# Properties

 Label 160.6.n.a.63.4 Level $160$ Weight $6$ Character 160.63 Analytic conductor $25.661$ Analytic rank $0$ Dimension $14$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$160 = 2^{5} \cdot 5$$ Weight: $$k$$ $$=$$ $$6$$ Character orbit: $$[\chi]$$ $$=$$ 160.n (of order $$4$$, degree $$2$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$25.6614111701$$ Analytic rank: $$0$$ Dimension: $$14$$ Relative dimension: $$7$$ over $$\Q(i)$$ Coefficient field: $$\mathbb{Q}[x]/(x^{14} - \cdots)$$ Defining polynomial: $$x^{14} - 4 x^{13} + 8 x^{12} - 4626 x^{11} + 149441 x^{10} - 2113414 x^{9} + 17958066 x^{8} - 97717112 x^{7} + 355171384 x^{6} - 910571904 x^{5} + 2428303248 x^{4} - 9166992192 x^{3} + 32237484304 x^{2} - 66916821408 x + 69451154208$$ Coefficient ring: $$\Z[a_1, \ldots, a_{9}]$$ Coefficient ring index: $$2^{31}\cdot 5^{3}$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

## Embedding invariants

 Embedding label 63.4 Root $$6.86993 + 6.86993i$$ of defining polynomial Character $$\chi$$ $$=$$ 160.63 Dual form 160.6.n.a.127.4

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-1.47740 + 1.47740i) q^{3} +(55.2474 - 8.52775i) q^{5} +(-156.265 - 156.265i) q^{7} +238.635i q^{9} +O(q^{10})$$ $$q+(-1.47740 + 1.47740i) q^{3} +(55.2474 - 8.52775i) q^{5} +(-156.265 - 156.265i) q^{7} +238.635i q^{9} -35.4820i q^{11} +(-247.384 - 247.384i) q^{13} +(-69.0238 + 94.2216i) q^{15} +(-1193.47 + 1193.47i) q^{17} +1010.27 q^{19} +461.733 q^{21} +(-2033.39 + 2033.39i) q^{23} +(2979.55 - 942.273i) q^{25} +(-711.568 - 711.568i) q^{27} +2206.91i q^{29} -6179.11i q^{31} +(52.4213 + 52.4213i) q^{33} +(-9965.84 - 7300.66i) q^{35} +(-9466.02 + 9466.02i) q^{37} +730.972 q^{39} -9004.04 q^{41} +(-15902.9 + 15902.9i) q^{43} +(2035.02 + 13183.9i) q^{45} +(-7193.64 - 7193.64i) q^{47} +32030.6i q^{49} -3526.47i q^{51} +(-12995.3 - 12995.3i) q^{53} +(-302.582 - 1960.29i) q^{55} +(-1492.57 + 1492.57i) q^{57} -40515.4 q^{59} +29233.6 q^{61} +(37290.3 - 37290.3i) q^{63} +(-15777.0 - 11557.7i) q^{65} +(-18221.2 - 18221.2i) q^{67} -6008.26i q^{69} +26609.8i q^{71} +(36402.4 + 36402.4i) q^{73} +(-3009.89 + 5794.12i) q^{75} +(-5544.61 + 5544.61i) q^{77} +5089.11 q^{79} -55885.7 q^{81} +(-20395.0 + 20395.0i) q^{83} +(-55758.6 + 76113.8i) q^{85} +(-3260.49 - 3260.49i) q^{87} -59348.0i q^{89} +77315.1i q^{91} +(9129.03 + 9129.03i) q^{93} +(55814.6 - 8615.30i) q^{95} +(69542.4 - 69542.4i) q^{97} +8467.24 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$14q - 10q^{3} + 42q^{5} - 66q^{7} + O(q^{10})$$ $$14q - 10q^{3} + 42q^{5} - 66q^{7} - 414q^{13} - 278q^{15} + 1222q^{17} - 5672q^{19} + 5924q^{21} - 2902q^{23} - 4466q^{25} + 2168q^{27} - 2444q^{33} + 2618q^{35} - 1790q^{37} + 11076q^{39} + 11644q^{41} + 3982q^{43} + 14704q^{45} + 1278q^{47} + 5882q^{53} - 65608q^{55} - 14552q^{57} + 8504q^{59} + 20564q^{61} - 19422q^{63} + 40798q^{65} - 107926q^{67} - 16418q^{73} - 66586q^{75} - 13348q^{77} + 146544q^{79} + 173806q^{81} + 36398q^{83} - 66262q^{85} - 124384q^{87} - 306620q^{93} - 173768q^{95} - 60314q^{97} + 388628q^{99} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/160\mathbb{Z}\right)^\times$$.

 $$n$$ $$31$$ $$97$$ $$101$$ $$\chi(n)$$ $$-1$$ $$e\left(\frac{3}{4}\right)$$ $$1$$

## Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0 0
$$3$$ −1.47740 + 1.47740i −0.0947754 + 0.0947754i −0.752905 0.658129i $$-0.771348\pi$$
0.658129 + 0.752905i $$0.271348\pi$$
$$4$$ 0 0
$$5$$ 55.2474 8.52775i 0.988296 0.152549i
$$6$$ 0 0
$$7$$ −156.265 156.265i −1.20536 1.20536i −0.972513 0.232848i $$-0.925196\pi$$
−0.232848 0.972513i $$-0.574804\pi$$
$$8$$ 0 0
$$9$$ 238.635i 0.982035i
$$10$$ 0 0
$$11$$ 35.4820i 0.0884152i −0.999022 0.0442076i $$-0.985924\pi$$
0.999022 0.0442076i $$-0.0140763\pi$$
$$12$$ 0 0
$$13$$ −247.384 247.384i −0.405988 0.405988i 0.474349 0.880337i $$-0.342684\pi$$
−0.880337 + 0.474349i $$0.842684\pi$$
$$14$$ 0 0
$$15$$ −69.0238 + 94.2216i −0.0792083 + 0.108124i
$$16$$ 0 0
$$17$$ −1193.47 + 1193.47i −1.00159 + 1.00159i −0.00159016 + 0.999999i $$0.500506\pi$$
−0.999999 + 0.00159016i $$0.999494\pi$$
$$18$$ 0 0
$$19$$ 1010.27 0.642025 0.321012 0.947075i $$-0.395977\pi$$
0.321012 + 0.947075i $$0.395977\pi$$
$$20$$ 0 0
$$21$$ 461.733 0.228477
$$22$$ 0 0
$$23$$ −2033.39 + 2033.39i −0.801494 + 0.801494i −0.983329 0.181835i $$-0.941796\pi$$
0.181835 + 0.983329i $$0.441796\pi$$
$$24$$ 0 0
$$25$$ 2979.55 942.273i 0.953458 0.301527i
$$26$$ 0 0
$$27$$ −711.568 711.568i −0.187848 0.187848i
$$28$$ 0 0
$$29$$ 2206.91i 0.487291i 0.969864 + 0.243646i $$0.0783434\pi$$
−0.969864 + 0.243646i $$0.921657\pi$$
$$30$$ 0 0
$$31$$ 6179.11i 1.15484i −0.816448 0.577419i $$-0.804060\pi$$
0.816448 0.577419i $$-0.195940\pi$$
$$32$$ 0 0
$$33$$ 52.4213 + 52.4213i 0.00837959 + 0.00837959i
$$34$$ 0 0
$$35$$ −9965.84 7300.66i −1.37513 1.00738i
$$36$$ 0 0
$$37$$ −9466.02 + 9466.02i −1.13674 + 1.13674i −0.147715 + 0.989030i $$0.547192\pi$$
−0.989030 + 0.147715i $$0.952808\pi$$
$$38$$ 0 0
$$39$$ 730.972 0.0769554
$$40$$ 0 0
$$41$$ −9004.04 −0.836523 −0.418261 0.908327i $$-0.637360\pi$$
−0.418261 + 0.908327i $$0.637360\pi$$
$$42$$ 0 0
$$43$$ −15902.9 + 15902.9i −1.31161 + 1.31161i −0.391383 + 0.920228i $$0.628003\pi$$
−0.920228 + 0.391383i $$0.871997\pi$$
$$44$$ 0 0
$$45$$ 2035.02 + 13183.9i 0.149809 + 0.970541i
$$46$$ 0 0
$$47$$ −7193.64 7193.64i −0.475011 0.475011i 0.428521 0.903532i $$-0.359035\pi$$
−0.903532 + 0.428521i $$0.859035\pi$$
$$48$$ 0 0
$$49$$ 32030.6i 1.90579i
$$50$$ 0 0
$$51$$ 3526.47i 0.189852i
$$52$$ 0 0
$$53$$ −12995.3 12995.3i −0.635474 0.635474i 0.313962 0.949436i $$-0.398344\pi$$
−0.949436 + 0.313962i $$0.898344\pi$$
$$54$$ 0 0
$$55$$ −302.582 1960.29i −0.0134877 0.0873804i
$$56$$ 0 0
$$57$$ −1492.57 + 1492.57i −0.0608482 + 0.0608482i
$$58$$ 0 0
$$59$$ −40515.4 −1.51527 −0.757636 0.652677i $$-0.773646\pi$$
−0.757636 + 0.652677i $$0.773646\pi$$
$$60$$ 0 0
$$61$$ 29233.6 1.00591 0.502954 0.864313i $$-0.332247\pi$$
0.502954 + 0.864313i $$0.332247\pi$$
$$62$$ 0 0
$$63$$ 37290.3 37290.3i 1.18371 1.18371i
$$64$$ 0 0
$$65$$ −15777.0 11557.7i −0.463170 0.339303i
$$66$$ 0 0
$$67$$ −18221.2 18221.2i −0.495894 0.495894i 0.414263 0.910157i $$-0.364039\pi$$
−0.910157 + 0.414263i $$0.864039\pi$$
$$68$$ 0 0
$$69$$ 6008.26i 0.151924i
$$70$$ 0 0
$$71$$ 26609.8i 0.626463i 0.949677 + 0.313232i $$0.101412\pi$$
−0.949677 + 0.313232i $$0.898588\pi$$
$$72$$ 0 0
$$73$$ 36402.4 + 36402.4i 0.799507 + 0.799507i 0.983018 0.183511i $$-0.0587462\pi$$
−0.183511 + 0.983018i $$0.558746\pi$$
$$74$$ 0 0
$$75$$ −3009.89 + 5794.12i −0.0617870 + 0.118942i
$$76$$ 0 0
$$77$$ −5544.61 + 5544.61i −0.106572 + 0.106572i
$$78$$ 0 0
$$79$$ 5089.11 0.0917432 0.0458716 0.998947i $$-0.485393\pi$$
0.0458716 + 0.998947i $$0.485393\pi$$
$$80$$ 0 0
$$81$$ −55885.7 −0.946428
$$82$$ 0 0
$$83$$ −20395.0 + 20395.0i −0.324958 + 0.324958i −0.850666 0.525707i $$-0.823801\pi$$
0.525707 + 0.850666i $$0.323801\pi$$
$$84$$ 0 0
$$85$$ −55758.6 + 76113.8i −0.837075 + 1.14266i
$$86$$ 0 0
$$87$$ −3260.49 3260.49i −0.0461832 0.0461832i
$$88$$ 0 0
$$89$$ 59348.0i 0.794202i −0.917775 0.397101i $$-0.870016\pi$$
0.917775 0.397101i $$-0.129984\pi$$
$$90$$ 0 0
$$91$$ 77315.1i 0.978725i
$$92$$ 0 0
$$93$$ 9129.03 + 9129.03i 0.109450 + 0.109450i
$$94$$ 0 0
$$95$$ 55814.6 8615.30i 0.634511 0.0979403i
$$96$$ 0 0
$$97$$ 69542.4 69542.4i 0.750447 0.750447i −0.224115 0.974563i $$-0.571949\pi$$
0.974563 + 0.224115i $$0.0719492\pi$$
$$98$$ 0 0
$$99$$ 8467.24 0.0868268
$$100$$ 0 0
$$101$$ 51962.3 0.506857 0.253428 0.967354i $$-0.418442\pi$$
0.253428 + 0.967354i $$0.418442\pi$$
$$102$$ 0 0
$$103$$ 95475.1 95475.1i 0.886742 0.886742i −0.107467 0.994209i $$-0.534274\pi$$
0.994209 + 0.107467i $$0.0342740\pi$$
$$104$$ 0 0
$$105$$ 25509.6 3937.55i 0.225803 0.0348540i
$$106$$ 0 0
$$107$$ −47628.0 47628.0i −0.402164 0.402164i 0.476831 0.878995i $$-0.341785\pi$$
−0.878995 + 0.476831i $$0.841785\pi$$
$$108$$ 0 0
$$109$$ 207149.i 1.67000i −0.550249 0.835000i $$-0.685467\pi$$
0.550249 0.835000i $$-0.314533\pi$$
$$110$$ 0 0
$$111$$ 27970.2i 0.215471i
$$112$$ 0 0
$$113$$ −69766.1 69766.1i −0.513983 0.513983i 0.401762 0.915744i $$-0.368398\pi$$
−0.915744 + 0.401762i $$0.868398\pi$$
$$114$$ 0 0
$$115$$ −94999.2 + 129680.i −0.669846 + 0.914381i
$$116$$ 0 0
$$117$$ 59034.4 59034.4i 0.398695 0.398695i
$$118$$ 0 0
$$119$$ 372996. 2.41455
$$120$$ 0 0
$$121$$ 159792. 0.992183
$$122$$ 0 0
$$123$$ 13302.6 13302.6i 0.0792818 0.0792818i
$$124$$ 0 0
$$125$$ 156577. 77467.0i 0.896301 0.443447i
$$126$$ 0 0
$$127$$ 211933. + 211933.i 1.16598 + 1.16598i 0.983144 + 0.182831i $$0.0585261\pi$$
0.182831 + 0.983144i $$0.441474\pi$$
$$128$$ 0 0
$$129$$ 46990.0i 0.248617i
$$130$$ 0 0
$$131$$ 231312.i 1.17766i 0.808258 + 0.588829i $$0.200411\pi$$
−0.808258 + 0.588829i $$0.799589\pi$$
$$132$$ 0 0
$$133$$ −157869. 157869.i −0.773872 0.773872i
$$134$$ 0 0
$$135$$ −45380.4 33244.2i −0.214306 0.156994i
$$136$$ 0 0
$$137$$ −148753. + 148753.i −0.677119 + 0.677119i −0.959347 0.282228i $$-0.908926\pi$$
0.282228 + 0.959347i $$0.408926\pi$$
$$138$$ 0 0
$$139$$ 28622.8 0.125653 0.0628267 0.998024i $$-0.479988\pi$$
0.0628267 + 0.998024i $$0.479988\pi$$
$$140$$ 0 0
$$141$$ 21255.8 0.0900388
$$142$$ 0 0
$$143$$ −8777.70 + 8777.70i −0.0358955 + 0.0358955i
$$144$$ 0 0
$$145$$ 18819.9 + 121926.i 0.0743358 + 0.481588i
$$146$$ 0 0
$$147$$ −47322.1 47322.1i −0.180622 0.180622i
$$148$$ 0 0
$$149$$ 168468.i 0.621658i 0.950466 + 0.310829i $$0.100607\pi$$
−0.950466 + 0.310829i $$0.899393\pi$$
$$150$$ 0 0
$$151$$ 114484.i 0.408604i −0.978908 0.204302i $$-0.934508\pi$$
0.978908 0.204302i $$-0.0654924\pi$$
$$152$$ 0 0
$$153$$ −284803. 284803.i −0.983596 0.983596i
$$154$$ 0 0
$$155$$ −52693.9 341380.i −0.176170 1.14132i
$$156$$ 0 0
$$157$$ −148793. + 148793.i −0.481762 + 0.481762i −0.905694 0.423932i $$-0.860650\pi$$
0.423932 + 0.905694i $$0.360650\pi$$
$$158$$ 0 0
$$159$$ 38398.7 0.120455
$$160$$ 0 0
$$161$$ 635495. 1.93218
$$162$$ 0 0
$$163$$ 14195.8 14195.8i 0.0418496 0.0418496i −0.685872 0.727722i $$-0.740579\pi$$
0.727722 + 0.685872i $$0.240579\pi$$
$$164$$ 0 0
$$165$$ 3343.17 + 2449.10i 0.00955981 + 0.00700321i
$$166$$ 0 0
$$167$$ −129380. 129380.i −0.358985 0.358985i 0.504453 0.863439i $$-0.331694\pi$$
−0.863439 + 0.504453i $$0.831694\pi$$
$$168$$ 0 0
$$169$$ 248895.i 0.670347i
$$170$$ 0 0
$$171$$ 241084.i 0.630491i
$$172$$ 0 0
$$173$$ 152149. + 152149.i 0.386505 + 0.386505i 0.873439 0.486934i $$-0.161885\pi$$
−0.486934 + 0.873439i $$0.661885\pi$$
$$174$$ 0 0
$$175$$ −612845. 318356.i −1.51271 0.785811i
$$176$$ 0 0
$$177$$ 59857.6 59857.6i 0.143611 0.143611i
$$178$$ 0 0
$$179$$ 293286. 0.684161 0.342081 0.939671i $$-0.388868\pi$$
0.342081 + 0.939671i $$0.388868\pi$$
$$180$$ 0 0
$$181$$ −35244.3 −0.0799635 −0.0399818 0.999200i $$-0.512730\pi$$
−0.0399818 + 0.999200i $$0.512730\pi$$
$$182$$ 0 0
$$183$$ −43189.8 + 43189.8i −0.0953353 + 0.0953353i
$$184$$ 0 0
$$185$$ −442249. + 603697.i −0.950031 + 1.29685i
$$186$$ 0 0
$$187$$ 42346.8 + 42346.8i 0.0885557 + 0.0885557i
$$188$$ 0 0
$$189$$ 222387.i 0.452850i
$$190$$ 0 0
$$191$$ 862350.i 1.71041i 0.518291 + 0.855204i $$0.326568\pi$$
−0.518291 + 0.855204i $$0.673432\pi$$
$$192$$ 0 0
$$193$$ −87253.9 87253.9i −0.168613 0.168613i 0.617756 0.786370i $$-0.288042\pi$$
−0.786370 + 0.617756i $$0.788042\pi$$
$$194$$ 0 0
$$195$$ 40384.3 6233.55i 0.0760547 0.0117395i
$$196$$ 0 0
$$197$$ −113501. + 113501.i −0.208369 + 0.208369i −0.803574 0.595205i $$-0.797071\pi$$
0.595205 + 0.803574i $$0.297071\pi$$
$$198$$ 0 0
$$199$$ −497444. −0.890455 −0.445227 0.895418i $$-0.646877\pi$$
−0.445227 + 0.895418i $$0.646877\pi$$
$$200$$ 0 0
$$201$$ 53840.0 0.0939971
$$202$$ 0 0
$$203$$ 344863. 344863.i 0.587362 0.587362i
$$204$$ 0 0
$$205$$ −497450. + 76784.2i −0.826732 + 0.127611i
$$206$$ 0 0
$$207$$ −485236. 485236.i −0.787096 0.787096i
$$208$$ 0 0
$$209$$ 35846.3i 0.0567648i
$$210$$ 0 0
$$211$$ 359007.i 0.555133i −0.960706 0.277566i $$-0.910472\pi$$
0.960706 0.277566i $$-0.0895278\pi$$
$$212$$ 0 0
$$213$$ −39313.4 39313.4i −0.0593733 0.0593733i
$$214$$ 0 0
$$215$$ −742978. + 1.01421e6i −1.09617 + 1.49634i
$$216$$ 0 0
$$217$$ −965579. + 965579.i −1.39200 + 1.39200i
$$218$$ 0 0
$$219$$ −107562. −0.151547
$$220$$ 0 0
$$221$$ 590492. 0.813267
$$222$$ 0 0
$$223$$ 927233. 927233.i 1.24861 1.24861i 0.292276 0.956334i $$-0.405587\pi$$
0.956334 0.292276i $$-0.0944126\pi$$
$$224$$ 0 0
$$225$$ 224859. + 711025.i 0.296110 + 0.936329i
$$226$$ 0 0
$$227$$ −1.02849e6 1.02849e6i −1.32475 1.32475i −0.909880 0.414871i $$-0.863827\pi$$
−0.414871 0.909880i $$-0.636173\pi$$
$$228$$ 0 0
$$229$$ 624395.i 0.786812i −0.919365 0.393406i $$-0.871297\pi$$
0.919365 0.393406i $$-0.128703\pi$$
$$230$$ 0 0
$$231$$ 16383.2i 0.0202009i
$$232$$ 0 0
$$233$$ 73769.5 + 73769.5i 0.0890199 + 0.0890199i 0.750214 0.661195i $$-0.229950\pi$$
−0.661195 + 0.750214i $$0.729950\pi$$
$$234$$ 0 0
$$235$$ −458776. 336084.i −0.541914 0.396989i
$$236$$ 0 0
$$237$$ −7518.66 + 7518.66i −0.00869500 + 0.00869500i
$$238$$ 0 0
$$239$$ −1.58693e6 −1.79706 −0.898529 0.438914i $$-0.855363\pi$$
−0.898529 + 0.438914i $$0.855363\pi$$
$$240$$ 0 0
$$241$$ 217448. 0.241165 0.120582 0.992703i $$-0.461524\pi$$
0.120582 + 0.992703i $$0.461524\pi$$
$$242$$ 0 0
$$243$$ 255477. 255477.i 0.277546 0.277546i
$$244$$ 0 0
$$245$$ 273149. + 1.76961e6i 0.290727 + 1.88349i
$$246$$ 0 0
$$247$$ −249924. 249924.i −0.260655 0.260655i
$$248$$ 0 0
$$249$$ 60263.1i 0.0615961i
$$250$$ 0 0
$$251$$ 1.84448e6i 1.84794i 0.382460 + 0.923972i $$0.375077\pi$$
−0.382460 + 0.923972i $$0.624923\pi$$
$$252$$ 0 0
$$253$$ 72148.7 + 72148.7i 0.0708643 + 0.0708643i
$$254$$ 0 0
$$255$$ −30072.9 194829.i −0.0289617 0.187630i
$$256$$ 0 0
$$257$$ 934464. 934464.i 0.882531 0.882531i −0.111261 0.993791i $$-0.535489\pi$$
0.993791 + 0.111261i $$0.0354888\pi$$
$$258$$ 0 0
$$259$$ 2.95842e6 2.74038
$$260$$ 0 0
$$261$$ −526644. −0.478537
$$262$$ 0 0
$$263$$ −545731. + 545731.i −0.486508 + 0.486508i −0.907202 0.420695i $$-0.861786\pi$$
0.420695 + 0.907202i $$0.361786\pi$$
$$264$$ 0 0
$$265$$ −828779. 607137.i −0.724977 0.531095i
$$266$$ 0 0
$$267$$ 87680.8 + 87680.8i 0.0752708 + 0.0752708i
$$268$$ 0 0
$$269$$ 1.62710e6i 1.37099i −0.728078 0.685495i $$-0.759586\pi$$
0.728078 0.685495i $$-0.240414\pi$$
$$270$$ 0 0
$$271$$ 344866.i 0.285251i 0.989777 + 0.142626i $$0.0455545\pi$$
−0.989777 + 0.142626i $$0.954446\pi$$
$$272$$ 0 0
$$273$$ −114225. 114225.i −0.0927591 0.0927591i
$$274$$ 0 0
$$275$$ −33433.8 105721.i −0.0266596 0.0843001i
$$276$$ 0 0
$$277$$ −1.31320e6 + 1.31320e6i −1.02833 + 1.02833i −0.0287441 + 0.999587i $$0.509151\pi$$
−0.999587 + 0.0287441i $$0.990849\pi$$
$$278$$ 0 0
$$279$$ 1.47455e6 1.13409
$$280$$ 0 0
$$281$$ 592433. 0.447583 0.223791 0.974637i $$-0.428157\pi$$
0.223791 + 0.974637i $$0.428157\pi$$
$$282$$ 0 0
$$283$$ 898854. 898854.i 0.667149 0.667149i −0.289906 0.957055i $$-0.593624\pi$$
0.957055 + 0.289906i $$0.0936240\pi$$
$$284$$ 0 0
$$285$$ −69732.4 + 95188.9i −0.0508537 + 0.0694183i
$$286$$ 0 0
$$287$$ 1.40702e6 + 1.40702e6i 1.00831 + 1.00831i
$$288$$ 0 0
$$289$$ 1.42889e6i 1.00636i
$$290$$ 0 0
$$291$$ 205484.i 0.142248i
$$292$$ 0 0
$$293$$ −1.69674e6 1.69674e6i −1.15464 1.15464i −0.985611 0.169032i $$-0.945936\pi$$
−0.169032 0.985611i $$-0.554064\pi$$
$$294$$ 0 0
$$295$$ −2.23837e6 + 345506.i −1.49754 + 0.231153i
$$296$$ 0 0
$$297$$ −25247.9 + 25247.9i −0.0166086 + 0.0166086i
$$298$$ 0 0
$$299$$ 1.00606e6 0.650795
$$300$$ 0 0
$$301$$ 4.97014e6 3.16193
$$302$$ 0 0
$$303$$ −76769.3 + 76769.3i −0.0480375 + 0.0480375i
$$304$$ 0 0
$$305$$ 1.61508e6 249297.i 0.994135 0.153450i
$$306$$ 0 0
$$307$$ −149779. 149779.i −0.0906992 0.0906992i 0.660301 0.751001i $$-0.270429\pi$$
−0.751001 + 0.660301i $$0.770429\pi$$
$$308$$ 0 0
$$309$$ 282110.i 0.168083i
$$310$$ 0 0
$$311$$ 384127.i 0.225203i 0.993640 + 0.112601i $$0.0359183\pi$$
−0.993640 + 0.112601i $$0.964082\pi$$
$$312$$ 0 0
$$313$$ −661386. 661386.i −0.381588 0.381588i 0.490086 0.871674i $$-0.336965\pi$$
−0.871674 + 0.490086i $$0.836965\pi$$
$$314$$ 0 0
$$315$$ 1.74219e6 2.37819e6i 0.989279 1.35043i
$$316$$ 0 0
$$317$$ 1.48199e6 1.48199e6i 0.828319 0.828319i −0.158965 0.987284i $$-0.550816\pi$$
0.987284 + 0.158965i $$0.0508159\pi$$
$$318$$ 0 0
$$319$$ 78305.5 0.0430840
$$320$$ 0 0
$$321$$ 140732. 0.0762305
$$322$$ 0 0
$$323$$ −1.20572e6 + 1.20572e6i −0.643045 + 0.643045i
$$324$$ 0 0
$$325$$ −970198. 503991.i −0.509509 0.264676i
$$326$$ 0 0
$$327$$ 306042. + 306042.i 0.158275 + 0.158275i
$$328$$ 0 0
$$329$$ 2.24823e6i 1.14512i
$$330$$ 0 0
$$331$$ 1.76606e6i 0.886004i 0.896521 + 0.443002i $$0.146087\pi$$
−0.896521 + 0.443002i $$0.853913\pi$$
$$332$$ 0 0
$$333$$ −2.25892e6 2.25892e6i −1.11632 1.11632i
$$334$$ 0 0
$$335$$ −1.16206e6 851286.i −0.565738 0.414442i
$$336$$ 0 0
$$337$$ −239492. + 239492.i −0.114872 + 0.114872i −0.762206 0.647334i $$-0.775884\pi$$
0.647334 + 0.762206i $$0.275884\pi$$
$$338$$ 0 0
$$339$$ 206145. 0.0974258
$$340$$ 0 0
$$341$$ −219247. −0.102105
$$342$$ 0 0
$$343$$ 2.37892e6 2.37892e6i 1.09180 1.09180i
$$344$$ 0 0
$$345$$ −51237.0 331941.i −0.0231758 0.150146i
$$346$$ 0 0
$$347$$ −111547. 111547.i −0.0497316 0.0497316i 0.681804 0.731535i $$-0.261196\pi$$
−0.731535 + 0.681804i $$0.761196\pi$$
$$348$$ 0 0
$$349$$ 726170.i 0.319135i −0.987187 0.159568i $$-0.948990\pi$$
0.987187 0.159568i $$-0.0510100\pi$$
$$350$$ 0 0
$$351$$ 352061.i 0.152528i
$$352$$ 0 0
$$353$$ −254625. 254625.i −0.108759 0.108759i 0.650633 0.759392i $$-0.274504\pi$$
−0.759392 + 0.650633i $$0.774504\pi$$
$$354$$ 0 0
$$355$$ 226922. + 1.47012e6i 0.0955664 + 0.619131i
$$356$$ 0 0
$$357$$ −551065. + 551065.i −0.228840 + 0.228840i
$$358$$ 0 0
$$359$$ 3.35115e6 1.37233 0.686163 0.727447i $$-0.259293\pi$$
0.686163 + 0.727447i $$0.259293\pi$$
$$360$$ 0 0
$$361$$ −1.45546e6 −0.587804
$$362$$ 0 0
$$363$$ −236077. + 236077.i −0.0940345 + 0.0940345i
$$364$$ 0 0
$$365$$ 2.32157e6 + 1.70071e6i 0.912114 + 0.668186i
$$366$$ 0 0
$$367$$ 2.84683e6 + 2.84683e6i 1.10331 + 1.10331i 0.994009 + 0.109299i $$0.0348605\pi$$
0.109299 + 0.994009i $$0.465139\pi$$
$$368$$ 0 0
$$369$$ 2.14868e6i 0.821495i
$$370$$ 0 0
$$371$$ 4.06144e6i 1.53195i
$$372$$ 0 0
$$373$$ 450340. + 450340.i 0.167598 + 0.167598i 0.785923 0.618325i $$-0.212188\pi$$
−0.618325 + 0.785923i $$0.712188\pi$$
$$374$$ 0 0
$$375$$ −116878. + 345778.i −0.0429194 + 0.126975i
$$376$$ 0 0
$$377$$ 545954. 545954.i 0.197835 0.197835i
$$378$$ 0 0
$$379$$ −3.33522e6 −1.19269 −0.596343 0.802729i $$-0.703380\pi$$
−0.596343 + 0.802729i $$0.703380\pi$$
$$380$$ 0 0
$$381$$ −626221. −0.221012
$$382$$ 0 0
$$383$$ 1.03183e6 1.03183e6i 0.359427 0.359427i −0.504175 0.863602i $$-0.668203\pi$$
0.863602 + 0.504175i $$0.168203\pi$$
$$384$$ 0 0
$$385$$ −259042. + 353608.i −0.0890674 + 0.121582i
$$386$$ 0 0
$$387$$ −3.79498e6 3.79498e6i −1.28805 1.28805i
$$388$$ 0 0
$$389$$ 695763.i 0.233124i 0.993183 + 0.116562i $$0.0371874\pi$$
−0.993183 + 0.116562i $$0.962813\pi$$
$$390$$ 0 0
$$391$$ 4.85358e6i 1.60554i
$$392$$ 0 0
$$393$$ −341740. 341740.i −0.111613 0.111613i
$$394$$ 0 0
$$395$$ 281160. 43398.6i 0.0906694 0.0139953i
$$396$$ 0 0
$$397$$ 752665. 752665.i 0.239677 0.239677i −0.577040 0.816716i $$-0.695792\pi$$
0.816716 + 0.577040i $$0.195792\pi$$
$$398$$ 0 0
$$399$$ 466473. 0.146688
$$400$$ 0 0
$$401$$ 5.46256e6 1.69643 0.848214 0.529654i $$-0.177678\pi$$
0.848214 + 0.529654i $$0.177678\pi$$
$$402$$ 0 0
$$403$$ −1.52861e6 + 1.52861e6i −0.468851 + 0.468851i
$$404$$ 0 0
$$405$$ −3.08754e6 + 476579.i −0.935351 + 0.144377i
$$406$$ 0 0
$$407$$ 335874. + 335874.i 0.100506 + 0.100506i
$$408$$ 0 0
$$409$$ 2.57791e6i 0.762008i −0.924573 0.381004i $$-0.875578\pi$$
0.924573 0.381004i $$-0.124422\pi$$
$$410$$ 0 0
$$411$$ 439537.i 0.128348i
$$412$$ 0 0
$$413$$ 6.33115e6 + 6.33115e6i 1.82645 + 1.82645i
$$414$$ 0 0
$$415$$ −952846. + 1.30069e6i −0.271583 + 0.370727i
$$416$$ 0 0
$$417$$ −42287.3 + 42287.3i −0.0119089 + 0.0119089i
$$418$$ 0 0
$$419$$ −1.48123e6 −0.412181 −0.206090 0.978533i $$-0.566074\pi$$
−0.206090 + 0.978533i $$0.566074\pi$$
$$420$$ 0 0
$$421$$ −6.15274e6 −1.69186 −0.845928 0.533297i $$-0.820953\pi$$
−0.845928 + 0.533297i $$0.820953\pi$$
$$422$$ 0 0
$$423$$ 1.71665e6 1.71665e6i 0.466478 0.466478i
$$424$$ 0 0
$$425$$ −2.43144e6 + 4.68059e6i −0.652966 + 1.25698i
$$426$$ 0 0
$$427$$ −4.56820e6 4.56820e6i −1.21248 1.21248i
$$428$$ 0 0
$$429$$ 25936.4i 0.00680403i
$$430$$ 0 0
$$431$$ 3.08017e6i 0.798695i −0.916800 0.399348i $$-0.869237\pi$$
0.916800 0.399348i $$-0.130763\pi$$
$$432$$ 0 0
$$433$$ 1.51152e6 + 1.51152e6i 0.387430 + 0.387430i 0.873770 0.486340i $$-0.161668\pi$$
−0.486340 + 0.873770i $$0.661668\pi$$
$$434$$ 0 0
$$435$$ −207938. 152329.i −0.0526879 0.0385975i
$$436$$ 0 0
$$437$$ −2.05426e6 + 2.05426e6i −0.514579 + 0.514579i
$$438$$ 0 0
$$439$$ −5.41400e6 −1.34078 −0.670389 0.742010i $$-0.733873\pi$$
−0.670389 + 0.742010i $$0.733873\pi$$
$$440$$ 0 0
$$441$$ −7.64361e6 −1.87155
$$442$$ 0 0
$$443$$ −5.09102e6 + 5.09102e6i −1.23252 + 1.23252i −0.269533 + 0.962991i $$0.586869\pi$$
−0.962991 + 0.269533i $$0.913131\pi$$
$$444$$ 0 0
$$445$$ −506105. 3.27882e6i −0.121155 0.784906i
$$446$$ 0 0
$$447$$ −248895. 248895.i −0.0589179 0.0589179i
$$448$$ 0 0
$$449$$ 3.85655e6i 0.902783i 0.892326 + 0.451392i $$0.149072\pi$$
−0.892326 + 0.451392i $$0.850928\pi$$
$$450$$ 0 0
$$451$$ 319482.i 0.0739613i
$$452$$ 0 0
$$453$$ 169139. + 169139.i 0.0387256 + 0.0387256i
$$454$$ 0 0
$$455$$ 659324. + 4.27146e6i 0.149304 + 0.967270i
$$456$$ 0 0
$$457$$ −5.72418e6 + 5.72418e6i −1.28210 + 1.28210i −0.342634 + 0.939469i $$0.611319\pi$$
−0.939469 + 0.342634i $$0.888681\pi$$
$$458$$ 0 0
$$459$$ 1.69847e6 0.376293
$$460$$ 0 0
$$461$$ −1.28502e6 −0.281615 −0.140808 0.990037i $$-0.544970\pi$$
−0.140808 + 0.990037i $$0.544970\pi$$
$$462$$ 0 0
$$463$$ 3.79316e6 3.79316e6i 0.822334 0.822334i −0.164108 0.986442i $$-0.552475\pi$$
0.986442 + 0.164108i $$0.0524747\pi$$
$$464$$ 0 0
$$465$$ 582205. + 426505.i 0.124866 + 0.0914728i
$$466$$ 0 0
$$467$$ −2.71510e6 2.71510e6i −0.576095 0.576095i 0.357730 0.933825i $$-0.383551\pi$$
−0.933825 + 0.357730i $$0.883551\pi$$
$$468$$ 0 0
$$469$$ 5.69467e6i 1.19546i
$$470$$ 0 0
$$471$$ 439653.i 0.0913184i
$$472$$ 0 0
$$473$$ 564267. + 564267.i 0.115966 + 0.115966i
$$474$$ 0 0
$$475$$ 3.01014e6 951946.i 0.612143 0.193588i
$$476$$ 0 0
$$477$$ 3.10113e6 3.10113e6i 0.624058 0.624058i
$$478$$ 0 0
$$479$$ −7.87712e6 −1.56866 −0.784329 0.620345i $$-0.786993\pi$$
−0.784329 + 0.620345i $$0.786993\pi$$
$$480$$ 0 0
$$481$$ 4.68349e6 0.923010
$$482$$ 0 0
$$483$$ −938882. + 938882.i −0.183123 + 0.183123i
$$484$$ 0 0
$$485$$ 3.24900e6 4.43508e6i 0.627184 0.856144i
$$486$$ 0 0
$$487$$ 2.23639e6 + 2.23639e6i 0.427292 + 0.427292i 0.887705 0.460413i $$-0.152299\pi$$
−0.460413 + 0.887705i $$0.652299\pi$$
$$488$$ 0 0
$$489$$ 41945.9i 0.00793263i
$$490$$ 0 0
$$491$$ 5.93940e6i 1.11183i 0.831239 + 0.555916i $$0.187632\pi$$
−0.831239 + 0.555916i $$0.812368\pi$$
$$492$$ 0 0
$$493$$ −2.63388e6 2.63388e6i −0.488066 0.488066i
$$494$$ 0 0
$$495$$ 467793. 72206.5i 0.0858106 0.0132454i
$$496$$ 0 0
$$497$$ 4.15818e6 4.15818e6i 0.755114 0.755114i
$$498$$ 0 0
$$499$$ 41191.0 0.00740545 0.00370272 0.999993i $$-0.498821\pi$$
0.00370272 + 0.999993i $$0.498821\pi$$
$$500$$ 0 0
$$501$$ 382293. 0.0680460
$$502$$ 0 0
$$503$$ −1.52979e6 + 1.52979e6i −0.269596 + 0.269596i −0.828937 0.559342i $$-0.811054\pi$$
0.559342 + 0.828937i $$0.311054\pi$$
$$504$$ 0 0
$$505$$ 2.87078e6 443122.i 0.500924 0.0773205i
$$506$$ 0 0
$$507$$ 367718. + 367718.i 0.0635324 + 0.0635324i
$$508$$ 0 0
$$509$$ 2.48052e6i 0.424374i 0.977229 + 0.212187i $$0.0680586\pi$$
−0.977229 + 0.212187i $$0.931941\pi$$
$$510$$ 0 0
$$511$$ 1.13768e7i 1.92739i
$$512$$ 0 0
$$513$$ −718873. 718873.i −0.120603 0.120603i
$$514$$ 0 0
$$515$$ 4.46057e6 6.08894e6i 0.741092 1.01163i
$$516$$ 0 0
$$517$$ −255245. + 255245.i −0.0419982 + 0.0419982i
$$518$$ 0 0
$$519$$ −449572. −0.0732624
$$520$$ 0 0
$$521$$ −949964. −0.153325 −0.0766624 0.997057i $$-0.524426\pi$$
−0.0766624 + 0.997057i $$0.524426\pi$$
$$522$$ 0 0
$$523$$ −3.91973e6 + 3.91973e6i −0.626617 + 0.626617i −0.947215 0.320598i $$-0.896116\pi$$
0.320598 + 0.947215i $$0.396116\pi$$
$$524$$ 0 0
$$525$$ 1.37576e6 435079.i 0.217843 0.0688921i
$$526$$ 0 0
$$527$$ 7.37458e6 + 7.37458e6i 1.15667 + 1.15667i
$$528$$ 0 0
$$529$$ 1.83298e6i 0.284786i
$$530$$ 0 0
$$531$$ 9.66839e6i 1.48805i
$$532$$ 0 0
$$533$$ 2.22746e6 + 2.22746e6i 0.339619 + 0.339619i
$$534$$ 0 0
$$535$$ −3.03749e6 2.22517e6i −0.458807 0.336107i
$$536$$ 0 0
$$537$$ −433301. + 433301.i −0.0648416 + 0.0648416i
$$538$$ 0 0
$$539$$ 1.13651e6 0.168501
$$540$$ 0 0
$$541$$ −7.07953e6 −1.03995 −0.519973 0.854182i $$-0.674058\pi$$
−0.519973 + 0.854182i $$0.674058\pi$$
$$542$$ 0 0
$$543$$ 52070.0 52070.0i 0.00757858 0.00757858i
$$544$$ 0 0
$$545$$ −1.76652e6 1.14444e7i −0.254757 1.65045i
$$546$$ 0 0
$$547$$ 8.01896e6 + 8.01896e6i 1.14591 + 1.14591i 0.987350 + 0.158559i $$0.0506848\pi$$
0.158559 + 0.987350i $$0.449315\pi$$
$$548$$ 0 0
$$549$$ 6.97616e6i 0.987837i
$$550$$ 0 0
$$551$$ 2.22956e6i 0.312853i
$$552$$ 0 0
$$553$$ −795250. 795250.i −0.110584 0.110584i
$$554$$ 0 0
$$555$$ −238523. 1.54528e6i −0.0328699 0.212949i
$$556$$ 0 0
$$557$$ 687054. 687054.i 0.0938324 0.0938324i −0.658632 0.752465i $$-0.728865\pi$$
0.752465 + 0.658632i $$0.228865\pi$$
$$558$$ 0 0
$$559$$ 7.86825e6 1.06500
$$560$$ 0 0
$$561$$ −125126. −0.0167858
$$562$$ 0 0
$$563$$ −7.17411e6 + 7.17411e6i −0.953888 + 0.953888i −0.998983 0.0450948i $$-0.985641\pi$$
0.0450948 + 0.998983i $$0.485641\pi$$
$$564$$ 0 0
$$565$$ −4.44935e6 3.25945e6i −0.586375 0.429559i
$$566$$ 0 0
$$567$$ 8.73298e6 + 8.73298e6i 1.14079 + 1.14079i
$$568$$ 0 0
$$569$$ 8.08487e6i 1.04687i 0.852066 + 0.523435i $$0.175350\pi$$
−0.852066 + 0.523435i $$0.824650\pi$$
$$570$$ 0 0
$$571$$ 3.00555e6i 0.385774i −0.981221 0.192887i $$-0.938215\pi$$
0.981221 0.192887i $$-0.0617851\pi$$
$$572$$ 0 0
$$573$$ −1.27404e6 1.27404e6i −0.162105 0.162105i
$$574$$ 0 0
$$575$$ −4.14258e6 + 7.97459e6i −0.522518 + 1.00586i
$$576$$ 0 0
$$577$$ 4.07557e6 4.07557e6i 0.509622 0.509622i −0.404788 0.914410i $$-0.632655\pi$$
0.914410 + 0.404788i $$0.132655\pi$$
$$578$$ 0 0
$$579$$ 257818. 0.0319608
$$580$$ 0 0
$$581$$ 6.37405e6 0.783384
$$582$$ 0 0
$$583$$ −461101. + 461101.i −0.0561855 + 0.0561855i
$$584$$ 0 0
$$585$$ 2.75807e6 3.76493e6i 0.333208 0.454849i
$$586$$ 0 0
$$587$$ −3.45341e6 3.45341e6i −0.413669 0.413669i 0.469346 0.883014i $$-0.344490\pi$$
−0.883014 + 0.469346i $$0.844490\pi$$
$$588$$ 0 0
$$589$$ 6.24254e6i 0.741435i
$$590$$ 0 0
$$591$$ 335373.i 0.0394965i
$$592$$ 0 0
$$593$$ 4.96777e6 + 4.96777e6i 0.580129 + 0.580129i 0.934939 0.354810i $$-0.115454\pi$$
−0.354810 + 0.934939i $$0.615454\pi$$
$$594$$ 0 0
$$595$$ 2.06071e7 3.18082e6i 2.38629 0.368338i
$$596$$ 0 0
$$597$$ 734926. 734926.i 0.0843932 0.0843932i
$$598$$ 0 0
$$599$$ −8.61814e6 −0.981401 −0.490701 0.871328i $$-0.663259\pi$$
−0.490701 + 0.871328i $$0.663259\pi$$
$$600$$ 0 0
$$601$$ −1.36092e7 −1.53690 −0.768451 0.639909i $$-0.778972\pi$$
−0.768451 + 0.639909i $$0.778972\pi$$
$$602$$ 0 0
$$603$$ 4.34820e6 4.34820e6i 0.486986 0.486986i
$$604$$ 0 0
$$605$$ 8.82810e6 1.36267e6i 0.980570 0.151357i
$$606$$ 0 0
$$607$$ −7.54202e6 7.54202e6i −0.830837 0.830837i 0.156794 0.987631i $$-0.449884\pi$$
−0.987631 + 0.156794i $$0.949884\pi$$
$$608$$ 0 0
$$609$$ 1.01900e6i 0.111335i
$$610$$ 0 0
$$611$$ 3.55918e6i 0.385698i
$$612$$ 0 0
$$613$$ −2.33571e6 2.33571e6i −0.251054 0.251054i 0.570349 0.821403i $$-0.306808\pi$$
−0.821403 + 0.570349i $$0.806808\pi$$
$$614$$ 0 0
$$615$$ 621493. 848375.i 0.0662595 0.0904483i
$$616$$ 0 0
$$617$$ 9.52103e6 9.52103e6i 1.00686 1.00686i 0.00688826 0.999976i $$-0.497807\pi$$
0.999976 0.00688826i $$-0.00219262\pi$$
$$618$$ 0 0
$$619$$ 1.71115e7 1.79499 0.897494 0.441027i $$-0.145386\pi$$
0.897494 + 0.441027i $$0.145386\pi$$
$$620$$ 0 0
$$621$$ 2.89379e6 0.301119
$$622$$ 0 0
$$623$$ −9.27402e6 + 9.27402e6i −0.957300 + 0.957300i
$$624$$ 0 0
$$625$$ 7.98987e6 5.61511e6i 0.818163 0.574987i
$$626$$ 0 0
$$627$$ 52959.4 + 52959.4i 0.00537990 + 0.00537990i
$$628$$ 0 0
$$629$$ 2.25948e7i 2.27710i
$$630$$ 0 0
$$631$$ 1.54863e7i 1.54837i −0.632958 0.774186i $$-0.718159\pi$$
0.632958 0.774186i $$-0.281841\pi$$
$$632$$ 0 0
$$633$$ 530398. + 530398.i 0.0526129 + 0.0526129i
$$634$$ 0 0
$$635$$ 1.35161e7 + 9.90144e6i 1.33020 + 0.974460i
$$636$$ 0 0
$$637$$ 7.92387e6 7.92387e6i 0.773729 0.773729i
$$638$$ 0 0
$$639$$ −6.35001e6 −0.615209
$$640$$ 0 0
$$641$$ −8.16308e6 −0.784709 −0.392355 0.919814i $$-0.628339\pi$$
−0.392355 + 0.919814i $$0.628339\pi$$
$$642$$ 0 0
$$643$$ 6.82289e6 6.82289e6i 0.650791 0.650791i −0.302393 0.953183i $$-0.597785\pi$$
0.953183 + 0.302393i $$0.0977854\pi$$
$$644$$ 0 0
$$645$$ −400719. 2.59607e6i −0.0379263 0.245707i
$$646$$ 0 0
$$647$$ 1.04574e7 + 1.04574e7i 0.982113 + 0.982113i 0.999843 0.0177299i $$-0.00564390\pi$$
−0.0177299 + 0.999843i $$0.505644\pi$$
$$648$$ 0 0
$$649$$ 1.43757e6i 0.133973i
$$650$$ 0 0
$$651$$ 2.85310e6i 0.263854i
$$652$$ 0 0
$$653$$ 8.91308e6 + 8.91308e6i 0.817984 + 0.817984i 0.985816 0.167831i $$-0.0536764\pi$$
−0.167831 + 0.985816i $$0.553676\pi$$
$$654$$ 0 0
$$655$$ 1.97257e6 + 1.27794e7i 0.179651 + 1.16387i
$$656$$ 0 0
$$657$$ −8.68686e6 + 8.68686e6i −0.785144 + 0.785144i
$$658$$ 0 0
$$659$$ −4.26560e6 −0.382619 −0.191310 0.981530i $$-0.561273\pi$$
−0.191310 + 0.981530i $$0.561273\pi$$
$$660$$ 0 0
$$661$$ −5.64640e6 −0.502653 −0.251326 0.967902i $$-0.580867\pi$$
−0.251326 + 0.967902i $$0.580867\pi$$
$$662$$ 0 0
$$663$$ −872394. + 872394.i −0.0770777 + 0.0770777i
$$664$$ 0 0
$$665$$ −1.00682e7 7.37561e6i −0.882868 0.646761i
$$666$$ 0 0
$$667$$ −4.48749e6 4.48749e6i −0.390561 0.390561i
$$668$$ 0 0
$$669$$ 2.73979e6i 0.236675i
$$670$$ 0 0
$$671$$ 1.03727e6i 0.0889376i
$$672$$ 0 0
$$673$$ 6.79083e6 + 6.79083e6i 0.577943 + 0.577943i 0.934336 0.356393i $$-0.115994\pi$$
−0.356393 + 0.934336i $$0.615994\pi$$
$$674$$ 0 0
$$675$$ −2.79065e6 1.44967e6i −0.235747 0.122464i
$$676$$ 0 0
$$677$$ −1.14580e7 + 1.14580e7i −0.960807 + 0.960807i −0.999260 0.0384535i $$-0.987757\pi$$
0.0384535 + 0.999260i $$0.487757\pi$$
$$678$$ 0 0
$$679$$ −2.17341e7 −1.80912
$$680$$ 0 0
$$681$$ 3.03898e6 0.251108
$$682$$ 0 0
$$683$$ 9.47517e6 9.47517e6i 0.777204 0.777204i −0.202150 0.979354i $$-0.564793\pi$$
0.979354 + 0.202150i $$0.0647930\pi$$
$$684$$ 0 0
$$685$$ −6.94970e6 + 9.48676e6i −0.565900 + 0.772488i
$$686$$ 0 0
$$687$$ 922483. + 922483.i 0.0745704 + 0.0745704i
$$688$$ 0 0
$$689$$ 6.42968e6i 0.515990i
$$690$$ 0 0
$$691$$ 2.19649e7i 1.74998i 0.484137 + 0.874992i $$0.339133\pi$$
−0.484137 + 0.874992i $$0.660867\pi$$
$$692$$ 0 0
$$693$$ −1.32314e6 1.32314e6i −0.104658 0.104658i
$$694$$ 0 0
$$695$$ 1.58133e6 244088.i 0.124183 0.0191683i
$$696$$ 0 0
$$697$$ 1.07461e7 1.07461e7i 0.837852 0.837852i
$$698$$ 0 0
$$699$$ −217975. −0.0168738
$$700$$ 0 0
$$701$$ −9.21992e6 −0.708651 −0.354325 0.935122i $$-0.615289\pi$$
−0.354325 + 0.935122i $$0.615289\pi$$
$$702$$ 0 0
$$703$$ −9.56320e6 + 9.56320e6i −0.729818 + 0.729818i
$$704$$ 0 0
$$705$$ 1.17433e6 181264.i 0.0889850 0.0137353i
$$706$$ 0 0
$$707$$ −8.11990e6 8.11990e6i −0.610945 0.610945i
$$708$$ 0 0
$$709$$ 2.13169e7i 1.59260i 0.604900 + 0.796301i $$0.293213\pi$$
−0.604900 + 0.796301i $$0.706787\pi$$
$$710$$ 0 0
$$711$$ 1.21444e6i 0.0900951i
$$712$$ 0 0
$$713$$ 1.25645e7 + 1.25645e7i 0.925597 + 0.925597i
$$714$$ 0 0
$$715$$ −410091. + 559799.i −0.0299996 + 0.0409512i
$$716$$ 0 0
$$717$$ 2.34453e6 2.34453e6i 0.170317 0.170317i
$$718$$ 0 0
$$719$$ −5.27347e6 −0.380430 −0.190215 0.981742i $$-0.560918\pi$$
−0.190215 + 0.981742i $$0.560918\pi$$
$$720$$ 0 0
$$721$$ −2.98389e7 −2.13769
$$722$$ 0 0
$$723$$ −321259. + 321259.i −0.0228565 + 0.0228565i
$$724$$ 0 0
$$725$$ 2.07951e6 + 6.57560e6i 0.146932 + 0.464612i
$$726$$ 0 0
$$727$$ −8.91293e6 8.91293e6i −0.625438 0.625438i 0.321479 0.946917i $$-0.395820\pi$$
−0.946917 + 0.321479i $$0.895820\pi$$
$$728$$ 0 0
$$729$$ 1.28253e7i 0.893819i
$$730$$ 0 0
$$731$$ 3.79593e7i 2.62739i
$$732$$ 0 0
$$733$$ 3.62320e6 + 3.62320e6i 0.249076 + 0.249076i 0.820591 0.571515i $$-0.193644\pi$$
−0.571515 + 0.820591i $$0.693644\pi$$
$$734$$ 0 0
$$735$$ −3.01798e6 2.21087e6i −0.206062 0.150954i
$$736$$ 0 0
$$737$$ −646524. + 646524.i −0.0438446 + 0.0438446i
$$738$$ 0 0
$$739$$ −8.18176e6 −0.551106 −0.275553 0.961286i $$-0.588861\pi$$
−0.275553 + 0.961286i $$0.588861\pi$$
$$740$$ 0 0
$$741$$ 738476. 0.0494073
$$742$$ 0 0
$$743$$ 1.12407e7 1.12407e7i 0.747004 0.747004i −0.226911 0.973915i $$-0.572863\pi$$
0.973915 + 0.226911i $$0.0728627\pi$$
$$744$$ 0 0
$$745$$ 1.43665e6 + 9.30742e6i 0.0948333 + 0.614382i
$$746$$ 0 0
$$747$$ −4.86694e6 4.86694e6i −0.319121 0.319121i
$$748$$ 0 0
$$749$$ 1.48852e7i 0.969506i
$$750$$ 0 0
$$751$$ 1.89630e7i 1.22689i −0.789736 0.613447i $$-0.789783\pi$$
0.789736 0.613447i $$-0.210217\pi$$
$$752$$ 0 0
$$753$$ −2.72503e6 2.72503e6i −0.175140 0.175140i
$$754$$ 0 0
$$755$$ −976291. 6.32495e6i −0.0623321 0.403822i
$$756$$ 0 0
$$757$$ 9.61677e6 9.61677e6i 0.609943 0.609943i −0.332988 0.942931i $$-0.608057\pi$$
0.942931 + 0.332988i $$0.108057\pi$$
$$758$$ 0 0
$$759$$ −213185. −0.0134324
$$760$$ 0 0
$$761$$ 2.07945e7 1.30163 0.650814 0.759238i $$-0.274428\pi$$
0.650814 + 0.759238i $$0.274428\pi$$
$$762$$ 0 0
$$763$$ −3.23702e7 + 3.23702e7i −2.01295 + 2.01295i
$$764$$ 0 0
$$765$$ −1.81634e7 1.33059e7i −1.12213 0.822037i
$$766$$ 0 0
$$767$$ 1.00229e7 + 1.00229e7i 0.615183 + 0.615183i
$$768$$ 0 0
$$769$$ 1.39172e7i 0.848667i 0.905506 + 0.424334i $$0.139492\pi$$
−0.905506 + 0.424334i $$0.860508\pi$$
$$770$$ 0 0
$$771$$ 2.76116e6i 0.167284i
$$772$$ 0 0
$$773$$ −3.19729e6 3.19729e6i −0.192457 0.192457i 0.604300 0.796757i $$-0.293453\pi$$
−0.796757 + 0.604300i $$0.793453\pi$$
$$774$$ 0 0
$$775$$ −5.82240e6 1.84110e7i −0.348215 1.10109i
$$776$$ 0 0
$$777$$ −4.37077e6 + 4.37077e6i −0.259720 + 0.259720i
$$778$$ 0 0
$$779$$ −9.09648e6 −0.537069
$$780$$ 0 0
$$781$$ 944170. 0.0553889
$$782$$ 0 0
$$783$$ 1.57036e6 1.57036e6i 0.0915368 0.0915368i
$$784$$ 0 0
$$785$$ −6.95154e6 + 9.48928e6i −0.402631 + 0.549616i
$$786$$ 0 0
$$787$$ 5.00799e6 + 5.00799e6i 0.288222 + 0.288222i 0.836377 0.548155i $$-0.184670\pi$$
−0.548155 + 0.836377i $$0.684670\pi$$
$$788$$ 0 0
$$789$$ 1.61253e6i 0.0922179i
$$790$$ 0 0
$$791$$ 2.18040e7i 1.23907i
$$792$$ 0