# Properties

 Label 384.3.l.a.223.2 Level $384$ Weight $3$ Character 384.223 Analytic conductor $10.463$ Analytic rank $0$ Dimension $16$ CM no Inner twists $2$

# Learn more about

## Newspace parameters

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

## Newform invariants

 Self dual: no Analytic conductor: $$10.4632421514$$ Analytic rank: $$0$$ Dimension: $$16$$ Relative dimension: $$8$$ over $$\Q(i)$$ Coefficient field: $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ Defining polynomial: $$x^{16} - 6 x^{14} - 4 x^{13} + 10 x^{12} + 56 x^{11} + 88 x^{10} - 128 x^{9} - 496 x^{8} - 512 x^{7} + 1408 x^{6} + 3584 x^{5} + 2560 x^{4} - 4096 x^{3} - 24576 x^{2} + 65536$$ Coefficient ring: $$\Z[a_1, \ldots, a_{7}]$$ Coefficient ring index: $$2^{24}$$ Twist minimal: no (minimal twist has level 48) Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

## Embedding invariants

 Embedding label 223.2 Root $$1.78012 + 0.911682i$$ of defining polynomial Character $$\chi$$ $$=$$ 384.223 Dual form 384.3.l.a.31.2

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-1.22474 + 1.22474i) q^{3} +(-1.00772 + 1.00772i) q^{5} +10.0236 q^{7} -3.00000i q^{9} +O(q^{10})$$ $$q+(-1.22474 + 1.22474i) q^{3} +(-1.00772 + 1.00772i) q^{5} +10.0236 q^{7} -3.00000i q^{9} +(-2.26517 - 2.26517i) q^{11} +(6.88229 + 6.88229i) q^{13} -2.46840i q^{15} -22.3801 q^{17} +(16.8918 - 16.8918i) q^{19} +(-12.2763 + 12.2763i) q^{21} +33.2007 q^{23} +22.9690i q^{25} +(3.67423 + 3.67423i) q^{27} +(24.6412 + 24.6412i) q^{29} +41.3761i q^{31} +5.54852 q^{33} +(-10.1010 + 10.1010i) q^{35} +(6.60031 - 6.60031i) q^{37} -16.8581 q^{39} +47.1477i q^{41} +(48.8218 + 48.8218i) q^{43} +(3.02316 + 3.02316i) q^{45} -45.6048i q^{47} +51.4717 q^{49} +(27.4100 - 27.4100i) q^{51} +(-25.1401 + 25.1401i) q^{53} +4.56532 q^{55} +41.3762i q^{57} +(-6.23974 - 6.23974i) q^{59} +(-35.9513 - 35.9513i) q^{61} -30.0707i q^{63} -13.8709 q^{65} +(-10.2045 + 10.2045i) q^{67} +(-40.6624 + 40.6624i) q^{69} +11.9529 q^{71} -111.332i q^{73} +(-28.1312 - 28.1312i) q^{75} +(-22.7051 - 22.7051i) q^{77} -4.46031i q^{79} -9.00000 q^{81} +(-10.1751 + 10.1751i) q^{83} +(22.5530 - 22.5530i) q^{85} -60.3583 q^{87} +21.9364i q^{89} +(68.9850 + 68.9850i) q^{91} +(-50.6752 - 50.6752i) q^{93} +34.0444i q^{95} +107.309 q^{97} +(-6.79552 + 6.79552i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$16q + O(q^{10})$$ $$16q - 32q^{11} + 32q^{19} - 128q^{23} - 32q^{29} - 96q^{35} + 96q^{37} - 160q^{43} + 112q^{49} + 96q^{51} + 160q^{53} - 256q^{55} + 128q^{59} + 32q^{61} - 32q^{65} - 320q^{67} - 96q^{69} + 512q^{71} - 192q^{75} - 224q^{77} - 144q^{81} + 160q^{83} - 160q^{85} + 480q^{91} - 96q^{99} + O(q^{100})$$

## Character values

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

 $$n$$ $$127$$ $$133$$ $$257$$ $$\chi(n)$$ $$-1$$ $$e\left(\frac{3}{4}\right)$$ $$1$$

## 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
$$3$$ −1.22474 + 1.22474i −0.408248 + 0.408248i
$$4$$ 0 0
$$5$$ −1.00772 + 1.00772i −0.201544 + 0.201544i −0.800661 0.599117i $$-0.795518\pi$$
0.599117 + 0.800661i $$0.295518\pi$$
$$6$$ 0 0
$$7$$ 10.0236 1.43194 0.715969 0.698133i $$-0.245985\pi$$
0.715969 + 0.698133i $$0.245985\pi$$
$$8$$ 0 0
$$9$$ 3.00000i 0.333333i
$$10$$ 0 0
$$11$$ −2.26517 2.26517i −0.205925 0.205925i 0.596608 0.802533i $$-0.296515\pi$$
−0.802533 + 0.596608i $$0.796515\pi$$
$$12$$ 0 0
$$13$$ 6.88229 + 6.88229i 0.529407 + 0.529407i 0.920395 0.390989i $$-0.127867\pi$$
−0.390989 + 0.920395i $$0.627867\pi$$
$$14$$ 0 0
$$15$$ 2.46840i 0.164560i
$$16$$ 0 0
$$17$$ −22.3801 −1.31648 −0.658240 0.752809i $$-0.728699\pi$$
−0.658240 + 0.752809i $$0.728699\pi$$
$$18$$ 0 0
$$19$$ 16.8918 16.8918i 0.889041 0.889041i −0.105390 0.994431i $$-0.533609\pi$$
0.994431 + 0.105390i $$0.0336092\pi$$
$$20$$ 0 0
$$21$$ −12.2763 + 12.2763i −0.584586 + 0.584586i
$$22$$ 0 0
$$23$$ 33.2007 1.44351 0.721755 0.692149i $$-0.243336\pi$$
0.721755 + 0.692149i $$0.243336\pi$$
$$24$$ 0 0
$$25$$ 22.9690i 0.918760i
$$26$$ 0 0
$$27$$ 3.67423 + 3.67423i 0.136083 + 0.136083i
$$28$$ 0 0
$$29$$ 24.6412 + 24.6412i 0.849696 + 0.849696i 0.990095 0.140399i $$-0.0448385\pi$$
−0.140399 + 0.990095i $$0.544839\pi$$
$$30$$ 0 0
$$31$$ 41.3761i 1.33471i 0.744738 + 0.667357i $$0.232574\pi$$
−0.744738 + 0.667357i $$0.767426\pi$$
$$32$$ 0 0
$$33$$ 5.54852 0.168137
$$34$$ 0 0
$$35$$ −10.1010 + 10.1010i −0.288599 + 0.288599i
$$36$$ 0 0
$$37$$ 6.60031 6.60031i 0.178387 0.178387i −0.612266 0.790652i $$-0.709742\pi$$
0.790652 + 0.612266i $$0.209742\pi$$
$$38$$ 0 0
$$39$$ −16.8581 −0.432259
$$40$$ 0 0
$$41$$ 47.1477i 1.14994i 0.818173 + 0.574972i $$0.194987\pi$$
−0.818173 + 0.574972i $$0.805013\pi$$
$$42$$ 0 0
$$43$$ 48.8218 + 48.8218i 1.13539 + 1.13539i 0.989266 + 0.146124i $$0.0466799\pi$$
0.146124 + 0.989266i $$0.453320\pi$$
$$44$$ 0 0
$$45$$ 3.02316 + 3.02316i 0.0671814 + 0.0671814i
$$46$$ 0 0
$$47$$ 45.6048i 0.970315i −0.874427 0.485157i $$-0.838762\pi$$
0.874427 0.485157i $$-0.161238\pi$$
$$48$$ 0 0
$$49$$ 51.4717 1.05044
$$50$$ 0 0
$$51$$ 27.4100 27.4100i 0.537450 0.537450i
$$52$$ 0 0
$$53$$ −25.1401 + 25.1401i −0.474341 + 0.474341i −0.903316 0.428975i $$-0.858875\pi$$
0.428975 + 0.903316i $$0.358875\pi$$
$$54$$ 0 0
$$55$$ 4.56532 0.0830059
$$56$$ 0 0
$$57$$ 41.3762i 0.725899i
$$58$$ 0 0
$$59$$ −6.23974 6.23974i −0.105758 0.105758i 0.652248 0.758006i $$-0.273826\pi$$
−0.758006 + 0.652248i $$0.773826\pi$$
$$60$$ 0 0
$$61$$ −35.9513 35.9513i −0.589366 0.589366i 0.348093 0.937460i $$-0.386829\pi$$
−0.937460 + 0.348093i $$0.886829\pi$$
$$62$$ 0 0
$$63$$ 30.0707i 0.477312i
$$64$$ 0 0
$$65$$ −13.8709 −0.213398
$$66$$ 0 0
$$67$$ −10.2045 + 10.2045i −0.152307 + 0.152307i −0.779147 0.626841i $$-0.784348\pi$$
0.626841 + 0.779147i $$0.284348\pi$$
$$68$$ 0 0
$$69$$ −40.6624 + 40.6624i −0.589310 + 0.589310i
$$70$$ 0 0
$$71$$ 11.9529 0.168350 0.0841752 0.996451i $$-0.473174\pi$$
0.0841752 + 0.996451i $$0.473174\pi$$
$$72$$ 0 0
$$73$$ 111.332i 1.52510i −0.646929 0.762550i $$-0.723947\pi$$
0.646929 0.762550i $$-0.276053\pi$$
$$74$$ 0 0
$$75$$ −28.1312 28.1312i −0.375082 0.375082i
$$76$$ 0 0
$$77$$ −22.7051 22.7051i −0.294871 0.294871i
$$78$$ 0 0
$$79$$ 4.46031i 0.0564596i −0.999601 0.0282298i $$-0.991013\pi$$
0.999601 0.0282298i $$-0.00898702\pi$$
$$80$$ 0 0
$$81$$ −9.00000 −0.111111
$$82$$ 0 0
$$83$$ −10.1751 + 10.1751i −0.122592 + 0.122592i −0.765741 0.643149i $$-0.777627\pi$$
0.643149 + 0.765741i $$0.277627\pi$$
$$84$$ 0 0
$$85$$ 22.5530 22.5530i 0.265329 0.265329i
$$86$$ 0 0
$$87$$ −60.3583 −0.693774
$$88$$ 0 0
$$89$$ 21.9364i 0.246476i 0.992377 + 0.123238i $$0.0393279\pi$$
−0.992377 + 0.123238i $$0.960672\pi$$
$$90$$ 0 0
$$91$$ 68.9850 + 68.9850i 0.758077 + 0.758077i
$$92$$ 0 0
$$93$$ −50.6752 50.6752i −0.544895 0.544895i
$$94$$ 0 0
$$95$$ 34.0444i 0.358362i
$$96$$ 0 0
$$97$$ 107.309 1.10628 0.553140 0.833088i $$-0.313429\pi$$
0.553140 + 0.833088i $$0.313429\pi$$
$$98$$ 0 0
$$99$$ −6.79552 + 6.79552i −0.0686416 + 0.0686416i
$$100$$ 0 0
$$101$$ 100.780 100.780i 0.997824 0.997824i −0.00217389 0.999998i $$-0.500692\pi$$
0.999998 + 0.00217389i $$0.000691973\pi$$
$$102$$ 0 0
$$103$$ 58.0562 0.563653 0.281826 0.959465i $$-0.409060\pi$$
0.281826 + 0.959465i $$0.409060\pi$$
$$104$$ 0 0
$$105$$ 24.7422i 0.235640i
$$106$$ 0 0
$$107$$ −112.747 112.747i −1.05371 1.05371i −0.998473 0.0552381i $$-0.982408\pi$$
−0.0552381 0.998473i $$-0.517592\pi$$
$$108$$ 0 0
$$109$$ 81.1384 + 81.1384i 0.744389 + 0.744389i 0.973419 0.229030i $$-0.0735554\pi$$
−0.229030 + 0.973419i $$0.573555\pi$$
$$110$$ 0 0
$$111$$ 16.1674i 0.145652i
$$112$$ 0 0
$$113$$ −171.844 −1.52074 −0.760371 0.649489i $$-0.774983\pi$$
−0.760371 + 0.649489i $$0.774983\pi$$
$$114$$ 0 0
$$115$$ −33.4571 + 33.4571i −0.290931 + 0.290931i
$$116$$ 0 0
$$117$$ 20.6469 20.6469i 0.176469 0.176469i
$$118$$ 0 0
$$119$$ −224.329 −1.88512
$$120$$ 0 0
$$121$$ 110.738i 0.915190i
$$122$$ 0 0
$$123$$ −57.7439 57.7439i −0.469463 0.469463i
$$124$$ 0 0
$$125$$ −48.3394 48.3394i −0.386715 0.386715i
$$126$$ 0 0
$$127$$ 36.8333i 0.290026i 0.989430 + 0.145013i $$0.0463224\pi$$
−0.989430 + 0.145013i $$0.953678\pi$$
$$128$$ 0 0
$$129$$ −119.588 −0.927042
$$130$$ 0 0
$$131$$ 12.3686 12.3686i 0.0944170 0.0944170i −0.658321 0.752738i $$-0.728733\pi$$
0.752738 + 0.658321i $$0.228733\pi$$
$$132$$ 0 0
$$133$$ 169.316 169.316i 1.27305 1.27305i
$$134$$ 0 0
$$135$$ −7.40521 −0.0548534
$$136$$ 0 0
$$137$$ 145.679i 1.06335i −0.846949 0.531674i $$-0.821563\pi$$
0.846949 0.531674i $$-0.178437\pi$$
$$138$$ 0 0
$$139$$ −82.5709 82.5709i −0.594035 0.594035i 0.344684 0.938719i $$-0.387986\pi$$
−0.938719 + 0.344684i $$0.887986\pi$$
$$140$$ 0 0
$$141$$ 55.8542 + 55.8542i 0.396129 + 0.396129i
$$142$$ 0 0
$$143$$ 31.1791i 0.218036i
$$144$$ 0 0
$$145$$ −49.6629 −0.342503
$$146$$ 0 0
$$147$$ −63.0398 + 63.0398i −0.428842 + 0.428842i
$$148$$ 0 0
$$149$$ −196.248 + 196.248i −1.31710 + 1.31710i −0.401043 + 0.916059i $$0.631352\pi$$
−0.916059 + 0.401043i $$0.868648\pi$$
$$150$$ 0 0
$$151$$ 64.5007 0.427157 0.213578 0.976926i $$-0.431488\pi$$
0.213578 + 0.976926i $$0.431488\pi$$
$$152$$ 0 0
$$153$$ 67.1404i 0.438826i
$$154$$ 0 0
$$155$$ −41.6956 41.6956i −0.269004 0.269004i
$$156$$ 0 0
$$157$$ −54.4202 54.4202i −0.346625 0.346625i 0.512226 0.858851i $$-0.328821\pi$$
−0.858851 + 0.512226i $$0.828821\pi$$
$$158$$ 0 0
$$159$$ 61.5803i 0.387298i
$$160$$ 0 0
$$161$$ 332.789 2.06701
$$162$$ 0 0
$$163$$ −104.803 + 104.803i −0.642961 + 0.642961i −0.951282 0.308321i $$-0.900233\pi$$
0.308321 + 0.951282i $$0.400233\pi$$
$$164$$ 0 0
$$165$$ −5.59136 + 5.59136i −0.0338870 + 0.0338870i
$$166$$ 0 0
$$167$$ 53.3110 0.319228 0.159614 0.987180i $$-0.448975\pi$$
0.159614 + 0.987180i $$0.448975\pi$$
$$168$$ 0 0
$$169$$ 74.2683i 0.439457i
$$170$$ 0 0
$$171$$ −50.6753 50.6753i −0.296347 0.296347i
$$172$$ 0 0
$$173$$ 41.5780 + 41.5780i 0.240335 + 0.240335i 0.816989 0.576654i $$-0.195642\pi$$
−0.576654 + 0.816989i $$0.695642\pi$$
$$174$$ 0 0
$$175$$ 230.231i 1.31561i
$$176$$ 0 0
$$177$$ 15.2842 0.0863513
$$178$$ 0 0
$$179$$ −53.0709 + 53.0709i −0.296486 + 0.296486i −0.839636 0.543150i $$-0.817231\pi$$
0.543150 + 0.839636i $$0.317231\pi$$
$$180$$ 0 0
$$181$$ 66.6042 66.6042i 0.367979 0.367979i −0.498761 0.866740i $$-0.666211\pi$$
0.866740 + 0.498761i $$0.166211\pi$$
$$182$$ 0 0
$$183$$ 88.0625 0.481216
$$184$$ 0 0
$$185$$ 13.3025i 0.0719056i
$$186$$ 0 0
$$187$$ 50.6949 + 50.6949i 0.271096 + 0.271096i
$$188$$ 0 0
$$189$$ 36.8289 + 36.8289i 0.194862 + 0.194862i
$$190$$ 0 0
$$191$$ 113.753i 0.595567i −0.954633 0.297784i $$-0.903753\pi$$
0.954633 0.297784i $$-0.0962474\pi$$
$$192$$ 0 0
$$193$$ −26.5596 −0.137615 −0.0688073 0.997630i $$-0.521919\pi$$
−0.0688073 + 0.997630i $$0.521919\pi$$
$$194$$ 0 0
$$195$$ 16.9883 16.9883i 0.0871193 0.0871193i
$$196$$ 0 0
$$197$$ −51.8935 + 51.8935i −0.263419 + 0.263419i −0.826442 0.563023i $$-0.809638\pi$$
0.563023 + 0.826442i $$0.309638\pi$$
$$198$$ 0 0
$$199$$ −136.741 −0.687140 −0.343570 0.939127i $$-0.611636\pi$$
−0.343570 + 0.939127i $$0.611636\pi$$
$$200$$ 0 0
$$201$$ 24.9959i 0.124358i
$$202$$ 0 0
$$203$$ 246.992 + 246.992i 1.21671 + 1.21671i
$$204$$ 0 0
$$205$$ −47.5118 47.5118i −0.231765 0.231765i
$$206$$ 0 0
$$207$$ 99.6022i 0.481170i
$$208$$ 0 0
$$209$$ −76.5255 −0.366151
$$210$$ 0 0
$$211$$ 141.171 141.171i 0.669057 0.669057i −0.288441 0.957498i $$-0.593137\pi$$
0.957498 + 0.288441i $$0.0931368\pi$$
$$212$$ 0 0
$$213$$ −14.6392 + 14.6392i −0.0687288 + 0.0687288i
$$214$$ 0 0
$$215$$ −98.3975 −0.457663
$$216$$ 0 0
$$217$$ 414.736i 1.91123i
$$218$$ 0 0
$$219$$ 136.354 + 136.354i 0.622620 + 0.622620i
$$220$$ 0 0
$$221$$ −154.027 154.027i −0.696953 0.696953i
$$222$$ 0 0
$$223$$ 122.607i 0.549806i −0.961472 0.274903i $$-0.911354\pi$$
0.961472 0.274903i $$-0.0886457\pi$$
$$224$$ 0 0
$$225$$ 68.9070 0.306253
$$226$$ 0 0
$$227$$ 295.844 295.844i 1.30328 1.30328i 0.377112 0.926168i $$-0.376917\pi$$
0.926168 0.377112i $$-0.123083\pi$$
$$228$$ 0 0
$$229$$ −73.3817 + 73.3817i −0.320444 + 0.320444i −0.848937 0.528493i $$-0.822757\pi$$
0.528493 + 0.848937i $$0.322757\pi$$
$$230$$ 0 0
$$231$$ 55.6159 0.240761
$$232$$ 0 0
$$233$$ 156.229i 0.670509i 0.942128 + 0.335255i $$0.108822\pi$$
−0.942128 + 0.335255i $$0.891178\pi$$
$$234$$ 0 0
$$235$$ 45.9569 + 45.9569i 0.195561 + 0.195561i
$$236$$ 0 0
$$237$$ 5.46274 + 5.46274i 0.0230495 + 0.0230495i
$$238$$ 0 0
$$239$$ 13.1716i 0.0551113i −0.999620 0.0275557i $$-0.991228\pi$$
0.999620 0.0275557i $$-0.00877235\pi$$
$$240$$ 0 0
$$241$$ −189.519 −0.786386 −0.393193 0.919456i $$-0.628630\pi$$
−0.393193 + 0.919456i $$0.628630\pi$$
$$242$$ 0 0
$$243$$ 11.0227 11.0227i 0.0453609 0.0453609i
$$244$$ 0 0
$$245$$ −51.8692 + 51.8692i −0.211711 + 0.211711i
$$246$$ 0 0
$$247$$ 232.508 0.941328
$$248$$ 0 0
$$249$$ 24.9238i 0.100096i
$$250$$ 0 0
$$251$$ 27.4434 + 27.4434i 0.109336 + 0.109336i 0.759658 0.650322i $$-0.225366\pi$$
−0.650322 + 0.759658i $$0.725366\pi$$
$$252$$ 0 0
$$253$$ −75.2053 75.2053i −0.297254 0.297254i
$$254$$ 0 0
$$255$$ 55.2432i 0.216640i
$$256$$ 0 0
$$257$$ 135.375 0.526752 0.263376 0.964693i $$-0.415164\pi$$
0.263376 + 0.964693i $$0.415164\pi$$
$$258$$ 0 0
$$259$$ 66.1586 66.1586i 0.255438 0.255438i
$$260$$ 0 0
$$261$$ 73.9236 73.9236i 0.283232 0.283232i
$$262$$ 0 0
$$263$$ 31.6123 0.120199 0.0600994 0.998192i $$-0.480858\pi$$
0.0600994 + 0.998192i $$0.480858\pi$$
$$264$$ 0 0
$$265$$ 50.6684i 0.191201i
$$266$$ 0 0
$$267$$ −26.8665 26.8665i −0.100624 0.100624i
$$268$$ 0 0
$$269$$ 194.213 + 194.213i 0.721981 + 0.721981i 0.969008 0.247028i $$-0.0794538\pi$$
−0.247028 + 0.969008i $$0.579454\pi$$
$$270$$ 0 0
$$271$$ 291.647i 1.07619i −0.842884 0.538095i $$-0.819144\pi$$
0.842884 0.538095i $$-0.180856\pi$$
$$272$$ 0 0
$$273$$ −168.978 −0.618967
$$274$$ 0 0
$$275$$ 52.0287 52.0287i 0.189195 0.189195i
$$276$$ 0 0
$$277$$ −305.166 + 305.166i −1.10168 + 1.10168i −0.107475 + 0.994208i $$0.534277\pi$$
−0.994208 + 0.107475i $$0.965723\pi$$
$$278$$ 0 0
$$279$$ 124.128 0.444905
$$280$$ 0 0
$$281$$ 211.861i 0.753955i 0.926222 + 0.376978i $$0.123037\pi$$
−0.926222 + 0.376978i $$0.876963\pi$$
$$282$$ 0 0
$$283$$ −105.325 105.325i −0.372175 0.372175i 0.496094 0.868269i $$-0.334767\pi$$
−0.868269 + 0.496094i $$0.834767\pi$$
$$284$$ 0 0
$$285$$ −41.6957 41.6957i −0.146301 0.146301i
$$286$$ 0 0
$$287$$ 472.588i 1.64665i
$$288$$ 0 0
$$289$$ 211.871 0.733117
$$290$$ 0 0
$$291$$ −131.426 + 131.426i −0.451637 + 0.451637i
$$292$$ 0 0
$$293$$ 171.289 171.289i 0.584603 0.584603i −0.351562 0.936165i $$-0.614349\pi$$
0.936165 + 0.351562i $$0.114349\pi$$
$$294$$ 0 0
$$295$$ 12.5758 0.0426300
$$296$$ 0 0
$$297$$ 16.6455i 0.0560456i
$$298$$ 0 0
$$299$$ 228.497 + 228.497i 0.764204 + 0.764204i
$$300$$ 0 0
$$301$$ 489.368 + 489.368i 1.62581 + 1.62581i
$$302$$ 0 0
$$303$$ 246.860i 0.814720i
$$304$$ 0 0
$$305$$ 72.4579 0.237567
$$306$$ 0 0
$$307$$ 27.1124 27.1124i 0.0883140 0.0883140i −0.661570 0.749884i $$-0.730109\pi$$
0.749884 + 0.661570i $$0.230109\pi$$
$$308$$ 0 0
$$309$$ −71.1041 + 71.1041i −0.230110 + 0.230110i
$$310$$ 0 0
$$311$$ 371.124 1.19333 0.596663 0.802492i $$-0.296493\pi$$
0.596663 + 0.802492i $$0.296493\pi$$
$$312$$ 0 0
$$313$$ 374.501i 1.19649i 0.801313 + 0.598245i $$0.204135\pi$$
−0.801313 + 0.598245i $$0.795865\pi$$
$$314$$ 0 0
$$315$$ 30.3029 + 30.3029i 0.0961996 + 0.0961996i
$$316$$ 0 0
$$317$$ 48.5840 + 48.5840i 0.153262 + 0.153262i 0.779573 0.626311i $$-0.215436\pi$$
−0.626311 + 0.779573i $$0.715436\pi$$
$$318$$ 0 0
$$319$$ 111.633i 0.349947i
$$320$$ 0 0
$$321$$ 276.173 0.860352
$$322$$ 0 0
$$323$$ −378.040 + 378.040i −1.17040 + 1.17040i
$$324$$ 0 0
$$325$$ −158.079 + 158.079i −0.486398 + 0.486398i
$$326$$ 0 0
$$327$$ −198.748 −0.607791
$$328$$ 0 0
$$329$$ 457.122i 1.38943i
$$330$$ 0 0
$$331$$ 1.88883 + 1.88883i 0.00570644 + 0.00570644i 0.709954 0.704248i $$-0.248716\pi$$
−0.704248 + 0.709954i $$0.748716\pi$$
$$332$$ 0 0
$$333$$ −19.8009 19.8009i −0.0594622 0.0594622i
$$334$$ 0 0
$$335$$ 20.5667i 0.0613931i
$$336$$ 0 0
$$337$$ −386.980 −1.14831 −0.574154 0.818747i $$-0.694669\pi$$
−0.574154 + 0.818747i $$0.694669\pi$$
$$338$$ 0 0
$$339$$ 210.465 210.465i 0.620840 0.620840i
$$340$$ 0 0
$$341$$ 93.7240 93.7240i 0.274851 0.274851i
$$342$$ 0 0
$$343$$ 24.7757 0.0722325
$$344$$ 0 0
$$345$$ 81.9528i 0.237544i
$$346$$ 0 0
$$347$$ −441.887 441.887i −1.27345 1.27345i −0.944266 0.329183i $$-0.893227\pi$$
−0.329183 0.944266i $$-0.606773\pi$$
$$348$$ 0 0
$$349$$ −119.382 119.382i −0.342068 0.342068i 0.515076 0.857144i $$-0.327764\pi$$
−0.857144 + 0.515076i $$0.827764\pi$$
$$350$$ 0 0
$$351$$ 50.5743i 0.144086i
$$352$$ 0 0
$$353$$ −515.642 −1.46074 −0.730371 0.683050i $$-0.760653\pi$$
−0.730371 + 0.683050i $$0.760653\pi$$
$$354$$ 0 0
$$355$$ −12.0452 + 12.0452i −0.0339301 + 0.0339301i
$$356$$ 0 0
$$357$$ 274.745 274.745i 0.769595 0.769595i
$$358$$ 0 0
$$359$$ 428.264 1.19294 0.596468 0.802637i $$-0.296570\pi$$
0.596468 + 0.802637i $$0.296570\pi$$
$$360$$ 0 0
$$361$$ 209.664i 0.580786i
$$362$$ 0 0
$$363$$ 135.626 + 135.626i 0.373625 + 0.373625i
$$364$$ 0 0
$$365$$ 112.192 + 112.192i 0.307375 + 0.307375i
$$366$$ 0 0
$$367$$ 219.482i 0.598043i −0.954246 0.299021i $$-0.903340\pi$$
0.954246 0.299021i $$-0.0966602\pi$$
$$368$$ 0 0
$$369$$ 141.443 0.383315
$$370$$ 0 0
$$371$$ −251.993 + 251.993i −0.679226 + 0.679226i
$$372$$ 0 0
$$373$$ −425.005 + 425.005i −1.13942 + 1.13942i −0.150870 + 0.988554i $$0.548207\pi$$
−0.988554 + 0.150870i $$0.951793\pi$$
$$374$$ 0 0
$$375$$ 118.407 0.315752
$$376$$ 0 0
$$377$$ 339.175i 0.899669i
$$378$$ 0 0
$$379$$ −365.916 365.916i −0.965476 0.965476i 0.0339473 0.999424i $$-0.489192\pi$$
−0.999424 + 0.0339473i $$0.989192\pi$$
$$380$$ 0 0
$$381$$ −45.1114 45.1114i −0.118403 0.118403i
$$382$$ 0 0
$$383$$ 213.276i 0.556857i −0.960457 0.278428i $$-0.910187\pi$$
0.960457 0.278428i $$-0.0898135\pi$$
$$384$$ 0 0
$$385$$ 45.7608 0.118859
$$386$$ 0 0
$$387$$ 146.465 146.465i 0.378464 0.378464i
$$388$$ 0 0
$$389$$ 210.798 210.798i 0.541898 0.541898i −0.382187 0.924085i $$-0.624829\pi$$
0.924085 + 0.382187i $$0.124829\pi$$
$$390$$ 0 0
$$391$$ −743.037 −1.90035
$$392$$ 0 0
$$393$$ 30.2968i 0.0770912i
$$394$$ 0 0
$$395$$ 4.49475 + 4.49475i 0.0113791 + 0.0113791i
$$396$$ 0 0
$$397$$ −392.907 392.907i −0.989690 0.989690i 0.0102579 0.999947i $$-0.496735\pi$$
−0.999947 + 0.0102579i $$0.996735\pi$$
$$398$$ 0 0
$$399$$ 414.737i 1.03944i
$$400$$ 0 0
$$401$$ 29.3290 0.0731396 0.0365698 0.999331i $$-0.488357\pi$$
0.0365698 + 0.999331i $$0.488357\pi$$
$$402$$ 0 0
$$403$$ −284.762 + 284.762i −0.706606 + 0.706606i
$$404$$ 0 0
$$405$$ 9.06949 9.06949i 0.0223938 0.0223938i
$$406$$ 0 0
$$407$$ −29.9017 −0.0734684
$$408$$ 0 0
$$409$$ 601.115i 1.46972i −0.678219 0.734860i $$-0.737248\pi$$
0.678219 0.734860i $$-0.262752\pi$$
$$410$$ 0 0
$$411$$ 178.419 + 178.419i 0.434110 + 0.434110i
$$412$$ 0 0
$$413$$ −62.5444 62.5444i −0.151439 0.151439i
$$414$$ 0 0
$$415$$ 20.5073i 0.0494153i
$$416$$ 0 0
$$417$$ 202.257 0.485028
$$418$$ 0 0
$$419$$ 518.885 518.885i 1.23839 1.23839i 0.277729 0.960659i $$-0.410418\pi$$
0.960659 0.277729i $$-0.0895819\pi$$
$$420$$ 0 0
$$421$$ 411.213 411.213i 0.976754 0.976754i −0.0229817 0.999736i $$-0.507316\pi$$
0.999736 + 0.0229817i $$0.00731596\pi$$
$$422$$ 0 0
$$423$$ −136.814 −0.323438
$$424$$ 0 0
$$425$$ 514.049i 1.20953i
$$426$$ 0 0
$$427$$ −360.360 360.360i −0.843936 0.843936i
$$428$$ 0 0
$$429$$ 38.1865 + 38.1865i 0.0890128 + 0.0890128i
$$430$$ 0 0
$$431$$ 41.1083i 0.0953789i −0.998862 0.0476895i $$-0.984814\pi$$
0.998862 0.0476895i $$-0.0151858\pi$$
$$432$$ 0 0
$$433$$ −351.682 −0.812199 −0.406100 0.913829i $$-0.633111\pi$$
−0.406100 + 0.913829i $$0.633111\pi$$
$$434$$ 0 0
$$435$$ 60.8244 60.8244i 0.139826 0.139826i
$$436$$ 0 0
$$437$$ 560.819 560.819i 1.28334 1.28334i
$$438$$ 0 0
$$439$$ −775.613 −1.76677 −0.883386 0.468646i $$-0.844742\pi$$
−0.883386 + 0.468646i $$0.844742\pi$$
$$440$$ 0 0
$$441$$ 154.415i 0.350148i
$$442$$ 0 0
$$443$$ 241.372 + 241.372i 0.544858 + 0.544858i 0.924949 0.380091i $$-0.124107\pi$$
−0.380091 + 0.924949i $$0.624107\pi$$
$$444$$ 0 0
$$445$$ −22.1058 22.1058i −0.0496759 0.0496759i
$$446$$ 0 0
$$447$$ 480.708i 1.07541i
$$448$$ 0 0
$$449$$ 266.360 0.593228 0.296614 0.954997i $$-0.404142\pi$$
0.296614 + 0.954997i $$0.404142\pi$$
$$450$$ 0 0
$$451$$ 106.798 106.798i 0.236802 0.236802i
$$452$$ 0 0
$$453$$ −78.9969 + 78.9969i −0.174386 + 0.174386i
$$454$$ 0 0
$$455$$ −139.035 −0.305572
$$456$$ 0 0
$$457$$ 515.244i 1.12745i 0.825963 + 0.563725i $$0.190632\pi$$
−0.825963 + 0.563725i $$0.809368\pi$$
$$458$$ 0 0
$$459$$ −82.2299 82.2299i −0.179150 0.179150i
$$460$$ 0 0
$$461$$ −5.67717 5.67717i −0.0123149 0.0123149i 0.700923 0.713237i $$-0.252772\pi$$
−0.713237 + 0.700923i $$0.752772\pi$$
$$462$$ 0 0
$$463$$ 464.510i 1.00326i 0.865082 + 0.501631i $$0.167267\pi$$
−0.865082 + 0.501631i $$0.832733\pi$$
$$464$$ 0 0
$$465$$ 102.133 0.219641
$$466$$ 0 0
$$467$$ −495.985 + 495.985i −1.06207 + 1.06207i −0.0641248 + 0.997942i $$0.520426\pi$$
−0.997942 + 0.0641248i $$0.979574\pi$$
$$468$$ 0 0
$$469$$ −102.286 + 102.286i −0.218094 + 0.218094i
$$470$$ 0 0
$$471$$ 133.302 0.283018
$$472$$ 0 0
$$473$$ 221.180i 0.467610i
$$474$$ 0 0
$$475$$ 387.987 + 387.987i 0.816815 + 0.816815i
$$476$$ 0 0
$$477$$ 75.4202 + 75.4202i 0.158114 + 0.158114i
$$478$$ 0 0
$$479$$ 378.802i 0.790818i 0.918505 + 0.395409i $$0.129397\pi$$
−0.918505 + 0.395409i $$0.870603\pi$$
$$480$$ 0 0
$$481$$ 90.8504 0.188878
$$482$$ 0 0
$$483$$ −407.582 + 407.582i −0.843855 + 0.843855i
$$484$$ 0 0
$$485$$ −108.138 + 108.138i −0.222964 + 0.222964i
$$486$$ 0 0
$$487$$ 147.446 0.302764 0.151382 0.988475i $$-0.451628\pi$$
0.151382 + 0.988475i $$0.451628\pi$$
$$488$$ 0 0
$$489$$ 256.713i 0.524976i
$$490$$ 0 0
$$491$$ −109.547 109.547i −0.223110 0.223110i 0.586697 0.809807i $$-0.300428\pi$$
−0.809807 + 0.586697i $$0.800428\pi$$
$$492$$ 0 0
$$493$$ −551.473 551.473i −1.11861 1.11861i
$$494$$ 0 0
$$495$$ 13.6960i 0.0276686i
$$496$$ 0 0
$$497$$ 119.810 0.241067
$$498$$ 0 0
$$499$$ 360.523 360.523i 0.722491 0.722491i −0.246621 0.969112i $$-0.579320\pi$$
0.969112 + 0.246621i $$0.0793202\pi$$
$$500$$ 0 0
$$501$$ −65.2924 + 65.2924i −0.130324 + 0.130324i
$$502$$ 0 0
$$503$$ −927.420 −1.84378 −0.921889 0.387454i $$-0.873355\pi$$
−0.921889 + 0.387454i $$0.873355\pi$$
$$504$$ 0 0
$$505$$ 203.117i 0.402211i
$$506$$ 0 0
$$507$$ 90.9597 + 90.9597i 0.179408 + 0.179408i
$$508$$ 0 0
$$509$$ −677.931 677.931i −1.33189 1.33189i −0.903680 0.428208i $$-0.859145\pi$$
−0.428208 0.903680i $$-0.640855\pi$$
$$510$$ 0 0
$$511$$ 1115.95i 2.18385i
$$512$$ 0 0
$$513$$ 124.129 0.241966
$$514$$ 0 0
$$515$$ −58.5045 + 58.5045i −0.113601 + 0.113601i
$$516$$ 0 0
$$517$$ −103.303 + 103.303i −0.199812 + 0.199812i
$$518$$ 0 0
$$519$$ −101.845 −0.196233
$$520$$ 0 0
$$521$$ 143.173i 0.274804i 0.990515 + 0.137402i $$0.0438753\pi$$
−0.990515 + 0.137402i $$0.956125\pi$$
$$522$$ 0 0
$$523$$ −226.187 226.187i −0.432481 0.432481i 0.456991 0.889471i $$-0.348927\pi$$
−0.889471 + 0.456991i $$0.848927\pi$$
$$524$$ 0 0
$$525$$ −281.974 281.974i −0.537094 0.537094i
$$526$$ 0 0
$$527$$ 926.004i 1.75712i
$$528$$ 0 0
$$529$$ 573.288 1.08372
$$530$$ 0 0
$$531$$ −18.7192 + 18.7192i −0.0352528 + 0.0352528i
$$532$$ 0 0
$$533$$ −324.484 + 324.484i −0.608788 + 0.608788i
$$534$$ 0 0
$$535$$ 227.235 0.424739
$$536$$ 0 0
$$537$$ 129.997i 0.242080i
$$538$$ 0 0
$$539$$ −116.592 116.592i −0.216312 0.216312i
$$540$$ 0 0
$$541$$ 156.708 + 156.708i 0.289663 + 0.289663i 0.836947 0.547284i $$-0.184338\pi$$
−0.547284 + 0.836947i $$0.684338\pi$$
$$542$$ 0 0
$$543$$ 163.146i 0.300454i
$$544$$ 0 0
$$545$$ −163.530 −0.300055
$$546$$ 0 0
$$547$$ −247.357 + 247.357i −0.452207 + 0.452207i −0.896086 0.443880i $$-0.853602\pi$$
0.443880 + 0.896086i $$0.353602\pi$$
$$548$$ 0 0
$$549$$ −107.854 + 107.854i −0.196455 + 0.196455i
$$550$$ 0 0
$$551$$ 832.466 1.51083
$$552$$ 0 0
$$553$$ 44.7082i 0.0808466i
$$554$$ 0 0
$$555$$ −16.2922 16.2922i −0.0293553 0.0293553i
$$556$$ 0 0
$$557$$ 661.193 + 661.193i 1.18706 + 1.18706i 0.977876 + 0.209184i $$0.0670808\pi$$
0.209184 + 0.977876i $$0.432919\pi$$
$$558$$ 0 0
$$559$$ 672.011i 1.20217i
$$560$$ 0 0
$$561$$ −124.177 −0.221349
$$562$$ 0 0
$$563$$ −246.685 + 246.685i −0.438162 + 0.438162i −0.891393 0.453231i $$-0.850271\pi$$
0.453231 + 0.891393i $$0.350271\pi$$
$$564$$ 0 0
$$565$$ 173.171 173.171i 0.306497 0.306497i
$$566$$ 0 0
$$567$$ −90.2120 −0.159104
$$568$$ 0 0
$$569$$ 243.567i 0.428061i 0.976827 + 0.214030i $$0.0686592\pi$$
−0.976827 + 0.214030i $$0.931341\pi$$
$$570$$ 0 0
$$571$$ −59.9229 59.9229i −0.104944 0.104944i 0.652685 0.757629i $$-0.273642\pi$$
−0.757629 + 0.652685i $$0.773642\pi$$
$$572$$ 0 0
$$573$$ 139.319 + 139.319i 0.243139 + 0.243139i
$$574$$ 0 0
$$575$$ 762.587i 1.32624i
$$576$$ 0 0
$$577$$ 136.609 0.236757 0.118378 0.992969i $$-0.462230\pi$$
0.118378 + 0.992969i $$0.462230\pi$$
$$578$$ 0 0
$$579$$ 32.5287 32.5287i 0.0561809 0.0561809i
$$580$$ 0 0
$$581$$ −101.991 + 101.991i −0.175543 + 0.175543i
$$582$$ 0 0
$$583$$ 113.893 0.195357
$$584$$ 0 0
$$585$$ 41.6126i 0.0711326i
$$586$$ 0 0
$$587$$ 331.817 + 331.817i 0.565276 + 0.565276i 0.930801 0.365525i $$-0.119111\pi$$
−0.365525 + 0.930801i $$0.619111\pi$$
$$588$$ 0 0
$$589$$ 698.916 + 698.916i 1.18661 + 1.18661i
$$590$$ 0 0
$$591$$ 127.113i 0.215081i
$$592$$ 0 0
$$593$$ 131.285 0.221391 0.110695 0.993854i $$-0.464692\pi$$
0.110695 + 0.993854i $$0.464692\pi$$
$$594$$ 0 0
$$595$$ 226.061 226.061i 0.379934 0.379934i
$$596$$ 0 0
$$597$$ 167.473 167.473i 0.280524 0.280524i
$$598$$ 0 0
$$599$$ −136.119 −0.227243 −0.113621 0.993524i $$-0.536245\pi$$
−0.113621 + 0.993524i $$0.536245\pi$$
$$600$$ 0 0
$$601$$ 498.566i 0.829561i 0.909922 + 0.414780i $$0.136142\pi$$
−0.909922 + 0.414780i $$0.863858\pi$$
$$602$$ 0 0
$$603$$ 30.6136 + 30.6136i 0.0507689 + 0.0507689i
$$604$$ 0 0
$$605$$ 111.593 + 111.593i 0.184451 + 0.184451i
$$606$$ 0 0
$$607$$ 568.740i 0.936969i 0.883472 + 0.468484i $$0.155200\pi$$
−0.883472 + 0.468484i $$0.844800\pi$$
$$608$$ 0 0
$$609$$ −605.005 −0.993441
$$610$$ 0 0
$$611$$ 313.865 313.865i 0.513691 0.513691i
$$612$$ 0 0
$$613$$ 168.441 168.441i 0.274782 0.274782i −0.556240 0.831022i $$-0.687756\pi$$
0.831022 + 0.556240i $$0.187756\pi$$
$$614$$ 0 0
$$615$$ 116.380 0.189235
$$616$$ 0 0
$$617$$ 599.157i 0.971081i −0.874214 0.485541i $$-0.838623\pi$$
0.874214 0.485541i $$-0.161377\pi$$
$$618$$ 0 0
$$619$$ −126.719 126.719i −0.204715 0.204715i 0.597301 0.802017i $$-0.296240\pi$$
−0.802017 + 0.597301i $$0.796240\pi$$
$$620$$ 0 0
$$621$$ 121.987 + 121.987i 0.196437 + 0.196437i
$$622$$ 0 0
$$623$$ 219.881i 0.352939i
$$624$$ 0 0
$$625$$ −476.800 −0.762879
$$626$$ 0 0
$$627$$ 93.7242 93.7242i 0.149480 0.149480i
$$628$$ 0 0
$$629$$ −147.716 + 147.716i −0.234842 + 0.234842i
$$630$$ 0 0
$$631$$ 668.283 1.05909 0.529543 0.848283i $$-0.322363\pi$$
0.529543 + 0.848283i $$0.322363\pi$$
$$632$$ 0 0
$$633$$ 345.797i 0.546283i
$$634$$ 0 0
$$635$$ −37.1177 37.1177i −0.0584531 0.0584531i
$$636$$ 0 0
$$637$$ 354.243 + 354.243i 0.556112 + 0.556112i
$$638$$ 0 0
$$639$$ 35.8586i 0.0561168i
$$640$$ 0 0
$$641$$ 484.574 0.755966 0.377983 0.925813i $$-0.376618\pi$$
0.377983 + 0.925813i $$0.376618\pi$$
$$642$$ 0 0
$$643$$ −75.2980 + 75.2980i −0.117104 + 0.117104i −0.763230 0.646126i $$-0.776388\pi$$
0.646126 + 0.763230i $$0.276388\pi$$
$$644$$ 0 0
$$645$$ 120.512 120.512i 0.186840 0.186840i
$$646$$ 0 0
$$647$$ −582.307 −0.900011 −0.450006 0.893026i $$-0.648578\pi$$
−0.450006 + 0.893026i $$0.648578\pi$$
$$648$$ 0 0
$$649$$ 28.2682i 0.0435565i
$$650$$ 0 0
$$651$$ −507.946 507.946i −0.780255 0.780255i
$$652$$ 0 0
$$653$$ −457.453 457.453i −0.700541 0.700541i 0.263986 0.964527i $$-0.414963\pi$$
−0.964527 + 0.263986i $$0.914963\pi$$
$$654$$ 0 0
$$655$$ 24.9283i 0.0380584i
$$656$$ 0 0
$$657$$ −333.997 −0.508367
$$658$$ 0 0
$$659$$ 430.079 430.079i 0.652623 0.652623i −0.301001 0.953624i $$-0.597321\pi$$
0.953624 + 0.301001i $$0.0973207\pi$$
$$660$$ 0 0
$$661$$ 513.622 513.622i 0.777038 0.777038i −0.202288 0.979326i $$-0.564838\pi$$
0.979326 + 0.202288i $$0.0648376\pi$$
$$662$$ 0 0
$$663$$ 377.287 0.569060
$$664$$ 0 0
$$665$$ 341.246i 0.513152i
$$666$$ 0 0
$$667$$ 818.105 + 818.105i 1.22654 + 1.22654i
$$668$$ 0 0
$$669$$ 150.162 + 150.162i 0.224457 + 0.224457i
$$670$$ 0 0
$$671$$ 162.872i 0.242730i
$$672$$ 0 0
$$673$$ −1112.68 −1.65332 −0.826659 0.562703i $$-0.809761\pi$$
−0.826659 + 0.562703i $$0.809761\pi$$
$$674$$ 0 0
$$675$$ −84.3935 + 84.3935i −0.125027 + 0.125027i
$$676$$ 0 0
$$677$$ −633.271 + 633.271i −0.935408 + 0.935408i −0.998037 0.0626291i $$-0.980051\pi$$
0.0626291 + 0.998037i $$0.480051\pi$$
$$678$$ 0 0
$$679$$ 1075.62 1.58412
$$680$$ 0 0
$$681$$ 724.668i 1.06412i
$$682$$ 0 0
$$683$$ 429.651 + 429.651i 0.629065 + 0.629065i 0.947833 0.318768i $$-0.103269\pi$$
−0.318768 + 0.947833i $$0.603269\pi$$
$$684$$ 0 0
$$685$$ 146.803 + 146.803i 0.214312 + 0.214312i
$$686$$ 0 0
$$687$$ 179.748i 0.261642i
$$688$$ 0 0
$$689$$ −346.042 −0.502239
$$690$$ 0 0
$$691$$ 151.617 151.617i 0.219417 0.219417i −0.588836 0.808253i $$-0.700414\pi$$
0.808253 + 0.588836i $$0.200414\pi$$
$$692$$ 0 0
$$693$$ −68.1153 + 68.1153i −0.0982904 + 0.0982904i
$$694$$ 0 0
$$695$$ 166.417 0.239449
$$696$$ 0 0
$$697$$ 1055.17i 1.51388i
$$698$$ 0 0
$$699$$ −191.340 191.340i −0.273734 0.273734i
$$700$$ 0 0
$$701$$ 920.704 + 920.704i 1.31341 + 1.31341i 0.918882 + 0.394533i $$0.129094\pi$$
0.394533 + 0.918882i $$0.370906\pi$$
$$702$$ 0 0
$$703$$ 222.982i 0.317186i
$$704$$ 0 0
$$705$$ −112.571 −0.159675
$$706$$ 0 0
$$707$$ 1010.18 1010.18i 1.42882 1.42882i
$$708$$ 0 0
$$709$$ −405.348 + 405.348i −0.571718 + 0.571718i −0.932608 0.360890i $$-0.882473\pi$$
0.360890 + 0.932608i $$0.382473\pi$$
$$710$$ 0 0
$$711$$ −13.3809 −0.0188199
$$712$$ 0 0
$$713$$ 1373.72i 1.92667i
$$714$$ 0 0
$$715$$ 31.4199 + 31.4199i 0.0439439 + 0.0439439i
$$716$$ 0 0
$$717$$ 16.1319 + 16.1319i 0.0224991 + 0.0224991i
$$718$$ 0 0
$$719$$ 880.704i 1.22490i −0.790509 0.612450i $$-0.790184\pi$$
0.790509 0.612450i $$-0.209816\pi$$
$$720$$ 0 0
$$721$$ 581.930 0.807115
$$722$$ 0 0
$$723$$ 232.112 232.112i 0.321041 0.321041i
$$724$$ 0 0
$$725$$ −565.983 + 565.983i −0.780667 + 0.780667i
$$726$$ 0 0
$$727$$ 1000.46 1.37615 0.688077 0.725637i $$-0.258455\pi$$
0.688077 + 0.725637i $$0.258455\pi$$
$$728$$ 0 0
$$729$$ 27.0000i 0.0370370i
$$730$$ 0 0
$$731$$ −1092.64 1092.64i −1.49472 1.49472i
$$732$$ 0 0
$$733$$ −540.306 540.306i −0.737116 0.737116i 0.234903 0.972019i $$-0.424523\pi$$
−0.972019 + 0.234903i $$0.924523\pi$$
$$734$$ 0 0
$$735$$ 127.053i 0.172861i
$$736$$ 0 0
$$737$$ 46.2301 0.0627274
$$738$$ 0 0
$$739$$ −893.726 + 893.726i −1.20937 + 1.20937i −0.238142 + 0.971230i $$0.576538\pi$$
−0.971230 + 0.238142i $$0.923462\pi$$
$$740$$ 0 0
$$741$$ −284.763 + 284.763i −0.384296 + 0.384296i
$$742$$ 0 0
$$743$$ 1295.75 1.74394 0.871969 0.489561i $$-0.162843\pi$$
0.871969 + 0.489561i $$0.162843\pi$$
$$744$$ 0 0
$$745$$ 395.527i 0.530909i
$$746$$ 0 0
$$747$$ 30.5253 + 30.5253i 0.0408639 + 0.0408639i
$$748$$ 0 0
$$749$$ −1130.13 1130.13i −1.50885 1.50885i
$$750$$ 0 0
$$751$$ 229.818i 0.306016i 0.988225 + 0.153008i $$0.0488961\pi$$
−0.988225 + 0.153008i $$0.951104\pi$$
$$752$$ 0 0
$$753$$ −67.2223 −0.0892726
$$754$$ 0 0
$$755$$ −64.9987 + 64.9987i −0.0860910 + 0.0860910i
$$756$$ 0 0
$$757$$ 373.678 373.678i 0.493630 0.493630i −0.415818 0.909448i $$-0.636505\pi$$
0.909448 + 0.415818i $$0.136505\pi$$
$$758$$ 0 0
$$759$$ 184.215 0.242707
$$760$$ 0 0
$$761$$ 384.012i 0.504615i −0.967647 0.252307i $$-0.918811\pi$$
0.967647 0.252307i $$-0.0811894\pi$$
$$762$$ 0 0
$$763$$ 813.296 + 813.296i 1.06592 + 1.06592i
$$764$$ 0 0
$$765$$ −67.6589 67.6589i −0.0884429 0.0884429i
$$766$$ 0 0
$$767$$ 85.8874i 0.111978i
$$768$$ 0 0
$$769$$ 865.026 1.12487 0.562436 0.826841i $$-0.309864\pi$$
0.562436 + 0.826841i $$0.309864\pi$$
$$770$$ 0 0
$$771$$ −165.800 + 165.800i −0.215045 + 0.215045i
$$772$$ 0 0
$$773$$ 1.78859 1.78859i 0.00231383 0.00231383i −0.705949 0.708263i $$-0.749479\pi$$
0.708263 + 0.705949i $$0.249479\pi$$
$$774$$ 0 0
$$775$$ −950.368 −1.22628
$$776$$ 0 0
$$777$$ 162.055i 0.208565i
$$778$$ 0 0
$$779$$ 796.409 + 796.409i 1.02235 + 1.02235i
$$780$$ 0 0
$$781$$ −27.0753 27.0753i −0.0346675 0.0346675i
$$782$$ 0 0
$$783$$ 181.075i 0.231258i
$$784$$ 0 0
$$785$$ 109.681 0.139721
$$786$$ 0 0
$$787$$ −143.702 + 143.702i −0.182595 + 0.182595i −0.792485 0.609891i $$-0.791213\pi$$
0.609891 + 0.792485i $$0.291213\pi$$
$$788$$ 0 0
$$789$$ −38.7170 + 38.7170i −0.0490710 + 0.0490710i
$$790$$ 0 0
$$791$$ −1722.49 −2.17761
$$792$$ 0 0
$$793$$ 494.855i 0.624029i
$$794$$ 0 0
$$795$$