# Properties

 Label 160.6.n.b.63.2 Level $160$ Weight $6$ Character 160.63 Analytic conductor $25.661$ Analytic rank $0$ Dimension $14$ CM no Inner twists $2$

# Learn more about

## 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 63.2 Root $$3.77108 + 3.77108i$$ of defining polynomial Character $$\chi$$ $$=$$ 160.63 Dual form 160.6.n.b.127.2

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-13.4331 + 13.4331i) q^{3} +(15.0352 + 53.8418i) q^{5} +(-76.4413 - 76.4413i) q^{7} -117.896i q^{9} +O(q^{10})$$ $$q+(-13.4331 + 13.4331i) q^{3} +(15.0352 + 53.8418i) q^{5} +(-76.4413 - 76.4413i) q^{7} -117.896i q^{9} -622.995i q^{11} +(-293.552 - 293.552i) q^{13} +(-925.232 - 521.293i) q^{15} +(-1153.02 + 1153.02i) q^{17} +2003.44 q^{19} +2053.69 q^{21} +(1392.29 - 1392.29i) q^{23} +(-2672.88 + 1619.05i) q^{25} +(-1680.53 - 1680.53i) q^{27} +305.819i q^{29} +2108.06i q^{31} +(8368.75 + 8368.75i) q^{33} +(2966.43 - 5265.05i) q^{35} +(9903.12 - 9903.12i) q^{37} +7886.62 q^{39} +16996.0 q^{41} +(-2031.28 + 2031.28i) q^{43} +(6347.74 - 1772.59i) q^{45} +(-682.885 - 682.885i) q^{47} -5120.46i q^{49} -30977.2i q^{51} +(21092.5 + 21092.5i) q^{53} +(33543.2 - 9366.86i) q^{55} +(-26912.4 + 26912.4i) q^{57} +11617.4 q^{59} -1309.80 q^{61} +(-9012.12 + 9012.12i) q^{63} +(11391.8 - 20219.0i) q^{65} +(-39870.6 - 39870.6i) q^{67} +37405.7i q^{69} +25454.3i q^{71} +(1031.25 + 1031.25i) q^{73} +(14156.3 - 57653.9i) q^{75} +(-47622.5 + 47622.5i) q^{77} -11849.6 q^{79} +73798.3 q^{81} +(45180.7 - 45180.7i) q^{83} +(-79416.5 - 44744.7i) q^{85} +(-4108.09 - 4108.09i) q^{87} -143889. i q^{89} +44879.0i q^{91} +(-28317.8 - 28317.8i) q^{93} +(30122.1 + 107869. i) q^{95} +(-24390.9 + 24390.9i) q^{97} -73448.7 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$14q + 10q^{3} + 42q^{5} + 66q^{7} + O(q^{10})$$ $$14q + 10q^{3} + 42q^{5} + 66q^{7} - 414q^{13} + 278q^{15} + 1222q^{17} + 5672q^{19} + 5924q^{21} + 2902q^{23} - 4466q^{25} - 2168q^{27} - 2444q^{33} - 2618q^{35} - 1790q^{37} - 11076q^{39} + 11644q^{41} - 3982q^{43} + 14704q^{45} - 1278q^{47} + 5882q^{53} + 65608q^{55} - 14552q^{57} - 8504q^{59} + 20564q^{61} + 19422q^{63} + 40798q^{65} + 107926q^{67} - 16418q^{73} + 66586q^{75} - 13348q^{77} - 146544q^{79} + 173806q^{81} - 36398q^{83} - 66262q^{85} + 124384q^{87} - 306620q^{93} + 173768q^{95} - 60314q^{97} - 388628q^{99} + O(q^{100})$$

## 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
$$3$$ −13.4331 + 13.4331i −0.861733 + 0.861733i −0.991539 0.129806i $$-0.958565\pi$$
0.129806 + 0.991539i $$0.458565\pi$$
$$4$$ 0 0
$$5$$ 15.0352 + 53.8418i 0.268958 + 0.963152i
$$6$$ 0 0
$$7$$ −76.4413 76.4413i −0.589634 0.589634i 0.347898 0.937532i $$-0.386896\pi$$
−0.937532 + 0.347898i $$0.886896\pi$$
$$8$$ 0 0
$$9$$ 117.896i 0.485169i
$$10$$ 0 0
$$11$$ 622.995i 1.55240i −0.630488 0.776199i $$-0.717145\pi$$
0.630488 0.776199i $$-0.282855\pi$$
$$12$$ 0 0
$$13$$ −293.552 293.552i −0.481755 0.481755i 0.423937 0.905692i $$-0.360648\pi$$
−0.905692 + 0.423937i $$0.860648\pi$$
$$14$$ 0 0
$$15$$ −925.232 521.293i −1.06175 0.598210i
$$16$$ 0 0
$$17$$ −1153.02 + 1153.02i −0.967640 + 0.967640i −0.999493 0.0318524i $$-0.989859\pi$$
0.0318524 + 0.999493i $$0.489859\pi$$
$$18$$ 0 0
$$19$$ 2003.44 1.27319 0.636593 0.771200i $$-0.280343\pi$$
0.636593 + 0.771200i $$0.280343\pi$$
$$20$$ 0 0
$$21$$ 2053.69 1.01622
$$22$$ 0 0
$$23$$ 1392.29 1392.29i 0.548797 0.548797i −0.377296 0.926093i $$-0.623146\pi$$
0.926093 + 0.377296i $$0.123146\pi$$
$$24$$ 0 0
$$25$$ −2672.88 + 1619.05i −0.855323 + 0.518095i
$$26$$ 0 0
$$27$$ −1680.53 1680.53i −0.443647 0.443647i
$$28$$ 0 0
$$29$$ 305.819i 0.0675257i 0.999430 + 0.0337629i $$0.0107491\pi$$
−0.999430 + 0.0337629i $$0.989251\pi$$
$$30$$ 0 0
$$31$$ 2108.06i 0.393985i 0.980405 + 0.196992i $$0.0631174\pi$$
−0.980405 + 0.196992i $$0.936883\pi$$
$$32$$ 0 0
$$33$$ 8368.75 + 8368.75i 1.33775 + 1.33775i
$$34$$ 0 0
$$35$$ 2966.43 5265.05i 0.409321 0.726494i
$$36$$ 0 0
$$37$$ 9903.12 9903.12i 1.18924 1.18924i 0.211957 0.977279i $$-0.432016\pi$$
0.977279 0.211957i $$-0.0679835\pi$$
$$38$$ 0 0
$$39$$ 7886.62 0.830289
$$40$$ 0 0
$$41$$ 16996.0 1.57902 0.789511 0.613736i $$-0.210334\pi$$
0.789511 + 0.613736i $$0.210334\pi$$
$$42$$ 0 0
$$43$$ −2031.28 + 2031.28i −0.167533 + 0.167533i −0.785894 0.618361i $$-0.787797\pi$$
0.618361 + 0.785894i $$0.287797\pi$$
$$44$$ 0 0
$$45$$ 6347.74 1772.59i 0.467291 0.130490i
$$46$$ 0 0
$$47$$ −682.885 682.885i −0.0450924 0.0450924i 0.684201 0.729293i $$-0.260151\pi$$
−0.729293 + 0.684201i $$0.760151\pi$$
$$48$$ 0 0
$$49$$ 5120.46i 0.304663i
$$50$$ 0 0
$$51$$ 30977.2i 1.66770i
$$52$$ 0 0
$$53$$ 21092.5 + 21092.5i 1.03143 + 1.03143i 0.999490 + 0.0319374i $$0.0101677\pi$$
0.0319374 + 0.999490i $$0.489832\pi$$
$$54$$ 0 0
$$55$$ 33543.2 9366.86i 1.49519 0.417530i
$$56$$ 0 0
$$57$$ −26912.4 + 26912.4i −1.09715 + 1.09715i
$$58$$ 0 0
$$59$$ 11617.4 0.434490 0.217245 0.976117i $$-0.430293\pi$$
0.217245 + 0.976117i $$0.430293\pi$$
$$60$$ 0 0
$$61$$ −1309.80 −0.0450694 −0.0225347 0.999746i $$-0.507174\pi$$
−0.0225347 + 0.999746i $$0.507174\pi$$
$$62$$ 0 0
$$63$$ −9012.12 + 9012.12i −0.286072 + 0.286072i
$$64$$ 0 0
$$65$$ 11391.8 20219.0i 0.334432 0.593576i
$$66$$ 0 0
$$67$$ −39870.6 39870.6i −1.08509 1.08509i −0.996026 0.0890646i $$-0.971612\pi$$
−0.0890646 0.996026i $$-0.528388\pi$$
$$68$$ 0 0
$$69$$ 37405.7i 0.945833i
$$70$$ 0 0
$$71$$ 25454.3i 0.599259i 0.954056 + 0.299630i $$0.0968631\pi$$
−0.954056 + 0.299630i $$0.903137\pi$$
$$72$$ 0 0
$$73$$ 1031.25 + 1031.25i 0.0226495 + 0.0226495i 0.718341 0.695691i $$-0.244902\pi$$
−0.695691 + 0.718341i $$0.744902\pi$$
$$74$$ 0 0
$$75$$ 14156.3 57653.9i 0.290601 1.18352i
$$76$$ 0 0
$$77$$ −47622.5 + 47622.5i −0.915347 + 0.915347i
$$78$$ 0 0
$$79$$ −11849.6 −0.213617 −0.106808 0.994280i $$-0.534063\pi$$
−0.106808 + 0.994280i $$0.534063\pi$$
$$80$$ 0 0
$$81$$ 73798.3 1.24978
$$82$$ 0 0
$$83$$ 45180.7 45180.7i 0.719876 0.719876i −0.248703 0.968580i $$-0.580004\pi$$
0.968580 + 0.248703i $$0.0800044\pi$$
$$84$$ 0 0
$$85$$ −79416.5 44744.7i −1.19224 0.671730i
$$86$$ 0 0
$$87$$ −4108.09 4108.09i −0.0581892 0.0581892i
$$88$$ 0 0
$$89$$ 143889.i 1.92553i −0.270332 0.962767i $$-0.587133\pi$$
0.270332 0.962767i $$-0.412867\pi$$
$$90$$ 0 0
$$91$$ 44879.0i 0.568119i
$$92$$ 0 0
$$93$$ −28317.8 28317.8i −0.339510 0.339510i
$$94$$ 0 0
$$95$$ 30122.1 + 107869.i 0.342434 + 1.22627i
$$96$$ 0 0
$$97$$ −24390.9 + 24390.9i −0.263207 + 0.263207i −0.826356 0.563148i $$-0.809590\pi$$
0.563148 + 0.826356i $$0.309590\pi$$
$$98$$ 0 0
$$99$$ −73448.7 −0.753175
$$100$$ 0 0
$$101$$ 169993. 1.65816 0.829082 0.559127i $$-0.188864\pi$$
0.829082 + 0.559127i $$0.188864\pi$$
$$102$$ 0 0
$$103$$ −116026. + 116026.i −1.07761 + 1.07761i −0.0808914 + 0.996723i $$0.525777\pi$$
−0.996723 + 0.0808914i $$0.974223\pi$$
$$104$$ 0 0
$$105$$ 30877.6 + 110574.i 0.273319 + 0.978770i
$$106$$ 0 0
$$107$$ −68471.5 68471.5i −0.578163 0.578163i 0.356234 0.934397i $$-0.384061\pi$$
−0.934397 + 0.356234i $$0.884061\pi$$
$$108$$ 0 0
$$109$$ 20202.8i 0.162872i −0.996679 0.0814360i $$-0.974049\pi$$
0.996679 0.0814360i $$-0.0259506\pi$$
$$110$$ 0 0
$$111$$ 266059.i 2.04961i
$$112$$ 0 0
$$113$$ −79268.7 79268.7i −0.583990 0.583990i 0.352007 0.935997i $$-0.385499\pi$$
−0.935997 + 0.352007i $$0.885499\pi$$
$$114$$ 0 0
$$115$$ 95897.1 + 54030.2i 0.676178 + 0.380971i
$$116$$ 0 0
$$117$$ −34608.6 + 34608.6i −0.233733 + 0.233733i
$$118$$ 0 0
$$119$$ 176276. 1.14111
$$120$$ 0 0
$$121$$ −227072. −1.40994
$$122$$ 0 0
$$123$$ −228309. + 228309.i −1.36070 + 1.36070i
$$124$$ 0 0
$$125$$ −127360. 119570.i −0.729050 0.684460i
$$126$$ 0 0
$$127$$ 133983. + 133983.i 0.737121 + 0.737121i 0.972020 0.234898i $$-0.0754758\pi$$
−0.234898 + 0.972020i $$0.575476\pi$$
$$128$$ 0 0
$$129$$ 54572.8i 0.288737i
$$130$$ 0 0
$$131$$ 358577.i 1.82559i −0.408414 0.912797i $$-0.633918\pi$$
0.408414 0.912797i $$-0.366082\pi$$
$$132$$ 0 0
$$133$$ −153145. 153145.i −0.750715 0.750715i
$$134$$ 0 0
$$135$$ 65215.8 115750.i 0.307977 0.546622i
$$136$$ 0 0
$$137$$ −156028. + 156028.i −0.710232 + 0.710232i −0.966584 0.256352i $$-0.917479\pi$$
0.256352 + 0.966584i $$0.417479\pi$$
$$138$$ 0 0
$$139$$ −211815. −0.929865 −0.464932 0.885346i $$-0.653921\pi$$
−0.464932 + 0.885346i $$0.653921\pi$$
$$140$$ 0 0
$$141$$ 18346.5 0.0777152
$$142$$ 0 0
$$143$$ −182881. + 182881.i −0.747876 + 0.747876i
$$144$$ 0 0
$$145$$ −16465.8 + 4598.05i −0.0650375 + 0.0181616i
$$146$$ 0 0
$$147$$ 68783.7 + 68783.7i 0.262538 + 0.262538i
$$148$$ 0 0
$$149$$ 55272.1i 0.203958i −0.994787 0.101979i $$-0.967483\pi$$
0.994787 0.101979i $$-0.0325174\pi$$
$$150$$ 0 0
$$151$$ 358721.i 1.28031i −0.768247 0.640154i $$-0.778871\pi$$
0.768247 0.640154i $$-0.221129\pi$$
$$152$$ 0 0
$$153$$ 135936. + 135936.i 0.469469 + 0.469469i
$$154$$ 0 0
$$155$$ −113502. + 31695.2i −0.379467 + 0.105965i
$$156$$ 0 0
$$157$$ 355644. 355644.i 1.15151 1.15151i 0.165255 0.986251i $$-0.447155\pi$$
0.986251 0.165255i $$-0.0528447\pi$$
$$158$$ 0 0
$$159$$ −566675. −1.77763
$$160$$ 0 0
$$161$$ −212858. −0.647179
$$162$$ 0 0
$$163$$ 288242. 288242.i 0.849745 0.849745i −0.140356 0.990101i $$-0.544825\pi$$
0.990101 + 0.140356i $$0.0448248\pi$$
$$164$$ 0 0
$$165$$ −324763. + 576415.i −0.928660 + 1.64826i
$$166$$ 0 0
$$167$$ 78292.2 + 78292.2i 0.217234 + 0.217234i 0.807332 0.590098i $$-0.200911\pi$$
−0.590098 + 0.807332i $$0.700911\pi$$
$$168$$ 0 0
$$169$$ 198947.i 0.535823i
$$170$$ 0 0
$$171$$ 236197.i 0.617711i
$$172$$ 0 0
$$173$$ −242048. 242048.i −0.614875 0.614875i 0.329337 0.944212i $$-0.393175\pi$$
−0.944212 + 0.329337i $$0.893175\pi$$
$$174$$ 0 0
$$175$$ 328081. + 80556.7i 0.809814 + 0.198841i
$$176$$ 0 0
$$177$$ −156058. + 156058.i −0.374414 + 0.374414i
$$178$$ 0 0
$$179$$ 28397.8 0.0662448 0.0331224 0.999451i $$-0.489455\pi$$
0.0331224 + 0.999451i $$0.489455\pi$$
$$180$$ 0 0
$$181$$ 637320. 1.44598 0.722988 0.690861i $$-0.242768\pi$$
0.722988 + 0.690861i $$0.242768\pi$$
$$182$$ 0 0
$$183$$ 17594.7 17594.7i 0.0388378 0.0388378i
$$184$$ 0 0
$$185$$ 682098. + 384307.i 1.46527 + 0.825560i
$$186$$ 0 0
$$187$$ 718325. + 718325.i 1.50216 + 1.50216i
$$188$$ 0 0
$$189$$ 256924.i 0.523179i
$$190$$ 0 0
$$191$$ 618423.i 1.22660i −0.789851 0.613299i $$-0.789842\pi$$
0.789851 0.613299i $$-0.210158\pi$$
$$192$$ 0 0
$$193$$ 21641.0 + 21641.0i 0.0418199 + 0.0418199i 0.727708 0.685888i $$-0.240586\pi$$
−0.685888 + 0.727708i $$0.740586\pi$$
$$194$$ 0 0
$$195$$ 118577. + 424630.i 0.223313 + 0.799695i
$$196$$ 0 0
$$197$$ 38033.2 38033.2i 0.0698227 0.0698227i −0.671333 0.741156i $$-0.734278\pi$$
0.741156 + 0.671333i $$0.234278\pi$$
$$198$$ 0 0
$$199$$ 258481. 0.462696 0.231348 0.972871i $$-0.425686\pi$$
0.231348 + 0.972871i $$0.425686\pi$$
$$200$$ 0 0
$$201$$ 1.07117e6 1.87012
$$202$$ 0 0
$$203$$ 23377.2 23377.2i 0.0398155 0.0398155i
$$204$$ 0 0
$$205$$ 255539. + 915098.i 0.424691 + 1.52084i
$$206$$ 0 0
$$207$$ −164146. 164146.i −0.266259 0.266259i
$$208$$ 0 0
$$209$$ 1.24813e6i 1.97649i
$$210$$ 0 0
$$211$$ 185768.i 0.287253i −0.989632 0.143626i $$-0.954124\pi$$
0.989632 0.143626i $$-0.0458764\pi$$
$$212$$ 0 0
$$213$$ −341930. 341930.i −0.516402 0.516402i
$$214$$ 0 0
$$215$$ −139909. 78827.2i −0.206419 0.116300i
$$216$$ 0 0
$$217$$ 161143. 161143.i 0.232307 0.232307i
$$218$$ 0 0
$$219$$ −27705.8 −0.0390356
$$220$$ 0 0
$$221$$ 676942. 0.932332
$$222$$ 0 0
$$223$$ 759885. 759885.i 1.02326 1.02326i 0.0235364 0.999723i $$-0.492507\pi$$
0.999723 0.0235364i $$-0.00749255\pi$$
$$224$$ 0 0
$$225$$ 190879. + 315122.i 0.251363 + 0.414976i
$$226$$ 0 0
$$227$$ 35910.4 + 35910.4i 0.0462547 + 0.0462547i 0.729856 0.683601i $$-0.239587\pi$$
−0.683601 + 0.729856i $$0.739587\pi$$
$$228$$ 0 0
$$229$$ 1.54665e6i 1.94896i 0.224469 + 0.974481i $$0.427935\pi$$
−0.224469 + 0.974481i $$0.572065\pi$$
$$230$$ 0 0
$$231$$ 1.27944e6i 1.57757i
$$232$$ 0 0
$$233$$ −389263. 389263.i −0.469735 0.469735i 0.432093 0.901829i $$-0.357775\pi$$
−0.901829 + 0.432093i $$0.857775\pi$$
$$234$$ 0 0
$$235$$ 26500.5 47035.1i 0.0313028 0.0555587i
$$236$$ 0 0
$$237$$ 159176. 159176.i 0.184081 0.184081i
$$238$$ 0 0
$$239$$ −823778. −0.932858 −0.466429 0.884559i $$-0.654460\pi$$
−0.466429 + 0.884559i $$0.654460\pi$$
$$240$$ 0 0
$$241$$ −139658. −0.154890 −0.0774451 0.996997i $$-0.524676\pi$$
−0.0774451 + 0.996997i $$0.524676\pi$$
$$242$$ 0 0
$$243$$ −582969. + 582969.i −0.633330 + 0.633330i
$$244$$ 0 0
$$245$$ 275695. 76987.3i 0.293436 0.0819415i
$$246$$ 0 0
$$247$$ −588113. 588113.i −0.613365 0.613365i
$$248$$ 0 0
$$249$$ 1.21383e6i 1.24068i
$$250$$ 0 0
$$251$$ 1.26857e6i 1.27096i −0.772118 0.635480i $$-0.780802\pi$$
0.772118 0.635480i $$-0.219198\pi$$
$$252$$ 0 0
$$253$$ −867393. 867393.i −0.851951 0.851951i
$$254$$ 0 0
$$255$$ 1.66787e6 465749.i 1.60624 0.448540i
$$256$$ 0 0
$$257$$ 79307.5 79307.5i 0.0749000 0.0749000i −0.668664 0.743564i $$-0.733134\pi$$
0.743564 + 0.668664i $$0.233134\pi$$
$$258$$ 0 0
$$259$$ −1.51401e6 −1.40243
$$260$$ 0 0
$$261$$ 36054.8 0.0327614
$$262$$ 0 0
$$263$$ −750568. + 750568.i −0.669115 + 0.669115i −0.957511 0.288396i $$-0.906878\pi$$
0.288396 + 0.957511i $$0.406878\pi$$
$$264$$ 0 0
$$265$$ −818529. + 1.45279e6i −0.716010 + 1.27083i
$$266$$ 0 0
$$267$$ 1.93287e6 + 1.93287e6i 1.65930 + 1.65930i
$$268$$ 0 0
$$269$$ 2.07912e6i 1.75186i −0.482441 0.875928i $$-0.660250\pi$$
0.482441 0.875928i $$-0.339750\pi$$
$$270$$ 0 0
$$271$$ 826197.i 0.683377i −0.939813 0.341689i $$-0.889001\pi$$
0.939813 0.341689i $$-0.110999\pi$$
$$272$$ 0 0
$$273$$ −602863. 602863.i −0.489567 0.489567i
$$274$$ 0 0
$$275$$ 1.00866e6 + 1.66519e6i 0.804289 + 1.32780i
$$276$$ 0 0
$$277$$ −1.13631e6 + 1.13631e6i −0.889808 + 0.889808i −0.994504 0.104696i $$-0.966613\pi$$
0.104696 + 0.994504i $$0.466613\pi$$
$$278$$ 0 0
$$279$$ 248532. 0.191149
$$280$$ 0 0
$$281$$ 812.516 0.000613856 0.000306928 1.00000i $$-0.499902\pi$$
0.000306928 1.00000i $$0.499902\pi$$
$$282$$ 0 0
$$283$$ 129621. 129621.i 0.0962076 0.0962076i −0.657365 0.753572i $$-0.728329\pi$$
0.753572 + 0.657365i $$0.228329\pi$$
$$284$$ 0 0
$$285$$ −1.85365e6 1.04438e6i −1.35181 0.761633i
$$286$$ 0 0
$$287$$ −1.29920e6 1.29920e6i −0.931046 0.931046i
$$288$$ 0 0
$$289$$ 1.23905e6i 0.872655i
$$290$$ 0 0
$$291$$ 655290.i 0.453629i
$$292$$ 0 0
$$293$$ 1.81804e6 + 1.81804e6i 1.23719 + 1.23719i 0.961147 + 0.276039i $$0.0890218\pi$$
0.276039 + 0.961147i $$0.410978\pi$$
$$294$$ 0 0
$$295$$ 174670. + 625503.i 0.116860 + 0.418480i
$$296$$ 0 0
$$297$$ −1.04696e6 + 1.04696e6i −0.688717 + 0.688717i
$$298$$ 0 0
$$299$$ −817422. −0.528772
$$300$$ 0 0
$$301$$ 310548. 0.197566
$$302$$ 0 0
$$303$$ −2.28353e6 + 2.28353e6i −1.42890 + 1.42890i
$$304$$ 0 0
$$305$$ −19693.2 70522.2i −0.0121218 0.0434087i
$$306$$ 0 0
$$307$$ 1.39031e6 + 1.39031e6i 0.841907 + 0.841907i 0.989107 0.147199i $$-0.0470259\pi$$
−0.147199 + 0.989107i $$0.547026\pi$$
$$308$$ 0 0
$$309$$ 3.11718e6i 1.85723i
$$310$$ 0 0
$$311$$ 2.77199e6i 1.62514i 0.582863 + 0.812570i $$0.301932\pi$$
−0.582863 + 0.812570i $$0.698068\pi$$
$$312$$ 0 0
$$313$$ −393418. 393418.i −0.226983 0.226983i 0.584448 0.811431i $$-0.301311\pi$$
−0.811431 + 0.584448i $$0.801311\pi$$
$$314$$ 0 0
$$315$$ −620728. 349730.i −0.352472 0.198590i
$$316$$ 0 0
$$317$$ 594016. 594016.i 0.332009 0.332009i −0.521340 0.853349i $$-0.674568\pi$$
0.853349 + 0.521340i $$0.174568\pi$$
$$318$$ 0 0
$$319$$ 190524. 0.104827
$$320$$ 0 0
$$321$$ 1.83957e6 0.996445
$$322$$ 0 0
$$323$$ −2.31000e6 + 2.31000e6i −1.23199 + 1.23199i
$$324$$ 0 0
$$325$$ 1.25990e6 + 309356.i 0.661652 + 0.162462i
$$326$$ 0 0
$$327$$ 271387. + 271387.i 0.140352 + 0.140352i
$$328$$ 0 0
$$329$$ 104401.i 0.0531760i
$$330$$ 0 0
$$331$$ 2.17459e6i 1.09096i 0.838124 + 0.545479i $$0.183652\pi$$
−0.838124 + 0.545479i $$0.816348\pi$$
$$332$$ 0 0
$$333$$ −1.16754e6 1.16754e6i −0.576980 0.576980i
$$334$$ 0 0
$$335$$ 1.54724e6 2.74617e6i 0.753263 1.33695i
$$336$$ 0 0
$$337$$ −603974. + 603974.i −0.289696 + 0.289696i −0.836960 0.547264i $$-0.815669\pi$$
0.547264 + 0.836960i $$0.315669\pi$$
$$338$$ 0 0
$$339$$ 2.12965e6 1.00649
$$340$$ 0 0
$$341$$ 1.31331e6 0.611621
$$342$$ 0 0
$$343$$ −1.67616e6 + 1.67616e6i −0.769274 + 0.769274i
$$344$$ 0 0
$$345$$ −2.01399e6 + 562402.i −0.910981 + 0.254389i
$$346$$ 0 0
$$347$$ −2.94638e6 2.94638e6i −1.31361 1.31361i −0.918738 0.394869i $$-0.870790\pi$$
−0.394869 0.918738i $$-0.629210\pi$$
$$348$$ 0 0
$$349$$ 1.01585e6i 0.446443i −0.974768 0.223221i $$-0.928343\pi$$
0.974768 0.223221i $$-0.0716573\pi$$
$$350$$ 0 0
$$351$$ 986648.i 0.427459i
$$352$$ 0 0
$$353$$ −3.05696e6 3.05696e6i −1.30573 1.30573i −0.924468 0.381259i $$-0.875491\pi$$
−0.381259 0.924468i $$-0.624509\pi$$
$$354$$ 0 0
$$355$$ −1.37050e6 + 382710.i −0.577178 + 0.161176i
$$356$$ 0 0
$$357$$ −2.36794e6 + 2.36794e6i −0.983331 + 0.983331i
$$358$$ 0 0
$$359$$ −1.01289e6 −0.414787 −0.207393 0.978258i $$-0.566498\pi$$
−0.207393 + 0.978258i $$0.566498\pi$$
$$360$$ 0 0
$$361$$ 1.53767e6 0.621005
$$362$$ 0 0
$$363$$ 3.05028e6 3.05028e6i 1.21499 1.21499i
$$364$$ 0 0
$$365$$ −40019.4 + 71029.6i −0.0157231 + 0.0279066i
$$366$$ 0 0
$$367$$ 1.78687e6 + 1.78687e6i 0.692511 + 0.692511i 0.962784 0.270272i $$-0.0871138\pi$$
−0.270272 + 0.962784i $$0.587114\pi$$
$$368$$ 0 0
$$369$$ 2.00377e6i 0.766092i
$$370$$ 0 0
$$371$$ 3.22468e6i 1.21633i
$$372$$ 0 0
$$373$$ 382840. + 382840.i 0.142477 + 0.142477i 0.774748 0.632270i $$-0.217877\pi$$
−0.632270 + 0.774748i $$0.717877\pi$$
$$374$$ 0 0
$$375$$ 3.31704e6 104637.i 1.21807 0.0384245i
$$376$$ 0 0
$$377$$ 89773.7 89773.7i 0.0325309 0.0325309i
$$378$$ 0 0
$$379$$ −2.37584e6 −0.849610 −0.424805 0.905285i $$-0.639657\pi$$
−0.424805 + 0.905285i $$0.639657\pi$$
$$380$$ 0 0
$$381$$ −3.59960e6 −1.27040
$$382$$ 0 0
$$383$$ −748285. + 748285.i −0.260657 + 0.260657i −0.825321 0.564664i $$-0.809006\pi$$
0.564664 + 0.825321i $$0.309006\pi$$
$$384$$ 0 0
$$385$$ −3.28010e6 1.84807e6i −1.12781 0.635428i
$$386$$ 0 0
$$387$$ 239480. + 239480.i 0.0812816 + 0.0812816i
$$388$$ 0 0
$$389$$ 3.04186e6i 1.01921i 0.860407 + 0.509607i $$0.170209\pi$$
−0.860407 + 0.509607i $$0.829791\pi$$
$$390$$ 0 0
$$391$$ 3.21068e6i 1.06208i
$$392$$ 0 0
$$393$$ 4.81680e6 + 4.81680e6i 1.57317 + 1.57317i
$$394$$ 0 0
$$395$$ −178161. 638003.i −0.0574539 0.205745i
$$396$$ 0 0
$$397$$ −3.19165e6 + 3.19165e6i −1.01634 + 1.01634i −0.0164751 + 0.999864i $$0.505244\pi$$
−0.999864 + 0.0164751i $$0.994756\pi$$
$$398$$ 0 0
$$399$$ 4.11443e6 1.29383
$$400$$ 0 0
$$401$$ 4.27231e6 1.32679 0.663395 0.748270i $$-0.269115\pi$$
0.663395 + 0.748270i $$0.269115\pi$$
$$402$$ 0 0
$$403$$ 618826. 618826.i 0.189804 0.189804i
$$404$$ 0 0
$$405$$ 1.10957e6 + 3.97343e6i 0.336138 + 1.20373i
$$406$$ 0 0
$$407$$ −6.16960e6 6.16960e6i −1.84617 1.84617i
$$408$$ 0 0
$$409$$ 4.39056e6i 1.29781i 0.760869 + 0.648906i $$0.224773\pi$$
−0.760869 + 0.648906i $$0.775227\pi$$
$$410$$ 0 0
$$411$$ 4.19187e6i 1.22406i
$$412$$ 0 0
$$413$$ −888050. 888050.i −0.256190 0.256190i
$$414$$ 0 0
$$415$$ 3.11191e6 + 1.75331e6i 0.886967 + 0.499734i
$$416$$ 0 0
$$417$$ 2.84533e6 2.84533e6i 0.801295 0.801295i
$$418$$ 0 0
$$419$$ −5.83290e6 −1.62312 −0.811558 0.584271i $$-0.801380\pi$$
−0.811558 + 0.584271i $$0.801380\pi$$
$$420$$ 0 0
$$421$$ −741629. −0.203930 −0.101965 0.994788i $$-0.532513\pi$$
−0.101965 + 0.994788i $$0.532513\pi$$
$$422$$ 0 0
$$423$$ −80509.4 + 80509.4i −0.0218774 + 0.0218774i
$$424$$ 0 0
$$425$$ 1.21509e6 4.94868e6i 0.326316 1.32897i
$$426$$ 0 0
$$427$$ 100123. + 100123.i 0.0265745 + 0.0265745i
$$428$$ 0 0
$$429$$ 4.91333e6i 1.28894i
$$430$$ 0 0
$$431$$ 12397.3i 0.00321464i −0.999999 0.00160732i $$-0.999488\pi$$
0.999999 0.00160732i $$-0.000511626\pi$$
$$432$$ 0 0
$$433$$ −203088. 203088.i −0.0520552 0.0520552i 0.680600 0.732655i $$-0.261719\pi$$
−0.732655 + 0.680600i $$0.761719\pi$$
$$434$$ 0 0
$$435$$ 159421. 282953.i 0.0403946 0.0716954i
$$436$$ 0 0
$$437$$ 2.78938e6 2.78938e6i 0.698721 0.698721i
$$438$$ 0 0
$$439$$ 6.21348e6 1.53877 0.769384 0.638786i $$-0.220563\pi$$
0.769384 + 0.638786i $$0.220563\pi$$
$$440$$ 0 0
$$441$$ −603682. −0.147813
$$442$$ 0 0
$$443$$ 4.93074e6 4.93074e6i 1.19372 1.19372i 0.217705 0.976015i $$-0.430143\pi$$
0.976015 0.217705i $$-0.0698571\pi$$
$$444$$ 0 0
$$445$$ 7.74722e6 2.16340e6i 1.85458 0.517888i
$$446$$ 0 0
$$447$$ 742475. + 742475.i 0.175757 + 0.175757i
$$448$$ 0 0
$$449$$ 3.32541e6i 0.778449i 0.921143 + 0.389224i $$0.127257\pi$$
−0.921143 + 0.389224i $$0.872743\pi$$
$$450$$ 0 0
$$451$$ 1.05885e7i 2.45127i
$$452$$ 0 0
$$453$$ 4.81873e6 + 4.81873e6i 1.10328 + 1.10328i
$$454$$ 0 0
$$455$$ −2.41637e6 + 674765.i −0.547185 + 0.152800i
$$456$$ 0 0
$$457$$ 1.03786e6 1.03786e6i 0.232460 0.232460i −0.581259 0.813719i $$-0.697440\pi$$
0.813719 + 0.581259i $$0.197440\pi$$
$$458$$ 0 0
$$459$$ 3.87537e6 0.858582
$$460$$ 0 0
$$461$$ 4.98358e6 1.09217 0.546083 0.837731i $$-0.316118\pi$$
0.546083 + 0.837731i $$0.316118\pi$$
$$462$$ 0 0
$$463$$ −867273. + 867273.i −0.188020 + 0.188020i −0.794839 0.606820i $$-0.792445\pi$$
0.606820 + 0.794839i $$0.292445\pi$$
$$464$$ 0 0
$$465$$ 1.09892e6 1.95045e6i 0.235686 0.418313i
$$466$$ 0 0
$$467$$ 6.21652e6 + 6.21652e6i 1.31903 + 1.31903i 0.914543 + 0.404489i $$0.132551\pi$$
0.404489 + 0.914543i $$0.367449\pi$$
$$468$$ 0 0
$$469$$ 6.09552e6i 1.27961i
$$470$$ 0 0
$$471$$ 9.55479e6i 1.98458i
$$472$$ 0 0
$$473$$ 1.26548e6 + 1.26548e6i 0.260077 + 0.260077i
$$474$$ 0 0
$$475$$ −5.35496e6 + 3.24366e6i −1.08899 + 0.659632i
$$476$$ 0 0
$$477$$ 2.48672e6 2.48672e6i 0.500416 0.500416i
$$478$$ 0 0
$$479$$ −5.54732e6 −1.10470 −0.552350 0.833612i $$-0.686269\pi$$
−0.552350 + 0.833612i $$0.686269\pi$$
$$480$$ 0 0
$$481$$ −5.81416e6 −1.14584
$$482$$ 0 0
$$483$$ 2.85934e6 2.85934e6i 0.557696 0.557696i
$$484$$ 0 0
$$485$$ −1.67997e6 946528.i −0.324300 0.182717i
$$486$$ 0 0
$$487$$ −45082.0 45082.0i −0.00861353 0.00861353i 0.702787 0.711400i $$-0.251939\pi$$
−0.711400 + 0.702787i $$0.751939\pi$$
$$488$$ 0 0
$$489$$ 7.74397e6i 1.46451i
$$490$$ 0 0
$$491$$ 4.49346e6i 0.841157i 0.907256 + 0.420579i $$0.138173\pi$$
−0.907256 + 0.420579i $$0.861827\pi$$
$$492$$ 0 0
$$493$$ −352615. 352615.i −0.0653406 0.0653406i
$$494$$ 0 0
$$495$$ −1.10432e6 3.95461e6i −0.202572 0.725422i
$$496$$ 0 0
$$497$$ 1.94576e6 1.94576e6i 0.353344 0.353344i
$$498$$ 0 0
$$499$$ 1.35470e6 0.243552 0.121776 0.992558i $$-0.461141\pi$$
0.121776 + 0.992558i $$0.461141\pi$$
$$500$$ 0 0
$$501$$ −2.10341e6 −0.374395
$$502$$ 0 0
$$503$$ 5.30723e6 5.30723e6i 0.935294 0.935294i −0.0627366 0.998030i $$-0.519983\pi$$
0.998030 + 0.0627366i $$0.0199828\pi$$
$$504$$ 0 0
$$505$$ 2.55588e6 + 9.15273e6i 0.445976 + 1.59706i
$$506$$ 0 0
$$507$$ 2.67248e6 + 2.67248e6i 0.461737 + 0.461737i
$$508$$ 0 0
$$509$$ 7.90014e6i 1.35158i −0.737096 0.675788i $$-0.763803\pi$$
0.737096 0.675788i $$-0.236197\pi$$
$$510$$ 0 0
$$511$$ 157661.i 0.0267098i
$$512$$ 0 0
$$513$$ −3.36685e6 3.36685e6i −0.564846 0.564846i
$$514$$ 0 0
$$515$$ −7.99155e6 4.50259e6i −1.32774 0.748073i
$$516$$ 0 0
$$517$$ −425434. + 425434.i −0.0700013 + 0.0700013i
$$518$$ 0 0
$$519$$ 6.50292e6 1.05972
$$520$$ 0 0
$$521$$ −90092.2 −0.0145410 −0.00727048 0.999974i $$-0.502314\pi$$
−0.00727048 + 0.999974i $$0.502314\pi$$
$$522$$ 0 0
$$523$$ 1.47517e6 1.47517e6i 0.235824 0.235824i −0.579295 0.815118i $$-0.696672\pi$$
0.815118 + 0.579295i $$0.196672\pi$$
$$524$$ 0 0
$$525$$ −5.48926e6 + 3.32501e6i −0.869192 + 0.526496i
$$526$$ 0 0
$$527$$ −2.43064e6 2.43064e6i −0.381235 0.381235i
$$528$$ 0 0
$$529$$ 2.55937e6i 0.397644i
$$530$$ 0 0
$$531$$ 1.36965e6i 0.210801i
$$532$$ 0 0
$$533$$ −4.98922e6 4.98922e6i −0.760702 0.760702i
$$534$$ 0 0
$$535$$ 2.65715e6 4.71612e6i 0.401357 0.712361i
$$536$$ 0 0
$$537$$ −381470. + 381470.i −0.0570854 + 0.0570854i
$$538$$ 0 0
$$539$$ −3.19002e6 −0.472958
$$540$$ 0 0
$$541$$ −1.00732e7 −1.47970 −0.739852 0.672769i $$-0.765105\pi$$
−0.739852 + 0.672769i $$0.765105\pi$$
$$542$$ 0 0
$$543$$ −8.56118e6 + 8.56118e6i −1.24605 + 1.24605i
$$544$$ 0 0
$$545$$ 1.08776e6 303754.i 0.156870 0.0438057i
$$546$$ 0 0
$$547$$ −1.68628e6 1.68628e6i −0.240969 0.240969i 0.576282 0.817251i $$-0.304503\pi$$
−0.817251 + 0.576282i $$0.804503\pi$$
$$548$$ 0 0
$$549$$ 154421.i 0.0218663i
$$550$$ 0 0
$$551$$ 612689.i 0.0859728i
$$552$$ 0 0
$$553$$ 905796. + 905796.i 0.125956 + 0.125956i
$$554$$ 0 0
$$555$$ −1.43251e7 + 4.00026e6i −1.97408 + 0.551259i
$$556$$ 0 0
$$557$$ 5.82782e6 5.82782e6i 0.795917 0.795917i −0.186532 0.982449i $$-0.559725\pi$$
0.982449 + 0.186532i $$0.0597247\pi$$
$$558$$ 0 0
$$559$$ 1.19257e6 0.161420
$$560$$ 0 0
$$561$$ −1.92987e7 −2.58893
$$562$$ 0 0
$$563$$ 3.92139e6 3.92139e6i 0.521397 0.521397i −0.396596 0.917993i $$-0.629809\pi$$
0.917993 + 0.396596i $$0.129809\pi$$
$$564$$ 0 0
$$565$$ 3.07615e6 5.45979e6i 0.405402 0.719540i
$$566$$ 0 0
$$567$$ −5.64123e6 5.64123e6i −0.736913 0.736913i
$$568$$ 0 0
$$569$$ 9.00329e6i 1.16579i −0.812547 0.582895i $$-0.801920\pi$$
0.812547 0.582895i $$-0.198080\pi$$
$$570$$ 0 0
$$571$$ 1.33754e7i 1.71678i 0.512995 + 0.858392i $$0.328536\pi$$
−0.512995 + 0.858392i $$0.671464\pi$$
$$572$$ 0 0
$$573$$ 8.30734e6 + 8.30734e6i 1.05700 + 1.05700i
$$574$$ 0 0
$$575$$ −1.46725e6 + 5.97563e6i −0.185070 + 0.753727i
$$576$$ 0 0
$$577$$ 5.22216e6 5.22216e6i 0.652996 0.652996i −0.300717 0.953713i $$-0.597226\pi$$
0.953713 + 0.300717i $$0.0972261\pi$$
$$578$$ 0 0
$$579$$ −581410. −0.0720752
$$580$$ 0 0
$$581$$ −6.90734e6 −0.848928
$$582$$ 0 0
$$583$$ 1.31405e7 1.31405e7i 1.60119 1.60119i
$$584$$ 0 0
$$585$$ −2.38374e6 1.34304e6i −0.287984 0.162256i
$$586$$ 0 0
$$587$$ 3.91266e6 + 3.91266e6i 0.468680 + 0.468680i 0.901487 0.432807i $$-0.142477\pi$$
−0.432807 + 0.901487i $$0.642477\pi$$
$$588$$ 0 0
$$589$$ 4.22338e6i 0.501616i
$$590$$ 0 0
$$591$$ 1.02181e6i 0.120337i
$$592$$ 0 0
$$593$$ −377034. 377034.i −0.0440295 0.0440295i 0.684749 0.728779i $$-0.259912\pi$$
−0.728779 + 0.684749i $$0.759912\pi$$
$$594$$ 0 0
$$595$$ 2.65035e6 + 9.49104e6i 0.306910 + 1.09906i
$$596$$ 0 0
$$597$$ −3.47220e6 + 3.47220e6i −0.398721 + 0.398721i
$$598$$ 0 0
$$599$$ −3.69548e6 −0.420827 −0.210413 0.977613i $$-0.567481\pi$$
−0.210413 + 0.977613i $$0.567481\pi$$
$$600$$ 0 0
$$601$$ −5.53615e6 −0.625204 −0.312602 0.949884i $$-0.601201\pi$$
−0.312602 + 0.949884i $$0.601201\pi$$
$$602$$ 0 0
$$603$$ −4.70059e6 + 4.70059e6i −0.526452 + 0.526452i
$$604$$ 0 0
$$605$$ −3.41408e6 1.22260e7i −0.379214 1.35798i
$$606$$ 0 0
$$607$$ −851040. 851040.i −0.0937515 0.0937515i 0.658676 0.752427i $$-0.271117\pi$$
−0.752427 + 0.658676i $$0.771117\pi$$
$$608$$ 0 0
$$609$$ 628056.i 0.0686207i
$$610$$ 0 0
$$611$$ 400924.i 0.0434470i
$$612$$ 0 0
$$613$$ −2.99552e6 2.99552e6i −0.321974 0.321974i 0.527550 0.849524i $$-0.323111\pi$$
−0.849524 + 0.527550i $$0.823111\pi$$
$$614$$ 0 0
$$615$$ −1.57253e7 8.85992e6i −1.67653 0.944587i
$$616$$ 0 0
$$617$$ 2.10245e6 2.10245e6i 0.222337 0.222337i −0.587145 0.809482i $$-0.699748\pi$$
0.809482 + 0.587145i $$0.199748\pi$$
$$618$$ 0 0
$$619$$ 4.83196e6 0.506870 0.253435 0.967352i $$-0.418440\pi$$
0.253435 + 0.967352i $$0.418440\pi$$
$$620$$ 0 0
$$621$$ −4.67960e6 −0.486944
$$622$$ 0 0
$$623$$ −1.09990e7 + 1.09990e7i −1.13536 + 1.13536i
$$624$$ 0 0
$$625$$ 4.52300e6 8.65505e6i 0.463155 0.886277i
$$626$$ 0 0
$$627$$ 1.67663e7 + 1.67663e7i 1.70321 + 1.70321i
$$628$$ 0 0
$$629$$ 2.28370e7i 2.30150i
$$630$$ 0 0
$$631$$ 1.27571e7i 1.27550i 0.770244 + 0.637749i $$0.220134\pi$$
−0.770244 + 0.637749i $$0.779866\pi$$
$$632$$ 0 0
$$633$$ 2.49544e6 + 2.49544e6i 0.247535 + 0.247535i
$$634$$ 0 0
$$635$$ −5.19941e6 + 9.22832e6i −0.511705 + 0.908215i
$$636$$ 0 0
$$637$$ −1.50312e6 + 1.50312e6i −0.146773 + 0.146773i
$$638$$ 0 0
$$639$$ 3.00096e6 0.290742
$$640$$ 0 0
$$641$$ 7.64611e6 0.735014 0.367507 0.930021i $$-0.380211\pi$$
0.367507 + 0.930021i $$0.380211\pi$$
$$642$$ 0 0
$$643$$ −2.54976e6 + 2.54976e6i −0.243204 + 0.243204i −0.818174 0.574970i $$-0.805014\pi$$
0.574970 + 0.818174i $$0.305014\pi$$
$$644$$ 0 0
$$645$$ 2.93830e6 820514.i 0.278098 0.0776581i
$$646$$ 0 0
$$647$$ −3.90727e6 3.90727e6i −0.366954 0.366954i 0.499411 0.866365i $$-0.333550\pi$$
−0.866365 + 0.499411i $$0.833550\pi$$
$$648$$ 0 0
$$649$$ 7.23760e6i 0.674501i
$$650$$ 0 0
$$651$$ 4.32930e6i 0.400373i
$$652$$ 0 0
$$653$$ −4.91675e6 4.91675e6i −0.451227 0.451227i 0.444535 0.895762i $$-0.353369\pi$$
−0.895762 + 0.444535i $$0.853369\pi$$
$$654$$ 0 0
$$655$$ 1.93064e7 5.39128e6i 1.75832 0.491008i
$$656$$ 0 0
$$657$$ 121581. 121581.i 0.0109888 0.0109888i
$$658$$ 0 0
$$659$$ −1.22997e6 −0.110327 −0.0551636 0.998477i $$-0.517568\pi$$
−0.0551636 + 0.998477i $$0.517568\pi$$
$$660$$ 0 0
$$661$$ 2.50222e6 0.222752 0.111376 0.993778i $$-0.464474\pi$$
0.111376 + 0.993778i $$0.464474\pi$$
$$662$$ 0 0
$$663$$ −9.09342e6 + 9.09342e6i −0.803421 + 0.803421i
$$664$$ 0 0
$$665$$ 5.94306e6 1.05482e7i 0.521142 0.924963i
$$666$$ 0 0
$$667$$ 425790. + 425790.i 0.0370579 + 0.0370579i
$$668$$ 0 0
$$669$$ 2.04152e7i 1.76355i
$$670$$ 0 0
$$671$$ 816001.i 0.0699656i
$$672$$ 0 0
$$673$$ 4.60945e6 + 4.60945e6i 0.392294 + 0.392294i 0.875504 0.483210i $$-0.160529\pi$$
−0.483210 + 0.875504i $$0.660529\pi$$
$$674$$ 0 0
$$675$$ 7.21273e6 + 1.77101e6i 0.609313 + 0.149610i
$$676$$ 0 0
$$677$$ 1.03990e7 1.03990e7i 0.872006 0.872006i −0.120685 0.992691i $$-0.538509\pi$$
0.992691 + 0.120685i $$0.0385091\pi$$
$$678$$ 0 0
$$679$$ 3.72894e6 0.310392
$$680$$ 0 0
$$681$$ −964776. −0.0797185
$$682$$ 0 0
$$683$$ 1.39930e7 1.39930e7i 1.14778 1.14778i 0.160795 0.986988i $$-0.448594\pi$$
0.986988 0.160795i $$-0.0514059\pi$$
$$684$$ 0 0
$$685$$ −1.07467e7 6.05490e6i −0.875084 0.493038i
$$686$$ 0 0
$$687$$ −2.07763e7 2.07763e7i −1.67949 1.67949i
$$688$$ 0 0
$$689$$ 1.23835e7i 0.993791i
$$690$$ 0 0
$$691$$ 9.98056e6i 0.795169i 0.917565 + 0.397585i $$0.130152\pi$$
−0.917565 + 0.397585i $$0.869848\pi$$
$$692$$ 0 0
$$693$$ 5.61451e6 + 5.61451e6i 0.444098 + 0.444098i
$$694$$ 0 0
$$695$$ −3.18468e6 1.14045e7i −0.250095 0.895601i
$$696$$ 0 0
$$697$$ −1.95968e7 + 1.95968e7i −1.52793 + 1.52793i
$$698$$ 0 0
$$699$$ 1.04580e7 0.809573
$$700$$ 0 0
$$701$$ −7.67178e6 −0.589659 −0.294830 0.955550i $$-0.595263\pi$$
−0.294830 + 0.955550i $$0.595263\pi$$
$$702$$ 0 0
$$703$$ 1.98403e7 1.98403e7i 1.51412 1.51412i
$$704$$ 0 0
$$705$$ 275844. + 987810.i 0.0209021 + 0.0748515i
$$706$$ 0 0
$$707$$ −1.29945e7 1.29945e7i −0.977710 0.977710i
$$708$$ 0 0
$$709$$ 1.61069e7i 1.20336i −0.798737 0.601681i $$-0.794498\pi$$
0.798737 0.601681i $$-0.205502\pi$$
$$710$$ 0 0
$$711$$ 1.39702e6i 0.103640i
$$712$$ 0 0
$$713$$ 2.93505e6 + 2.93505e6i 0.216218 + 0.216218i
$$714$$ 0 0
$$715$$ −1.25963e7 7.09701e6i −0.921465 0.519171i
$$716$$ 0 0
$$717$$ 1.10659e7 1.10659e7i 0.803874 0.803874i
$$718$$ 0 0
$$719$$ 9.25776e6 0.667857 0.333929 0.942598i $$-0.391626\pi$$
0.333929 + 0.942598i $$0.391626\pi$$
$$720$$ 0 0
$$721$$ 1.77384e7 1.27080
$$722$$ 0 0
$$723$$ 1.87604e6 1.87604e6i 0.133474 0.133474i
$$724$$ 0 0
$$725$$ −495135. 817418.i −0.0349847 0.0577563i
$$726$$ 0 0
$$727$$ −1.17208e7 1.17208e7i −0.822475 0.822475i 0.163988 0.986462i $$-0.447564\pi$$
−0.986462 + 0.163988i $$0.947564\pi$$
$$728$$ 0 0
$$729$$ 2.27081e6i 0.158257i
$$730$$ 0 0
$$731$$ 4.68421e6i 0.324223i
$$732$$ 0 0
$$733$$ 5.35037e6 + 5.35037e6i 0.367811 + 0.367811i 0.866678 0.498868i $$-0.166251\pi$$
−0.498868 + 0.866678i $$0.666251\pi$$
$$734$$ 0 0
$$735$$ −2.66926e6 + 4.73762e6i −0.182252 + 0.323476i
$$736$$ 0 0
$$737$$ −2.48392e7 + 2.48392e7i −1.68449 + 1.68449i
$$738$$ 0 0
$$739$$ −2.80515e7 −1.88949 −0.944746 0.327803i $$-0.893692\pi$$
−0.944746 + 0.327803i $$0.893692\pi$$
$$740$$ 0 0
$$741$$ 1.58004e7 1.05711
$$742$$ 0 0
$$743$$ 3.89759e6 3.89759e6i 0.259014 0.259014i −0.565639 0.824653i $$-0.691370\pi$$
0.824653 + 0.565639i $$0.191370\pi$$
$$744$$ 0 0
$$745$$ 2.97595e6 831028.i 0.196442 0.0548561i
$$746$$ 0 0
$$747$$ −5.32663e6 5.32663e6i −0.349262 0.349262i
$$748$$ 0 0
$$749$$ 1.04681e7i 0.681810i
$$750$$ 0 0
$$751$$ 1.33082e6i 0.0861032i 0.999073 + 0.0430516i $$0.0137080\pi$$
−0.999073 + 0.0430516i $$0.986292\pi$$
$$752$$ 0 0
$$753$$ 1.70409e7 + 1.70409e7i 1.09523 + 1.09523i
$$754$$ 0 0
$$755$$ 1.93142e7 5.39344e6i 1.23313 0.344349i
$$756$$ 0 0
$$757$$ −4.82595e6 + 4.82595e6i −0.306085 + 0.306085i −0.843389 0.537303i $$-0.819443\pi$$
0.537303 + 0.843389i $$0.319443\pi$$
$$758$$ 0 0
$$759$$ 2.33035e7 1.46831
$$760$$ 0 0
$$761$$ −1.62700e7 −1.01842 −0.509210 0.860642i $$-0.670062\pi$$
−0.509210 + 0.860642i $$0.670062\pi$$
$$762$$ 0 0
$$763$$ −1.54433e6 + 1.54433e6i −0.0960349 + 0.0960349i
$$764$$ 0 0
$$765$$ −5.27523e6 + 9.36289e6i −0.325902 + 0.578437i
$$766$$ 0 0
$$767$$ −3.41032e6 3.41032e6i −0.209318 0.209318i
$$768$$ 0 0
$$769$$ 7.50924e6i 0.457910i 0.973437 + 0.228955i $$0.0735308\pi$$
−0.973437 + 0.228955i $$0.926469\pi$$
$$770$$ 0 0
$$771$$ 2.13069e6i 0.129088i
$$772$$ 0 0
$$773$$ −2.21009e6 2.21009e6i −0.133034 0.133034i 0.637454 0.770488i $$-0.279987\pi$$
−0.770488 + 0.637454i $$0.779987\pi$$
$$774$$ 0 0
$$775$$ −3.41305e6 5.63461e6i −0.204121 0.336984i
$$776$$ 0 0
$$777$$ 2.03379e7 2.03379e7i 1.20852 1.20852i
$$778$$ 0 0
$$779$$ 3.40505e7 2.01039
$$780$$ 0 0
$$781$$ 1.58579e7 0.930289
$$782$$ 0 0
$$783$$ 513939. 513939.i 0.0299576 0.0299576i
$$784$$ 0 0
$$785$$ 2.44957e7 + 1.38013e7i 1.41878 + 0.799368i
$$786$$ 0 0
$$787$$ −6.25543e6 6.25543e6i −0.360015 0.360015i 0.503803 0.863818i $$-0.331934\pi$$
−0.863818 + 0.503803i $$0.831934\pi$$
$$788$$ 0 0
$$789$$ 2.01649e7i 1.15320i
$$790$$ 0 0
$$791$$ 1.21188e7i 0.688681i
$$792$$ 0 0