Properties

 Label 300.3.c.g.151.7 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 151.7 Root $$1.65359 + 0.954702i$$ of defining polynomial Character $$\chi$$ $$=$$ 300.151 Dual form 300.3.c.g.151.8

$q$-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 $$-0.618542\pi$$
0.363861 0.931453i $$-0.381458\pi$$
$$12$$ −2.09288 6.60453i −0.174407 0.550378i
$$13$$ 0.416712 0.0320548 0.0160274 0.999872i $$-0.494898\pi$$
0.0160274 + 0.999872i $$0.494898\pi$$
$$14$$ 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 $$-0.315877\pi$$
0.546717 + 0.837317i $$0.315877\pi$$
$$18$$ −5.92951 + 0.917019i −0.329417 + 0.0509455i
$$19$$ 12.4503i 0.655281i 0.944803 + 0.327640i $$0.106253\pi$$
−0.944803 + 0.327640i $$0.893747\pi$$
$$20$$ 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 $$-0.762995\pi$$
0.735377 0.677658i $$-0.237005\pi$$
$$32$$ 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 $$-0.741750\pi$$
−0.688545 + 0.725194i $$0.741750\pi$$
$$38$$ 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 $$-0.408744\pi$$
0.282777 + 0.959186i $$0.408744\pi$$
$$54$$ 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 $$0.0661083\pi$$
−0.978511 + 0.206196i $$0.933892\pi$$
$$60$$ 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 $$0.0892150\pi$$
−0.960979 + 0.276622i $$0.910785\pi$$
$$72$$ −21.5019 + 10.6615i −0.298638 + 0.148076i
$$73$$ 46.5814 0.638101 0.319051 0.947738i $$-0.396636\pi$$
0.319051 + 0.947738i $$0.396636\pi$$
$$74$$ −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 $$0.223168\pi$$
−0.764131 + 0.645062i $$0.776832\pi$$
$$80$$ 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 $$-0.663914\pi$$
−0.492494 + 0.870316i $$0.663914\pi$$
$$98$$ 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 $$-0.356100\pi$$
0.436834 + 0.899542i $$0.356100\pi$$
$$114$$ 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 $$-0.994583\pi$$
0.999855 0.0170157i $$-0.00541653\pi$$
$$132$$ −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 $$-0.269224\pi$$
0.663139 + 0.748496i $$0.269224\pi$$
$$138$$ 79.5270 12.2991i 0.576282 0.0891241i
$$139$$ 223.419i 1.60733i −0.595083 0.803664i $$-0.702881\pi$$
0.595083 0.803664i $$-0.297119\pi$$
$$140$$ 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 $$0.0810797\pi$$
−0.967734 + 0.251974i $$0.918920\pi$$
$$152$$ 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 $$-0.534834\pi$$
−0.109217 + 0.994018i $$0.534834\pi$$
$$158$$ 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 $$-0.688244\pi$$
−0.557513 + 0.830168i $$0.688244\pi$$
$$174$$ 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 $$-0.890311\pi$$
0.941211 0.337819i $$-0.109689\pi$$
$$180$$ 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 $$0.261513\pi$$
−0.681075 + 0.732214i $$0.738487\pi$$
$$192$$ −88.2355 67.1006i −0.459560 0.349482i
$$193$$ 102.534 0.531263 0.265632 0.964075i $$-0.414420\pi$$
0.265632 + 0.964075i $$0.414420\pi$$
$$194$$ −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 $$-0.531530\pi$$
−0.0988913 + 0.995098i $$0.531530\pi$$
$$198$$ 18.7915 + 121.507i 0.0949067 + 0.613673i
$$199$$ 147.646i 0.741940i −0.928645 0.370970i $$-0.879025\pi$$
0.928645 0.370970i $$-0.120975\pi$$
$$200$$ 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 $$-0.813510\pi$$
0.833229 0.552928i $$-0.186490\pi$$
$$212$$ 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 $$-0.594708\pi$$
−0.293164 + 0.956062i $$0.594708\pi$$
$$234$$ −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 $$-0.962312\pi$$
0.992999 0.118124i $$-0.0376880\pi$$
$$240$$ 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 $$-0.710877\pi$$
0.615081 0.788464i $$-0.289123\pi$$
$$252$$ −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 $$-0.568511\pi$$
−0.213576 + 0.976927i $$0.568511\pi$$
$$258$$ 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 $$0.208126\pi$$
−0.793750 + 0.608245i $$0.791874\pi$$
$$272$$ 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 $$-0.684976\pi$$
−0.548960 + 0.835849i $$0.684976\pi$$
$$278$$ −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 $$-0.732041\pi$$
−0.666108 + 0.745855i $$0.732041\pi$$
$$294$$ −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 $$0.0548205\pi$$
−0.985206 + 0.171373i $$0.945180\pi$$
$$312$$ −2.56504 5.17312i −0.00822127 0.0165805i
$$313$$ 46.2243 0.147682 0.0738408 0.997270i $$-0.476474\pi$$
0.0738408 + 0.997270i $$0.476474\pi$$
$$314$$ −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 $$-0.495799\pi$$
0.0131984 + 0.999913i $$0.495799\pi$$
$$318$$ −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 $$-0.946339\pi$$
0.985824 0.167782i $$-0.0536605\pi$$
$$332$$ 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 $$-0.388220\pi$$
0.343995 + 0.938972i $$0.388220\pi$$
$$338$$ −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 $$-0.580128\pi$$
−0.249081 + 0.968483i $$0.580128\pi$$
$$354$$ 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 $$0.159863\pi$$
−0.876514 + 0.481377i $$0.840137\pi$$
$$360$$ 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 $$-0.480071\pi$$
0.0625668 + 0.998041i $$0.480071\pi$$
$$374$$ −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 $$0.0495970\pi$$
−0.987886 + 0.155184i $$0.950403\pi$$
$$380$$ 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 $$-0.458260\pi$$
0.130754 + 0.991415i $$0.458260\pi$$
$$398$$ −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 $$0.0642572\pi$$
−0.979693 + 0.200502i $$0.935743\pi$$
$$420$$ 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 $$0.0494643\pi$$
−0.987950 + 0.154772i $$0.950536\pi$$
$$432$$ 47.8826 + 67.9651i 0.110839 + 0.157327i
$$433$$ −706.716 −1.63214 −0.816069 0.577954i $$-0.803851\pi$$
−0.816069 + 0.577954i $$0.803851\pi$$
$$434$$ 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 $$-0.803831\pi$$
0.816033 0.578005i $$-0.196169\pi$$
$$440$$ 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 $$-0.673088\pi$$
−0.517367 + 0.855764i $$0.673088\pi$$
$$458$$ 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 $$0.194101\pi$$
−0.819770 + 0.572693i $$0.805899\pi$$
$$480$$ 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 $$-0.719916\pi$$
0.637220 0.770682i $$-0.280084\pi$$
$$492$$ −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 $$0.250570\pi$$
−0.705838 + 0.708373i $$0.749430\pi$$
$$500$$ 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 $$-0.509103\pi$$
−0.0285941 + 0.999591i $$0.509103\pi$$
$$558$$ 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 $$-0.925200\pi$$
0.972517 0.232833i $$-0.0747995\pi$$
$$572$$ −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 $$-0.538183\pi$$
−0.119668 + 0.992814i $$0.538183\pi$$
$$578$$ 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 $$-0.404534\pi$$
0.295440 + 0.955361i $$0.404534\pi$$
$$594$$ 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 $$-0.925798\pi$$
0.972952 0.231006i $$-0.0742017\pi$$
$$600$$ 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 $$-0.805950\pi$$
−0.819862 + 0.572561i $$0.805950\pi$$
$$614$$ 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 $$-0.642247\pi$$
−0.432157 + 0.901798i $$0.642247\pi$$
$$618$$ −541.568 + 83.7553i −0.876324 + 0.135526i
$$619$$ 1136.85i 1.83659i −0.395900 0.918294i $$-0.629567\pi$$
0.395900 0.918294i $$-0.370433\pi$$
$$620$$ 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 $$0.266248\pi$$
−0.670107 + 0.742265i $$0.733752\pi$$
$$632$$ 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 $$-0.370606\pi$$
0.395399 + 0.918510i $$0.370606\pi$$
$$654$$ 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 $$-0.930592\pi$$
0.976321 0.216326i $$-0.0694076\pi$$
$$660$$ 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 $$-0.857625\pi$$
−0.901626 + 0.432517i $$0.857625\pi$$
$$674$$ 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 $$-0.440443\pi$$
0.186014 + 0.982547i $$0.440443\pi$$
$$678$$ −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 $$0.157002\pi$$
−0.880805 + 0.473479i $$0.842998\pi$$
$$692$$ −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 $$-0.986628\pi$$
0.999118 0.0419965i $$-0.0133718\pi$$
$$720$$ 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 $$-0.206689\pi$$
0.796488 + 0.604654i $$0.206689\pi$$
$$734$$ 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 $$0.0172347\pi$$
−0.998535 + 0.0541179i $$0.982765\pi$$
$$740$$ 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 $$0.0124534\pi$$
−0.999235 + 0.0391136i $$0.987547\pi$$
$$752$$ 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 $$-0.741301\pi$$
−0.687522 + 0.726164i $$0.741301\pi$$
$$758$$ 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 $$-0.709926\pi$$
−0.612724 + 0.790297i $$0.709926\pi$$
$$774$$ −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