# Properties

 Label 384.3.i.a.353.1 Level $384$ Weight $3$ Character 384.353 Analytic conductor $10.463$ Analytic rank $0$ Dimension $8$ CM no Inner twists $4$

# Learn more

## 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: $$x^{8} - 2 x^{6} + 2 x^{4} - 8 x^{2} + 16$$ 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 353.1 Root $$-1.38255 + 0.297594i$$ of defining polynomial Character $$\chi$$ $$=$$ 384.353 Dual form 384.3.i.a.161.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-2.90783 + 0.737922i) q^{3} +(-1.57472 + 1.57472i) q^{5} -3.64575i q^{7} +(7.91094 - 4.29150i) q^{9} +O(q^{10})$$ $$q+(-2.90783 + 0.737922i) q^{3} +(-1.57472 + 1.57472i) q^{5} -3.64575i q^{7} +(7.91094 - 4.29150i) q^{9} +(-1.19038 + 1.19038i) q^{11} +(14.6458 - 14.6458i) q^{13} +(3.41699 - 5.74103i) q^{15} +28.0726i q^{17} +(-12.5830 + 12.5830i) q^{19} +(2.69028 + 10.6012i) q^{21} -29.2630 q^{23} +20.0405i q^{25} +(-19.8369 + 18.3166i) q^{27} +(19.3557 + 19.3557i) q^{29} +11.6458 q^{31} +(2.58301 - 4.33981i) q^{33} +(5.74103 + 5.74103i) q^{35} +(-0.771243 - 0.771243i) q^{37} +(-31.7799 + 53.3948i) q^{39} -25.6919 q^{41} +(40.5830 + 40.5830i) q^{43} +(-5.69960 + 19.2154i) q^{45} +50.2681i q^{47} +35.7085 q^{49} +(-20.7154 - 81.6304i) q^{51} +(-46.2379 + 46.2379i) q^{53} -3.74902i q^{55} +(27.3040 - 45.8745i) q^{57} +(-22.7533 + 22.7533i) q^{59} +(-12.7712 + 12.7712i) q^{61} +(-15.6458 - 28.8413i) q^{63} +46.1259i q^{65} +(-10.6863 + 10.6863i) q^{67} +(85.0919 - 21.5938i) q^{69} +122.086 q^{71} -15.0405i q^{73} +(-14.7883 - 58.2744i) q^{75} +(4.33981 + 4.33981i) q^{77} -51.3948 q^{79} +(44.1660 - 67.8997i) q^{81} +(37.8680 + 37.8680i) q^{83} +(-44.2065 - 44.2065i) q^{85} +(-70.5659 - 42.0000i) q^{87} +5.45550 q^{89} +(-53.3948 - 53.3948i) q^{91} +(-33.8639 + 8.59366i) q^{93} -39.6294i q^{95} -81.1660 q^{97} +(-4.30849 + 14.5255i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$8 q - 4 q^{3} + O(q^{10})$$ $$8 q - 4 q^{3} + 96 q^{13} + 112 q^{15} - 16 q^{19} + 32 q^{21} + 68 q^{27} + 72 q^{31} - 64 q^{33} - 112 q^{37} + 240 q^{43} + 112 q^{45} + 328 q^{49} + 32 q^{51} - 208 q^{61} - 104 q^{63} + 232 q^{67} - 324 q^{75} - 136 q^{79} + 184 q^{81} + 112 q^{85} - 152 q^{91} - 64 q^{93} - 480 q^{97} - 160 q^{99} + O(q^{100})$$

## 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
$$3$$ −2.90783 + 0.737922i −0.969276 + 0.245974i
$$4$$ 0 0
$$5$$ −1.57472 + 1.57472i −0.314944 + 0.314944i −0.846821 0.531877i $$-0.821487\pi$$
0.531877 + 0.846821i $$0.321487\pi$$
$$6$$ 0 0
$$7$$ 3.64575i 0.520822i −0.965498 0.260411i $$-0.916142\pi$$
0.965498 0.260411i $$-0.0838580\pi$$
$$8$$ 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 $$0.309200\pi$$
−0.564159 + 0.825666i $$0.690800\pi$$
$$18$$ 0 0
$$19$$ −12.5830 + 12.5830i −0.662263 + 0.662263i −0.955913 0.293650i $$-0.905130\pi$$
0.293650 + 0.955913i $$0.405130\pi$$
$$20$$ 0 0
$$21$$ 2.69028 + 10.6012i 0.128109 + 0.504820i
$$22$$ 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
$$27$$ −19.8369 + 18.3166i −0.734699 + 0.678393i
$$28$$ 0 0
$$29$$ 19.3557 + 19.3557i 0.667437 + 0.667437i 0.957122 0.289685i $$-0.0935506\pi$$
−0.289685 + 0.957122i $$0.593551\pi$$
$$30$$ 0 0
$$31$$ 11.6458 0.375669 0.187835 0.982201i $$-0.439853\pi$$
0.187835 + 0.982201i $$0.439853\pi$$
$$32$$ 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 $$-0.601440\pi$$
−0.313316 + 0.949649i $$0.601440\pi$$
$$42$$ 0 0
$$43$$ 40.5830 + 40.5830i 0.943791 + 0.943791i 0.998502 0.0547114i $$-0.0174239\pi$$
−0.0547114 + 0.998502i $$0.517424\pi$$
$$44$$ 0 0
$$45$$ −5.69960 + 19.2154i −0.126658 + 0.427009i
$$46$$ 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
$$51$$ −20.7154 81.6304i −0.406185 1.60060i
$$52$$ 0 0
$$53$$ −46.2379 + 46.2379i −0.872414 + 0.872414i −0.992735 0.120321i $$-0.961608\pi$$
0.120321 + 0.992735i $$0.461608\pi$$
$$54$$ 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 −0.782344 0.622847i $$-0.785976\pi$$
0.622847 + 0.782344i $$0.285976\pi$$
$$68$$ 0 0
$$69$$ 85.0919 21.5938i 1.23322 0.312954i
$$70$$ 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
$$75$$ −14.7883 58.2744i −0.197178 0.776992i
$$76$$ 0 0
$$77$$ 4.33981 + 4.33981i 0.0563612 + 0.0563612i
$$78$$ 0 0
$$79$$ −51.3948 −0.650567 −0.325283 0.945617i $$-0.605460\pi$$
−0.325283 + 0.945617i $$0.605460\pi$$
$$80$$ 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 $$-0.490243\pi$$
0.0306489 + 0.999530i $$0.490243\pi$$
$$90$$ 0 0
$$91$$ −53.3948 53.3948i −0.586756 0.586756i
$$92$$ 0 0
$$93$$ −33.8639 + 8.59366i −0.364127 + 0.0924049i
$$94$$ 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
$$99$$ −4.30849 + 14.5255i −0.0435201 + 0.146722i
$$100$$ 0 0
$$101$$ −32.4498 + 32.4498i −0.321285 + 0.321285i −0.849260 0.527975i $$-0.822952\pi$$
0.527975 + 0.849260i $$0.322952\pi$$
$$102$$ 0 0
$$103$$ 51.1882i 0.496973i −0.968635 0.248487i $$-0.920067\pi$$
0.968635 0.248487i $$-0.0799332\pi$$
$$104$$ 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 $$-0.894554\pi$$
0.945631 0.325241i $$-0.105446\pi$$
$$114$$ 0 0
$$115$$ 46.0810 46.0810i 0.400705 0.400705i
$$116$$ 0 0
$$117$$ 53.0094 178.714i 0.453072 1.52747i
$$118$$ 0 0
$$119$$ 102.346 0.860049
$$120$$ 0 0
$$121$$ 118.166i 0.976579i
$$122$$ 0 0
$$123$$ 74.7076 18.9586i 0.607379 0.154135i
$$124$$ 0 0
$$125$$ −70.9262 70.9262i −0.567409 0.567409i
$$126$$ 0 0
$$127$$ 73.9333 0.582152 0.291076 0.956700i $$-0.405987\pi$$
0.291076 + 0.956700i $$0.405987\pi$$
$$128$$ 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 $$-0.619835\pi$$
−0.367642 + 0.929968i $$0.619835\pi$$
$$138$$ 0 0
$$139$$ −18.2732 18.2732i −0.131462 0.131462i 0.638314 0.769776i $$-0.279632\pi$$
−0.769776 + 0.638314i $$0.779632\pi$$
$$140$$ 0 0
$$141$$ −37.0939 146.171i −0.263078 1.03667i
$$142$$ 0 0
$$143$$ 34.8679i 0.243831i
$$144$$ 0 0
$$145$$ −60.9595 −0.420410
$$146$$ 0 0
$$147$$ −103.834 + 26.3501i −0.706355 + 0.179252i
$$148$$ 0 0
$$149$$ −44.9729 + 44.9729i −0.301831 + 0.301831i −0.841730 0.539899i $$-0.818463\pi$$
0.539899 + 0.841730i $$0.318463\pi$$
$$150$$ 0 0
$$151$$ 28.1033i 0.186114i −0.995661 0.0930572i $$-0.970336\pi$$
0.995661 0.0930572i $$-0.0296639\pi$$
$$152$$ 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 −0.848199 0.529678i $$-0.822313\pi$$
0.529678 + 0.848199i $$0.322313\pi$$
$$164$$ 0 0
$$165$$ 2.76648 + 10.9015i 0.0167666 + 0.0660697i
$$166$$ 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
$$171$$ −45.5434 + 153.543i −0.266336 + 0.897915i
$$172$$ 0 0
$$173$$ −112.600 112.600i −0.650868 0.650868i 0.302334 0.953202i $$-0.402234\pi$$
−0.953202 + 0.302334i $$0.902234\pi$$
$$174$$ 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
$$189$$ 66.7778 + 72.3203i 0.353322 + 0.382647i
$$190$$ 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
$$195$$ −34.0373 134.126i −0.174550 0.687827i
$$196$$ 0 0
$$197$$ 136.258 136.258i 0.691667 0.691667i −0.270932 0.962599i $$-0.587332\pi$$
0.962599 + 0.270932i $$0.0873318\pi$$
$$198$$ 0 0
$$199$$ 144.767i 0.727474i 0.931502 + 0.363737i $$0.118499\pi$$
−0.931502 + 0.363737i $$0.881501\pi$$
$$200$$ 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 −0.0671538 0.997743i $$-0.521392\pi$$
0.997743 + 0.0671538i $$0.0213918\pi$$
$$212$$ 0 0
$$213$$ −355.005 + 90.0899i −1.66669 + 0.422957i
$$214$$ 0 0
$$215$$ −127.814 −0.594482
$$216$$ 0 0
$$217$$ 42.4575i 0.195657i
$$218$$ 0 0
$$219$$ 11.0987 + 43.7353i 0.0506791 + 0.199704i
$$220$$ 0 0
$$221$$ 411.145 + 411.145i 1.86038 + 1.86038i
$$222$$ 0 0
$$223$$ −375.261 −1.68279 −0.841393 0.540423i $$-0.818264\pi$$
−0.841393 + 0.540423i $$0.818264\pi$$
$$224$$ 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 $$-0.535442\pi$$
−0.111114 + 0.993808i $$0.535442\pi$$
$$234$$ 0 0
$$235$$ −79.1581 79.1581i −0.336843 0.336843i
$$236$$ 0 0
$$237$$ 149.447 37.9253i 0.630579 0.160022i
$$238$$ 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
$$243$$ −78.3226 + 230.032i −0.322315 + 0.946632i
$$244$$ 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 $$0.113354\pi$$
−0.937259 + 0.348633i $$0.886646\pi$$
$$258$$ 0 0
$$259$$ −2.81176 + 2.81176i −0.0108562 + 0.0108562i
$$260$$ 0 0
$$261$$ 236.186 + 70.0567i 0.904929 + 0.268416i
$$262$$ 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
$$267$$ −15.8637 + 4.02573i −0.0594145 + 0.0150777i
$$268$$ 0 0
$$269$$ −33.7631 33.7631i −0.125513 0.125513i 0.641560 0.767073i $$-0.278288\pi$$
−0.767073 + 0.641560i $$0.778288\pi$$
$$270$$ 0 0
$$271$$ 329.269 1.21502 0.607508 0.794314i $$-0.292169\pi$$
0.607508 + 0.794314i $$0.292169\pi$$
$$272$$ 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 $$-0.401106\pi$$
0.305711 + 0.952124i $$0.401106\pi$$
$$282$$ 0 0
$$283$$ 193.476 + 193.476i 0.683660 + 0.683660i 0.960823 0.277163i $$-0.0893942\pi$$
−0.277163 + 0.960823i $$0.589394\pi$$
$$284$$ 0 0
$$285$$ 29.2434 + 115.236i 0.102608 + 0.404335i
$$286$$ 0 0
$$287$$ 93.6662i 0.326363i
$$288$$ 0 0
$$289$$ −499.073 −1.72690
$$290$$ 0 0
$$291$$ 236.017 59.8942i 0.811055 0.205822i
$$292$$ 0 0
$$293$$ −73.4937 + 73.4937i −0.250832 + 0.250832i −0.821312 0.570480i $$-0.806757\pi$$
0.570480 + 0.821312i $$0.306757\pi$$
$$294$$ 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 −0.997171 0.0751680i $$-0.976051\pi$$
0.0751680 + 0.997171i $$0.476051\pi$$
$$308$$ 0 0
$$309$$ 37.7729 + 148.847i 0.122242 + 0.481704i
$$310$$ 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
$$315$$ 70.0547 + 20.7793i 0.222396 + 0.0659661i
$$316$$ 0 0
$$317$$ −319.550 319.550i −1.00804 1.00804i −0.999967 0.00807607i $$-0.997429\pi$$
−0.00807607 0.999967i $$-0.502571\pi$$
$$318$$ 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 0.985230 0.171238i $$-0.0547766\pi$$
−0.171238 + 0.985230i $$0.554777\pi$$
$$332$$ 0 0
$$333$$ −9.41106 2.79147i −0.0282614 0.00838279i
$$334$$ 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
$$339$$ 54.2406 + 213.739i 0.160002 + 0.630497i
$$340$$ 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 $$-0.864525\pi$$
0.910789 0.412873i $$-0.135475\pi$$
$$354$$ 0 0
$$355$$ −192.251 + 192.251i −0.541552 + 0.541552i
$$356$$ 0 0
$$357$$ −297.604 + 75.5233i −0.833626 + 0.211550i
$$358$$ 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
$$363$$ −87.1973 343.607i −0.240213 0.946575i
$$364$$ 0 0
$$365$$ 23.6846 + 23.6846i 0.0648893 + 0.0648893i
$$366$$ 0 0
$$367$$ 340.678 0.928279 0.464140 0.885762i $$-0.346364\pi$$
0.464140 + 0.885762i $$0.346364\pi$$
$$368$$ 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 0.144327 0.989530i $$-0.453898\pi$$
−0.989530 + 0.144327i $$0.953898\pi$$
$$380$$ 0 0
$$381$$ −214.985 + 54.5570i −0.564266 + 0.143194i
$$382$$ 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
$$387$$ 495.212 + 146.888i 1.27962 + 0.379555i
$$388$$ 0 0
$$389$$ 424.351 424.351i 1.09088 1.09088i 0.0954418 0.995435i $$-0.469574\pi$$
0.995435 0.0954418i $$-0.0304264\pi$$
$$390$$ 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 $$-0.756228\pi$$
0.720806 0.693137i $$-0.243772\pi$$
$$402$$ 0 0
$$403$$ 170.561 170.561i 0.423228 0.423228i
$$404$$ 0 0
$$405$$ 37.3738 + 176.472i 0.0922811 + 0.435733i
$$406$$ 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
$$411$$ 292.917 74.3337i 0.712693 0.180861i
$$412$$ 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
$$429$$ −25.7298 101.390i −0.0599762 0.236340i
$$430$$ 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
$$435$$ 177.260 44.9833i 0.407494 0.103410i
$$436$$ 0 0
$$437$$ 368.217 368.217i 0.842601 0.842601i
$$438$$ 0 0
$$439$$ 434.893i 0.990644i 0.868709 + 0.495322i $$0.164950\pi$$
−0.868709 + 0.495322i $$0.835050\pi$$
$$440$$ 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 $$-0.964854\pi$$
0.993911 0.110190i $$-0.0351459\pi$$
$$450$$ 0 0
$$451$$ 30.5830 30.5830i 0.0678115 0.0678115i
$$452$$ 0 0
$$453$$ 20.7380 + 81.7195i 0.0457793 + 0.180396i
$$454$$ 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
$$459$$ −514.196 556.873i −1.12025 1.21323i
$$460$$ 0 0
$$461$$ −328.278 328.278i −0.712099 0.712099i 0.254875 0.966974i $$-0.417966\pi$$
−0.966974 + 0.254875i $$0.917966\pi$$
$$462$$ 0 0
$$463$$ −848.427 −1.83246 −0.916228 0.400657i $$-0.868782\pi$$
−0.916228 + 0.400657i $$0.868782\pi$$
$$464$$ 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
$$477$$ −167.355 + 564.216i −0.350850 + 1.18284i
$$478$$ 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
$$483$$ −78.7257 310.224i −0.162993 0.642285i
$$484$$ 0 0
$$485$$ 127.814 127.814i 0.263533 0.263533i
$$486$$ 0 0
$$487$$ 176.783i 0.363004i −0.983391 0.181502i $$-0.941904\pi$$
0.983391 0.181502i $$-0.0580959\pi$$
$$488$$ 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 −0.224250 0.974532i $$-0.571993\pi$$
0.974532 + 0.224250i $$0.0719931\pi$$
$$500$$ 0 0
$$501$$ −167.297 + 42.4551i −0.333926 + 0.0847407i
$$502$$ 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
$$507$$ 191.857 + 756.024i 0.378416 + 1.49117i
$$508$$ 0 0
$$509$$ −41.6258 41.6258i −0.0817796 0.0817796i 0.665034 0.746813i $$-0.268417\pi$$
−0.746813 + 0.665034i $$0.768417\pi$$
$$510$$ 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 $$-0.427996\pi$$
0.224284 + 0.974524i $$0.427996\pi$$
$$522$$ 0 0
$$523$$ 219.506 + 219.506i 0.419705 + 0.419705i 0.885102 0.465397i $$-0.154088\pi$$
−0.465397 + 0.885102i $$0.654088\pi$$
$$524$$ 0 0
$$525$$ −212.454 + 53.9146i −0.404674 + 0.102694i
$$526$$ 0 0
$$527$$ 326.927i 0.620355i
$$528$$ 0 0
$$529$$ 327.324 0.618760
$$530$$ 0 0
$$531$$ −82.3542 + 277.646i −0.155093 + 0.522873i
$$532$$ 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 −0.708475 0.705736i $$-0.750616\pi$$
0.705736 + 0.708475i $$0.250616\pi$$
$$548$$ 0 0
$$549$$ −46.2247 + 155.840i −0.0841981 + 0.283862i
$$550$$ 0 0
$$551$$ −487.105 −0.884038
$$552$$ 0 0
$$553$$ 187.373i 0.338829i
$$554$$ 0 0
$$555$$ −7.06307 + 1.79240i −0.0127263 + 0.00322955i
$$556$$ 0 0
$$557$$ 322.326 + 322.326i 0.578682 + 0.578682i 0.934540 0.355858i $$-0.115811\pi$$
−0.355858 + 0.934540i $$0.615811\pi$$
$$558$$ 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 $$-0.735754\pi$$
−0.674762 + 0.738035i $$0.735754\pi$$
$$570$$ 0 0
$$571$$ 3.43922 + 3.43922i 0.00602316 + 0.00602316i 0.710112 0.704089i $$-0.248644\pi$$
−0.704089 + 0.710112i $$0.748644\pi$$
$$572$$ 0 0
$$573$$ −141.439 557.350i −0.246840 0.972688i
$$574$$ 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
$$579$$ −141.400 + 35.8833i −0.244215 + 0.0619746i
$$580$$ 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 $$0.249804\pi$$
−0.707542 + 0.706671i $$0.750196\pi$$
$$594$$ 0 0
$$595$$ −161.166 + 161.166i −0.270867 + 0.270867i
$$596$$ 0 0
$$597$$ −106.827 420.959i −0.178940 0.705123i
$$598$$ 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
$$603$$ −38.6783 + 130.399i −0.0641431 + 0.216250i
$$604$$ 0 0
$$605$$ −186.078 186.078i −0.307567 0.307567i
$$606$$ 0 0
$$607$$ −103.217 −0.170044 −0.0850222 0.996379i $$-0.527096\pi$$
−0.0850222 + 0.996379i $$0.527096\pi$$
$$608$$ 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 $$-0.303795\pi$$
0.578098 + 0.815967i $$0.303795\pi$$
$$618$$ 0 0
$$619$$ 399.763 + 399.763i 0.645821 + 0.645821i 0.951980 0.306159i $$-0.0990440\pi$$
−0.306159 + 0.951980i $$0.599044\pi$$
$$620$$ 0 0
$$621$$ 580.487 535.999i 0.934761 0.863123i
$$622$$ 0 0
$$623$$ 19.8894i 0.0319252i
$$624$$ 0 0
$$625$$ −277.635 −0.444217
$$626$$ 0 0
$$627$$ 22.1059 + 87.1099i 0.0352567 + 0.138931i
$$628$$ 0 0
$$629$$ 21.6508 21.6508i 0.0344210 0.0344210i
$$630$$ 0 0
$$631$$ 934.242i 1.48057i 0.672291 + 0.740287i $$0.265310\pi$$
−0.672291 + 0.740287i $$0.734690\pi$$
$$632$$ 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 $$0.00650162\pi$$
−0.999791 + 0.0204240i $$0.993498\pi$$
$$642$$ 0 0
$$643$$ −625.336 + 625.336i −0.972529 + 0.972529i −0.999633 0.0271039i $$-0.991371\pi$$
0.0271039 + 0.999633i $$0.491371\pi$$
$$644$$ 0 0
$$645$$ 371.660 94.3165i 0.576218 0.146227i
$$646$$ 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
$$651$$ 31.3303 + 123.459i 0.0481265 + 0.189645i
$$652$$ 0 0
$$653$$ 129.213 + 129.213i 0.197875 + 0.197875i 0.799089 0.601213i $$-0.205316\pi$$
−0.601213 + 0.799089i $$0.705316\pi$$
$$654$$ 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
$$669$$ 1091.20 276.914i 1.63109 0.413922i
$$670$$ 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
$$675$$ −367.074 397.541i −0.543814 0.588950i
$$676$$ 0 0
$$677$$ −813.520 + 813.520i −1.20165 + 1.20165i −0.227991 + 0.973663i $$0.573216\pi$$
−0.973663 + 0.227991i $$0.926784\pi$$
$$678$$ 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 −0.334378 0.942439i $$-0.608526\pi$$
0.942439 + 0.334378i $$0.108526\pi$$
$$692$$ 0 0
$$693$$ 52.9563 + 15.7077i 0.0764161 + 0.0226662i
$$694$$ 0 0
$$695$$ 57.5504 0.0828063
$$696$$ 0 0
$$697$$ 721.239i 1.03478i
$$698$$ 0 0
$$699$$ 150.565 38.2089i 0.215400 0.0546622i
$$700$$ 0 0
$$701$$ 774.018 + 774.018i 1.10416 + 1.10416i 0.993903 + 0.110260i $$0.0351684\pi$$
0.110260 + 0.993903i $$0.464832\pi$$
$$702$$ 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
$$717$$ 184.406 + 726.665i 0.257192 + 1.01348i
$$718$$ 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
$$723$$ −1286.80 + 326.553i −1.77981 + 0.451664i
$$724$$ 0 0
$$725$$ −387.898 + 387.898i −0.535031 + 0.535031i
$$726$$ 0 0
$$727$$ 789.136i 1.08547i −0.839904 0.542734i $$-0.817389\pi$$
0.839904 0.542734i $$-0.182611\pi$$
$$728$$ 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 −0.805647 0.592395i $$-0.798182\pi$$
0.592395 + 0.805647i $$0.298182\pi$$
$$740$$ 0 0
$$741$$ −271.980 1071.75i −0.367044 1.44636i
$$742$$ 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
$$747$$ 462.082 + 137.061i 0.618583 + 0.183482i
$$748$$ 0 0
$$749$$ −311.601 311.601i −0.416023 0.416023i
$$750$$ 0 0
$$751$$ 793.800 1.05699 0.528495 0.848936i $$-0.322756\pi$$
0.528495 + 0.848936i $$0.322756\pi$$
$$752$$ 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 $$-0.256084\pi$$
0.693462 + 0.720493i $$0.256084\pi$$
$$762$$ 0 0
$$763$$ −192.686 192.686i −0.252538 0.252538i
$$764$$ 0 0
$$765$$ −539.428 160.003i −0.705134 0.209154i
$$766$$ 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
$$771$$ −132.234 521.076i −0.171509 0.675844i
$$772$$ 0 0
$$773$$ −894.518 + 894.518i −1.15720 + 1.15720i −0.172129 + 0.985074i $$0.555065\pi$$
−0.985074 + 0.172129i $$0.944935\pi$$
$$774$$ 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 −0.00992500 0.999951i $$-0.503159\pi$$
0.999951 + 0.00992500i $$0.00315928\pi$$
$$788$$ 0 0
$$789$$ 1219.77 309.542i 1.54597 0.392322i
$$790$$ 0 0
$$791$$ −267.979 −0.338785
$$792$$ 0 0
$$793$$ 374.089i 0.471739i
$$794$$ 0 0