# Properties

 Label 84.9.m.b.73.2 Level $84$ Weight $9$ Character 84.73 Analytic conductor $34.220$ Analytic rank $0$ Dimension $12$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$84 = 2^{2} \cdot 3 \cdot 7$$ Weight: $$k$$ $$=$$ $$9$$ Character orbit: $$[\chi]$$ $$=$$ 84.m (of order $$6$$, degree $$2$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$34.2198032451$$ Analytic rank: $$0$$ Dimension: $$12$$ Relative dimension: $$6$$ over $$\Q(\zeta_{6})$$ Coefficient field: $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ Defining polynomial: $$x^{12} - 3 x^{11} + 148097 x^{10} + 46071824 x^{9} + 21578502553 x^{8} + 3561445462121 x^{7} + 576413321817541 x^{6} + \cdots + 45\!\cdots\!96$$ x^12 - 3*x^11 + 148097*x^10 + 46071824*x^9 + 21578502553*x^8 + 3561445462121*x^7 + 576413321817541*x^6 + 47217566733462528*x^5 + 5214056955297543333*x^4 + 358752845334081085965*x^3 + 30962072851910211245661*x^2 + 1221542968331193193318500*x + 45396580558961892385326096 Coefficient ring: $$\Z[a_1, \ldots, a_{13}]$$ Coefficient ring index: $$2^{20}\cdot 3^{10}\cdot 7^{4}$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

## Embedding invariants

 Embedding label 73.2 Root $$-72.3408 + 125.298i$$ of defining polynomial Character $$\chi$$ $$=$$ 84.73 Dual form 84.9.m.b.61.2

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(40.5000 + 23.3827i) q^{3} +(-225.043 + 129.928i) q^{5} +(597.275 + 2325.52i) q^{7} +(1093.50 + 1894.00i) q^{9} +O(q^{10})$$ $$q+(40.5000 + 23.3827i) q^{3} +(-225.043 + 129.928i) q^{5} +(597.275 + 2325.52i) q^{7} +(1093.50 + 1894.00i) q^{9} +(9723.49 - 16841.6i) q^{11} +46381.7i q^{13} -12152.3 q^{15} +(-105886. - 61133.6i) q^{17} +(18446.7 - 10650.2i) q^{19} +(-30187.4 + 108150. i) q^{21} +(152199. + 263616. i) q^{23} +(-161550. + 279812. i) q^{25} +102276. i q^{27} +88119.4 q^{29} +(-1.54998e6 - 894884. i) q^{31} +(787602. - 454722. i) q^{33} +(-436564. - 445739. i) q^{35} +(755092. + 1.30786e6i) q^{37} +(-1.08453e6 + 1.87846e6i) q^{39} +188022. i q^{41} -123402. q^{43} +(-492168. - 284153. i) q^{45} +(-5.58909e6 + 3.22686e6i) q^{47} +(-5.05133e6 + 2.77796e6i) q^{49} +(-2.85893e6 - 4.95182e6i) q^{51} +(-6.88508e6 + 1.19253e7i) q^{53} +5.05343e6i q^{55} +996123. q^{57} +(1.00305e7 + 5.79109e6i) q^{59} +(-1.92663e7 + 1.11234e7i) q^{61} +(-3.75142e6 + 3.67420e6i) q^{63} +(-6.02630e6 - 1.04379e7i) q^{65} +(5.75873e6 - 9.97442e6i) q^{67} +1.42353e7i q^{69} -3.11345e7 q^{71} +(-1.08437e7 - 6.26059e6i) q^{73} +(-1.30855e7 + 7.55493e6i) q^{75} +(4.49731e7 + 1.25532e7i) q^{77} +(2.13222e7 + 3.69312e7i) q^{79} +(-2.39148e6 + 4.14217e6i) q^{81} -7.19982e7i q^{83} +3.17720e7 q^{85} +(3.56884e6 + 2.06047e6i) q^{87} +(4.37683e7 - 2.52696e7i) q^{89} +(-1.07862e8 + 2.77026e7i) q^{91} +(-4.18496e7 - 7.24856e7i) q^{93} +(-2.76753e6 + 4.79351e6i) q^{95} -1.16642e8i q^{97} +4.25305e7 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$12 q + 486 q^{3} + 285 q^{5} + 198 q^{7} + 13122 q^{9}+O(q^{10})$$ 12 * q + 486 * q^3 + 285 * q^5 + 198 * q^7 + 13122 * q^9 $$12 q + 486 q^{3} + 285 q^{5} + 198 q^{7} + 13122 q^{9} - 17919 q^{11} + 15390 q^{15} - 205782 q^{17} + 74313 q^{19} - 39609 q^{21} - 62832 q^{23} + 878679 q^{25} - 575454 q^{29} + 1442952 q^{31} - 1451439 q^{33} - 3989514 q^{35} - 2058621 q^{37} - 930933 q^{39} + 7721322 q^{43} + 623295 q^{45} + 12088194 q^{47} - 16964694 q^{49} - 5556114 q^{51} - 5506743 q^{53} + 4012902 q^{57} + 7511901 q^{59} - 37215576 q^{61} - 3641355 q^{63} + 5047122 q^{65} - 36824553 q^{67} - 30011556 q^{71} + 95080185 q^{73} + 71172999 q^{75} - 38333727 q^{77} + 8514456 q^{79} - 28697814 q^{81} + 20121540 q^{85} - 23305887 q^{87} + 83038554 q^{89} - 198538635 q^{91} + 38959704 q^{93} - 221605224 q^{95} - 78377706 q^{99}+O(q^{100})$$ 12 * q + 486 * q^3 + 285 * q^5 + 198 * q^7 + 13122 * q^9 - 17919 * q^11 + 15390 * q^15 - 205782 * q^17 + 74313 * q^19 - 39609 * q^21 - 62832 * q^23 + 878679 * q^25 - 575454 * q^29 + 1442952 * q^31 - 1451439 * q^33 - 3989514 * q^35 - 2058621 * q^37 - 930933 * q^39 + 7721322 * q^43 + 623295 * q^45 + 12088194 * q^47 - 16964694 * q^49 - 5556114 * q^51 - 5506743 * q^53 + 4012902 * q^57 + 7511901 * q^59 - 37215576 * q^61 - 3641355 * q^63 + 5047122 * q^65 - 36824553 * q^67 - 30011556 * q^71 + 95080185 * q^73 + 71172999 * q^75 - 38333727 * q^77 + 8514456 * q^79 - 28697814 * q^81 + 20121540 * q^85 - 23305887 * q^87 + 83038554 * q^89 - 198538635 * q^91 + 38959704 * q^93 - 221605224 * q^95 - 78377706 * q^99

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/84\mathbb{Z}\right)^\times$$.

 $$n$$ $$29$$ $$43$$ $$73$$ $$\chi(n)$$ $$1$$ $$1$$ $$e\left(\frac{1}{6}\right)$$

## 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
$$3$$ 40.5000 + 23.3827i 0.500000 + 0.288675i
$$4$$ 0 0
$$5$$ −225.043 + 129.928i −0.360068 + 0.207885i −0.669111 0.743163i $$-0.733325\pi$$
0.309042 + 0.951048i $$0.399991\pi$$
$$6$$ 0 0
$$7$$ 597.275 + 2325.52i 0.248761 + 0.968565i
$$8$$ 0 0
$$9$$ 1093.50 + 1894.00i 0.166667 + 0.288675i
$$10$$ 0 0
$$11$$ 9723.49 16841.6i 0.664127 1.15030i −0.315394 0.948961i $$-0.602137\pi$$
0.979521 0.201341i $$-0.0645300\pi$$
$$12$$ 0 0
$$13$$ 46381.7i 1.62395i 0.583690 + 0.811976i $$0.301608\pi$$
−0.583690 + 0.811976i $$0.698392\pi$$
$$14$$ 0 0
$$15$$ −12152.3 −0.240045
$$16$$ 0 0
$$17$$ −105886. 61133.6i −1.26778 0.731955i −0.293215 0.956047i $$-0.594725\pi$$
−0.974568 + 0.224092i $$0.928058\pi$$
$$18$$ 0 0
$$19$$ 18446.7 10650.2i 0.141548 0.0817230i −0.427553 0.903990i $$-0.640624\pi$$
0.569102 + 0.822267i $$0.307291\pi$$
$$20$$ 0 0
$$21$$ −30187.4 + 108150.i −0.155220 + 0.556094i
$$22$$ 0 0
$$23$$ 152199. + 263616.i 0.543876 + 0.942020i 0.998677 + 0.0514271i $$0.0163770\pi$$
−0.454801 + 0.890593i $$0.650290\pi$$
$$24$$ 0 0
$$25$$ −161550. + 279812.i −0.413567 + 0.716320i
$$26$$ 0 0
$$27$$ 102276.i 0.192450i
$$28$$ 0 0
$$29$$ 88119.4 0.124589 0.0622945 0.998058i $$-0.480158\pi$$
0.0622945 + 0.998058i $$0.480158\pi$$
$$30$$ 0 0
$$31$$ −1.54998e6 894884.i −1.67834 0.968991i −0.962718 0.270505i $$-0.912809\pi$$
−0.715624 0.698486i $$-0.753857\pi$$
$$32$$ 0 0
$$33$$ 787602. 454722.i 0.664127 0.383434i
$$34$$ 0 0
$$35$$ −436564. 445739.i −0.290921 0.297036i
$$36$$ 0 0
$$37$$ 755092. + 1.30786e6i 0.402896 + 0.697836i 0.994074 0.108705i $$-0.0346703\pi$$
−0.591178 + 0.806541i $$0.701337\pi$$
$$38$$ 0 0
$$39$$ −1.08453e6 + 1.87846e6i −0.468795 + 0.811976i
$$40$$ 0 0
$$41$$ 188022.i 0.0665385i 0.999446 + 0.0332692i $$0.0105919\pi$$
−0.999446 + 0.0332692i $$0.989408\pi$$
$$42$$ 0 0
$$43$$ −123402. −0.0360953 −0.0180476 0.999837i $$-0.505745\pi$$
−0.0180476 + 0.999837i $$0.505745\pi$$
$$44$$ 0 0
$$45$$ −492168. 284153.i −0.120023 0.0692952i
$$46$$ 0 0
$$47$$ −5.58909e6 + 3.22686e6i −1.14538 + 0.661285i −0.947757 0.318993i $$-0.896655\pi$$
−0.197623 + 0.980278i $$0.563322\pi$$
$$48$$ 0 0
$$49$$ −5.05133e6 + 2.77796e6i −0.876236 + 0.481882i
$$50$$ 0 0
$$51$$ −2.85893e6 4.95182e6i −0.422594 0.731955i
$$52$$ 0 0
$$53$$ −6.88508e6 + 1.19253e7i −0.872580 + 1.51135i −0.0132616 + 0.999912i $$0.504221\pi$$
−0.859318 + 0.511441i $$0.829112\pi$$
$$54$$ 0 0
$$55$$ 5.05343e6i 0.552250i
$$56$$ 0 0
$$57$$ 996123. 0.0943656
$$58$$ 0 0
$$59$$ 1.00305e7 + 5.79109e6i 0.827776 + 0.477917i 0.853090 0.521763i $$-0.174725\pi$$
−0.0253148 + 0.999680i $$0.508059\pi$$
$$60$$ 0 0
$$61$$ −1.92663e7 + 1.11234e7i −1.39149 + 0.803375i −0.993480 0.114007i $$-0.963631\pi$$
−0.398007 + 0.917383i $$0.630298\pi$$
$$62$$ 0 0
$$63$$ −3.75142e6 + 3.67420e6i −0.238140 + 0.233239i
$$64$$ 0 0
$$65$$ −6.02630e6 1.04379e7i −0.337596 0.584734i
$$66$$ 0 0
$$67$$ 5.75873e6 9.97442e6i 0.285777 0.494981i −0.687020 0.726638i $$-0.741082\pi$$
0.972797 + 0.231658i $$0.0744149\pi$$
$$68$$ 0 0
$$69$$ 1.42353e7i 0.628013i
$$70$$ 0 0
$$71$$ −3.11345e7 −1.22520 −0.612602 0.790392i $$-0.709877\pi$$
−0.612602 + 0.790392i $$0.709877\pi$$
$$72$$ 0 0
$$73$$ −1.08437e7 6.26059e6i −0.381843 0.220457i 0.296777 0.954947i $$-0.404088\pi$$
−0.678620 + 0.734490i $$0.737422\pi$$
$$74$$ 0 0
$$75$$ −1.30855e7 + 7.55493e6i −0.413567 + 0.238773i
$$76$$ 0 0
$$77$$ 4.49731e7 + 1.25532e7i 1.27935 + 0.357100i
$$78$$ 0 0
$$79$$ 2.13222e7 + 3.69312e7i 0.547424 + 0.948167i 0.998450 + 0.0556558i $$0.0177249\pi$$
−0.451026 + 0.892511i $$0.648942\pi$$
$$80$$ 0 0
$$81$$ −2.39148e6 + 4.14217e6i −0.0555556 + 0.0962250i
$$82$$ 0 0
$$83$$ 7.19982e7i 1.51708i −0.651625 0.758541i $$-0.725912\pi$$
0.651625 0.758541i $$-0.274088\pi$$
$$84$$ 0 0
$$85$$ 3.17720e7 0.608651
$$86$$ 0 0
$$87$$ 3.56884e6 + 2.06047e6i 0.0622945 + 0.0359657i
$$88$$ 0 0
$$89$$ 4.37683e7 2.52696e7i 0.697589 0.402753i −0.108860 0.994057i $$-0.534720\pi$$
0.806449 + 0.591304i $$0.201387\pi$$
$$90$$ 0 0
$$91$$ −1.07862e8 + 2.77026e7i −1.57290 + 0.403976i
$$92$$ 0 0
$$93$$ −4.18496e7 7.24856e7i −0.559447 0.968991i
$$94$$ 0 0
$$95$$ −2.76753e6 + 4.79351e6i −0.0339781 + 0.0588517i
$$96$$ 0 0
$$97$$ 1.16642e8i 1.31755i −0.752339 0.658776i $$-0.771075\pi$$
0.752339 0.658776i $$-0.228925\pi$$
$$98$$ 0 0
$$99$$ 4.25305e7 0.442751
$$100$$ 0 0
$$101$$ 9.23786e7 + 5.33348e7i 0.887740 + 0.512537i 0.873203 0.487357i $$-0.162039\pi$$
0.0145374 + 0.999894i $$0.495372\pi$$
$$102$$ 0 0
$$103$$ 1.77725e8 1.02609e8i 1.57906 0.911671i 0.584070 0.811703i $$-0.301459\pi$$
0.994991 0.0999675i $$-0.0318739\pi$$
$$104$$ 0 0
$$105$$ −7.25827e6 2.82605e7i −0.0597139 0.232500i
$$106$$ 0 0
$$107$$ 8.90703e7 + 1.54274e8i 0.679513 + 1.17695i 0.975128 + 0.221644i $$0.0711423\pi$$
−0.295615 + 0.955307i $$0.595524\pi$$
$$108$$ 0 0
$$109$$ −5.48168e7 + 9.49454e7i −0.388336 + 0.672617i −0.992226 0.124450i $$-0.960283\pi$$
0.603890 + 0.797068i $$0.293617\pi$$
$$110$$ 0 0
$$111$$ 7.06243e7i 0.465224i
$$112$$ 0 0
$$113$$ 2.74592e8 1.68413 0.842063 0.539379i $$-0.181341\pi$$
0.842063 + 0.539379i $$0.181341\pi$$
$$114$$ 0 0
$$115$$ −6.85024e7 3.95499e7i −0.391665 0.226128i
$$116$$ 0 0
$$117$$ −8.78469e7 + 5.07184e7i −0.468795 + 0.270659i
$$118$$ 0 0
$$119$$ 7.89243e7 2.82755e8i 0.393571 1.41001i
$$120$$ 0 0
$$121$$ −8.19129e7 1.41877e8i −0.382130 0.661868i
$$122$$ 0 0
$$123$$ −4.39645e6 + 7.61488e6i −0.0192080 + 0.0332692i
$$124$$ 0 0
$$125$$ 1.85466e8i 0.759669i
$$126$$ 0 0
$$127$$ −3.97605e7 −0.152840 −0.0764199 0.997076i $$-0.524349\pi$$
−0.0764199 + 0.997076i $$0.524349\pi$$
$$128$$ 0 0
$$129$$ −4.99780e6 2.88548e6i −0.0180476 0.0104198i
$$130$$ 0 0
$$131$$ 3.31807e7 1.91569e7i 0.112668 0.0650490i −0.442607 0.896716i $$-0.645946\pi$$
0.555275 + 0.831667i $$0.312613\pi$$
$$132$$ 0 0
$$133$$ 3.57851e7 + 3.65372e7i 0.114366 + 0.116769i
$$134$$ 0 0
$$135$$ −1.32885e7 2.30164e7i −0.0400076 0.0692952i
$$136$$ 0 0
$$137$$ 2.07018e8 3.58565e8i 0.587659 1.01786i −0.406879 0.913482i $$-0.633383\pi$$
0.994538 0.104374i $$-0.0332838\pi$$
$$138$$ 0 0
$$139$$ 2.15646e8i 0.577674i 0.957378 + 0.288837i $$0.0932686\pi$$
−0.957378 + 0.288837i $$0.906731\pi$$
$$140$$ 0 0
$$141$$ −3.01811e8 −0.763587
$$142$$ 0 0
$$143$$ 7.81141e8 + 4.50992e8i 1.86804 + 1.07851i
$$144$$ 0 0
$$145$$ −1.98306e7 + 1.14492e7i −0.0448605 + 0.0259002i
$$146$$ 0 0
$$147$$ −2.69535e8 5.60637e6i −0.577225 0.0120064i
$$148$$ 0 0
$$149$$ −2.59668e8 4.49759e8i −0.526834 0.912503i −0.999511 0.0312676i $$-0.990046\pi$$
0.472677 0.881236i $$-0.343288\pi$$
$$150$$ 0 0
$$151$$ −1.65131e8 + 2.86015e8i −0.317630 + 0.550151i −0.979993 0.199032i $$-0.936220\pi$$
0.662363 + 0.749183i $$0.269554\pi$$
$$152$$ 0 0
$$153$$ 2.67398e8i 0.487970i
$$154$$ 0 0
$$155$$ 4.65083e8 0.805757
$$156$$ 0 0
$$157$$ −2.58909e8 1.49481e8i −0.426137 0.246030i 0.271563 0.962421i $$-0.412460\pi$$
−0.697700 + 0.716390i $$0.745793\pi$$
$$158$$ 0 0
$$159$$ −5.57691e8 + 3.21983e8i −0.872580 + 0.503784i
$$160$$ 0 0
$$161$$ −5.22141e8 + 5.11393e8i −0.777113 + 0.761117i
$$162$$ 0 0
$$163$$ 2.92142e8 + 5.06004e8i 0.413850 + 0.716810i 0.995307 0.0967676i $$-0.0308504\pi$$
−0.581457 + 0.813577i $$0.697517\pi$$
$$164$$ 0 0
$$165$$ −1.18163e8 + 2.04664e8i −0.159421 + 0.276125i
$$166$$ 0 0
$$167$$ 7.46657e8i 0.959965i 0.877278 + 0.479983i $$0.159357\pi$$
−0.877278 + 0.479983i $$0.840643\pi$$
$$168$$ 0 0
$$169$$ −1.33553e9 −1.63722
$$170$$ 0 0
$$171$$ 4.03430e7 + 2.32920e7i 0.0471828 + 0.0272410i
$$172$$ 0 0
$$173$$ 9.08205e8 5.24352e8i 1.01391 0.585381i 0.101576 0.994828i $$-0.467612\pi$$
0.912334 + 0.409447i $$0.134278\pi$$
$$174$$ 0 0
$$175$$ −7.47200e8 2.08563e8i −0.796681 0.222374i
$$176$$ 0 0
$$177$$ 2.70822e8 + 4.69078e8i 0.275925 + 0.477917i
$$178$$ 0 0
$$179$$ −1.24237e8 + 2.15185e8i −0.121015 + 0.209604i −0.920168 0.391523i $$-0.871948\pi$$
0.799153 + 0.601127i $$0.205282\pi$$
$$180$$ 0 0
$$181$$ 4.91957e8i 0.458366i −0.973383 0.229183i $$-0.926394\pi$$
0.973383 0.229183i $$-0.0736055\pi$$
$$182$$ 0 0
$$183$$ −1.04038e9 −0.927658
$$184$$ 0 0
$$185$$ −3.39856e8 1.96216e8i −0.290140 0.167512i
$$186$$ 0 0
$$187$$ −2.05917e9 + 1.18886e9i −1.68394 + 0.972222i
$$188$$ 0 0
$$189$$ −2.37845e8 + 6.10868e7i −0.186400 + 0.0478741i
$$190$$ 0 0
$$191$$ 9.53669e8 + 1.65180e9i 0.716579 + 1.24115i 0.962347 + 0.271823i $$0.0876265\pi$$
−0.245768 + 0.969329i $$0.579040\pi$$
$$192$$ 0 0
$$193$$ −4.70293e8 + 8.14571e8i −0.338953 + 0.587083i −0.984236 0.176860i $$-0.943406\pi$$
0.645283 + 0.763943i $$0.276739\pi$$
$$194$$ 0 0
$$195$$ 5.63645e8i 0.389822i
$$196$$ 0 0
$$197$$ 1.22807e9 0.815379 0.407689 0.913121i $$-0.366335\pi$$
0.407689 + 0.913121i $$0.366335\pi$$
$$198$$ 0 0
$$199$$ 9.98896e7 + 5.76713e7i 0.0636954 + 0.0367745i 0.531509 0.847052i $$-0.321625\pi$$
−0.467814 + 0.883827i $$0.654958\pi$$
$$200$$ 0 0
$$201$$ 4.66457e8 2.69309e8i 0.285777 0.164994i
$$202$$ 0 0
$$203$$ 5.26315e7 + 2.04924e8i 0.0309929 + 0.120672i
$$204$$ 0 0
$$205$$ −2.44294e7 4.23129e7i −0.0138324 0.0239584i
$$206$$ 0 0
$$207$$ −3.32859e8 + 5.76528e8i −0.181292 + 0.314007i
$$208$$ 0 0
$$209$$ 4.14229e8i 0.217098i
$$210$$ 0 0
$$211$$ 2.33973e9 1.18042 0.590209 0.807250i $$-0.299045\pi$$
0.590209 + 0.807250i $$0.299045\pi$$
$$212$$ 0 0
$$213$$ −1.26095e9 7.28008e8i −0.612602 0.353686i
$$214$$ 0 0
$$215$$ 2.77708e7 1.60335e7i 0.0129968 0.00750368i
$$216$$ 0 0
$$217$$ 1.15531e9 4.13902e9i 0.521025 1.86663i
$$218$$ 0 0
$$219$$ −2.92779e8 5.07108e8i −0.127281 0.220457i
$$220$$ 0 0
$$221$$ 2.83548e9 4.91120e9i 1.18866 2.05882i
$$222$$ 0 0
$$223$$ 1.14133e9i 0.461523i 0.973010 + 0.230762i $$0.0741218\pi$$
−0.973010 + 0.230762i $$0.925878\pi$$
$$224$$ 0 0
$$225$$ −7.06618e8 −0.275712
$$226$$ 0 0
$$227$$ −1.82252e8 1.05223e8i −0.0686387 0.0396285i 0.465288 0.885159i $$-0.345951\pi$$
−0.533927 + 0.845531i $$0.679284\pi$$
$$228$$ 0 0
$$229$$ −3.18730e9 + 1.84019e9i −1.15899 + 0.669146i −0.951063 0.308997i $$-0.900007\pi$$
−0.207932 + 0.978143i $$0.566673\pi$$
$$230$$ 0 0
$$231$$ 1.52788e9 + 1.55999e9i 0.536590 + 0.547867i
$$232$$ 0 0
$$233$$ 1.42196e8 + 2.46291e8i 0.0482464 + 0.0835652i 0.889140 0.457635i $$-0.151303\pi$$
−0.840894 + 0.541200i $$0.817970\pi$$
$$234$$ 0 0
$$235$$ 8.38522e8 1.45236e9i 0.274943 0.476216i
$$236$$ 0 0
$$237$$ 1.99428e9i 0.632111i
$$238$$ 0 0
$$239$$ 2.62607e9 0.804850 0.402425 0.915453i $$-0.368167\pi$$
0.402425 + 0.915453i $$0.368167\pi$$
$$240$$ 0 0
$$241$$ 2.05781e8 + 1.18808e8i 0.0610011 + 0.0352190i 0.530190 0.847879i $$-0.322120\pi$$
−0.469189 + 0.883098i $$0.655454\pi$$
$$242$$ 0 0
$$243$$ −1.93710e8 + 1.11839e8i −0.0555556 + 0.0320750i
$$244$$ 0 0
$$245$$ 7.75828e8 1.28147e9i 0.215328 0.355667i
$$246$$ 0 0
$$247$$ 4.93976e8 + 8.55591e8i 0.132714 + 0.229868i
$$248$$ 0 0
$$249$$ 1.68351e9 2.91593e9i 0.437944 0.758541i
$$250$$ 0 0
$$251$$ 3.49203e9i 0.879797i −0.898047 0.439899i $$-0.855014\pi$$
0.898047 0.439899i $$-0.144986\pi$$
$$252$$ 0 0
$$253$$ 5.91961e9 1.44481
$$254$$ 0 0
$$255$$ 1.28676e9 + 7.42914e8i 0.304325 + 0.175702i
$$256$$ 0 0
$$257$$ −3.36384e9 + 1.94211e9i −0.771086 + 0.445187i −0.833262 0.552879i $$-0.813529\pi$$
0.0621759 + 0.998065i $$0.480196\pi$$
$$258$$ 0 0
$$259$$ −2.59046e9 + 2.53714e9i −0.575675 + 0.563825i
$$260$$ 0 0
$$261$$ 9.63585e7 + 1.66898e8i 0.0207648 + 0.0359657i
$$262$$ 0 0
$$263$$ −9.40863e8 + 1.62962e9i −0.196654 + 0.340615i −0.947442 0.319929i $$-0.896341\pi$$
0.750787 + 0.660544i $$0.229674\pi$$
$$264$$ 0 0
$$265$$ 3.57827e9i 0.725587i
$$266$$ 0 0
$$267$$ 2.36349e9 0.465059
$$268$$ 0 0
$$269$$ 2.78854e9 + 1.60997e9i 0.532559 + 0.307473i 0.742058 0.670336i $$-0.233850\pi$$
−0.209499 + 0.977809i $$0.567183\pi$$
$$270$$ 0 0
$$271$$ 4.42388e9 2.55413e9i 0.820212 0.473550i −0.0302773 0.999542i $$-0.509639\pi$$
0.850490 + 0.525992i $$0.176306\pi$$
$$272$$ 0 0
$$273$$ −5.01617e9 1.40014e9i −0.903070 0.252070i
$$274$$ 0 0
$$275$$ 3.14165e9 + 5.44150e9i 0.549323 + 0.951455i
$$276$$ 0 0
$$277$$ 5.20091e9 9.00825e9i 0.883406 1.53010i 0.0358772 0.999356i $$-0.488577\pi$$
0.847529 0.530749i $$-0.178089\pi$$
$$278$$ 0 0
$$279$$ 3.91422e9i 0.645994i
$$280$$ 0 0
$$281$$ −9.79146e9 −1.57044 −0.785222 0.619215i $$-0.787451\pi$$
−0.785222 + 0.619215i $$0.787451\pi$$
$$282$$ 0 0
$$283$$ −9.03261e8 5.21498e8i −0.140821 0.0813031i 0.427934 0.903810i $$-0.359242\pi$$
−0.568755 + 0.822507i $$0.692575\pi$$
$$284$$ 0 0
$$285$$ −2.24170e8 + 1.29425e8i −0.0339781 + 0.0196172i
$$286$$ 0 0
$$287$$ −4.37249e8 + 1.12301e8i −0.0644468 + 0.0165522i
$$288$$ 0 0
$$289$$ 3.98675e9 + 6.90526e9i 0.571515 + 0.989893i
$$290$$ 0 0
$$291$$ 2.72740e9 4.72400e9i 0.380344 0.658776i
$$292$$ 0 0
$$293$$ 2.83834e9i 0.385118i −0.981285 0.192559i $$-0.938321\pi$$
0.981285 0.192559i $$-0.0616787\pi$$
$$294$$ 0 0
$$295$$ −3.00971e9 −0.397408
$$296$$ 0 0
$$297$$ 1.72249e9 + 9.94478e8i 0.221376 + 0.127811i
$$298$$ 0 0
$$299$$ −1.22270e10 + 7.05924e9i −1.52980 + 0.883228i
$$300$$ 0 0
$$301$$ −7.37052e7 2.86975e8i −0.00897909 0.0349606i
$$302$$ 0 0
$$303$$ 2.49422e9 + 4.32012e9i 0.295913 + 0.512537i
$$304$$ 0 0
$$305$$ 2.89049e9 5.00648e9i 0.334020 0.578540i
$$306$$ 0 0
$$307$$ 1.01655e10i 1.14439i 0.820116 + 0.572197i $$0.193909\pi$$
−0.820116 + 0.572197i $$0.806091\pi$$
$$308$$ 0 0
$$309$$ 9.59713e9 1.05271
$$310$$ 0 0
$$311$$ −9.35774e9 5.40269e9i −1.00030 0.577522i −0.0919614 0.995763i $$-0.529314\pi$$
−0.908336 + 0.418240i $$0.862647\pi$$
$$312$$ 0 0
$$313$$ −7.81261e9 + 4.51061e9i −0.813989 + 0.469957i −0.848339 0.529453i $$-0.822397\pi$$
0.0343502 + 0.999410i $$0.489064\pi$$
$$314$$ 0 0
$$315$$ 3.66846e8 1.31427e9i 0.0372599 0.133488i
$$316$$ 0 0
$$317$$ 2.10486e9 + 3.64573e9i 0.208443 + 0.361034i 0.951224 0.308500i $$-0.0998271\pi$$
−0.742781 + 0.669534i $$0.766494\pi$$
$$318$$ 0 0
$$319$$ 8.56828e8 1.48407e9i 0.0827429 0.143315i
$$320$$ 0 0
$$321$$ 8.33081e9i 0.784634i
$$322$$ 0 0
$$323$$ −2.60435e9 −0.239270
$$324$$ 0 0
$$325$$ −1.29782e10 7.49295e9i −1.16327 0.671614i
$$326$$ 0 0
$$327$$ −4.44016e9 + 2.56353e9i −0.388336 + 0.224206i
$$328$$ 0 0
$$329$$ −1.08424e10 1.10702e10i −0.925424 0.944873i
$$330$$ 0 0
$$331$$ 5.98155e9 + 1.03603e10i 0.498312 + 0.863102i 0.999998 0.00194777i $$-0.000619995\pi$$
−0.501686 + 0.865050i $$0.667287\pi$$
$$332$$ 0 0
$$333$$ −1.65139e9 + 2.86028e9i −0.134299 + 0.232612i
$$334$$ 0 0
$$335$$ 2.99289e9i 0.237636i
$$336$$ 0 0
$$337$$ 8.47484e9 0.657070 0.328535 0.944492i $$-0.393445\pi$$
0.328535 + 0.944492i $$0.393445\pi$$
$$338$$ 0 0
$$339$$ 1.11210e10 + 6.42071e9i 0.842063 + 0.486165i
$$340$$ 0 0
$$341$$ −3.01425e10 + 1.74028e10i −2.22927 + 1.28707i
$$342$$ 0 0
$$343$$ −9.47723e9 1.00878e10i −0.684708 0.728818i
$$344$$ 0 0
$$345$$ −1.84956e9 3.20354e9i −0.130555 0.226128i
$$346$$ 0 0
$$347$$ −7.92809e9 + 1.37319e10i −0.546828 + 0.947134i 0.451661 + 0.892190i $$0.350832\pi$$
−0.998489 + 0.0549447i $$0.982502\pi$$
$$348$$ 0 0
$$349$$ 7.90260e9i 0.532682i −0.963879 0.266341i $$-0.914185\pi$$
0.963879 0.266341i $$-0.0858148\pi$$
$$350$$ 0 0
$$351$$ −4.74373e9 −0.312530
$$352$$ 0 0
$$353$$ 8.28745e9 + 4.78476e9i 0.533731 + 0.308150i 0.742534 0.669808i $$-0.233624\pi$$
−0.208804 + 0.977958i $$0.566957\pi$$
$$354$$ 0 0
$$355$$ 7.00658e9 4.04525e9i 0.441157 0.254702i
$$356$$ 0 0
$$357$$ 9.80801e9 9.60612e9i 0.603821 0.591392i
$$358$$ 0 0
$$359$$ 5.12021e9 + 8.86847e9i 0.308255 + 0.533914i 0.977981 0.208695i $$-0.0669216\pi$$
−0.669726 + 0.742609i $$0.733588\pi$$
$$360$$ 0 0
$$361$$ −8.26493e9 + 1.43153e10i −0.486643 + 0.842890i
$$362$$ 0 0
$$363$$ 7.66138e9i 0.441246i
$$364$$ 0 0
$$365$$ 3.25371e9 0.183319
$$366$$ 0 0
$$367$$ 2.80339e10 + 1.61854e10i 1.54532 + 0.892193i 0.998489 + 0.0549514i $$0.0175004\pi$$
0.546834 + 0.837241i $$0.315833\pi$$
$$368$$ 0 0
$$369$$ −3.56113e8 + 2.05602e8i −0.0192080 + 0.0110897i
$$370$$ 0 0
$$371$$ −3.18449e10 8.88873e9i −1.68091 0.469185i
$$372$$ 0 0
$$373$$ 1.25975e10 + 2.18195e10i 0.650803 + 1.12722i 0.982928 + 0.183988i $$0.0589008\pi$$
−0.332126 + 0.943235i $$0.607766\pi$$
$$374$$ 0 0
$$375$$ 4.33670e9 7.51138e9i 0.219298 0.379835i
$$376$$ 0 0
$$377$$ 4.08713e9i 0.202327i
$$378$$ 0 0
$$379$$ −6.03658e9 −0.292573 −0.146287 0.989242i $$-0.546732\pi$$
−0.146287 + 0.989242i $$0.546732\pi$$
$$380$$ 0 0
$$381$$ −1.61030e9 9.29707e8i −0.0764199 0.0441211i
$$382$$ 0 0
$$383$$ −9.57427e9 + 5.52771e9i −0.444949 + 0.256892i −0.705695 0.708516i $$-0.749365\pi$$
0.260745 + 0.965408i $$0.416032\pi$$
$$384$$ 0 0
$$385$$ −1.17519e10 + 3.01829e9i −0.534890 + 0.137378i
$$386$$ 0 0
$$387$$ −1.34941e8 2.33724e8i −0.00601588 0.0104198i
$$388$$ 0 0
$$389$$ 1.58412e10 2.74378e10i 0.691814 1.19826i −0.279428 0.960167i $$-0.590145\pi$$
0.971243 0.238091i $$-0.0765217\pi$$
$$390$$ 0 0
$$391$$ 3.72178e10i 1.59237i
$$392$$ 0 0
$$393$$ 1.79176e9 0.0751121
$$394$$ 0 0
$$395$$ −9.59682e9 5.54072e9i −0.394220 0.227603i
$$396$$ 0 0
$$397$$ −1.81623e10 + 1.04860e10i −0.731155 + 0.422132i −0.818844 0.574015i $$-0.805385\pi$$
0.0876897 + 0.996148i $$0.472052\pi$$
$$398$$ 0 0
$$399$$ 5.94960e8 + 2.31651e9i 0.0234745 + 0.0913992i
$$400$$ 0 0
$$401$$ −5.84375e9 1.01217e10i −0.226003 0.391449i 0.730617 0.682788i $$-0.239233\pi$$
−0.956620 + 0.291339i $$0.905899\pi$$
$$402$$ 0 0
$$403$$ 4.15062e10 7.18909e10i 1.57360 2.72555i
$$404$$ 0 0
$$405$$ 1.24289e9i 0.0461968i
$$406$$ 0 0
$$407$$ 2.93685e10 1.07030
$$408$$ 0 0
$$409$$ 2.98804e10 + 1.72515e10i 1.06781 + 0.616499i 0.927582 0.373620i $$-0.121884\pi$$
0.140226 + 0.990119i $$0.455217\pi$$
$$410$$ 0 0
$$411$$ 1.67684e10 9.68127e9i 0.587659 0.339285i
$$412$$ 0 0
$$413$$ −7.47637e9 + 2.67849e10i −0.256975 + 0.920642i
$$414$$ 0 0
$$415$$ 9.35461e9 + 1.62027e10i 0.315379 + 0.546253i
$$416$$ 0 0
$$417$$ −5.04239e9 + 8.73368e9i −0.166760 + 0.288837i
$$418$$ 0 0
$$419$$ 1.71261e10i 0.555652i −0.960631 0.277826i $$-0.910386\pi$$
0.960631 0.277826i $$-0.0896139\pi$$
$$420$$ 0 0
$$421$$ 3.64524e10 1.16037 0.580187 0.814484i $$-0.302980\pi$$
0.580187 + 0.814484i $$0.302980\pi$$
$$422$$ 0 0
$$423$$ −1.22233e10 7.05715e9i −0.381793 0.220428i
$$424$$ 0 0
$$425$$ 3.42119e10 1.97522e10i 1.04863 0.605425i
$$426$$ 0 0
$$427$$ −3.73750e10 3.81605e10i −1.12427 1.14790i
$$428$$ 0 0
$$429$$ 2.10908e10 + 3.65303e10i 0.622679 + 1.07851i
$$430$$ 0 0
$$431$$ 1.09904e10 1.90360e10i 0.318497 0.551654i −0.661677 0.749789i $$-0.730155\pi$$
0.980175 + 0.198135i $$0.0634884\pi$$
$$432$$ 0 0
$$433$$ 1.35544e10i 0.385593i −0.981239 0.192796i $$-0.938244\pi$$
0.981239 0.192796i $$-0.0617557\pi$$
$$434$$ 0 0
$$435$$ −1.07085e9 −0.0299070
$$436$$ 0 0
$$437$$ 5.61514e9 + 3.24190e9i 0.153969 + 0.0888943i
$$438$$ 0 0
$$439$$ −4.13004e10 + 2.38448e10i −1.11198 + 0.642001i −0.939341 0.342985i $$-0.888562\pi$$
−0.172637 + 0.984986i $$0.555229\pi$$
$$440$$ 0 0
$$441$$ −1.07851e10 6.52950e9i −0.285147 0.172634i
$$442$$ 0 0
$$443$$ 9.20913e9 + 1.59507e10i 0.239113 + 0.414156i 0.960460 0.278418i $$-0.0898100\pi$$
−0.721347 + 0.692574i $$0.756477\pi$$
$$444$$ 0 0
$$445$$ −6.56648e9 + 1.13735e10i −0.167453 + 0.290037i
$$446$$ 0 0
$$447$$ 2.42870e10i 0.608336i
$$448$$ 0 0
$$449$$ 4.72530e10 1.16264 0.581319 0.813676i $$-0.302537\pi$$
0.581319 + 0.813676i $$0.302537\pi$$
$$450$$ 0 0
$$451$$ 3.16658e9 + 1.82823e9i 0.0765393 + 0.0441900i
$$452$$ 0 0
$$453$$ −1.33756e10 + 7.72242e9i −0.317630 + 0.183384i
$$454$$ 0 0
$$455$$ 2.06741e10 2.02486e10i 0.482372 0.472443i
$$456$$ 0 0
$$457$$ 9.30524e9 + 1.61172e10i 0.213335 + 0.369508i 0.952756 0.303736i $$-0.0982340\pi$$
−0.739421 + 0.673243i $$0.764901\pi$$
$$458$$ 0 0
$$459$$ 6.25249e9 1.08296e10i 0.140865 0.243985i
$$460$$ 0 0
$$461$$ 9.20893e9i 0.203895i −0.994790 0.101947i $$-0.967493\pi$$
0.994790 0.101947i $$-0.0325073\pi$$
$$462$$ 0 0
$$463$$ −1.42010e10 −0.309025 −0.154513 0.987991i $$-0.549381\pi$$
−0.154513 + 0.987991i $$0.549381\pi$$
$$464$$ 0 0
$$465$$ 1.88359e10 + 1.08749e10i 0.402878 + 0.232602i
$$466$$ 0 0
$$467$$ −2.95507e10 + 1.70611e10i −0.621299 + 0.358707i −0.777374 0.629038i $$-0.783449\pi$$
0.156076 + 0.987745i $$0.450116\pi$$
$$468$$ 0 0
$$469$$ 2.66353e10 + 7.43460e9i 0.550511 + 0.153662i
$$470$$ 0 0
$$471$$ −6.99056e9 1.21080e10i −0.142046 0.246030i
$$472$$ 0 0
$$473$$ −1.19990e9 + 2.07829e9i −0.0239718 + 0.0415204i
$$474$$ 0 0
$$475$$ 6.88216e9i 0.135192i
$$476$$ 0 0
$$477$$ −3.01153e10 −0.581720
$$478$$ 0 0
$$479$$ 7.59507e9 + 4.38502e9i 0.144275 + 0.0832970i 0.570400 0.821367i $$-0.306788\pi$$
−0.426125 + 0.904664i $$0.640122\pi$$
$$480$$ 0 0
$$481$$ −6.06607e10 + 3.50225e10i −1.13325 + 0.654284i
$$482$$ 0 0
$$483$$ −3.31044e10 + 8.50236e9i −0.608272 + 0.156225i
$$484$$ 0 0
$$485$$ 1.51551e10 + 2.62494e10i 0.273900 + 0.474408i
$$486$$ 0 0
$$487$$ −6.41038e9 + 1.11031e10i −0.113964 + 0.197392i −0.917365 0.398047i $$-0.869688\pi$$
0.803401 + 0.595438i $$0.203022\pi$$
$$488$$ 0 0
$$489$$ 2.73242e10i 0.477873i
$$490$$ 0 0
$$491$$ 6.34320e10 1.09140 0.545698 0.837982i $$-0.316265\pi$$
0.545698 + 0.837982i $$0.316265\pi$$
$$492$$ 0 0
$$493$$ −9.33065e9 5.38705e9i −0.157952 0.0911934i
$$494$$ 0 0
$$495$$ −9.57118e9 + 5.52592e9i −0.159421 + 0.0920416i
$$496$$ 0 0
$$497$$ −1.85958e10 7.24040e10i −0.304783 1.18669i
$$498$$ 0 0
$$499$$ −3.36380e10 5.82628e10i −0.542536 0.939700i −0.998758 0.0498336i $$-0.984131\pi$$
0.456222 0.889866i $$-0.349202\pi$$
$$500$$ 0 0
$$501$$ −1.74589e10 + 3.02396e10i −0.277118 + 0.479983i
$$502$$ 0 0
$$503$$ 1.04697e11i 1.63554i −0.575542 0.817772i $$-0.695209\pi$$
0.575542 0.817772i $$-0.304791\pi$$
$$504$$ 0 0
$$505$$ −2.77188e10 −0.426196
$$506$$ 0 0
$$507$$ −5.40891e10 3.12283e10i −0.818611 0.472625i
$$508$$ 0 0
$$509$$ −4.94469e10 + 2.85482e10i −0.736662 + 0.425312i −0.820854 0.571137i $$-0.806502\pi$$
0.0841923 + 0.996450i $$0.473169\pi$$
$$510$$ 0 0
$$511$$ 8.08251e9 2.89565e10i 0.118539 0.424680i
$$512$$ 0 0
$$513$$ 1.08926e9 + 1.88666e9i 0.0157276 + 0.0272410i
$$514$$ 0 0
$$515$$ −2.66637e10 + 4.61830e10i −0.379046 + 0.656527i
$$516$$ 0 0
$$517$$ 1.25505e11i 1.75671i
$$518$$ 0 0
$$519$$ 4.90430e10 0.675940
$$520$$ 0 0
$$521$$ 7.48609e10 + 4.32210e10i 1.01602 + 0.586602i 0.912950 0.408072i $$-0.133799\pi$$
0.103074 + 0.994674i $$0.467132\pi$$
$$522$$ 0 0
$$523$$ 1.27623e10 7.36833e9i 0.170578 0.0984832i −0.412280 0.911057i $$-0.635268\pi$$
0.582858 + 0.812574i $$0.301934\pi$$
$$524$$ 0 0
$$525$$ −2.53848e10 2.59183e10i −0.334147 0.341169i
$$526$$ 0 0
$$527$$ 1.09415e11 + 1.89512e11i 1.41852 + 2.45694i
$$528$$ 0 0
$$529$$ −7.17338e9 + 1.24247e10i −0.0916012 + 0.158658i
$$530$$ 0 0
$$531$$ 2.53302e10i 0.318611i
$$532$$ 0 0
$$533$$ −8.72077e9 −0.108055
$$534$$ 0 0
$$535$$ −4.00892e10 2.31455e10i −0.489342 0.282522i
$$536$$ 0 0
$$537$$ −1.00632e10 + 5.80999e9i −0.121015 + 0.0698679i
$$538$$ 0 0
$$539$$ −2.33136e9 + 1.12084e11i −0.0276220 + 1.32797i
$$540$$ 0 0
$$541$$ −5.99660e10 1.03864e11i −0.700029 1.21249i −0.968456 0.249185i $$-0.919837\pi$$
0.268427 0.963300i $$-0.413496\pi$$
$$542$$ 0 0
$$543$$ 1.15033e10 1.99243e10i 0.132319 0.229183i
$$544$$ 0 0
$$545$$ 2.84890e10i 0.322917i
$$546$$ 0 0
$$547$$ −7.72241e10 −0.862588 −0.431294 0.902211i $$-0.641943\pi$$
−0.431294 + 0.902211i $$0.641943\pi$$
$$548$$ 0 0
$$549$$ −4.21354e10 2.43269e10i −0.463829 0.267792i
$$550$$ 0 0
$$551$$ 1.62551e9 9.38491e8i 0.0176354 0.0101818i
$$552$$ 0 0
$$553$$ −7.31491e10 + 7.16434e10i −0.782183 + 0.766083i
$$554$$ 0 0
$$555$$ −9.17610e9 1.58935e10i −0.0967133 0.167512i
$$556$$ 0 0
$$557$$ 8.89933e10 1.54141e11i 0.924564 1.60139i 0.132302 0.991209i $$-0.457763\pi$$
0.792262 0.610182i $$-0.208904\pi$$
$$558$$ 0 0
$$559$$ 5.72362e9i 0.0586170i
$$560$$ 0 0
$$561$$ −1.11195e11 −1.12263
$$562$$ 0 0
$$563$$ −1.36022e11 7.85323e10i −1.35386 0.781654i −0.365076 0.930978i $$-0.618957\pi$$
−0.988788 + 0.149323i $$0.952290\pi$$
$$564$$ 0 0
$$565$$ −6.17950e10 + 3.56774e10i −0.606400 + 0.350105i
$$566$$ 0 0
$$567$$ −1.10611e10 3.08744e9i −0.107020 0.0298721i
$$568$$ 0 0
$$569$$ −2.78668e8 4.82667e8i −0.00265851 0.00460467i 0.864693 0.502301i $$-0.167513\pi$$
−0.867352 + 0.497696i $$0.834180\pi$$
$$570$$ 0 0
$$571$$ 1.85718e10 3.21672e10i 0.174706 0.302600i −0.765353 0.643610i $$-0.777436\pi$$
0.940060 + 0.341010i $$0.110769\pi$$
$$572$$ 0 0
$$573$$ 8.91974e10i 0.827434i
$$574$$ 0 0
$$575$$ −9.83506e10 −0.899716
$$576$$ 0 0
$$577$$ 3.46036e10 + 1.99784e10i 0.312189 + 0.180243i 0.647906 0.761721i $$-0.275645\pi$$
−0.335716 + 0.941963i $$0.608978\pi$$
$$578$$ 0 0
$$579$$ −3.80937e10 + 2.19934e10i −0.338953 + 0.195694i
$$580$$ 0 0
$$581$$ 1.67434e11 4.30027e10i 1.46939 0.377391i
$$582$$ 0 0
$$583$$ 1.33894e11 + 2.31911e11i 1.15901 + 2.00746i
$$584$$ 0 0
$$585$$ 1.31795e10 2.28276e10i 0.112532 0.194911i
$$586$$ 0 0
$$587$$ 1.12252e11i 0.945460i 0.881207 + 0.472730i $$0.156731\pi$$
−0.881207 + 0.472730i $$0.843269\pi$$
$$588$$ 0 0
$$589$$ −3.81229e10 −0.316756
$$590$$ 0 0
$$591$$ 4.97370e10 + 2.87156e10i 0.407689 + 0.235380i
$$592$$ 0 0
$$593$$ 4.84487e10 2.79719e10i 0.391799 0.226205i −0.291140 0.956680i $$-0.594035\pi$$
0.682939 + 0.730475i $$0.260701\pi$$
$$594$$ 0 0
$$595$$ 1.89766e10 + 7.38865e10i 0.151409 + 0.589518i
$$596$$ 0 0
$$597$$ 2.69702e9 + 4.67137e9i 0.0212318 + 0.0367745i
$$598$$ 0 0
$$599$$ 1.46361e10 2.53505e10i 0.113689 0.196916i −0.803566 0.595216i $$-0.797067\pi$$
0.917255 + 0.398300i $$0.130400\pi$$
$$600$$ 0 0
$$601$$ 3.04406e10i 0.233322i 0.993172 + 0.116661i $$0.0372191\pi$$
−0.993172 + 0.116661i $$0.962781\pi$$
$$602$$ 0 0
$$603$$ 2.51887e10 0.190518
$$604$$ 0 0
$$605$$ 3.68678e10 + 2.12856e10i 0.275186 + 0.158879i
$$606$$ 0 0
$$607$$ 1.87228e11 1.08096e11i 1.37917 0.796262i 0.387107 0.922035i $$-0.373474\pi$$
0.992059 + 0.125772i $$0.0401409\pi$$
$$608$$ 0 0
$$609$$ −2.66009e9 + 9.53008e9i −0.0193387 + 0.0692831i
$$610$$ 0 0
$$611$$ −1.49667e11 2.59232e11i −1.07390 1.86004i
$$612$$ 0 0
$$613$$ 3.15010e10 5.45613e10i 0.223091 0.386405i −0.732654 0.680601i $$-0.761719\pi$$
0.955745 + 0.294196i $$0.0950519\pi$$
$$614$$ 0 0
$$615$$ 2.28490e9i 0.0159723i
$$616$$ 0 0
$$617$$ 2.31396e11 1.59667 0.798336 0.602213i $$-0.205714\pi$$
0.798336 + 0.602213i $$0.205714\pi$$
$$618$$ 0 0
$$619$$ −8.62110e10 4.97739e10i −0.587219 0.339031i 0.176778 0.984251i $$-0.443432\pi$$
−0.763997 + 0.645220i $$0.776766\pi$$
$$620$$ 0 0
$$621$$ −2.69615e10 + 1.55663e10i −0.181292 + 0.104669i
$$622$$ 0 0
$$623$$ 8.49068e10 + 8.66913e10i 0.563625 + 0.575471i
$$624$$ 0 0
$$625$$ −3.90080e10 6.75639e10i −0.255643 0.442787i
$$626$$ 0 0
$$627$$ 9.68579e9 1.67763e10i 0.0626708 0.108549i
$$628$$ 0 0
$$629$$ 1.84646e11i 1.17961i
$$630$$ 0 0
$$631$$ −3.88355e10 −0.244969 −0.122485 0.992470i $$-0.539086\pi$$
−0.122485 + 0.992470i $$0.539086\pi$$
$$632$$ 0 0
$$633$$ 9.47590e10 + 5.47092e10i 0.590209 + 0.340757i
$$634$$ 0 0
$$635$$ 8.94780e9 5.16602e9i 0.0550328 0.0317732i
$$636$$ 0 0
$$637$$ −1.28846e11 2.34289e11i −0.782554 1.42297i
$$638$$ 0 0
$$639$$ −3.40455e10 5.89686e10i −0.204201 0.353686i
$$640$$ 0 0
$$641$$ −1.01203e11 + 1.75289e11i −0.599462 + 1.03830i 0.393439 + 0.919351i $$0.371285\pi$$
−0.992901 + 0.118948i $$0.962048\pi$$
$$642$$ 0 0
$$643$$ 1.46591e11i 0.857558i −0.903409 0.428779i $$-0.858944\pi$$
0.903409 0.428779i $$-0.141056\pi$$
$$644$$ 0 0
$$645$$ 1.49962e9 0.00866450
$$646$$ 0 0
$$647$$ 2.40431e11 + 1.38813e11i 1.37206 + 0.792158i 0.991187 0.132470i $$-0.0422907\pi$$
0.380871 + 0.924628i $$0.375624\pi$$
$$648$$ 0 0
$$649$$ 1.95062e11 1.12619e11i 1.09950 0.634795i
$$650$$ 0 0
$$651$$ 1.43571e11 1.40616e11i 0.799362 0.782908i
$$652$$ 0 0
$$653$$ −1.35533e11 2.34750e11i −0.745406 1.29108i −0.950005 0.312236i $$-0.898922\pi$$
0.204598 0.978846i $$-0.434411\pi$$
$$654$$ 0 0
$$655$$ −4.97805e9 + 8.62224e9i −0.0270455 + 0.0468441i
$$656$$ 0 0
$$657$$ 2.73838e10i 0.146971i
$$658$$ 0 0
$$659$$ 8.76828e10 0.464914 0.232457 0.972607i $$-0.425324\pi$$
0.232457 + 0.972607i $$0.425324\pi$$
$$660$$ 0 0
$$661$$ −3.77894e10 2.18177e10i −0.197954 0.114289i 0.397747 0.917495i $$-0.369792\pi$$
−0.595701 + 0.803206i $$0.703126\pi$$
$$662$$ 0 0
$$663$$ 2.29674e11 1.32602e11i 1.18866 0.686273i
$$664$$ 0 0
$$665$$ −1.28004e10 3.57292e9i −0.0654541 0.0182699i
$$666$$ 0 0
$$667$$ 1.34117e10 + 2.32297e10i 0.0677609 + 0.117365i
$$668$$ 0 0
$$669$$ −2.66875e10 + 4.62241e10i −0.133230 + 0.230762i
$$670$$ 0 0
$$671$$ 4.32633e11i 2.13417i
$$672$$ 0 0
$$673$$ 1.88626e11 0.919480 0.459740 0.888054i $$-0.347943\pi$$
0.459740 + 0.888054i $$0.347943\pi$$
$$674$$ 0 0
$$675$$ −2.86180e10 1.65226e10i −0.137856 0.0795911i
$$676$$ 0 0
$$677$$ 3.41068e10 1.96916e10i 0.162363 0.0937401i −0.416617 0.909082i $$-0.636784\pi$$
0.578980 + 0.815342i $$0.303451\pi$$
$$678$$ 0 0
$$679$$ 2.71253e11 6.96673e10i 1.27613 0.327755i
$$680$$ 0 0
$$681$$ −4.92080e9 8.52308e9i −0.0228796 0.0396285i
$$682$$ 0 0
$$683$$ −1.05360e11 + 1.82490e11i −0.484167 + 0.838601i −0.999835 0.0181874i $$-0.994210\pi$$
0.515668 + 0.856788i $$0.327544\pi$$
$$684$$ 0 0
$$685$$ 1.07590e11i 0.488663i
$$686$$ 0 0
$$687$$ −1.72114e11 −0.772663
$$688$$ 0 0
$$689$$ −5.53116e11 3.19342e11i −2.45437 1.41703i
$$690$$ 0 0
$$691$$ −3.03078e10 + 1.74982e10i −0.132936 + 0.0767505i −0.564993 0.825096i $$-0.691121\pi$$
0.432057 + 0.901846i $$0.357788\pi$$
$$692$$ 0 0
$$693$$ 2.54024e10 + 9.89058e10i 0.110139 + 0.428834i
$$694$$ 0 0
$$695$$ −2.80186e10 4.85296e10i −0.120090 0.208002i
$$696$$ 0 0
$$697$$ 1.14944e10 1.99090e10i 0.0487031 0.0843563i
$$698$$ 0 0
$$699$$ 1.32997e10i 0.0557101i
$$700$$ 0 0
$$701$$ 8.58032e10 0.355330 0.177665 0.984091i $$-0.443146\pi$$
0.177665 + 0.984091i $$0.443146\pi$$
$$702$$ 0 0
$$703$$ 2.78580e10 + 1.60838e10i 0.114059 + 0.0658517i
$$704$$ 0 0
$$705$$ 6.79203e10 3.92138e10i 0.274943 0.158739i
$$706$$ 0 0
$$707$$ −6.88559e10 + 2.46684e11i −0.275590 + 0.987333i
$$708$$ 0 0
$$709$$ 9.74057e10 + 1.68712e11i 0.385478 + 0.667668i 0.991835 0.127525i $$-0.0407032\pi$$
−0.606357 + 0.795192i $$0.707370\pi$$
$$710$$ 0 0
$$711$$ −4.66317e10 + 8.07685e10i −0.182475 + 0.316056i
$$712$$ 0 0
$$713$$ 5.44801e11i 2.10804i
$$714$$ 0 0
$$715$$ −2.34387e11 −0.896827
$$716$$ 0 0
$$717$$ 1.06356e11 + 6.14046e10i 0.402425 + 0.232340i
$$718$$ 0 0
$$719$$ −2.89871e11 + 1.67357e11i −1.08465 + 0.626222i −0.932147 0.362081i $$-0.882066\pi$$
−0.152502 + 0.988303i $$0.548733\pi$$
$$720$$ 0 0
$$721$$ 3.44771e11 + 3.52017e11i 1.27582 + 1.30263i
$$722$$ 0 0
$$723$$ 5.55609e9 + 9.62343e9i 0.0203337 + 0.0352190i
$$724$$ 0 0
$$725$$ −1.42357e10 + 2.46569e10i −0.0515259 + 0.0892455i
$$726$$ 0 0
$$727$$ 9.86180e10i 0.353035i 0.984297 + 0.176518i $$0.0564833\pi$$
−0.984297 + 0.176518i $$0.943517\pi$$
$$728$$ 0 0
$$729$$ −1.04604e10 −0.0370370
$$730$$ 0 0
$$731$$ 1.30667e10 + 7.54404e9i 0.0457609 + 0.0264201i
$$732$$ 0 0
$$733$$ 2.61192e11 1.50799e11i 0.904782 0.522376i 0.0260337 0.999661i $$-0.491712\pi$$
0.878749 + 0.477285i $$0.158379\pi$$
$$734$$ 0 0
$$735$$ 6.13852e10 3.37586e10i 0.210336 0.115674i
$$736$$ 0 0
$$737$$ −1.11990e11 1.93972e11i −0.379585 0.657460i
$$738$$ 0 0
$$739$$ −1.82846e11 + 3.16698e11i −0.613065 + 1.06186i 0.377655 + 0.925946i $$0.376730\pi$$
−0.990721 + 0.135914i $$0.956603\pi$$
$$740$$ 0 0
$$741$$ 4.62019e10i 0.153245i
$$742$$ 0 0
$$743$$ −3.52082e11 −1.15528 −0.577642 0.816290i $$-0.696027\pi$$
−0.577642 + 0.816290i $$0.696027\pi$$
$$744$$ 0 0
$$745$$ 1.16873e11 + 6.74766e10i 0.379392 + 0.219042i
$$746$$ 0 0
$$747$$ 1.36364e11 7.87300e10i 0.437944 0.252847i
$$748$$ 0 0
$$749$$ −3.05569e11 + 2.99279e11i −0.970917 + 0.950932i
$$750$$ 0 0
$$751$$ −1.44039e11 2.49484e11i −0.452816 0.784300i 0.545744 0.837952i $$-0.316247\pi$$
−0.998560 + 0.0536517i $$0.982914\pi$$
$$752$$ 0 0
$$753$$ 8.16530e10 1.41427e11i 0.253976 0.439899i
$$754$$ 0 0
$$755$$ 8.58209e10i 0.264122i
$$756$$ 0 0
$$757$$ −5.34615e11 −1.62801 −0.814006 0.580857i $$-0.802718\pi$$
−0.814006 + 0.580857i $$0.802718\pi$$
$$758$$ 0 0
$$759$$ 2.39744e11 + 1.38416e11i 0.722405 + 0.417081i
$$760$$ 0 0
$$761$$ 2.20516e10 1.27315e10i 0.0657507 0.0379612i −0.466764 0.884382i $$-0.654580\pi$$
0.532515 + 0.846421i $$0.321247\pi$$
$$762$$ 0 0
$$763$$ −2.53539e11 7.07692e10i −0.748076 0.208807i
$$764$$ 0 0
$$765$$ 3.47426e10 + 6.01760e10i 0.101442 + 0.175702i
$$766$$ 0 0
$$767$$ −2.68601e11 + 4.65230e11i −0.776114 + 1.34427i
$$768$$ 0 0
$$769$$ 1.61134e11i 0.460768i 0.973100 + 0.230384i $$0.0739982\pi$$
−0.973100 + 0.230384i $$0.926002\pi$$
$$770$$ 0 0
$$771$$ −1.81647e11 −0.514057
$$772$$ 0 0
$$773$$ −2.00134e11 1.15547e11i −0.560535 0.323625i 0.192825 0.981233i $$-0.438235\pi$$
−0.753360 + 0.657608i $$0.771568\pi$$
$$774$$ 0 0
$$775$$ 5.00799e11 2.89136e11i 1.38821 0.801486i
$$776$$ 0 0
$$777$$ −1.64239e11 + 4.21821e10i −0.450600 + 0.115730i
$$778$$ 0 0
$$779$$ 2.00247e9 + 3.46839e9i 0.00543772 + 0.00941841i
$$780$$ 0 0
$$781$$ −3.02736e11 + 5.24353e11i −0.8136