# Properties

 Label 882.4.g.ba.361.2 Level $882$ Weight $4$ Character 882.361 Analytic conductor $52.040$ Analytic rank $0$ Dimension $4$ CM no Inner twists $4$

# Learn more

## Newspace parameters

 Level: $$N$$ $$=$$ $$882 = 2 \cdot 3^{2} \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 882.g (of order $$3$$, degree $$2$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$52.0396846251$$ Analytic rank: $$0$$ Dimension: $$4$$ Relative dimension: $$2$$ over $$\Q(\zeta_{3})$$ Coefficient field: $$\Q(\sqrt{2}, \sqrt{-3})$$ Defining polynomial: $$x^{4} + 2x^{2} + 4$$ x^4 + 2*x^2 + 4 Coefficient ring: $$\Z[a_1, \ldots, a_{25}]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 98) Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 361.2 Root $$0.707107 + 1.22474i$$ of defining polynomial Character $$\chi$$ $$=$$ 882.361 Dual form 882.4.g.ba.667.2

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-1.00000 - 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} +(9.89949 + 17.1464i) q^{5} +8.00000 q^{8} +O(q^{10})$$ $$q+(-1.00000 - 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} +(9.89949 + 17.1464i) q^{5} +8.00000 q^{8} +(19.7990 - 34.2929i) q^{10} +(-7.00000 + 12.1244i) q^{11} -50.9117 q^{13} +(-8.00000 - 13.8564i) q^{16} +(-0.707107 + 1.22474i) q^{17} +(-0.707107 - 1.22474i) q^{19} -79.1960 q^{20} +28.0000 q^{22} +(70.0000 + 121.244i) q^{23} +(-133.500 + 231.229i) q^{25} +(50.9117 + 88.1816i) q^{26} +286.000 q^{29} +(-46.6690 + 80.8332i) q^{31} +(-16.0000 + 27.7128i) q^{32} +2.82843 q^{34} +(19.0000 + 32.9090i) q^{37} +(-1.41421 + 2.44949i) q^{38} +(79.1960 + 137.171i) q^{40} -125.865 q^{41} -34.0000 q^{43} +(-28.0000 - 48.4974i) q^{44} +(140.000 - 242.487i) q^{46} +(-261.630 - 453.156i) q^{47} +534.000 q^{50} +(101.823 - 176.363i) q^{52} +(-37.0000 + 64.0859i) q^{53} -277.186 q^{55} +(-286.000 - 495.367i) q^{58} +(-217.082 + 375.997i) q^{59} +(7.07107 + 12.2474i) q^{61} +186.676 q^{62} +64.0000 q^{64} +(-504.000 - 872.954i) q^{65} +(-342.000 + 592.361i) q^{67} +(-2.82843 - 4.89898i) q^{68} -588.000 q^{71} +(-135.057 + 233.926i) q^{73} +(38.0000 - 65.8179i) q^{74} +5.65685 q^{76} +(-610.000 - 1056.55i) q^{79} +(158.392 - 274.343i) q^{80} +(125.865 + 218.005i) q^{82} +422.850 q^{83} -28.0000 q^{85} +(34.0000 + 58.8897i) q^{86} +(-56.0000 + 96.9948i) q^{88} +(-309.006 - 535.214i) q^{89} -560.000 q^{92} +(-523.259 + 906.311i) q^{94} +(14.0000 - 24.2487i) q^{95} -1483.51 q^{97} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4 q - 4 q^{2} - 8 q^{4} + 32 q^{8}+O(q^{10})$$ 4 * q - 4 * q^2 - 8 * q^4 + 32 * q^8 $$4 q - 4 q^{2} - 8 q^{4} + 32 q^{8} - 28 q^{11} - 32 q^{16} + 112 q^{22} + 280 q^{23} - 534 q^{25} + 1144 q^{29} - 64 q^{32} + 76 q^{37} - 136 q^{43} - 112 q^{44} + 560 q^{46} + 2136 q^{50} - 148 q^{53} - 1144 q^{58} + 256 q^{64} - 2016 q^{65} - 1368 q^{67} - 2352 q^{71} + 152 q^{74} - 2440 q^{79} - 112 q^{85} + 136 q^{86} - 224 q^{88} - 2240 q^{92} + 56 q^{95}+O(q^{100})$$ 4 * q - 4 * q^2 - 8 * q^4 + 32 * q^8 - 28 * q^11 - 32 * q^16 + 112 * q^22 + 280 * q^23 - 534 * q^25 + 1144 * q^29 - 64 * q^32 + 76 * q^37 - 136 * q^43 - 112 * q^44 + 560 * q^46 + 2136 * q^50 - 148 * q^53 - 1144 * q^58 + 256 * q^64 - 2016 * q^65 - 1368 * q^67 - 2352 * q^71 + 152 * q^74 - 2440 * q^79 - 112 * q^85 + 136 * q^86 - 224 * q^88 - 2240 * q^92 + 56 * q^95

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/882\mathbb{Z}\right)^\times$$.

 $$n$$ $$199$$ $$785$$ $$\chi(n)$$ $$e\left(\frac{2}{3}\right)$$ $$1$$

## Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −1.00000 1.73205i −0.353553 0.612372i
$$3$$ 0 0
$$4$$ −2.00000 + 3.46410i −0.250000 + 0.433013i
$$5$$ 9.89949 + 17.1464i 0.885438 + 1.53362i 0.845211 + 0.534433i $$0.179475\pi$$
0.0402266 + 0.999191i $$0.487192\pi$$
$$6$$ 0 0
$$7$$ 0 0
$$8$$ 8.00000 0.353553
$$9$$ 0 0
$$10$$ 19.7990 34.2929i 0.626099 1.08444i
$$11$$ −7.00000 + 12.1244i −0.191871 + 0.332330i −0.945870 0.324545i $$-0.894789\pi$$
0.753999 + 0.656875i $$0.228122\pi$$
$$12$$ 0 0
$$13$$ −50.9117 −1.08618 −0.543091 0.839674i $$-0.682746\pi$$
−0.543091 + 0.839674i $$0.682746\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ −8.00000 13.8564i −0.125000 0.216506i
$$17$$ −0.707107 + 1.22474i −0.0100882 + 0.0174732i −0.871025 0.491238i $$-0.836545\pi$$
0.860937 + 0.508711i $$0.169878\pi$$
$$18$$ 0 0
$$19$$ −0.707107 1.22474i −0.00853797 0.0147882i 0.861725 0.507376i $$-0.169384\pi$$
−0.870263 + 0.492588i $$0.836051\pi$$
$$20$$ −79.1960 −0.885438
$$21$$ 0 0
$$22$$ 28.0000 0.271346
$$23$$ 70.0000 + 121.244i 0.634609 + 1.09918i 0.986598 + 0.163171i $$0.0521722\pi$$
−0.351989 + 0.936004i $$0.614494\pi$$
$$24$$ 0 0
$$25$$ −133.500 + 231.229i −1.06800 + 1.84983i
$$26$$ 50.9117 + 88.1816i 0.384023 + 0.665148i
$$27$$ 0 0
$$28$$ 0 0
$$29$$ 286.000 1.83134 0.915670 0.401931i $$-0.131661\pi$$
0.915670 + 0.401931i $$0.131661\pi$$
$$30$$ 0 0
$$31$$ −46.6690 + 80.8332i −0.270387 + 0.468325i −0.968961 0.247213i $$-0.920485\pi$$
0.698574 + 0.715538i $$0.253818\pi$$
$$32$$ −16.0000 + 27.7128i −0.0883883 + 0.153093i
$$33$$ 0 0
$$34$$ 2.82843 0.0142668
$$35$$ 0 0
$$36$$ 0 0
$$37$$ 19.0000 + 32.9090i 0.0844211 + 0.146222i 0.905144 0.425104i $$-0.139763\pi$$
−0.820723 + 0.571326i $$0.806429\pi$$
$$38$$ −1.41421 + 2.44949i −0.00603726 + 0.0104568i
$$39$$ 0 0
$$40$$ 79.1960 + 137.171i 0.313050 + 0.542218i
$$41$$ −125.865 −0.479434 −0.239717 0.970843i $$-0.577055\pi$$
−0.239717 + 0.970843i $$0.577055\pi$$
$$42$$ 0 0
$$43$$ −34.0000 −0.120580 −0.0602901 0.998181i $$-0.519203\pi$$
−0.0602901 + 0.998181i $$0.519203\pi$$
$$44$$ −28.0000 48.4974i −0.0959354 0.166165i
$$45$$ 0 0
$$46$$ 140.000 242.487i 0.448736 0.777234i
$$47$$ −261.630 453.156i −0.811970 1.40637i −0.911483 0.411337i $$-0.865062\pi$$
0.0995134 0.995036i $$-0.468271\pi$$
$$48$$ 0 0
$$49$$ 0 0
$$50$$ 534.000 1.51038
$$51$$ 0 0
$$52$$ 101.823 176.363i 0.271545 0.470330i
$$53$$ −37.0000 + 64.0859i −0.0958932 + 0.166092i −0.909981 0.414650i $$-0.863904\pi$$
0.814088 + 0.580742i $$0.197237\pi$$
$$54$$ 0 0
$$55$$ −277.186 −0.679559
$$56$$ 0 0
$$57$$ 0 0
$$58$$ −286.000 495.367i −0.647477 1.12146i
$$59$$ −217.082 + 375.997i −0.479011 + 0.829671i −0.999710 0.0240689i $$-0.992338\pi$$
0.520699 + 0.853740i $$0.325671\pi$$
$$60$$ 0 0
$$61$$ 7.07107 + 12.2474i 0.0148419 + 0.0257070i 0.873351 0.487091i $$-0.161942\pi$$
−0.858509 + 0.512798i $$0.828609\pi$$
$$62$$ 186.676 0.382385
$$63$$ 0 0
$$64$$ 64.0000 0.125000
$$65$$ −504.000 872.954i −0.961746 1.66579i
$$66$$ 0 0
$$67$$ −342.000 + 592.361i −0.623611 + 1.08013i 0.365196 + 0.930930i $$0.381002\pi$$
−0.988808 + 0.149196i $$0.952332\pi$$
$$68$$ −2.82843 4.89898i −0.00504408 0.00873660i
$$69$$ 0 0
$$70$$ 0 0
$$71$$ −588.000 −0.982856 −0.491428 0.870918i $$-0.663525\pi$$
−0.491428 + 0.870918i $$0.663525\pi$$
$$72$$ 0 0
$$73$$ −135.057 + 233.926i −0.216538 + 0.375055i −0.953747 0.300610i $$-0.902810\pi$$
0.737209 + 0.675664i $$0.236143\pi$$
$$74$$ 38.0000 65.8179i 0.0596947 0.103394i
$$75$$ 0 0
$$76$$ 5.65685 0.00853797
$$77$$ 0 0
$$78$$ 0 0
$$79$$ −610.000 1056.55i −0.868739 1.50470i −0.863286 0.504715i $$-0.831598\pi$$
−0.00545246 0.999985i $$-0.501736\pi$$
$$80$$ 158.392 274.343i 0.221359 0.383406i
$$81$$ 0 0
$$82$$ 125.865 + 218.005i 0.169506 + 0.293592i
$$83$$ 422.850 0.559202 0.279601 0.960116i $$-0.409798\pi$$
0.279601 + 0.960116i $$0.409798\pi$$
$$84$$ 0 0
$$85$$ −28.0000 −0.0357297
$$86$$ 34.0000 + 58.8897i 0.0426316 + 0.0738400i
$$87$$ 0 0
$$88$$ −56.0000 + 96.9948i −0.0678366 + 0.117496i
$$89$$ −309.006 535.214i −0.368028 0.637444i 0.621229 0.783629i $$-0.286634\pi$$
−0.989257 + 0.146185i $$0.953300\pi$$
$$90$$ 0 0
$$91$$ 0 0
$$92$$ −560.000 −0.634609
$$93$$ 0 0
$$94$$ −523.259 + 906.311i −0.574149 + 0.994456i
$$95$$ 14.0000 24.2487i 0.0151197 0.0261881i
$$96$$ 0 0
$$97$$ −1483.51 −1.55286 −0.776431 0.630202i $$-0.782972\pi$$
−0.776431 + 0.630202i $$0.782972\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ −534.000 924.915i −0.534000 0.924915i
$$101$$ −564.271 + 977.346i −0.555912 + 0.962867i 0.441920 + 0.897054i $$0.354297\pi$$
−0.997832 + 0.0658130i $$0.979036\pi$$
$$102$$ 0 0
$$103$$ −434.164 751.993i −0.415334 0.719380i 0.580129 0.814524i $$-0.303002\pi$$
−0.995463 + 0.0951446i $$0.969669\pi$$
$$104$$ −407.294 −0.384023
$$105$$ 0 0
$$106$$ 148.000 0.135613
$$107$$ −842.000 1458.39i −0.760740 1.31764i −0.942469 0.334292i $$-0.891503\pi$$
0.181729 0.983349i $$-0.441831\pi$$
$$108$$ 0 0
$$109$$ 409.000 708.409i 0.359405 0.622507i −0.628457 0.777844i $$-0.716313\pi$$
0.987861 + 0.155337i $$0.0496465\pi$$
$$110$$ 277.186 + 480.100i 0.240260 + 0.416143i
$$111$$ 0 0
$$112$$ 0 0
$$113$$ 540.000 0.449548 0.224774 0.974411i $$-0.427836\pi$$
0.224774 + 0.974411i $$0.427836\pi$$
$$114$$ 0 0
$$115$$ −1385.93 + 2400.50i −1.12381 + 1.94650i
$$116$$ −572.000 + 990.733i −0.457835 + 0.792994i
$$117$$ 0 0
$$118$$ 868.327 0.677424
$$119$$ 0 0
$$120$$ 0 0
$$121$$ 567.500 + 982.939i 0.426371 + 0.738496i
$$122$$ 14.1421 24.4949i 0.0104948 0.0181776i
$$123$$ 0 0
$$124$$ −186.676 323.333i −0.135194 0.234162i
$$125$$ −2811.46 −2.01171
$$126$$ 0 0
$$127$$ 1720.00 1.20177 0.600887 0.799334i $$-0.294814\pi$$
0.600887 + 0.799334i $$0.294814\pi$$
$$128$$ −64.0000 110.851i −0.0441942 0.0765466i
$$129$$ 0 0
$$130$$ −1008.00 + 1745.91i −0.680057 + 1.17789i
$$131$$ 867.620 + 1502.76i 0.578659 + 1.00227i 0.995634 + 0.0933484i $$0.0297571\pi$$
−0.416975 + 0.908918i $$0.636910\pi$$
$$132$$ 0 0
$$133$$ 0 0
$$134$$ 1368.00 0.881919
$$135$$ 0 0
$$136$$ −5.65685 + 9.79796i −0.00356670 + 0.00617771i
$$137$$ 414.000 717.069i 0.258178 0.447178i −0.707576 0.706638i $$-0.750211\pi$$
0.965754 + 0.259460i $$0.0835445\pi$$
$$138$$ 0 0
$$139$$ 425.678 0.259752 0.129876 0.991530i $$-0.458542\pi$$
0.129876 + 0.991530i $$0.458542\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 588.000 + 1018.45i 0.347492 + 0.601874i
$$143$$ 356.382 617.271i 0.208407 0.360971i
$$144$$ 0 0
$$145$$ 2831.26 + 4903.88i 1.62154 + 2.80859i
$$146$$ 540.230 0.306231
$$147$$ 0 0
$$148$$ −152.000 −0.0844211
$$149$$ 1025.00 + 1775.35i 0.563566 + 0.976124i 0.997182 + 0.0750264i $$0.0239041\pi$$
−0.433616 + 0.901098i $$0.642763\pi$$
$$150$$ 0 0
$$151$$ 236.000 408.764i 0.127188 0.220296i −0.795398 0.606087i $$-0.792738\pi$$
0.922586 + 0.385791i $$0.126071\pi$$
$$152$$ −5.65685 9.79796i −0.00301863 0.00522842i
$$153$$ 0 0
$$154$$ 0 0
$$155$$ −1848.00 −0.957645
$$156$$ 0 0
$$157$$ −1105.92 + 1915.50i −0.562176 + 0.973717i 0.435130 + 0.900367i $$0.356702\pi$$
−0.997306 + 0.0733498i $$0.976631\pi$$
$$158$$ −1220.00 + 2113.10i −0.614291 + 1.06398i
$$159$$ 0 0
$$160$$ −633.568 −0.313050
$$161$$ 0 0
$$162$$ 0 0
$$163$$ −1643.00 2845.76i −0.789507 1.36747i −0.926269 0.376863i $$-0.877003\pi$$
0.136762 0.990604i $$-0.456331\pi$$
$$164$$ 251.730 436.009i 0.119859 0.207601i
$$165$$ 0 0
$$166$$ −422.850 732.397i −0.197708 0.342440i
$$167$$ −1490.58 −0.690686 −0.345343 0.938476i $$-0.612237\pi$$
−0.345343 + 0.938476i $$0.612237\pi$$
$$168$$ 0 0
$$169$$ 395.000 0.179791
$$170$$ 28.0000 + 48.4974i 0.0126324 + 0.0218799i
$$171$$ 0 0
$$172$$ 68.0000 117.779i 0.0301451 0.0522128i
$$173$$ 1035.20 + 1793.03i 0.454943 + 0.787984i 0.998685 0.0512682i $$-0.0163263\pi$$
−0.543742 + 0.839252i $$0.682993\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 224.000 0.0959354
$$177$$ 0 0
$$178$$ −618.011 + 1070.43i −0.260235 + 0.450741i
$$179$$ 270.000 467.654i 0.112742 0.195274i −0.804133 0.594449i $$-0.797370\pi$$
0.916875 + 0.399175i $$0.130703\pi$$
$$180$$ 0 0
$$181$$ −3784.44 −1.55412 −0.777058 0.629429i $$-0.783289\pi$$
−0.777058 + 0.629429i $$0.783289\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 560.000 + 969.948i 0.224368 + 0.388617i
$$185$$ −376.181 + 651.564i −0.149499 + 0.258940i
$$186$$ 0 0
$$187$$ −9.89949 17.1464i −0.00387124 0.00670519i
$$188$$ 2093.04 0.811970
$$189$$ 0 0
$$190$$ −56.0000 −0.0213825
$$191$$ 514.000 + 890.274i 0.194721 + 0.337267i 0.946809 0.321796i $$-0.104286\pi$$
−0.752088 + 0.659063i $$0.770953\pi$$
$$192$$ 0 0
$$193$$ −2296.00 + 3976.79i −0.856320 + 1.48319i 0.0190956 + 0.999818i $$0.493921\pi$$
−0.875415 + 0.483372i $$0.839412\pi$$
$$194$$ 1483.51 + 2569.51i 0.549020 + 0.950930i
$$195$$ 0 0
$$196$$ 0 0
$$197$$ −794.000 −0.287158 −0.143579 0.989639i $$-0.545861\pi$$
−0.143579 + 0.989639i $$0.545861\pi$$
$$198$$ 0 0
$$199$$ 1243.09 2153.10i 0.442817 0.766981i −0.555080 0.831797i $$-0.687312\pi$$
0.997897 + 0.0648153i $$0.0206458\pi$$
$$200$$ −1068.00 + 1849.83i −0.377595 + 0.654014i
$$201$$ 0 0
$$202$$ 2257.08 0.786178
$$203$$ 0 0
$$204$$ 0 0
$$205$$ −1246.00 2158.14i −0.424509 0.735272i
$$206$$ −868.327 + 1503.99i −0.293686 + 0.508678i
$$207$$ 0 0
$$208$$ 407.294 + 705.453i 0.135773 + 0.235165i
$$209$$ 19.7990 0.00655275
$$210$$ 0 0
$$211$$ −2748.00 −0.896588 −0.448294 0.893886i $$-0.647968\pi$$
−0.448294 + 0.893886i $$0.647968\pi$$
$$212$$ −148.000 256.344i −0.0479466 0.0830460i
$$213$$ 0 0
$$214$$ −1684.00 + 2916.77i −0.537925 + 0.931713i
$$215$$ −336.583 582.979i −0.106766 0.184925i
$$216$$ 0 0
$$217$$ 0 0
$$218$$ −1636.00 −0.508275
$$219$$ 0 0
$$220$$ 554.372 960.200i 0.169890 0.294258i
$$221$$ 36.0000 62.3538i 0.0109576 0.0189791i
$$222$$ 0 0
$$223$$ 3428.05 1.02941 0.514707 0.857366i $$-0.327901\pi$$
0.514707 + 0.857366i $$0.327901\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ −540.000 935.307i −0.158939 0.275291i
$$227$$ −2645.29 + 4581.77i −0.773453 + 1.33966i 0.162207 + 0.986757i $$0.448139\pi$$
−0.935660 + 0.352903i $$0.885195\pi$$
$$228$$ 0 0
$$229$$ −1374.62 2380.90i −0.396669 0.687051i 0.596644 0.802506i $$-0.296501\pi$$
−0.993313 + 0.115456i $$0.963167\pi$$
$$230$$ 5543.72 1.58931
$$231$$ 0 0
$$232$$ 2288.00 0.647477
$$233$$ 36.0000 + 62.3538i 0.0101221 + 0.0175319i 0.871042 0.491208i $$-0.163445\pi$$
−0.860920 + 0.508740i $$0.830111\pi$$
$$234$$ 0 0
$$235$$ 5180.00 8972.02i 1.43790 2.49051i
$$236$$ −868.327 1503.99i −0.239505 0.414836i
$$237$$ 0 0
$$238$$ 0 0
$$239$$ −4308.00 −1.16595 −0.582974 0.812491i $$-0.698111\pi$$
−0.582974 + 0.812491i $$0.698111\pi$$
$$240$$ 0 0
$$241$$ −770.039 + 1333.75i −0.205820 + 0.356490i −0.950394 0.311050i $$-0.899319\pi$$
0.744574 + 0.667540i $$0.232653\pi$$
$$242$$ 1135.00 1965.88i 0.301490 0.522196i
$$243$$ 0 0
$$244$$ −56.5685 −0.0148419
$$245$$ 0 0
$$246$$ 0 0
$$247$$ 36.0000 + 62.3538i 0.00927379 + 0.0160627i
$$248$$ −373.352 + 646.665i −0.0955964 + 0.165578i
$$249$$ 0 0
$$250$$ 2811.46 + 4869.59i 0.711249 + 1.23192i
$$251$$ 931.967 0.234363 0.117182 0.993110i $$-0.462614\pi$$
0.117182 + 0.993110i $$0.462614\pi$$
$$252$$ 0 0
$$253$$ −1960.00 −0.487052
$$254$$ −1720.00 2979.13i −0.424891 0.735933i
$$255$$ 0 0
$$256$$ −128.000 + 221.703i −0.0312500 + 0.0541266i
$$257$$ −468.812 812.006i −0.113789 0.197088i 0.803506 0.595296i $$-0.202965\pi$$
−0.917295 + 0.398209i $$0.869632\pi$$
$$258$$ 0 0
$$259$$ 0 0
$$260$$ 4032.00 0.961746
$$261$$ 0 0
$$262$$ 1735.24 3005.52i 0.409174 0.708709i
$$263$$ 3570.00 6183.42i 0.837018 1.44976i −0.0553595 0.998466i $$-0.517630\pi$$
0.892377 0.451291i $$-0.149036\pi$$
$$264$$ 0 0
$$265$$ −1465.13 −0.339630
$$266$$ 0 0
$$267$$ 0 0
$$268$$ −1368.00 2369.45i −0.311806 0.540063i
$$269$$ −2305.17 + 3992.67i −0.522485 + 0.904971i 0.477172 + 0.878810i $$0.341662\pi$$
−0.999658 + 0.0261615i $$0.991672\pi$$
$$270$$ 0 0
$$271$$ −1182.28 2047.77i −0.265013 0.459016i 0.702554 0.711630i $$-0.252043\pi$$
−0.967567 + 0.252614i $$0.918710\pi$$
$$272$$ 22.6274 0.00504408
$$273$$ 0 0
$$274$$ −1656.00 −0.365119
$$275$$ −1869.00 3237.20i −0.409836 0.709857i
$$276$$ 0 0
$$277$$ −2003.00 + 3469.30i −0.434472 + 0.752527i −0.997252 0.0740794i $$-0.976398\pi$$
0.562781 + 0.826606i $$0.309731\pi$$
$$278$$ −425.678 737.296i −0.0918363 0.159065i
$$279$$ 0 0
$$280$$ 0 0
$$281$$ 5984.00 1.27038 0.635188 0.772358i $$-0.280923\pi$$
0.635188 + 0.772358i $$0.280923\pi$$
$$282$$ 0 0
$$283$$ −2464.27 + 4268.24i −0.517617 + 0.896538i 0.482174 + 0.876075i $$0.339847\pi$$
−0.999791 + 0.0204627i $$0.993486\pi$$
$$284$$ 1176.00 2036.89i 0.245714 0.425589i
$$285$$ 0 0
$$286$$ −1425.53 −0.294731
$$287$$ 0 0
$$288$$ 0 0
$$289$$ 2455.50 + 4253.05i 0.499796 + 0.865673i
$$290$$ 5662.51 9807.76i 1.14660 1.98597i
$$291$$ 0 0
$$292$$ −540.230 935.705i −0.108269 0.187527i
$$293$$ 1971.41 0.393076 0.196538 0.980496i $$-0.437030\pi$$
0.196538 + 0.980496i $$0.437030\pi$$
$$294$$ 0 0
$$295$$ −8596.00 −1.69654
$$296$$ 152.000 + 263.272i 0.0298474 + 0.0516972i
$$297$$ 0 0
$$298$$ 2050.00 3550.70i 0.398501 0.690224i
$$299$$ −3563.82 6172.71i −0.689301 1.19390i
$$300$$ 0 0
$$301$$ 0 0
$$302$$ −944.000 −0.179871
$$303$$ 0 0
$$304$$ −11.3137 + 19.5959i −0.00213449 + 0.00369705i
$$305$$ −140.000 + 242.487i −0.0262832 + 0.0455238i
$$306$$ 0 0
$$307$$ 4767.31 0.886270 0.443135 0.896455i $$-0.353866\pi$$
0.443135 + 0.896455i $$0.353866\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 1848.00 + 3200.83i 0.338579 + 0.586435i
$$311$$ 3388.46 5868.98i 0.617819 1.07009i −0.372064 0.928207i $$-0.621350\pi$$
0.989883 0.141887i $$-0.0453169\pi$$
$$312$$ 0 0
$$313$$ −3095.01 5360.71i −0.558914 0.968068i −0.997587 0.0694210i $$-0.977885\pi$$
0.438673 0.898647i $$-0.355449\pi$$
$$314$$ 4423.66 0.795037
$$315$$ 0 0
$$316$$ 4880.00 0.868739
$$317$$ 4913.00 + 8509.57i 0.870478 + 1.50771i 0.861503 + 0.507753i $$0.169524\pi$$
0.00897524 + 0.999960i $$0.497143\pi$$
$$318$$ 0 0
$$319$$ −2002.00 + 3467.57i −0.351381 + 0.608609i
$$320$$ 633.568 + 1097.37i 0.110680 + 0.191703i
$$321$$ 0 0
$$322$$ 0 0
$$323$$ 2.00000 0.000344529
$$324$$ 0 0
$$325$$ 6796.71 11772.2i 1.16004 2.00925i
$$326$$ −3286.00 + 5691.52i −0.558266 + 0.966945i
$$327$$ 0 0
$$328$$ −1006.92 −0.169506
$$329$$ 0 0
$$330$$ 0 0
$$331$$ 2869.00 + 4969.25i 0.476418 + 0.825181i 0.999635 0.0270189i $$-0.00860142\pi$$
−0.523216 + 0.852200i $$0.675268\pi$$
$$332$$ −845.700 + 1464.79i −0.139801 + 0.242142i
$$333$$ 0 0
$$334$$ 1490.58 + 2581.76i 0.244195 + 0.422957i
$$335$$ −13542.5 −2.20868
$$336$$ 0 0
$$337$$ −2254.00 −0.364342 −0.182171 0.983267i $$-0.558312\pi$$
−0.182171 + 0.983267i $$0.558312\pi$$
$$338$$ −395.000 684.160i −0.0635656 0.110099i
$$339$$ 0 0
$$340$$ 56.0000 96.9948i 0.00893243 0.0154714i
$$341$$ −653.367 1131.66i −0.103759 0.179716i
$$342$$ 0 0
$$343$$ 0 0
$$344$$ −272.000 −0.0426316
$$345$$ 0 0
$$346$$ 2070.41 3586.05i 0.321693 0.557189i
$$347$$ −993.000 + 1719.93i −0.153623 + 0.266082i −0.932557 0.361024i $$-0.882427\pi$$
0.778934 + 0.627106i $$0.215761\pi$$
$$348$$ 0 0
$$349$$ −6771.25 −1.03856 −0.519279 0.854605i $$-0.673800\pi$$
−0.519279 + 0.854605i $$0.673800\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ −224.000 387.979i −0.0339183 0.0587482i
$$353$$ −3496.64 + 6056.36i −0.527217 + 0.913166i 0.472280 + 0.881449i $$0.343431\pi$$
−0.999497 + 0.0317177i $$0.989902\pi$$
$$354$$ 0 0
$$355$$ −5820.90 10082.1i −0.870258 1.50733i
$$356$$ 2472.05 0.368028
$$357$$ 0 0
$$358$$ −1080.00 −0.159441
$$359$$ 2972.00 + 5147.66i 0.436925 + 0.756777i 0.997451 0.0713606i $$-0.0227341\pi$$
−0.560525 + 0.828137i $$0.689401\pi$$
$$360$$ 0 0
$$361$$ 3428.50 5938.34i 0.499854 0.865773i
$$362$$ 3784.44 + 6554.83i 0.549463 + 0.951697i
$$363$$ 0 0
$$364$$ 0 0
$$365$$ −5348.00 −0.766924
$$366$$ 0 0
$$367$$ −421.436 + 729.948i −0.0599421 + 0.103823i −0.894439 0.447190i $$-0.852425\pi$$
0.834497 + 0.551012i $$0.185758\pi$$
$$368$$ 1120.00 1939.90i 0.158652 0.274794i
$$369$$ 0 0
$$370$$ 1504.72 0.211424
$$371$$ 0 0
$$372$$ 0 0
$$373$$ 2863.00 + 4958.86i 0.397428 + 0.688365i 0.993408 0.114634i $$-0.0365696\pi$$
−0.595980 + 0.802999i $$0.703236\pi$$
$$374$$ −19.7990 + 34.2929i −0.00273738 + 0.00474129i
$$375$$ 0 0
$$376$$ −2093.04 3625.24i −0.287075 0.497228i
$$377$$ −14560.7 −1.98917
$$378$$ 0 0
$$379$$ 10330.0 1.40004 0.700022 0.714122i $$-0.253174\pi$$
0.700022 + 0.714122i $$0.253174\pi$$
$$380$$ 56.0000 + 96.9948i 0.00755984 + 0.0130940i
$$381$$ 0 0
$$382$$ 1028.00 1780.55i 0.137689 0.238484i
$$383$$ −502.046 869.569i −0.0669800 0.116013i 0.830591 0.556884i $$-0.188003\pi$$
−0.897571 + 0.440871i $$0.854670\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 9184.00 1.21102
$$387$$ 0 0
$$388$$ 2967.02 5139.03i 0.388216 0.672409i
$$389$$ 2605.00 4511.99i 0.339534 0.588090i −0.644811 0.764342i $$-0.723064\pi$$
0.984345 + 0.176252i $$0.0563973\pi$$
$$390$$ 0 0
$$391$$ −197.990 −0.0256081
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 794.000 + 1375.25i 0.101526 + 0.175848i
$$395$$ 12077.4 20918.6i 1.53843 2.66464i
$$396$$ 0 0
$$397$$ −36.7696 63.6867i −0.00464839 0.00805125i 0.863692 0.504020i $$-0.168146\pi$$
−0.868340 + 0.495969i $$0.834813\pi$$
$$398$$ −4972.37 −0.626238
$$399$$ 0 0
$$400$$ 4272.00 0.534000
$$401$$ −249.000 431.281i −0.0310086 0.0537085i 0.850105 0.526614i $$-0.176539\pi$$
−0.881113 + 0.472905i $$0.843205\pi$$
$$402$$ 0 0
$$403$$ 2376.00 4115.35i 0.293690 0.508686i
$$404$$ −2257.08 3909.39i −0.277956 0.481434i
$$405$$ 0 0
$$406$$ 0 0
$$407$$ −532.000 −0.0647918
$$408$$ 0 0
$$409$$ 1677.96 2906.32i 0.202861 0.351365i −0.746588 0.665286i $$-0.768309\pi$$
0.949449 + 0.313921i $$0.101643\pi$$
$$410$$ −2492.00 + 4316.27i −0.300173 + 0.519916i
$$411$$ 0 0
$$412$$ 3473.31 0.415334
$$413$$ 0 0
$$414$$ 0 0
$$415$$ 4186.00 + 7250.36i 0.495139 + 0.857606i
$$416$$ 814.587 1410.91i 0.0960058 0.166287i
$$417$$ 0 0
$$418$$ −19.7990 34.2929i −0.00231675 0.00401272i
$$419$$ 14545.2 1.69589 0.847946 0.530082i $$-0.177839\pi$$
0.847946 + 0.530082i $$0.177839\pi$$
$$420$$ 0 0
$$421$$ 10854.0 1.25651 0.628256 0.778007i $$-0.283769\pi$$
0.628256 + 0.778007i $$0.283769\pi$$
$$422$$ 2748.00 + 4759.68i 0.316992 + 0.549046i
$$423$$ 0 0
$$424$$ −296.000 + 512.687i −0.0339034 + 0.0587224i
$$425$$ −188.798 327.007i −0.0215483 0.0373227i
$$426$$ 0 0
$$427$$ 0 0
$$428$$ 6736.00 0.760740
$$429$$ 0 0
$$430$$ −673.166 + 1165.96i −0.0754952 + 0.130762i
$$431$$ −2682.00 + 4645.36i −0.299739 + 0.519163i −0.976076 0.217429i $$-0.930233\pi$$
0.676337 + 0.736592i $$0.263566\pi$$
$$432$$ 0 0
$$433$$ 6487.00 0.719966 0.359983 0.932959i $$-0.382783\pi$$
0.359983 + 0.932959i $$0.382783\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 1636.00 + 2833.64i 0.179702 + 0.311253i
$$437$$ 98.9949 171.464i 0.0108365 0.0187694i
$$438$$ 0 0
$$439$$ 6966.42 + 12066.2i 0.757378 + 1.31182i 0.944183 + 0.329420i $$0.106853\pi$$
−0.186806 + 0.982397i $$0.559813\pi$$
$$440$$ −2217.49 −0.240260
$$441$$ 0 0
$$442$$ −144.000 −0.0154963
$$443$$ 2998.00 + 5192.69i 0.321533 + 0.556912i 0.980805 0.194993i $$-0.0624684\pi$$
−0.659271 + 0.751905i $$0.729135\pi$$
$$444$$ 0 0
$$445$$ 6118.00 10596.7i 0.651733 1.12883i
$$446$$ −3428.05 5937.56i −0.363953 0.630385i
$$447$$ 0 0
$$448$$ 0 0
$$449$$ −2622.00 −0.275590 −0.137795 0.990461i $$-0.544001\pi$$
−0.137795 + 0.990461i $$0.544001\pi$$
$$450$$ 0 0
$$451$$ 881.055 1526.03i 0.0919895 0.159330i
$$452$$ −1080.00 + 1870.61i −0.112387 + 0.194660i
$$453$$ 0 0
$$454$$ 10581.1 1.09383
$$455$$ 0 0
$$456$$ 0 0
$$457$$ −5604.00 9706.41i −0.573619 0.993538i −0.996190 0.0872080i $$-0.972206\pi$$
0.422571 0.906330i $$-0.361128\pi$$
$$458$$ −2749.23 + 4761.81i −0.280487 + 0.485818i
$$459$$ 0 0
$$460$$ −5543.72 9602.00i −0.561907 0.973251i
$$461$$ 9786.36 0.988712 0.494356 0.869260i $$-0.335404\pi$$
0.494356 + 0.869260i $$0.335404\pi$$
$$462$$ 0 0
$$463$$ 3952.00 0.396685 0.198342 0.980133i $$-0.436444\pi$$
0.198342 + 0.980133i $$0.436444\pi$$
$$464$$ −2288.00 3962.93i −0.228918 0.396497i
$$465$$ 0 0
$$466$$ 72.0000 124.708i 0.00715737 0.0123969i
$$467$$ −8753.27 15161.1i −0.867352 1.50230i −0.864693 0.502301i $$-0.832487\pi$$
−0.00265876 0.999996i $$-0.500846\pi$$
$$468$$ 0 0
$$469$$ 0 0
$$470$$ −20720.0 −2.03349
$$471$$ 0 0
$$472$$ −1736.65 + 3007.97i −0.169356 + 0.293333i
$$473$$ 238.000 412.228i 0.0231358 0.0400724i
$$474$$ 0 0
$$475$$ 377.595 0.0364742
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 4308.00 + 7461.67i 0.412225 + 0.713994i
$$479$$ −1144.10 + 1981.64i −0.109134 + 0.189026i −0.915420 0.402501i $$-0.868141\pi$$
0.806286 + 0.591526i $$0.201474\pi$$
$$480$$ 0 0
$$481$$ −967.322 1675.45i −0.0916967 0.158823i
$$482$$ 3080.16 0.291073
$$483$$ 0 0
$$484$$ −4540.00 −0.426371
$$485$$ −14686.0 25436.9i −1.37496 2.38151i
$$486$$ 0 0
$$487$$ −486.000 + 841.777i −0.0452213 + 0.0783256i −0.887750 0.460326i $$-0.847733\pi$$
0.842529 + 0.538651i $$0.181066\pi$$
$$488$$ 56.5685 + 97.9796i 0.00524741 + 0.00908879i
$$489$$ 0 0
$$490$$ 0 0
$$491$$ 7404.00 0.680525 0.340263 0.940330i $$-0.389484\pi$$
0.340263 + 0.940330i $$0.389484\pi$$
$$492$$ 0 0
$$493$$ −202.233 + 350.277i −0.0184748 + 0.0319994i
$$494$$ 72.0000 124.708i 0.00655756 0.0113580i
$$495$$ 0 0
$$496$$ 1493.41 0.135194
$$497$$ 0 0
$$498$$ 0 0
$$499$$ 6122.00 + 10603.6i 0.549215 + 0.951269i 0.998329 + 0.0577938i $$0.0184066\pi$$
−0.449113 + 0.893475i $$0.648260\pi$$
$$500$$ 5622.91 9739.17i 0.502929 0.871098i
$$501$$ 0 0
$$502$$ −931.967 1614.21i −0.0828600 0.143518i
$$503$$ −2415.48 −0.214117 −0.107058 0.994253i $$-0.534143\pi$$
−0.107058 + 0.994253i $$0.534143\pi$$
$$504$$ 0 0
$$505$$ −22344.0 −1.96890
$$506$$ 1960.00 + 3394.82i 0.172199 + 0.298257i
$$507$$ 0 0
$$508$$ −3440.00 + 5958.25i −0.300444 + 0.520383i
$$509$$ 2853.88 + 4943.07i 0.248519 + 0.430447i 0.963115 0.269090i $$-0.0867228\pi$$
−0.714596 + 0.699537i $$0.753390\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ 512.000 0.0441942
$$513$$ 0 0
$$514$$ −937.624 + 1624.01i −0.0804607 + 0.139362i
$$515$$ 8596.00 14888.7i 0.735505 1.27393i
$$516$$ 0 0
$$517$$ 7325.63 0.623173
$$518$$ 0 0
$$519$$ 0 0
$$520$$ −4032.00 6983.63i −0.340029 0.588947i
$$521$$ −0.707107 + 1.22474i −5.94605e−5 + 0.000102989i −0.866055 0.499949i $$-0.833352\pi$$
0.865996 + 0.500051i $$0.166686\pi$$
$$522$$ 0 0
$$523$$ −6128.49 10614.9i −0.512391 0.887487i −0.999897 0.0143672i $$-0.995427\pi$$
0.487506 0.873120i $$-0.337907\pi$$
$$524$$ −6940.96 −0.578659
$$525$$ 0 0
$$526$$ −14280.0 −1.18372
$$527$$ −66.0000 114.315i −0.00545542 0.00944906i
$$528$$ 0 0
$$529$$ −3716.50 + 6437.17i −0.305457 + 0.529068i
$$530$$ 1465.13 + 2537.67i 0.120077 + 0.207980i
$$531$$ 0 0
$$532$$ 0 0
$$533$$ 6408.00 0.520753
$$534$$ 0 0
$$535$$ 16670.7 28874.6i 1.34718 2.33338i
$$536$$ −2736.00 + 4738.89i −0.220480 + 0.381882i
$$537$$ 0 0
$$538$$ 9220.67 0.738906
$$539$$ 0 0
$$540$$ 0 0
$$541$$ −1025.00 1775.35i −0.0814569 0.141088i 0.822419 0.568882i $$-0.192624\pi$$
−0.903876 + 0.427795i $$0.859291\pi$$
$$542$$ −2364.57 + 4095.55i −0.187393 + 0.324573i
$$543$$ 0 0
$$544$$ −22.6274 39.1918i −0.00178335 0.00308885i
$$545$$ 16195.6 1.27292
$$546$$ 0 0
$$547$$ 14554.0 1.13763 0.568815 0.822465i $$-0.307402\pi$$
0.568815 + 0.822465i $$0.307402\pi$$
$$548$$ 1656.00 + 2868.28i 0.129089 + 0.223589i
$$549$$ 0 0
$$550$$ −3738.00 + 6474.41i −0.289798 + 0.501945i
$$551$$ −202.233 350.277i −0.0156359 0.0270822i
$$552$$ 0 0
$$553$$ 0 0
$$554$$ 8012.00 0.614435
$$555$$ 0 0
$$556$$ −851.357 + 1474.59i −0.0649381 + 0.112476i
$$557$$ 3477.00 6022.34i 0.264498 0.458123i −0.702934 0.711255i $$-0.748127\pi$$
0.967432 + 0.253131i $$0.0814605\pi$$
$$558$$ 0 0
$$559$$ 1731.00 0.130972
$$560$$ 0 0
$$561$$ 0 0
$$562$$ −5984.00 10364.6i −0.449146 0.777943i
$$563$$ 818.123 1417.03i 0.0612429 0.106076i −0.833778 0.552099i $$-0.813827\pi$$
0.895021 + 0.446024i $$0.147160\pi$$
$$564$$ 0 0
$$565$$ 5345.73 + 9259.07i 0.398047 + 0.689437i
$$566$$ 9857.07 0.732020
$$567$$ 0 0
$$568$$ −4704.00 −0.347492
$$569$$ −3571.00 6185.15i −0.263100 0.455703i 0.703964 0.710236i $$-0.251412\pi$$
−0.967064 + 0.254533i $$0.918078\pi$$
$$570$$ 0 0
$$571$$ 10303.0 17845.3i 0.755109 1.30789i −0.190211 0.981743i $$-0.560917\pi$$
0.945320 0.326144i $$-0.105749\pi$$
$$572$$ 1425.53 + 2469.09i 0.104203 + 0.180485i
$$573$$ 0 0
$$574$$ 0 0
$$575$$ −37380.0 −2.71105
$$576$$ 0 0
$$577$$ −4401.74 + 7624.04i −0.317585 + 0.550074i −0.979984 0.199078i $$-0.936205\pi$$
0.662398 + 0.749152i $$0.269539\pi$$
$$578$$ 4911.00 8506.10i 0.353409 0.612123i
$$579$$ 0 0
$$580$$ −22650.0 −1.62154
$$581$$ 0 0
$$582$$ 0 0
$$583$$ −518.000 897.202i −0.0367982 0.0637364i
$$584$$ −1080.46 + 1871.41i −0.0765577 + 0.132602i
$$585$$ 0 0
$$586$$ −1971.41 3414.59i −0.138973 0.240709i
$$587$$ 6503.97 0.457321 0.228661 0.973506i $$-0.426565\pi$$
0.228661 + 0.973506i $$0.426565\pi$$
$$588$$ 0 0
$$589$$ 132.000 0.00923424
$$590$$ 8596.00 + 14888.7i 0.599816 + 1.03891i
$$591$$ 0 0
$$592$$ 304.000 526.543i 0.0211053 0.0365554i
$$593$$ 11570.4 + 20040.5i 0.801246 + 1.38780i 0.918796 + 0.394732i $$0.129163\pi$$
−0.117550 + 0.993067i $$0.537504\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ −8200.00 −0.563566
$$597$$ 0 0
$$598$$ −7127.64 + 12345.4i −0.487409 + 0.844218i
$$599$$ −5648.00 + 9782.62i −0.385260 + 0.667291i −0.991805 0.127759i $$-0.959222\pi$$
0.606545 + 0.795049i $$0.292555\pi$$
$$600$$ 0 0
$$601$$ −8727.11 −0.592323 −0.296162 0.955138i $$-0.595707\pi$$
−0.296162 + 0.955138i $$0.595707\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ 944.000 + 1635.06i 0.0635941 + 0.110148i
$$605$$ −11235.9 + 19461.2i −0.755050 + 1.30779i
$$606$$ 0 0
$$607$$ 9868.38 + 17092.5i 0.659877 + 1.14294i 0.980647 + 0.195783i $$0.0627249\pi$$
−0.320770 + 0.947157i $$0.603942\pi$$
$$608$$ 45.2548 0.00301863
$$609$$ 0 0
$$610$$ 560.000 0.0371701
$$611$$ 13320.0 + 23070.9i 0.881947 + 1.52758i
$$612$$ 0 0
$$613$$ −8481.00 + 14689.5i −0.558800 + 0.967870i 0.438797 + 0.898586i $$0.355405\pi$$
−0.997597 + 0.0692837i $$0.977929\pi$$
$$614$$ −4767.31 8257.23i −0.313344 0.542727i
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 19034.0 1.24194 0.620972 0.783832i $$-0.286738\pi$$
0.620972 + 0.783832i $$0.286738\pi$$
$$618$$ 0 0
$$619$$ −9338.76 + 16175.2i −0.606392 + 1.05030i 0.385438 + 0.922734i $$0.374050\pi$$
−0.991830 + 0.127568i $$0.959283\pi$$
$$620$$ 3696.00 6401.66i 0.239411 0.414672i
$$621$$ 0 0
$$622$$ −13553.8 −0.873728
$$623$$ 0 0
$$624$$ 0 0
$$625$$ −11144.5 19302.8i −0.713248 1.23538i
$$626$$ −6190.01 + 10721.4i −0.395212 + 0.684527i
$$627$$ 0 0
$$628$$ −4423.66 7662.00i −0.281088 0.486859i
$$629$$ −53.7401 −0.00340661
$$630$$ 0 0
$$631$$ −14716.0 −0.928423 −0.464211 0.885724i $$-0.653662\pi$$
−0.464211 + 0.885724i $$0.653662\pi$$
$$632$$ −4880.00 8452.41i −0.307146 0.531992i
$$633$$ 0 0
$$634$$ 9826.00 17019.1i 0.615521 1.06611i
$$635$$ 17027.1 + 29491.9i 1.06410 + 1.84307i
$$636$$ 0 0
$$637$$ 0 0
$$638$$ 8008.00 0.496928
$$639$$ 0 0
$$640$$ 1267.14 2194.74i 0.0782624 0.135554i
$$641$$ 2365.00 4096.30i 0.145728 0.252409i −0.783916 0.620867i $$-0.786781\pi$$
0.929644 + 0.368458i $$0.120114\pi$$
$$642$$ 0 0
$$643$$ −19056.5 −1.16877 −0.584383 0.811478i $$-0.698663\pi$$
−0.584383 + 0.811478i $$0.698663\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ −2.00000 3.46410i −0.000121810 0.000210980i
$$647$$ −4671.15 + 8090.66i −0.283836 + 0.491618i −0.972326 0.233627i $$-0.924940\pi$$
0.688490 + 0.725245i $$0.258274\pi$$
$$648$$ 0 0
$$649$$ −3039.14 5263.95i −0.183816 0.318379i
$$650$$ −27186.8 −1.64055
$$651$$ 0 0
$$652$$ 13144.0 0.789507
$$653$$ 1887.00 + 3268.38i 0.113084 + 0.195868i 0.917012 0.398859i $$-0.130594\pi$$
−0.803928 + 0.594727i $$0.797260\pi$$
$$654$$ 0 0
$$655$$ −17178.0 + 29753.2i −1.02473 + 1.77489i
$$656$$ 1006.92 + 1744.04i 0.0599293 + 0.103801i
$$657$$ 0 0
$$658$$ 0 0
$$659$$ 21150.0 1.25021 0.625104 0.780541i $$-0.285057\pi$$
0.625104 + 0.780541i $$0.285057\pi$$
$$660$$ 0 0
$$661$$ −5188.75 + 8987.18i −0.305324 + 0.528836i −0.977333 0.211706i $$-0.932098\pi$$
0.672010 + 0.740542i $$0.265431\pi$$
$$662$$ 5738.00 9938.51i 0.336879 0.583491i
$$663$$ 0 0
$$664$$ 3382.80 0.197708
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 20020.0 + 34675.7i 1.16219 + 2.01296i
$$668$$ 2981.16 5163.52i 0.172672 0.299076i
$$669$$ 0 0
$$670$$ 13542.5 + 23456.3i 0.780885 + 1.35253i
$$671$$ −197.990 −0.0113909
$$672$$ 0 0
$$673$$ −1164.00 −0.0666700 −0.0333350 0.999444i $$-0.510613\pi$$
−0.0333350 + 0.999444i $$0.510613\pi$$
$$674$$ 2254.00 + 3904.04i 0.128814 + 0.223113i
$$675$$ 0 0
$$676$$ −790.000 + 1368.32i −0.0449477 + 0.0778516i
$$677$$ −13576.5 23515.1i −0.770732 1.33495i −0.937162 0.348893i $$-0.886558\pi$$
0.166431 0.986053i $$-0.446776\pi$$
$$678$$ 0 0
$$679$$ 0 0
$$680$$ −224.000 −0.0126324
$$681$$ 0 0
$$682$$ −1306.73 + 2263.33i −0.0733686 + 0.127078i
$$683$$ −8298.00 + 14372.6i −0.464882 + 0.805199i −0.999196 0.0400871i $$-0.987236\pi$$
0.534315 + 0.845286i $$0.320570\pi$$
$$684$$ 0 0
$$685$$ 16393.6 0.914403
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 272.000 + 471.118i 0.0150725 + 0.0261064i
$$689$$ 1883.73 3262.72i 0.104157 0.180406i
$$690$$ 0 0
$$691$$ 5649.08 + 9784.49i 0.311000 + 0.538668i 0.978579 0.205871i $$-0.0660028\pi$$
−0.667579 + 0.744539i $$0.732669\pi$$
$$692$$ −8281.63 −0.454943
$$693$$ 0 0
$$694$$ 3972.00 0.217255
$$695$$ 4214.00 + 7298.86i 0.229994 + 0.398362i
$$696$$ 0 0
$$697$$ 89.0000 154.153i 0.00483661 0.00837725i
$$698$$ 6771.25 + 11728.2i 0.367186 + 0.635985i
$$699$$ 0 0
$$700$$ 0 0
$$701$$ 2754.00 0.148384 0.0741920 0.997244i $$-0.476362\pi$$
0.0741920 + 0.997244i $$0.476362\pi$$
$$702$$ 0 0
$$703$$ 26.8701 46.5403i 0.00144157 0.00249687i
$$704$$ −448.000 + 775.959i −0.0239839 + 0.0415413i
$$705$$ 0 0
$$706$$ 13986.6 0.745597
$$707$$ 0 0
$$708$$ 0 0
$$709$$ −14717.0 25490.6i −0.779561 1.35024i −0.932195 0.361956i $$-0.882109\pi$$
0.152634 0.988283i $$-0.451224\pi$$
$$710$$ −11641.8 + 20164.2i −0.615365 + 1.06584i
$$711$$ 0 0
$$712$$ −2472.05 4281.71i −0.130118 0.225370i
$$713$$ −13067.3 −0.686361
$$714$$ 0 0
$$715$$ 14112.0 0.738124
$$716$$ 1080.00 + 1870.61i 0.0563708 + 0.0976371i
$$717$$ 0 0
$$718$$ 5944.00 10295.3i 0.308953 0.535122i
$$719$$ 8834.59 + 15302.0i 0.458240 + 0.793695i 0.998868 0.0475666i $$-0.0151466\pi$$
−0.540628 + 0.841262i $$0.681813\pi$$
$$720$$ 0 0
$$721$$ 0 0
$$722$$ −13714.0 −0.706901
$$723$$ 0 0
$$724$$ 7568.87 13109.7i 0.388529 0.672952i
$$725$$ −38181.0 + 66131.4i −1.95587 + 3.38767i
$$726$$ 0 0
$$727$$ −28445.5 −1.45115 −0.725574 0.688144i $$-0.758426\pi$$
−0.725574 + 0.688144i $$0.758426\pi$$
$$728$$ 0 0
$$729$$ 0 0
$$730$$ 5348.00 + 9263.01i 0.271148 + 0.469643i
$$731$$ 24.0416 41.6413i 0.00121643 0.00210692i
$$732$$ 0 0
$$733$$ 11170.9 + 19348.5i 0.562900 + 0.974971i 0.997242 + 0.0742230i $$0.0236477\pi$$
−0.434342 + 0.900748i $$0.643019\pi$$
$$734$$ 1685.74 0.0847710
$$735$$ 0 0
$$736$$ −4480.00 −0.224368
$$737$$ −4788.00 8293.06i −0.239306 0.414490i
$$738$$ 0 0
$$739$$ −10335.0 + 17900.7i −0.514451 + 0.891055i 0.485409 + 0.874287i $$0.338671\pi$$
−0.999859 + 0.0167675i $$0.994662\pi$$
$$740$$ −1504.72 2606.26i −0.0747496 0.129470i
$$741$$ 0 0
$$742$$ 0 0
$$743$$ 25400.0 1.25415 0.627076 0.778958i $$-0.284251\pi$$
0.627076 + 0.778958i $$0.284251\pi$$
$$744$$ 0 0
$$745$$ −20294.0 + 35150.2i −0.998004 + 1.72859i
$$746$$ 5726.00 9917.72i 0.281024 0.486748i
$$747$$ 0 0
$$748$$ 79.1960 0.00387124
$$749$$ 0 0
$$750$$ 0 0
$$751$$ −14590.0 25270.6i −0.708917 1.22788i −0.965259 0.261294i $$-0.915851\pi$$
0.256342 0.966586i $$-0.417483\pi$$
$$752$$ −4186.07 + 7250.49i −0.202992 + 0.351593i
$$753$$ 0 0
$$754$$ 14560.7 + 25219.9i 0.703277 + 1.21811i
$$755$$ 9345.12 0.450469
$$756$$ 0 0
$$757$$ −26206.0 −1.25822 −0.629110 0.777316i $$-0.716581\pi$$
−0.629110 + 0.777316i $$0.716581\pi$$
$$758$$ −10330.0 17892.1i −0.494990 0.857348i
$$759$$ 0 0
$$760$$ 112.000 193.990i 0.00534561 0.00925888i
$$761$$ −3431.59 5943.69i −0.163463 0.283125i 0.772646 0.634838i $$-0.218933\pi$$
−0.936108 + 0.351712i $$0.885600\pi$$
$$762$$ 0 0
$$763$$ 0 0
$$764$$ −4112.00 −0.194721
$$765$$ 0 0
$$766$$ −1004.09 + 1739.14i −0.0473620 + 0.0820334i
$$767$$ 11052.0 19142.6i 0.520293 0.901174i
$$768$$ 0 0
$$769$$ 9058.04 0.424761 0.212380 0.977187i $$-0.431878\pi$$
0.212380 + 0.977187i $$0.431878\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ −9184.00 15907.2i −0.428160 0.741595i
$$773$$ 66.4680 115.126i 0.00309274 0.00535679i −0.864475 0.502676i $$-0.832349\pi$$
0.867568 + 0.497319i $$0.165682\pi$$
$$774$$ 0 0
$$775$$ −12460.6 21582.5i −0.577547 1.00034i
$$776$$ −11868.1 −0.549020
$$777$$ 0 0
$$778$$ −10420.0 −0.480174
$$779$$ 89.0000 + 154.153i 0.00409340 + 0.00708997i
$$780$$ 0 0
$$781$$ 4116.00 7129.12i 0.188581 0.326633i
$$782$$ 197.990 + 342.929i 0.00905384 + 0.0156817i
$$783$$ 0 0
$$784$$ 0 0
$$785$$ −43792.0 −1.99109
$$786$$ 0 0
$$787$$ −4364.97 + 7560.35i −0.197706 + 0.342436i −0.947784 0.318913i $$-0.896682\pi$$
0.750078 + 0.661349i $$0.230016\pi$$
$$788$$ 1588.00 2750.50i 0.0717895 0.124343i
$$789$$ 0 0