.911i 0.435804i
$$680$$ 0 0
$$681$$ −660.276 + 392.988i −0.969568 + 0.577075i
$$682$$ 0 0
$$683$$ 427.362 427.362i 0.625713 0.625713i −0.321273 0.946986i $$-0.604111\pi$$
0.946986 + 0.321273i $$0.104111\pi$$
$$684$$ 0 0
$$685$$ 158.627 158.627i 0.231573 0.231573i
$$686$$ 0 0
$$687$$ 561.217 334.030i 0.816910 0.486215i
$$688$$ 0 0
$$689$$ 1354.38i 1.96572i
$$690$$ 0 0
$$691$$ −420.170 + 420.170i −0.608061 + 0.608061i −0.942439 0.334378i $$-0.891474\pi$$
0.334378 + 0.942439i $$0.391474\pi$$
$$692$$ 0 0
$$693$$ 15.7077 + 52.9563i 0.0226662 + 0.0764161i
$$694$$ 0 0
$$695$$ 57.5504 0.0828063
$$696$$ 0 0
$$697$$ 721.239i 1.03478i
$$698$$ 0 0
$$699$$ 38.2089 150.565i 0.0546622 0.215400i
$$700$$ 0 0
$$701$$ −774.018 774.018i −1.10416 1.10416i −0.993903 0.110260i $$-0.964832\pi$$
−0.110260 0.993903i $$-0.535168\pi$$
$$702$$ 0 0
$$703$$ −19.4091 −0.0276090
$$704$$ 0 0
$$705$$ 288.591 171.766i 0.409349 0.243639i
$$706$$ 0 0
$$707$$ 118.304 + 118.304i 0.167332 + 0.167332i
$$708$$ 0 0
$$709$$ −198.261 198.261i −0.279635 0.279635i 0.553328 0.832963i $$-0.313358\pi$$
−0.832963 + 0.553328i $$0.813358\pi$$
$$710$$ 0 0
$$711$$ −406.581 220.561i −0.571844 0.310212i
$$712$$ 0 0
$$713$$ 340.790 0.477966
$$714$$ 0 0
$$715$$ 54.9072 + 54.9072i 0.0767932 + 0.0767932i
$$716$$ 0 0
$$717$$ −726.665 184.406i −1.01348 0.257192i
$$718$$ 0 0
$$719$$ 639.218i 0.889037i 0.895770 + 0.444519i $$0.146625\pi$$
−0.895770 + 0.444519i $$0.853375\pi$$
$$720$$ 0 0
$$721$$ −186.620 −0.258834
$$722$$ 0 0
$$723$$ 326.553 1286.80i 0.451664 1.77981i
$$724$$ 0 0
$$725$$ 387.898 387.898i 0.535031 0.535031i
$$726$$ 0 0
$$727$$ 789.136i 1.08547i 0.839904 + 0.542734i $$0.182611\pi$$
−0.839904 + 0.542734i $$0.817389\pi$$
$$728$$ 0 0
$$729$$ −58.0032 726.689i −0.0795654 0.996830i
$$730$$ 0 0
$$731$$ −1139.27 + 1139.27i −1.55851 + 1.55851i
$$732$$ 0 0
$$733$$ 49.8641 49.8641i 0.0680274 0.0680274i −0.672275 0.740302i $$-0.734683\pi$$
0.740302 + 0.672275i $$0.234683\pi$$
$$734$$ 0 0
$$735$$ −122.016 205.004i −0.166008 0.278917i
$$736$$ 0 0
$$737$$ 25.4414i 0.0345202i
$$738$$ 0 0
$$739$$ 157.593 157.593i 0.213252 0.213252i −0.592395 0.805647i $$-0.701818\pi$$
0.805647 + 0.592395i $$0.201818\pi$$
$$740$$ 0 0
$$741$$ −1071.75 271.980i −1.44636 0.367044i
$$742$$ 0 0
$$743$$ 1305.03 1.75643 0.878216 0.478265i $$-0.158734\pi$$
0.878216 + 0.478265i $$0.158734\pi$$
$$744$$ 0 0
$$745$$ 141.639i 0.190120i
$$746$$ 0 0
$$747$$ −137.061 462.082i −0.183482 0.618583i
$$748$$ 0 0
$$749$$ 311.601 + 311.601i 0.416023 + 0.416023i
$$750$$ 0 0
$$751$$ −793.800 −1.05699 −0.528495 0.848936i $$-0.677244\pi$$
−0.528495 + 0.848936i $$0.677244\pi$$
$$752$$ 0 0
$$753$$ 94.0079 + 157.947i 0.124844 + 0.209756i
$$754$$ 0 0
$$755$$ 44.2548 + 44.2548i 0.0586156 + 0.0586156i
$$756$$ 0 0
$$757$$ 750.497 + 750.497i 0.991409 + 0.991409i 0.999963 0.00855438i $$-0.00272298\pi$$
−0.00855438 + 0.999963i $$0.502723\pi$$
$$758$$ 0 0
$$759$$ −75.5865 126.996i −0.0995870 0.167320i
$$760$$ 0 0
$$761$$ −1055.45 −1.38692 −0.693462 0.720493i $$-0.743916\pi$$
−0.693462 + 0.720493i $$0.743916\pi$$
$$762$$ 0 0
$$763$$ 192.686 + 192.686i 0.252538 + 0.252538i
$$764$$ 0 0
$$765$$ 160.003 + 539.428i 0.209154 + 0.705134i
$$766$$ 0 0
$$767$$ 666.478i 0.868942i
$$768$$ 0 0
$$769$$ 883.681 1.14913 0.574565 0.818459i $$-0.305171\pi$$
0.574565 + 0.818459i $$0.305171\pi$$
$$770$$ 0 0
$$771$$ −521.076 132.234i −0.675844 0.171509i
$$772$$ 0 0
$$773$$ 894.518 894.518i 1.15720 1.15720i 0.172129 0.985074i $$-0.444935\pi$$
0.985074 0.172129i $$-0.0550647\pi$$
$$774$$ 0 0
$$775$$ 233.387i 0.301144i
$$776$$ 0 0
$$777$$ −6.10126 10.2510i −0.00785233 0.0131930i
$$778$$ 0 0
$$779$$ 323.281 323.281i 0.414995 0.414995i
$$780$$ 0 0
$$781$$ −145.328 + 145.328i −0.186079 + 0.186079i
$$782$$ 0 0
$$783$$ 738.486 29.4256i 0.943150 0.0375806i
$$784$$ 0 0
$$785$$ 545.689i 0.695145i
$$786$$ 0 0
$$787$$ −779.150 + 779.150i −0.990026 + 0.990026i −0.999951 0.00992500i $$-0.996841\pi$$
0.00992500 + 0.999951i $$0.496841\pi$$
$$788$$ 0 0
$$789$$ −309.542 + 1219.77i −0.392322 + 1.54597i
$$790$$ 0 0
$$791$$ −267.979 −0.338785
$$792$$ 0 0
$$793$$ 374.089i 0.471739i