# Properties

 Label 300.3.c.e.151.1 Level $300$ Weight $3$ Character 300.151 Analytic conductor $8.174$ Analytic rank $0$ Dimension $8$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$300 = 2^{2} \cdot 3 \cdot 5^{2}$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 300.c (of order $$2$$, degree $$1$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$8.17440793081$$ Analytic rank: $$0$$ Dimension: $$8$$ Coefficient field: 8.0.4069419264.1 Defining polynomial: $$x^{8} - 7 x^{6} + 50 x^{4} - 84 x^{3} + 55 x^{2} - 12 x + 1$$ Coefficient ring: $$\Z[a_1, \ldots, a_{7}]$$ Coefficient ring index: $$2^{8}$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

## Embedding invariants

 Embedding label 151.1 Root $$1.65359 - 0.954702i$$ of defining polynomial Character $$\chi$$ $$=$$ 300.151 Dual form 300.3.c.e.151.2

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-1.97650 - 0.305673i) q^{2} -1.73205i q^{3} +(3.81313 + 1.20833i) q^{4} +(-0.529441 + 3.42340i) q^{6} +0.329898i q^{7} +(-7.16731 - 3.55383i) q^{8} -3.00000 q^{9} +O(q^{10})$$ $$q+(-1.97650 - 0.305673i) q^{2} -1.73205i q^{3} +(3.81313 + 1.20833i) q^{4} +(-0.529441 + 3.42340i) q^{6} +0.329898i q^{7} +(-7.16731 - 3.55383i) q^{8} -3.00000 q^{9} +20.4920i q^{11} +(2.09288 - 6.60453i) q^{12} -0.416712 q^{13} +(0.100841 - 0.652044i) q^{14} +(13.0799 + 9.21501i) q^{16} -18.5884 q^{17} +(5.92951 + 0.917019i) q^{18} -12.4503i q^{19} +0.571400 q^{21} +(6.26384 - 40.5024i) q^{22} +23.2304i q^{23} +(-6.15542 + 12.4141i) q^{24} +(0.823633 + 0.127378i) q^{26} +5.19615i q^{27} +(-0.398624 + 1.25794i) q^{28} -23.9166 q^{29} +42.0148i q^{31} +(-23.0357 - 22.2117i) q^{32} +35.4931 q^{33} +(36.7400 + 5.68197i) q^{34} +(-11.4394 - 3.62498i) q^{36} +50.9523 q^{37} +(-3.80573 + 24.6081i) q^{38} +0.721767i q^{39} +46.7073 q^{41} +(-1.12937 - 0.174661i) q^{42} +55.5866i q^{43} +(-24.7610 + 78.1385i) q^{44} +(7.10090 - 45.9149i) q^{46} +81.7616i q^{47} +(15.9609 - 22.6550i) q^{48} +48.8912 q^{49} +32.1960i q^{51} +(-1.58898 - 0.503524i) q^{52} -29.9744 q^{53} +(1.58832 - 10.2702i) q^{54} +(1.17240 - 2.36448i) q^{56} -21.5646 q^{57} +(47.2713 + 7.31067i) q^{58} -24.3311i q^{59} -74.8416 q^{61} +(12.8428 - 83.0424i) q^{62} -0.989693i q^{63} +(38.7406 + 50.9428i) q^{64} +(-70.1523 - 10.8493i) q^{66} +72.8008i q^{67} +(-70.8799 - 22.4608i) q^{68} +40.2362 q^{69} -39.2803i q^{71} +(21.5019 + 10.6615i) q^{72} -46.5814 q^{73} +(-100.707 - 15.5747i) q^{74} +(15.0441 - 47.4747i) q^{76} -6.76026 q^{77} +(0.220625 - 1.42657i) q^{78} -101.920i q^{79} +9.00000 q^{81} +(-92.3170 - 14.2771i) q^{82} +5.88913i q^{83} +(2.17882 + 0.690438i) q^{84} +(16.9913 - 109.867i) q^{86} +41.4248i q^{87} +(72.8250 - 146.872i) q^{88} -61.0100 q^{89} -0.137472i q^{91} +(-28.0699 + 88.5804i) q^{92} +72.7718 q^{93} +(24.9923 - 161.602i) q^{94} +(-38.4717 + 39.8989i) q^{96} +95.5437 q^{97} +(-96.6335 - 14.9447i) q^{98} -61.4759i q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$8q - 2q^{2} - 8q^{4} - 6q^{6} - 20q^{8} - 24q^{9} + O(q^{10})$$ $$8q - 2q^{2} - 8q^{4} - 6q^{6} - 20q^{8} - 24q^{9} - 8q^{13} + 22q^{14} + 40q^{16} + 6q^{18} + 24q^{21} - 4q^{22} - 36q^{24} - 66q^{26} - 104q^{28} - 32q^{29} - 112q^{32} + 124q^{34} + 24q^{36} + 176q^{37} + 170q^{38} - 16q^{41} - 54q^{42} + 40q^{44} - 76q^{46} - 24q^{48} + 16q^{49} - 56q^{52} + 304q^{53} + 18q^{54} - 172q^{56} - 72q^{57} + 12q^{58} + 136q^{61} + 238q^{62} + 16q^{64} - 108q^{66} - 88q^{68} - 96q^{69} + 60q^{72} - 240q^{73} - 108q^{74} + 120q^{76} + 384q^{77} - 150q^{78} + 72q^{81} - 320q^{82} - 144q^{84} + 214q^{86} + 200q^{88} + 128q^{89} - 312q^{92} - 72q^{93} + 12q^{94} + 96q^{96} - 216q^{97} - 60q^{98} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/300\mathbb{Z}\right)^\times$$.

 $$n$$ $$101$$ $$151$$ $$277$$ $$\chi(n)$$ $$1$$ $$-1$$ $$1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −1.97650 0.305673i −0.988251 0.152836i
$$3$$ 1.73205i 0.577350i
$$4$$ 3.81313 + 1.20833i 0.953282 + 0.302082i
$$5$$ 0 0
$$6$$ −0.529441 + 3.42340i −0.0882402 + 0.570567i
$$7$$ 0.329898i 0.0471283i 0.999722 + 0.0235641i $$0.00750139\pi$$
−0.999722 + 0.0235641i $$0.992499\pi$$
$$8$$ −7.16731 3.55383i −0.895913 0.444229i
$$9$$ −3.00000 −0.333333
$$10$$ 0 0
$$11$$ 20.4920i 1.86291i 0.363861 + 0.931453i $$0.381458\pi$$
−0.363861 + 0.931453i $$0.618542\pi$$
$$12$$ 2.09288 6.60453i 0.174407 0.550378i
$$13$$ −0.416712 −0.0320548 −0.0160274 0.999872i $$-0.505102\pi$$
−0.0160274 + 0.999872i $$0.505102\pi$$
$$14$$ 0.100841 0.652044i 0.00720292 0.0465746i
$$15$$ 0 0
$$16$$ 13.0799 + 9.21501i 0.817493 + 0.575938i
$$17$$ −18.5884 −1.09343 −0.546717 0.837317i $$-0.684123\pi$$
−0.546717 + 0.837317i $$0.684123\pi$$
$$18$$ 5.92951 + 0.917019i 0.329417 + 0.0509455i
$$19$$ 12.4503i 0.655281i −0.944803 0.327640i $$-0.893747\pi$$
0.944803 0.327640i $$-0.106253\pi$$
$$20$$ 0 0
$$21$$ 0.571400 0.0272095
$$22$$ 6.26384 40.5024i 0.284720 1.84102i
$$23$$ 23.2304i 1.01002i 0.863114 + 0.505008i $$0.168511\pi$$
−0.863114 + 0.505008i $$0.831489\pi$$
$$24$$ −6.15542 + 12.4141i −0.256476 + 0.517256i
$$25$$ 0 0
$$26$$ 0.823633 + 0.127378i 0.0316782 + 0.00489914i
$$27$$ 5.19615i 0.192450i
$$28$$ −0.398624 + 1.25794i −0.0142366 + 0.0449265i
$$29$$ −23.9166 −0.824712 −0.412356 0.911023i $$-0.635294\pi$$
−0.412356 + 0.911023i $$0.635294\pi$$
$$30$$ 0 0
$$31$$ 42.0148i 1.35532i 0.735377 + 0.677658i $$0.237005\pi$$
−0.735377 + 0.677658i $$0.762995\pi$$
$$32$$ −23.0357 22.2117i −0.719865 0.694115i
$$33$$ 35.4931 1.07555
$$34$$ 36.7400 + 5.68197i 1.08059 + 0.167117i
$$35$$ 0 0
$$36$$ −11.4394 3.62498i −0.317761 0.100694i
$$37$$ 50.9523 1.37709 0.688545 0.725194i $$-0.258250\pi$$
0.688545 + 0.725194i $$0.258250\pi$$
$$38$$ −3.80573 + 24.6081i −0.100151 + 0.647582i
$$39$$ 0.721767i 0.0185068i
$$40$$ 0 0
$$41$$ 46.7073 1.13920 0.569601 0.821921i $$-0.307098\pi$$
0.569601 + 0.821921i $$0.307098\pi$$
$$42$$ −1.12937 0.174661i −0.0268898 0.00415861i
$$43$$ 55.5866i 1.29271i 0.763036 + 0.646356i $$0.223708\pi$$
−0.763036 + 0.646356i $$0.776292\pi$$
$$44$$ −24.7610 + 78.1385i −0.562750 + 1.77588i
$$45$$ 0 0
$$46$$ 7.10090 45.9149i 0.154367 0.998151i
$$47$$ 81.7616i 1.73961i 0.493397 + 0.869804i $$0.335755\pi$$
−0.493397 + 0.869804i $$0.664245\pi$$
$$48$$ 15.9609 22.6550i 0.332518 0.471980i
$$49$$ 48.8912 0.997779
$$50$$ 0 0
$$51$$ 32.1960i 0.631295i
$$52$$ −1.58898 0.503524i −0.0305572 0.00968316i
$$53$$ −29.9744 −0.565554 −0.282777 0.959186i $$-0.591256\pi$$
−0.282777 + 0.959186i $$0.591256\pi$$
$$54$$ 1.58832 10.2702i 0.0294134 0.190189i
$$55$$ 0 0
$$56$$ 1.17240 2.36448i 0.0209357 0.0422228i
$$57$$ −21.5646 −0.378326
$$58$$ 47.2713 + 7.31067i 0.815023 + 0.126046i
$$59$$ 24.3311i 0.412391i −0.978511 0.206196i $$-0.933892\pi$$
0.978511 0.206196i $$-0.0661083\pi$$
$$60$$ 0 0
$$61$$ −74.8416 −1.22691 −0.613456 0.789729i $$-0.710221\pi$$
−0.613456 + 0.789729i $$0.710221\pi$$
$$62$$ 12.8428 83.0424i 0.207142 1.33939i
$$63$$ 0.989693i 0.0157094i
$$64$$ 38.7406 + 50.9428i 0.605321 + 0.795981i
$$65$$ 0 0
$$66$$ −70.1523 10.8493i −1.06291 0.164383i
$$67$$ 72.8008i 1.08658i 0.839545 + 0.543290i $$0.182822\pi$$
−0.839545 + 0.543290i $$0.817178\pi$$
$$68$$ −70.8799 22.4608i −1.04235 0.330307i
$$69$$ 40.2362 0.583133
$$70$$ 0 0
$$71$$ 39.2803i 0.553244i −0.960979 0.276622i $$-0.910785\pi$$
0.960979 0.276622i $$-0.0892150\pi$$
$$72$$ 21.5019 + 10.6615i 0.298638 + 0.148076i
$$73$$ −46.5814 −0.638101 −0.319051 0.947738i $$-0.603364\pi$$
−0.319051 + 0.947738i $$0.603364\pi$$
$$74$$ −100.707 15.5747i −1.36091 0.210469i
$$75$$ 0 0
$$76$$ 15.0441 47.4747i 0.197948 0.624667i
$$77$$ −6.76026 −0.0877955
$$78$$ 0.220625 1.42657i 0.00282852 0.0182894i
$$79$$ 101.920i 1.29012i −0.764131 0.645062i $$-0.776832\pi$$
0.764131 0.645062i $$-0.223168\pi$$
$$80$$ 0 0
$$81$$ 9.00000 0.111111
$$82$$ −92.3170 14.2771i −1.12582 0.174112i
$$83$$ 5.88913i 0.0709534i 0.999371 + 0.0354767i $$0.0112950\pi$$
−0.999371 + 0.0354767i $$0.988705\pi$$
$$84$$ 2.17882 + 0.690438i 0.0259383 + 0.00821950i
$$85$$ 0 0
$$86$$ 16.9913 109.867i 0.197574 1.27752i
$$87$$ 41.4248i 0.476148i
$$88$$ 72.8250 146.872i 0.827557 1.66900i
$$89$$ −61.0100 −0.685506 −0.342753 0.939426i $$-0.611359\pi$$
−0.342753 + 0.939426i $$0.611359\pi$$
$$90$$ 0 0
$$91$$ 0.137472i 0.00151069i
$$92$$ −28.0699 + 88.5804i −0.305108 + 0.962831i
$$93$$ 72.7718 0.782492
$$94$$ 24.9923 161.602i 0.265876 1.71917i
$$95$$ 0 0
$$96$$ −38.4717 + 39.8989i −0.400747 + 0.415614i
$$97$$ 95.5437 0.984987 0.492494 0.870316i $$-0.336086\pi$$
0.492494 + 0.870316i $$0.336086\pi$$
$$98$$ −96.6335 14.9447i −0.986057 0.152497i
$$99$$ 61.4759i 0.620969i
$$100$$ 0 0
$$101$$ 162.675 1.61064 0.805322 0.592838i $$-0.201992\pi$$
0.805322 + 0.592838i $$0.201992\pi$$
$$102$$ 9.84145 63.6355i 0.0964848 0.623878i
$$103$$ 158.196i 1.53588i −0.640521 0.767941i $$-0.721282\pi$$
0.640521 0.767941i $$-0.278718\pi$$
$$104$$ 2.98670 + 1.48092i 0.0287183 + 0.0142397i
$$105$$ 0 0
$$106$$ 59.2445 + 9.16236i 0.558910 + 0.0864373i
$$107$$ 18.1827i 0.169932i −0.996384 0.0849660i $$-0.972922\pi$$
0.996384 0.0849660i $$-0.0270782\pi$$
$$108$$ −6.27865 + 19.8136i −0.0581357 + 0.183459i
$$109$$ −156.842 −1.43891 −0.719457 0.694537i $$-0.755609\pi$$
−0.719457 + 0.694537i $$0.755609\pi$$
$$110$$ 0 0
$$111$$ 88.2520i 0.795063i
$$112$$ −3.04001 + 4.31503i −0.0271430 + 0.0385270i
$$113$$ −98.7245 −0.873668 −0.436834 0.899542i $$-0.643900\pi$$
−0.436834 + 0.899542i $$0.643900\pi$$
$$114$$ 42.6225 + 6.59172i 0.373882 + 0.0578221i
$$115$$ 0 0
$$116$$ −91.1972 28.8991i −0.786183 0.249130i
$$117$$ 1.25014 0.0106849
$$118$$ −7.43735 + 48.0904i −0.0630284 + 0.407546i
$$119$$ 6.13227i 0.0515317i
$$120$$ 0 0
$$121$$ −298.921 −2.47042
$$122$$ 147.925 + 22.8770i 1.21250 + 0.187517i
$$123$$ 80.8994i 0.657718i
$$124$$ −50.7676 + 160.208i −0.409416 + 1.29200i
$$125$$ 0 0
$$126$$ −0.302523 + 1.95613i −0.00240097 + 0.0155249i
$$127$$ 27.0938i 0.213337i −0.994295 0.106669i $$-0.965982\pi$$
0.994295 0.106669i $$-0.0340184\pi$$
$$128$$ −60.9990 112.531i −0.476555 0.879145i
$$129$$ 96.2789 0.746348
$$130$$ 0 0
$$131$$ 4.45811i 0.0340314i 0.999855 + 0.0170157i $$0.00541653\pi$$
−0.999855 + 0.0170157i $$0.994583\pi$$
$$132$$ 135.340 + 42.8873i 1.02530 + 0.324904i
$$133$$ 4.10734 0.0308822
$$134$$ 22.2533 143.891i 0.166069 1.07381i
$$135$$ 0 0
$$136$$ 133.229 + 66.0600i 0.979622 + 0.485735i
$$137$$ −181.700 −1.32628 −0.663139 0.748496i $$-0.730776\pi$$
−0.663139 + 0.748496i $$0.730776\pi$$
$$138$$ −79.5270 12.2991i −0.576282 0.0891241i
$$139$$ 223.419i 1.60733i 0.595083 + 0.803664i $$0.297119\pi$$
−0.595083 + 0.803664i $$0.702881\pi$$
$$140$$ 0 0
$$141$$ 141.615 1.00436
$$142$$ −12.0069 + 77.6377i −0.0845559 + 0.546744i
$$143$$ 8.53925i 0.0597151i
$$144$$ −39.2397 27.6450i −0.272498 0.191979i
$$145$$ 0 0
$$146$$ 92.0683 + 14.2387i 0.630604 + 0.0975251i
$$147$$ 84.6820i 0.576068i
$$148$$ 194.288 + 61.5670i 1.31275 + 0.415994i
$$149$$ 123.867 0.831324 0.415662 0.909519i $$-0.363550\pi$$
0.415662 + 0.909519i $$0.363550\pi$$
$$150$$ 0 0
$$151$$ 76.0961i 0.503948i −0.967734 0.251974i $$-0.918920\pi$$
0.967734 0.251974i $$-0.0810797\pi$$
$$152$$ −44.2464 + 89.2353i −0.291095 + 0.587075i
$$153$$ 55.7651 0.364478
$$154$$ 13.3617 + 2.06643i 0.0867641 + 0.0134184i
$$155$$ 0 0
$$156$$ −0.872130 + 2.75219i −0.00559058 + 0.0176422i
$$157$$ 34.2940 0.218433 0.109217 0.994018i $$-0.465166\pi$$
0.109217 + 0.994018i $$0.465166\pi$$
$$158$$ −31.1541 + 201.445i −0.197178 + 1.27497i
$$159$$ 51.9172i 0.326523i
$$160$$ 0 0
$$161$$ −7.66365 −0.0476003
$$162$$ −17.7885 2.75106i −0.109806 0.0169818i
$$163$$ 165.538i 1.01557i 0.861483 + 0.507786i $$0.169536\pi$$
−0.861483 + 0.507786i $$0.830464\pi$$
$$164$$ 178.101 + 56.4377i 1.08598 + 0.344132i
$$165$$ 0 0
$$166$$ 1.80015 11.6399i 0.0108443 0.0701198i
$$167$$ 83.6064i 0.500637i −0.968164 0.250319i $$-0.919465\pi$$
0.968164 0.250319i $$-0.0805353\pi$$
$$168$$ −4.09540 2.03066i −0.0243774 0.0120873i
$$169$$ −168.826 −0.998972
$$170$$ 0 0
$$171$$ 37.3510i 0.218427i
$$172$$ −67.1668 + 211.959i −0.390505 + 1.23232i
$$173$$ 192.900 1.11503 0.557513 0.830168i $$-0.311756\pi$$
0.557513 + 0.830168i $$0.311756\pi$$
$$174$$ 12.6625 81.8763i 0.0727727 0.470554i
$$175$$ 0 0
$$176$$ −188.834 + 268.033i −1.07292 + 1.52291i
$$177$$ −42.1427 −0.238094
$$178$$ 120.587 + 18.6491i 0.677452 + 0.104770i
$$179$$ 120.939i 0.675637i 0.941211 + 0.337819i $$0.109689\pi$$
−0.941211 + 0.337819i $$0.890311\pi$$
$$180$$ 0 0
$$181$$ −107.583 −0.594381 −0.297191 0.954818i $$-0.596050\pi$$
−0.297191 + 0.954818i $$0.596050\pi$$
$$182$$ −0.0420216 + 0.271715i −0.000230888 + 0.00149294i
$$183$$ 129.629i 0.708357i
$$184$$ 82.5569 166.499i 0.448679 0.904887i
$$185$$ 0 0
$$186$$ −143.834 22.2444i −0.773299 0.119593i
$$187$$ 380.913i 2.03697i
$$188$$ −98.7947 + 311.767i −0.525504 + 1.65834i
$$189$$ −1.71420 −0.00906984
$$190$$ 0 0
$$191$$ 279.706i 1.46443i −0.681075 0.732214i $$-0.738487\pi$$
0.681075 0.732214i $$-0.261513\pi$$
$$192$$ 88.2355 67.1006i 0.459560 0.349482i
$$193$$ −102.534 −0.531263 −0.265632 0.964075i $$-0.585580\pi$$
−0.265632 + 0.964075i $$0.585580\pi$$
$$194$$ −188.842 29.2051i −0.973415 0.150542i
$$195$$ 0 0
$$196$$ 186.428 + 59.0765i 0.951165 + 0.301411i
$$197$$ 38.9632 0.197783 0.0988913 0.995098i $$-0.468470\pi$$
0.0988913 + 0.995098i $$0.468470\pi$$
$$198$$ −18.7915 + 121.507i −0.0949067 + 0.613673i
$$199$$ 147.646i 0.741940i 0.928645 + 0.370970i $$0.120975\pi$$
−0.928645 + 0.370970i $$0.879025\pi$$
$$200$$ 0 0
$$201$$ 126.095 0.627337
$$202$$ −321.528 49.7254i −1.59172 0.246165i
$$203$$ 7.89005i 0.0388672i
$$204$$ −38.9033 + 122.768i −0.190703 + 0.601802i
$$205$$ 0 0
$$206$$ −48.3562 + 312.674i −0.234739 + 1.51784i
$$207$$ 69.6912i 0.336672i
$$208$$ −5.45055 3.84001i −0.0262046 0.0184616i
$$209$$ 255.132 1.22073
$$210$$ 0 0
$$211$$ 233.336i 1.10586i 0.833229 + 0.552928i $$0.186490\pi$$
−0.833229 + 0.552928i $$0.813510\pi$$
$$212$$ −114.296 36.2189i −0.539133 0.170844i
$$213$$ −68.0355 −0.319416
$$214$$ −5.55797 + 35.9382i −0.0259718 + 0.167936i
$$215$$ 0 0
$$216$$ 18.4663 37.2424i 0.0854919 0.172419i
$$217$$ −13.8606 −0.0638737
$$218$$ 309.998 + 47.9422i 1.42201 + 0.219918i
$$219$$ 80.6813i 0.368408i
$$220$$ 0 0
$$221$$ 7.74600 0.0350498
$$222$$ −26.9762 + 174.430i −0.121515 + 0.785722i
$$223$$ 82.7105i 0.370899i −0.982654 0.185450i $$-0.940626\pi$$
0.982654 0.185450i $$-0.0593741\pi$$
$$224$$ 7.32758 7.59941i 0.0327124 0.0339260i
$$225$$ 0 0
$$226$$ 195.129 + 30.1774i 0.863403 + 0.133528i
$$227$$ 361.534i 1.59266i −0.604862 0.796330i $$-0.706772\pi$$
0.604862 0.796330i $$-0.293228\pi$$
$$228$$ −82.2286 26.0571i −0.360652 0.114286i
$$229$$ 121.818 0.531955 0.265977 0.963979i $$-0.414305\pi$$
0.265977 + 0.963979i $$0.414305\pi$$
$$230$$ 0 0
$$231$$ 11.7091i 0.0506888i
$$232$$ 171.418 + 84.9957i 0.738870 + 0.366361i
$$233$$ 136.615 0.586329 0.293164 0.956062i $$-0.405292\pi$$
0.293164 + 0.956062i $$0.405292\pi$$
$$234$$ −2.47090 0.382133i −0.0105594 0.00163305i
$$235$$ 0 0
$$236$$ 29.3999 92.7775i 0.124576 0.393125i
$$237$$ −176.530 −0.744853
$$238$$ −1.87447 + 12.1204i −0.00787592 + 0.0509262i
$$239$$ 56.4632i 0.236248i 0.992999 + 0.118124i $$0.0376880\pi$$
−0.992999 + 0.118124i $$0.962312\pi$$
$$240$$ 0 0
$$241$$ −2.24158 −0.00930117 −0.00465059 0.999989i $$-0.501480\pi$$
−0.00465059 + 0.999989i $$0.501480\pi$$
$$242$$ 590.818 + 91.3720i 2.44140 + 0.377570i
$$243$$ 15.5885i 0.0641500i
$$244$$ −285.381 90.4331i −1.16959 0.370627i
$$245$$ 0 0
$$246$$ −24.7287 + 159.898i −0.100523 + 0.649991i
$$247$$ 5.18820i 0.0210049i
$$248$$ 149.314 301.133i 0.602071 1.21425i
$$249$$ 10.2003 0.0409650
$$250$$ 0 0
$$251$$ 395.809i 1.57693i 0.615081 + 0.788464i $$0.289123\pi$$
−0.615081 + 0.788464i $$0.710877\pi$$
$$252$$ 1.19587 3.77383i 0.00474553 0.0149755i
$$253$$ −476.036 −1.88157
$$254$$ −8.28184 + 53.5510i −0.0326057 + 0.210831i
$$255$$ 0 0
$$256$$ 86.1671 + 241.063i 0.336590 + 0.941651i
$$257$$ 109.778 0.427151 0.213576 0.976927i $$-0.431489\pi$$
0.213576 + 0.976927i $$0.431489\pi$$
$$258$$ −190.295 29.4298i −0.737579 0.114069i
$$259$$ 16.8091i 0.0648998i
$$260$$ 0 0
$$261$$ 71.7499 0.274904
$$262$$ 1.36272 8.81147i 0.00520124 0.0336316i
$$263$$ 327.702i 1.24601i −0.782216 0.623007i $$-0.785911\pi$$
0.782216 0.623007i $$-0.214089\pi$$
$$264$$ −254.390 126.137i −0.963599 0.477790i
$$265$$ 0 0
$$266$$ −8.11816 1.25550i −0.0305194 0.00471993i
$$267$$ 105.673i 0.395777i
$$268$$ −87.9672 + 277.599i −0.328236 + 1.03582i
$$269$$ −130.032 −0.483392 −0.241696 0.970352i $$-0.577704\pi$$
−0.241696 + 0.970352i $$0.577704\pi$$
$$270$$ 0 0
$$271$$ 329.669i 1.21649i −0.793750 0.608245i $$-0.791874\pi$$
0.793750 0.608245i $$-0.208126\pi$$
$$272$$ −243.134 171.292i −0.893875 0.629751i
$$273$$ −0.238109 −0.000872195
$$274$$ 359.131 + 55.5408i 1.31070 + 0.202704i
$$275$$ 0 0
$$276$$ 153.426 + 48.6185i 0.555891 + 0.176154i
$$277$$ 304.124 1.09792 0.548960 0.835849i $$-0.315024\pi$$
0.548960 + 0.835849i $$0.315024\pi$$
$$278$$ 68.2930 441.588i 0.245658 1.58844i
$$279$$ 126.044i 0.451772i
$$280$$ 0 0
$$281$$ 240.099 0.854446 0.427223 0.904146i $$-0.359492\pi$$
0.427223 + 0.904146i $$0.359492\pi$$
$$282$$ −279.903 43.2879i −0.992563 0.153503i
$$283$$ 86.6730i 0.306265i 0.988206 + 0.153133i $$0.0489362\pi$$
−0.988206 + 0.153133i $$0.951064\pi$$
$$284$$ 47.4635 149.781i 0.167125 0.527398i
$$285$$ 0 0
$$286$$ −2.61022 + 16.8779i −0.00912664 + 0.0590135i
$$287$$ 15.4086i 0.0536886i
$$288$$ 69.1070 + 66.6350i 0.239955 + 0.231372i
$$289$$ 56.5280 0.195599
$$290$$ 0 0
$$291$$ 165.487i 0.568683i
$$292$$ −177.621 56.2856i −0.608290 0.192759i
$$293$$ 390.339 1.33222 0.666108 0.745855i $$-0.267959\pi$$
0.666108 + 0.745855i $$0.267959\pi$$
$$294$$ −25.8850 + 167.374i −0.0880442 + 0.569300i
$$295$$ 0 0
$$296$$ −365.191 181.076i −1.23375 0.611743i
$$297$$ −106.479 −0.358517
$$298$$ −244.824 37.8629i −0.821557 0.127057i
$$299$$ 9.68038i 0.0323759i
$$300$$ 0 0
$$301$$ −18.3379 −0.0609233
$$302$$ −23.2605 + 150.404i −0.0770216 + 0.498027i
$$303$$ 281.761i 0.929906i
$$304$$ 114.730 162.849i 0.377401 0.535687i
$$305$$ 0 0
$$306$$ −110.220 17.0459i −0.360196 0.0557056i
$$307$$ 60.2318i 0.196195i 0.995177 + 0.0980973i $$0.0312757\pi$$
−0.995177 + 0.0980973i $$0.968724\pi$$
$$308$$ −25.7777 8.16860i −0.0836939 0.0265214i
$$309$$ −274.003 −0.886741
$$310$$ 0 0
$$311$$ 106.594i 0.342747i −0.985206 0.171373i $$-0.945180\pi$$
0.985206 0.171373i $$-0.0548205\pi$$
$$312$$ 2.56504 5.17312i 0.00822127 0.0165805i
$$313$$ −46.2243 −0.147682 −0.0738408 0.997270i $$-0.523526\pi$$
−0.0738408 + 0.997270i $$0.523526\pi$$
$$314$$ −67.7823 10.4828i −0.215867 0.0333846i
$$315$$ 0 0
$$316$$ 123.152 388.633i 0.389723 1.22985i
$$317$$ −8.36780 −0.0263969 −0.0131984 0.999913i $$-0.504201\pi$$
−0.0131984 + 0.999913i $$0.504201\pi$$
$$318$$ 15.8697 102.614i 0.0499046 0.322687i
$$319$$ 490.099i 1.53636i
$$320$$ 0 0
$$321$$ −31.4934 −0.0981103
$$322$$ 15.1472 + 2.34257i 0.0470411 + 0.00727507i
$$323$$ 231.432i 0.716506i
$$324$$ 34.3182 + 10.8749i 0.105920 + 0.0335646i
$$325$$ 0 0
$$326$$ 50.6006 327.187i 0.155217 1.00364i
$$327$$ 271.658i 0.830757i
$$328$$ −334.765 165.990i −1.02063 0.506066i
$$329$$ −26.9730 −0.0819847
$$330$$ 0 0
$$331$$ 111.072i 0.335564i 0.985824 + 0.167782i $$0.0536605\pi$$
−0.985824 + 0.167782i $$0.946339\pi$$
$$332$$ −7.11600 + 22.4560i −0.0214337 + 0.0676386i
$$333$$ −152.857 −0.459030
$$334$$ −25.5562 + 165.248i −0.0765156 + 0.494755i
$$335$$ 0 0
$$336$$ 7.47385 + 5.26546i 0.0222436 + 0.0156710i
$$337$$ −231.853 −0.687990 −0.343995 0.938972i $$-0.611780\pi$$
−0.343995 + 0.938972i $$0.611780\pi$$
$$338$$ 333.686 + 51.6057i 0.987236 + 0.152679i
$$339$$ 170.996i 0.504412i
$$340$$ 0 0
$$341$$ −860.966 −2.52483
$$342$$ 11.4172 73.8244i 0.0333836 0.215861i
$$343$$ 32.2941i 0.0941518i
$$344$$ 197.546 398.406i 0.574260 1.15816i
$$345$$ 0 0
$$346$$ −381.266 58.9642i −1.10193 0.170417i
$$347$$ 402.088i 1.15875i 0.815059 + 0.579377i $$0.196704\pi$$
−0.815059 + 0.579377i $$0.803296\pi$$
$$348$$ −50.0548 + 157.958i −0.143835 + 0.453903i
$$349$$ −163.284 −0.467864 −0.233932 0.972253i $$-0.575159\pi$$
−0.233932 + 0.972253i $$0.575159\pi$$
$$350$$ 0 0
$$351$$ 2.16530i 0.00616894i
$$352$$ 455.161 472.046i 1.29307 1.34104i
$$353$$ 175.851 0.498161 0.249081 0.968483i $$-0.419872\pi$$
0.249081 + 0.968483i $$0.419872\pi$$
$$354$$ 83.2951 + 12.8819i 0.235297 + 0.0363895i
$$355$$ 0 0
$$356$$ −232.639 73.7201i −0.653481 0.207079i
$$357$$ −10.6214 −0.0297518
$$358$$ 36.9678 239.037i 0.103262 0.667700i
$$359$$ 345.628i 0.962753i −0.876514 0.481377i $$-0.840137\pi$$
0.876514 0.481377i $$-0.159863\pi$$
$$360$$ 0 0
$$361$$ 205.989 0.570607
$$362$$ 212.638 + 32.8852i 0.587398 + 0.0908431i
$$363$$ 517.746i 1.42630i
$$364$$ 0.166112 0.524200i 0.000456351 0.00144011i
$$365$$ 0 0
$$366$$ 39.6242 256.213i 0.108263 0.700035i
$$367$$ 728.998i 1.98637i 0.116546 + 0.993185i $$0.462818\pi$$
−0.116546 + 0.993185i $$0.537182\pi$$
$$368$$ −214.068 + 303.851i −0.581707 + 0.825682i
$$369$$ −140.122 −0.379734
$$370$$ 0 0
$$371$$ 9.88848i 0.0266536i
$$372$$ 277.488 + 87.9321i 0.745936 + 0.236377i
$$373$$ −46.6749 −0.125134 −0.0625668 0.998041i $$-0.519929\pi$$
−0.0625668 + 0.998041i $$0.519929\pi$$
$$374$$ −116.435 + 752.875i −0.311323 + 2.01303i
$$375$$ 0 0
$$376$$ 290.567 586.010i 0.772784 1.55854i
$$377$$ 9.96635 0.0264360
$$378$$ 3.38812 + 0.523984i 0.00896328 + 0.00138620i
$$379$$ 117.629i 0.310368i −0.987886 0.155184i $$-0.950403\pi$$
0.987886 0.155184i $$-0.0495970\pi$$
$$380$$ 0 0
$$381$$ −46.9278 −0.123170
$$382$$ −85.4985 + 552.839i −0.223818 + 1.44722i
$$383$$ 251.669i 0.657100i −0.944487 0.328550i $$-0.893440\pi$$
0.944487 0.328550i $$-0.106560\pi$$
$$384$$ −194.909 + 105.653i −0.507575 + 0.275139i
$$385$$ 0 0
$$386$$ 202.658 + 31.3418i 0.525022 + 0.0811964i
$$387$$ 166.760i 0.430904i
$$388$$ 364.321 + 115.448i 0.938970 + 0.297547i
$$389$$ 356.890 0.917454 0.458727 0.888577i $$-0.348306\pi$$
0.458727 + 0.888577i $$0.348306\pi$$
$$390$$ 0 0
$$391$$ 431.815i 1.10439i
$$392$$ −350.418 173.751i −0.893923 0.443242i
$$393$$ 7.72168 0.0196480
$$394$$ −77.0108 11.9100i −0.195459 0.0302284i
$$395$$ 0 0
$$396$$ 74.2830 234.416i 0.187583 0.591958i
$$397$$ −103.819 −0.261508 −0.130754 0.991415i $$-0.541740\pi$$
−0.130754 + 0.991415i $$0.541740\pi$$
$$398$$ 45.1314 291.823i 0.113396 0.733224i
$$399$$ 7.11412i 0.0178299i
$$400$$ 0 0
$$401$$ −121.598 −0.303237 −0.151618 0.988439i $$-0.548449\pi$$
−0.151618 + 0.988439i $$0.548449\pi$$
$$402$$ −249.227 38.5438i −0.619967 0.0958800i
$$403$$ 17.5081i 0.0434444i
$$404$$ 620.301 + 196.565i 1.53540 + 0.486546i
$$405$$ 0 0
$$406$$ −2.41177 + 15.5947i −0.00594033 + 0.0384106i
$$407$$ 1044.11i 2.56539i
$$408$$ 114.419 230.759i 0.280439 0.565585i
$$409$$ 182.788 0.446915 0.223457 0.974714i $$-0.428266\pi$$
0.223457 + 0.974714i $$0.428266\pi$$
$$410$$ 0 0
$$411$$ 314.714i 0.765727i
$$412$$ 191.152 603.221i 0.463962 1.46413i
$$413$$ 8.02677 0.0194353
$$414$$ −21.3027 + 137.745i −0.0514558 + 0.332717i
$$415$$ 0 0
$$416$$ 9.59924 + 9.25587i 0.0230751 + 0.0222497i
$$417$$ 386.972 0.927991
$$418$$ −504.269 77.9869i −1.20638 0.186572i
$$419$$ 168.020i 0.401003i −0.979693 0.200502i $$-0.935743\pi$$
0.979693 0.200502i $$-0.0642572\pi$$
$$420$$ 0 0
$$421$$ 625.291 1.48525 0.742626 0.669706i $$-0.233580\pi$$
0.742626 + 0.669706i $$0.233580\pi$$
$$422$$ 71.3244 461.189i 0.169015 1.09286i
$$423$$ 245.285i 0.579869i
$$424$$ 214.836 + 106.524i 0.506688 + 0.251236i
$$425$$ 0 0
$$426$$ 134.472 + 20.7966i 0.315663 + 0.0488184i
$$427$$ 24.6901i 0.0578222i
$$428$$ 21.9707 69.3331i 0.0513334 0.161993i
$$429$$ −14.7904 −0.0344765
$$430$$ 0 0
$$431$$ 133.413i 0.309544i −0.987950 0.154772i $$-0.950536\pi$$
0.987950 0.154772i $$-0.0494643\pi$$
$$432$$ −47.8826 + 67.9651i −0.110839 + 0.157327i
$$433$$ 706.716 1.63214 0.816069 0.577954i $$-0.196149\pi$$
0.816069 + 0.577954i $$0.196149\pi$$
$$434$$ 27.3955 + 4.23681i 0.0631233 + 0.00976223i
$$435$$ 0 0
$$436$$ −598.057 189.516i −1.37169 0.434670i
$$437$$ 289.226 0.661844
$$438$$ 24.6621 159.467i 0.0563062 0.364080i
$$439$$ 507.488i 1.15601i 0.816033 + 0.578005i $$0.196169\pi$$
−0.816033 + 0.578005i $$0.803831\pi$$
$$440$$ 0 0
$$441$$ −146.674 −0.332593
$$442$$ −15.3100 2.36774i −0.0346380 0.00535689i
$$443$$ 412.172i 0.930410i 0.885203 + 0.465205i $$0.154019\pi$$
−0.885203 + 0.465205i $$0.845981\pi$$
$$444$$ 106.637 336.516i 0.240174 0.757919i
$$445$$ 0 0
$$446$$ −25.2824 + 163.478i −0.0566869 + 0.366542i
$$447$$ 214.544i 0.479965i
$$448$$ −16.8059 + 12.7804i −0.0375132 + 0.0285277i
$$449$$ −808.617 −1.80093 −0.900465 0.434929i $$-0.856773\pi$$
−0.900465 + 0.434929i $$0.856773\pi$$
$$450$$ 0 0
$$451$$ 957.124i 2.12223i
$$452$$ −376.449 119.291i −0.832852 0.263919i
$$453$$ −131.802 −0.290955
$$454$$ −110.511 + 714.573i −0.243417 + 1.57395i
$$455$$ 0 0
$$456$$ 154.560 + 76.6370i 0.338948 + 0.168064i
$$457$$ 472.873 1.03473 0.517367 0.855764i $$-0.326912\pi$$
0.517367 + 0.855764i $$0.326912\pi$$
$$458$$ −240.773 37.2364i −0.525705 0.0813021i
$$459$$ 96.5881i 0.210432i
$$460$$ 0 0
$$461$$ 433.776 0.940946 0.470473 0.882414i $$-0.344083\pi$$
0.470473 + 0.882414i $$0.344083\pi$$
$$462$$ 3.57916 23.1431i 0.00774709 0.0500933i
$$463$$ 530.624i 1.14606i 0.819536 + 0.573028i $$0.194231\pi$$
−0.819536 + 0.573028i $$0.805769\pi$$
$$464$$ −312.827 220.392i −0.674196 0.474983i
$$465$$ 0 0
$$466$$ −270.019 41.7594i −0.579440 0.0896124i
$$467$$ 355.266i 0.760741i −0.924834 0.380370i $$-0.875797\pi$$
0.924834 0.380370i $$-0.124203\pi$$
$$468$$ 4.76693 + 1.51057i 0.0101857 + 0.00322772i
$$469$$ −24.0168 −0.0512086
$$470$$ 0 0
$$471$$ 59.3990i 0.126113i
$$472$$ −86.4686 + 174.388i −0.183196 + 0.369467i
$$473$$ −1139.08 −2.40820
$$474$$ 348.912 + 53.9605i 0.736102 + 0.113841i
$$475$$ 0 0
$$476$$ 7.40978 23.3831i 0.0155668 0.0491242i
$$477$$ 89.9232 0.188518
$$478$$ 17.2593 111.600i 0.0361072 0.233472i
$$479$$ 548.640i 1.14539i −0.819770 0.572693i $$-0.805899\pi$$
0.819770 0.572693i $$-0.194101\pi$$
$$480$$ 0 0
$$481$$ −21.2324 −0.0441423
$$482$$ 4.43050 + 0.685191i 0.00919190 + 0.00142156i
$$483$$ 13.2738i 0.0274821i
$$484$$ −1139.82 361.194i −2.35501 0.746269i
$$485$$ 0 0
$$486$$ −4.76497 + 30.8106i −0.00980446 + 0.0633964i
$$487$$ 134.618i 0.276422i 0.990403 + 0.138211i $$0.0441352\pi$$
−0.990403 + 0.138211i $$0.955865\pi$$
$$488$$ 536.412 + 265.974i 1.09921 + 0.545029i
$$489$$ 286.721 0.586341
$$490$$ 0 0
$$491$$ 756.810i 1.54136i 0.637220 + 0.770682i $$0.280084\pi$$
−0.637220 + 0.770682i $$0.719916\pi$$
$$492$$ 97.7529 308.480i 0.198685 0.626991i
$$493$$ 444.572 0.901768
$$494$$ 1.58589 10.2545i 0.00321031 0.0207581i
$$495$$ 0 0
$$496$$ −387.167 + 549.549i −0.780579 + 1.10796i
$$497$$ 12.9585 0.0260734
$$498$$ −20.1609 3.11795i −0.0404837 0.00626094i
$$499$$ 706.956i 1.41675i −0.705838 0.708373i $$-0.749430\pi$$
0.705838 0.708373i $$-0.250570\pi$$
$$500$$ 0 0
$$501$$ −144.811 −0.289043
$$502$$ 120.988 782.318i 0.241012 1.55840i
$$503$$ 100.567i 0.199935i −0.994991 0.0999673i $$-0.968126\pi$$
0.994991 0.0999673i $$-0.0318738\pi$$
$$504$$ −3.51720 + 7.09344i −0.00697858 + 0.0140743i
$$505$$ 0 0
$$506$$ 940.887 + 145.511i 1.85946 + 0.287572i
$$507$$ 292.416i 0.576757i
$$508$$ 32.7382 103.312i 0.0644452 0.203370i
$$509$$ 753.185 1.47973 0.739867 0.672753i $$-0.234888\pi$$
0.739867 + 0.672753i $$0.234888\pi$$
$$510$$ 0 0
$$511$$ 15.3671i 0.0300726i
$$512$$ −96.6232 502.800i −0.188717 0.982031i
$$513$$ 64.6938 0.126109
$$514$$ −216.976 33.5561i −0.422133 0.0652843i
$$515$$ 0 0
$$516$$ 367.124 + 116.336i 0.711480 + 0.225458i
$$517$$ −1675.46 −3.24073
$$518$$ 5.13807 33.2231i 0.00991906 0.0641373i
$$519$$ 334.112i 0.643761i
$$520$$ 0 0
$$521$$ 117.708 0.225926 0.112963 0.993599i $$-0.463966\pi$$
0.112963 + 0.993599i $$0.463966\pi$$
$$522$$ −141.814 21.9320i −0.271674 0.0420153i
$$523$$ 617.411i 1.18052i −0.807214 0.590259i $$-0.799026\pi$$
0.807214 0.590259i $$-0.200974\pi$$
$$524$$ −5.38686 + 16.9994i −0.0102803 + 0.0324415i
$$525$$ 0 0
$$526$$ −100.170 + 647.704i −0.190437 + 1.23138i
$$527$$ 780.988i 1.48195i
$$528$$ 464.246 + 327.070i 0.879254 + 0.619450i
$$529$$ −10.6508 −0.0201338
$$530$$ 0 0
$$531$$ 72.9932i 0.137464i
$$532$$ 15.6618 + 4.96301i 0.0294395 + 0.00932896i
$$533$$ −19.4635 −0.0365169
$$534$$ 32.3012 208.862i 0.0604892 0.391127i
$$535$$ 0 0
$$536$$ 258.722 521.786i 0.482690 0.973481i
$$537$$ 209.473 0.390079
$$538$$ 257.009 + 39.7474i 0.477713 + 0.0738799i
$$539$$ 1001.88i 1.85877i
$$540$$ 0 0
$$541$$ 352.762 0.652056 0.326028 0.945360i $$-0.394290\pi$$
0.326028 + 0.945360i $$0.394290\pi$$
$$542$$ −100.771 + 651.591i −0.185924 + 1.20220i
$$543$$ 186.339i 0.343166i
$$544$$ 428.196 + 412.879i 0.787125 + 0.758969i
$$545$$ 0 0
$$546$$ 0.470623 + 0.0727835i 0.000861948 + 0.000133303i
$$547$$ 295.110i 0.539507i −0.962929 0.269753i $$-0.913058\pi$$
0.962929 0.269753i $$-0.0869422\pi$$
$$548$$ −692.846 219.553i −1.26432 0.400644i
$$549$$ 224.525 0.408970
$$550$$ 0 0
$$551$$ 297.770i 0.540418i
$$552$$ −288.385 142.993i −0.522437 0.259045i
$$553$$ 33.6231 0.0608013
$$554$$ −601.102 92.9624i −1.08502 0.167802i
$$555$$ 0 0
$$556$$ −269.963 + 851.924i −0.485545 + 1.53224i
$$557$$ 31.8538 0.0571882 0.0285941 0.999591i $$-0.490897\pi$$
0.0285941 + 0.999591i $$0.490897\pi$$
$$558$$ −38.5284 + 249.127i −0.0690473 + 0.446465i
$$559$$ 23.1636i 0.0414376i
$$560$$ 0 0
$$561$$ −659.760 −1.17604
$$562$$ −474.557 73.3919i −0.844408 0.130591i
$$563$$ 906.668i 1.61042i 0.592988 + 0.805211i $$0.297948\pi$$
−0.592988 + 0.805211i $$0.702052\pi$$
$$564$$ 539.997 + 171.117i 0.957441 + 0.303400i
$$565$$ 0 0
$$566$$ 26.4936 171.310i 0.0468085 0.302667i
$$567$$ 2.96908i 0.00523647i
$$568$$ −139.596 + 281.534i −0.245767 + 0.495659i
$$569$$ −465.009 −0.817239 −0.408620 0.912705i $$-0.633990\pi$$
−0.408620 + 0.912705i $$0.633990\pi$$
$$570$$ 0 0
$$571$$ 265.895i 0.465666i 0.972517 + 0.232833i $$0.0747995\pi$$
−0.972517 + 0.232833i $$0.925200\pi$$
$$572$$ 10.3182 32.5613i 0.0180388 0.0569253i
$$573$$ −484.464 −0.845488
$$574$$ 4.71000 30.4552i 0.00820557 0.0530578i
$$575$$ 0 0
$$576$$ −116.222 152.828i −0.201774 0.265327i
$$577$$ 138.097 0.239336 0.119668 0.992814i $$-0.461817\pi$$
0.119668 + 0.992814i $$0.461817\pi$$
$$578$$ −111.728 17.2791i −0.193301 0.0298946i
$$579$$ 177.594i 0.306725i
$$580$$ 0 0
$$581$$ −1.94281 −0.00334391
$$582$$ −50.5848 + 327.085i −0.0869154 + 0.562001i
$$583$$ 614.234i 1.05358i
$$584$$ 333.863 + 165.542i 0.571683 + 0.283463i
$$585$$ 0 0
$$586$$ −771.507 119.316i −1.31656 0.203611i
$$587$$ 648.473i 1.10472i −0.833604 0.552362i $$-0.813727\pi$$
0.833604 0.552362i $$-0.186273\pi$$
$$588$$ 102.324 322.903i 0.174020 0.549155i
$$589$$ 523.098 0.888113
$$590$$ 0 0
$$591$$ 67.4862i 0.114190i
$$592$$ 666.451 + 469.526i 1.12576 + 0.793118i
$$593$$ −350.392 −0.590880 −0.295440 0.955361i $$-0.595466\pi$$
−0.295440 + 0.955361i $$0.595466\pi$$
$$594$$ 210.457 + 32.5479i 0.354304 + 0.0547944i
$$595$$ 0 0
$$596$$ 472.322 + 149.672i 0.792486 + 0.251128i
$$597$$ 255.731 0.428359
$$598$$ −2.95903 + 19.1333i −0.00494821 + 0.0319955i
$$599$$ 276.745i 0.462012i 0.972952 + 0.231006i $$0.0742017\pi$$
−0.972952 + 0.231006i $$0.925798\pi$$
$$600$$ 0 0
$$601$$ 815.487 1.35688 0.678442 0.734654i $$-0.262656\pi$$
0.678442 + 0.734654i $$0.262656\pi$$
$$602$$ 36.2449 + 5.60540i 0.0602075 + 0.00931130i
$$603$$ 218.403i 0.362193i
$$604$$ 91.9490 290.164i 0.152233 0.480405i
$$605$$ 0 0
$$606$$ −86.1269 + 556.902i −0.142124 + 0.918981i
$$607$$ 247.049i 0.407001i 0.979075 + 0.203500i $$0.0652318\pi$$
−0.979075 + 0.203500i $$0.934768\pi$$
$$608$$ −276.543 + 286.802i −0.454840 + 0.471713i
$$609$$ −13.6660 −0.0224400
$$610$$ 0 0
$$611$$ 34.0710i 0.0557627i
$$612$$ 212.640 + 67.3825i 0.347450 + 0.110102i
$$613$$ 1005.15 1.63972 0.819862 0.572561i $$-0.194050\pi$$
0.819862 + 0.572561i $$0.194050\pi$$
$$614$$ 18.4112 119.048i 0.0299857 0.193890i
$$615$$ 0 0
$$616$$ 48.4528 + 24.0248i 0.0786572 + 0.0390013i
$$617$$ 533.282 0.864314 0.432157 0.901798i $$-0.357753\pi$$
0.432157 + 0.901798i $$0.357753\pi$$
$$618$$ 541.568 + 83.7553i 0.876324 + 0.135526i
$$619$$ 1136.85i 1.83659i 0.395900 + 0.918294i $$0.370433\pi$$
−0.395900 + 0.918294i $$0.629567\pi$$
$$620$$ 0 0
$$621$$ −120.709 −0.194378
$$622$$ −32.5830 + 210.684i −0.0523842 + 0.338720i
$$623$$ 20.1271i 0.0323067i
$$624$$ −6.65109 + 9.44063i −0.0106588 + 0.0151292i
$$625$$ 0 0
$$626$$ 91.3625 + 14.1295i 0.145946 + 0.0225711i
$$627$$ 441.901i 0.704787i
$$628$$ 130.768 + 41.4384i 0.208229 + 0.0659847i
$$629$$ −947.121 −1.50576
$$630$$ 0 0
$$631$$ 936.738i 1.48453i −0.670107 0.742265i $$-0.733752\pi$$
0.670107 0.742265i $$-0.266248\pi$$
$$632$$ −362.206 + 730.490i −0.573110 + 1.15584i
$$633$$ 404.149 0.638466
$$634$$ 16.5390 + 2.55781i 0.0260867 + 0.00403440i
$$635$$ 0 0
$$636$$ −62.7329 + 197.967i −0.0986366 + 0.311269i
$$637$$ −20.3735 −0.0319836
$$638$$ −149.810 + 968.682i −0.234812 + 1.51831i
$$639$$ 117.841i 0.184415i
$$640$$ 0 0
$$641$$ 214.558 0.334723 0.167362 0.985896i $$-0.446475\pi$$
0.167362 + 0.985896i $$0.446475\pi$$
$$642$$ 62.2468 + 9.62669i 0.0969577 + 0.0149948i
$$643$$ 786.394i 1.22301i 0.791241 + 0.611504i $$0.209435\pi$$
−0.791241 + 0.611504i $$0.790565\pi$$
$$644$$ −29.2225 9.26020i −0.0453765 0.0143792i
$$645$$ 0 0
$$646$$ 70.7424 457.425i 0.109508 0.708088i
$$647$$ 316.550i 0.489258i 0.969617 + 0.244629i $$0.0786661\pi$$
−0.969617 + 0.244629i $$0.921334\pi$$
$$648$$ −64.5058 31.9845i −0.0995459 0.0493588i
$$649$$ 498.592 0.768246
$$650$$ 0 0
$$651$$ 24.0073i 0.0368775i
$$652$$ −200.024 + 631.219i −0.306786 + 0.968127i
$$653$$ −516.391 −0.790797 −0.395399 0.918510i $$-0.629394\pi$$
−0.395399 + 0.918510i $$0.629394\pi$$
$$654$$ 83.0384 536.932i 0.126970 0.820997i
$$655$$ 0 0
$$656$$ 610.926 + 430.408i 0.931290 + 0.656110i
$$657$$ 139.744 0.212700
$$658$$ 53.3121 + 8.24491i 0.0810215 + 0.0125303i
$$659$$ 285.118i 0.432653i 0.976321 + 0.216326i $$0.0694076\pi$$
−0.976321 + 0.216326i $$0.930592\pi$$
$$660$$ 0 0
$$661$$ −391.847 −0.592809 −0.296405 0.955062i $$-0.595788\pi$$
−0.296405 + 0.955062i $$0.595788\pi$$
$$662$$ 33.9516 219.534i 0.0512865 0.331622i
$$663$$ 13.4165i 0.0202360i
$$664$$ 20.9290 42.2092i 0.0315196 0.0635681i
$$665$$ 0 0
$$666$$ 302.122 + 46.7242i 0.453637 + 0.0701565i
$$667$$ 555.593i 0.832973i
$$668$$ 101.024 318.802i 0.151233 0.477248i
$$669$$ −143.259 −0.214139
$$670$$ 0 0
$$671$$ 1533.65i 2.28562i
$$672$$ −13.1626 12.6917i −0.0195872 0.0188865i
$$673$$ 1213.59 1.80325 0.901626 0.432517i $$-0.142375\pi$$
0.901626 + 0.432517i $$0.142375\pi$$
$$674$$ 458.257 + 70.8711i 0.679907 + 0.105150i
$$675$$ 0 0
$$676$$ −643.756 203.997i −0.952303 0.301771i
$$677$$ −251.863 −0.372028 −0.186014 0.982547i $$-0.559557\pi$$
−0.186014 + 0.982547i $$0.559557\pi$$
$$678$$ 52.2688 337.974i 0.0770926 0.498486i
$$679$$ 31.5197i 0.0464207i
$$680$$ 0 0
$$681$$ −626.195 −0.919523
$$682$$ 1701.70 + 263.174i 2.49517 + 0.385886i
$$683$$ 664.793i 0.973342i −0.873585 0.486671i $$-0.838211\pi$$
0.873585 0.486671i $$-0.161789\pi$$
$$684$$ −45.1322 + 142.424i −0.0659828 + 0.208222i
$$685$$ 0 0
$$686$$ 9.87143 63.8293i 0.0143898 0.0930457i
$$687$$ 210.994i 0.307124i
$$688$$ −512.231 + 727.067i −0.744522 + 1.05678i
$$689$$ 12.4907 0.0181287
$$690$$ 0 0
$$691$$ 654.347i 0.946957i −0.880805 0.473479i $$-0.842998\pi$$
0.880805 0.473479i $$-0.157002\pi$$
$$692$$ 735.551 + 233.086i 1.06293 + 0.336829i
$$693$$ 20.2808 0.0292652
$$694$$ 122.907 794.728i 0.177100 1.14514i
$$695$$ 0 0
$$696$$ 147.217 296.904i 0.211519 0.426587i
$$697$$ −868.213 −1.24564
$$698$$ 322.732 + 49.9117i 0.462367 + 0.0715067i
$$699$$ 236.623i 0.338517i
$$700$$ 0 0
$$701$$ −1266.25 −1.80635 −0.903174 0.429275i $$-0.858769\pi$$
−0.903174 + 0.429275i $$0.858769\pi$$
$$702$$ −0.661874 + 4.27972i −0.000942840 + 0.00609647i
$$703$$ 634.373i 0.902380i
$$704$$ −1043.92 + 793.870i −1.48284 + 1.12766i
$$705$$ 0 0
$$706$$ −347.570 53.7529i −0.492309 0.0761372i
$$707$$ 53.6661i 0.0759068i
$$708$$ −160.695 50.9221i −0.226971 0.0719239i
$$709$$ −493.220 −0.695656 −0.347828 0.937558i $$-0.613081\pi$$
−0.347828 + 0.937558i $$0.613081\pi$$
$$710$$ 0 0
$$711$$ 305.759i 0.430041i
$$712$$ 437.278 + 216.819i 0.614154 + 0.304522i
$$713$$ −976.020 −1.36889
$$714$$ 20.9932 + 3.24667i 0.0294023 + 0.00454716i
$$715$$ 0 0
$$716$$ −146.134 + 461.156i −0.204098 + 0.644073i
$$717$$ 97.7971 0.136398
$$718$$ −105.649 + 683.135i −0.147144 + 0.951442i
$$719$$ 60.3910i 0.0839930i 0.999118 + 0.0419965i $$0.0133718\pi$$
−0.999118 + 0.0419965i $$0.986628\pi$$
$$720$$ 0 0
$$721$$ 52.1884 0.0723834
$$722$$ −407.138 62.9653i −0.563904 0.0872096i
$$723$$ 3.88254i 0.00537003i
$$724$$ −410.228 129.995i −0.566613 0.179552i
$$725$$ 0 0
$$726$$ 158.261 1023.33i 0.217990 1.40954i
$$727$$ 994.690i 1.36821i −0.729383 0.684106i $$-0.760193\pi$$
0.729383 0.684106i $$-0.239807\pi$$
$$728$$ −0.488554 + 0.985307i −0.000671090 + 0.00135344i
$$729$$ −27.0000 −0.0370370
$$730$$ 0 0
$$731$$ 1033.27i 1.41350i
$$732$$ −156.635 + 494.294i −0.213982 + 0.675264i
$$733$$ −1167.65 −1.59298 −0.796488 0.604654i $$-0.793311\pi$$
−0.796488 + 0.604654i $$0.793311\pi$$
$$734$$ 222.835 1440.87i 0.303590 1.96303i
$$735$$ 0 0
$$736$$ 515.986 535.127i 0.701067 0.727075i
$$737$$ −1491.83 −2.02420
$$738$$ 276.951 + 42.8314i 0.375273 + 0.0580372i
$$739$$ 79.9863i 0.108236i −0.998535 0.0541179i $$-0.982765\pi$$
0.998535 0.0541179i $$-0.0172347\pi$$
$$740$$ 0 0
$$741$$ 8.98623 0.0121272
$$742$$ −3.02264 + 19.5446i −0.00407364 + 0.0263405i
$$743$$ 402.122i 0.541214i −0.962690 0.270607i $$-0.912776\pi$$
0.962690 0.270607i $$-0.0872244\pi$$
$$744$$ −521.578 258.619i −0.701045 0.347606i
$$745$$ 0 0
$$746$$ 92.2530 + 14.2672i 0.123664 + 0.0191250i
$$747$$ 17.6674i 0.0236511i
$$748$$ 460.267 1452.47i 0.615330 1.94180i
$$749$$ 5.99844 0.00800860
$$750$$ 0 0
$$751$$ 58.7486i 0.0782271i −0.999235 0.0391136i $$-0.987547\pi$$
0.999235 0.0391136i $$-0.0124534\pi$$
$$752$$ −753.434 + 1069.43i −1.00191 + 1.42212i
$$753$$ 685.561 0.910440
$$754$$ −19.6985 3.04644i −0.0261254 0.00404038i
$$755$$ 0 0
$$756$$ −6.53646 2.07131i −0.00864611 0.00273983i
$$757$$ 1040.91 1.37504 0.687522 0.726164i $$-0.258699\pi$$
0.687522 + 0.726164i $$0.258699\pi$$
$$758$$ −35.9561 + 232.495i −0.0474355 + 0.306721i
$$759$$ 824.519i 1.08632i
$$760$$ 0 0
$$761$$ 750.095 0.985670 0.492835 0.870123i $$-0.335961\pi$$
0.492835 + 0.870123i $$0.335961\pi$$
$$762$$ 92.7530 + 14.3446i 0.121723 + 0.0188249i
$$763$$ 51.7417i 0.0678135i
$$764$$ 337.976 1066.55i 0.442377 1.39601i
$$765$$ 0 0
$$766$$ −76.9285 + 497.425i −0.100429 + 0.649380i
$$767$$ 10.1391i 0.0132191i
$$768$$ 417.533 149.246i 0.543663 0.194331i
$$769$$ 1065.98 1.38619 0.693094 0.720847i $$-0.256247\pi$$
0.693094 + 0.720847i $$0.256247\pi$$
$$770$$ 0 0
$$771$$ 190.141i 0.246616i
$$772$$ −390.975 123.894i −0.506444 0.160485i
$$773$$ 947.271 1.22545 0.612724 0.790297i $$-0.290074\pi$$
0.612724 + 0.790297i $$0.290074\pi$$
$$774$$ −50.9740 + 329.601i −0.0658579 + 0.425842i
$$775$$ 0 0
$$776$$ −684.791 339.546i −0.882463 0.437560i
$$777$$ 29.1141 0.0374699
$$778$$ −705.393 109.092i −0.906675 0.140220i
$$779$$ 581.521i 0.746497i
$$780$$ 0 0
$$781$$ 804.931 1.03064
$$782$$ −131.994 + 853.484i −0.168791 + 1.09141i
$$783$$ 124.275i 0.158716i
$$784$$ 639.491 + 450.533i 0.815678 + 0.574659i
$$785$$ 0 0
$$786$$ −15.2619 2.36031i −0.0194172 0.00300294i
$$787$$