# Properties

 Label 1344.4.p.d.223.12 Level $1344$ Weight $4$ Character 1344.223 Analytic conductor $79.299$ Analytic rank $0$ Dimension $32$ CM no Inner twists $4$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$1344 = 2^{6} \cdot 3 \cdot 7$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 1344.p (of order $$2$$, degree $$1$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$79.2985670477$$ Analytic rank: $$0$$ Dimension: $$32$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

## Embedding invariants

 Embedding label 223.12 Character $$\chi$$ $$=$$ 1344.223 Dual form 1344.4.p.d.223.11

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+3.00000i q^{3} +15.4018 q^{5} +(-6.29285 + 17.4184i) q^{7} -9.00000 q^{9} +O(q^{10})$$ $$q+3.00000i q^{3} +15.4018 q^{5} +(-6.29285 + 17.4184i) q^{7} -9.00000 q^{9} +16.8703 q^{11} +9.10290 q^{13} +46.2054i q^{15} -73.9573i q^{17} -151.262i q^{19} +(-52.2551 - 18.8786i) q^{21} -0.264643i q^{23} +112.215 q^{25} -27.0000i q^{27} -279.925i q^{29} -147.800 q^{31} +50.6110i q^{33} +(-96.9212 + 268.274i) q^{35} -418.498i q^{37} +27.3087i q^{39} -164.377i q^{41} +266.668 q^{43} -138.616 q^{45} +277.719 q^{47} +(-263.800 - 219.223i) q^{49} +221.872 q^{51} +276.852i q^{53} +259.833 q^{55} +453.785 q^{57} -212.008i q^{59} +174.541 q^{61} +(56.6357 - 156.765i) q^{63} +140.201 q^{65} -317.501 q^{67} +0.793928 q^{69} +106.093i q^{71} -755.118i q^{73} +336.645i q^{75} +(-106.163 + 293.854i) q^{77} +194.202i q^{79} +81.0000 q^{81} +997.764i q^{83} -1139.08i q^{85} +839.776 q^{87} +988.320i q^{89} +(-57.2832 + 158.558i) q^{91} -443.400i q^{93} -2329.70i q^{95} -1021.78i q^{97} -151.833 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$32q - 288q^{9} + O(q^{10})$$ $$32q - 288q^{9} + 224q^{13} + 72q^{21} + 1120q^{25} - 752q^{49} - 672q^{57} + 544q^{61} + 1536q^{65} + 144q^{69} + 1632q^{77} + 2592q^{81} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1344\mathbb{Z}\right)^\times$$.

 $$n$$ $$127$$ $$449$$ $$577$$ $$1093$$ $$\chi(n)$$ $$-1$$ $$1$$ $$-1$$ $$-1$$

## Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0 0
$$3$$ 3.00000i 0.577350i
$$4$$ 0 0
$$5$$ 15.4018 1.37758 0.688789 0.724962i $$-0.258143\pi$$
0.688789 + 0.724962i $$0.258143\pi$$
$$6$$ 0 0
$$7$$ −6.29285 + 17.4184i −0.339782 + 0.940504i
$$8$$ 0 0
$$9$$ −9.00000 −0.333333
$$10$$ 0 0
$$11$$ 16.8703 0.462418 0.231209 0.972904i $$-0.425732\pi$$
0.231209 + 0.972904i $$0.425732\pi$$
$$12$$ 0 0
$$13$$ 9.10290 0.194207 0.0971034 0.995274i $$-0.469042\pi$$
0.0971034 + 0.995274i $$0.469042\pi$$
$$14$$ 0 0
$$15$$ 46.2054i 0.795345i
$$16$$ 0 0
$$17$$ 73.9573i 1.05513i −0.849513 0.527567i $$-0.823104\pi$$
0.849513 0.527567i $$-0.176896\pi$$
$$18$$ 0 0
$$19$$ 151.262i 1.82641i −0.407499 0.913206i $$-0.633599\pi$$
0.407499 0.913206i $$-0.366401\pi$$
$$20$$ 0 0
$$21$$ −52.2551 18.8786i −0.543000 0.196173i
$$22$$ 0 0
$$23$$ 0.264643i 0.00239921i −0.999999 0.00119960i $$-0.999618\pi$$
0.999999 0.00119960i $$-0.000381846\pi$$
$$24$$ 0 0
$$25$$ 112.215 0.897721
$$26$$ 0 0
$$27$$ 27.0000i 0.192450i
$$28$$ 0 0
$$29$$ 279.925i 1.79244i −0.443607 0.896221i $$-0.646301\pi$$
0.443607 0.896221i $$-0.353699\pi$$
$$30$$ 0 0
$$31$$ −147.800 −0.856311 −0.428156 0.903705i $$-0.640836\pi$$
−0.428156 + 0.903705i $$0.640836\pi$$
$$32$$ 0 0
$$33$$ 50.6110i 0.266977i
$$34$$ 0 0
$$35$$ −96.9212 + 268.274i −0.468076 + 1.29562i
$$36$$ 0 0
$$37$$ 418.498i 1.85948i −0.368221 0.929738i $$-0.620033\pi$$
0.368221 0.929738i $$-0.379967\pi$$
$$38$$ 0 0
$$39$$ 27.3087i 0.112125i
$$40$$ 0 0
$$41$$ 164.377i 0.626131i −0.949731 0.313066i $$-0.898644\pi$$
0.949731 0.313066i $$-0.101356\pi$$
$$42$$ 0 0
$$43$$ 266.668 0.945731 0.472865 0.881135i $$-0.343220\pi$$
0.472865 + 0.881135i $$0.343220\pi$$
$$44$$ 0 0
$$45$$ −138.616 −0.459193
$$46$$ 0 0
$$47$$ 277.719 0.861903 0.430952 0.902375i $$-0.358178\pi$$
0.430952 + 0.902375i $$0.358178\pi$$
$$48$$ 0 0
$$49$$ −263.800 219.223i −0.769096 0.639133i
$$50$$ 0 0
$$51$$ 221.872 0.609182
$$52$$ 0 0
$$53$$ 276.852i 0.717519i 0.933430 + 0.358760i $$0.116800\pi$$
−0.933430 + 0.358760i $$0.883200\pi$$
$$54$$ 0 0
$$55$$ 259.833 0.637017
$$56$$ 0 0
$$57$$ 453.785 1.05448
$$58$$ 0 0
$$59$$ 212.008i 0.467815i −0.972259 0.233908i $$-0.924849\pi$$
0.972259 0.233908i $$-0.0751513\pi$$
$$60$$ 0 0
$$61$$ 174.541 0.366355 0.183177 0.983080i $$-0.441362\pi$$
0.183177 + 0.983080i $$0.441362\pi$$
$$62$$ 0 0
$$63$$ 56.6357 156.765i 0.113261 0.313501i
$$64$$ 0 0
$$65$$ 140.201 0.267535
$$66$$ 0 0
$$67$$ −317.501 −0.578940 −0.289470 0.957187i $$-0.593479\pi$$
−0.289470 + 0.957187i $$0.593479\pi$$
$$68$$ 0 0
$$69$$ 0.793928 0.00138518
$$70$$ 0 0
$$71$$ 106.093i 0.177338i 0.996061 + 0.0886688i $$0.0282613\pi$$
−0.996061 + 0.0886688i $$0.971739\pi$$
$$72$$ 0 0
$$73$$ 755.118i 1.21068i −0.795966 0.605342i $$-0.793036\pi$$
0.795966 0.605342i $$-0.206964\pi$$
$$74$$ 0 0
$$75$$ 336.645i 0.518299i
$$76$$ 0 0
$$77$$ −106.163 + 293.854i −0.157121 + 0.434906i
$$78$$ 0 0
$$79$$ 194.202i 0.276575i 0.990392 + 0.138288i $$0.0441598\pi$$
−0.990392 + 0.138288i $$0.955840\pi$$
$$80$$ 0 0
$$81$$ 81.0000 0.111111
$$82$$ 0 0
$$83$$ 997.764i 1.31950i 0.751484 + 0.659752i $$0.229339\pi$$
−0.751484 + 0.659752i $$0.770661\pi$$
$$84$$ 0 0
$$85$$ 1139.08i 1.45353i
$$86$$ 0 0
$$87$$ 839.776 1.03487
$$88$$ 0 0
$$89$$ 988.320i 1.17710i 0.808462 + 0.588549i $$0.200300\pi$$
−0.808462 + 0.588549i $$0.799700\pi$$
$$90$$ 0 0
$$91$$ −57.2832 + 158.558i −0.0659880 + 0.182652i
$$92$$ 0 0
$$93$$ 443.400i 0.494391i
$$94$$ 0 0
$$95$$ 2329.70i 2.51602i
$$96$$ 0 0
$$97$$ 1021.78i 1.06954i −0.844996 0.534772i $$-0.820398\pi$$
0.844996 0.534772i $$-0.179602\pi$$
$$98$$ 0 0
$$99$$ −151.833 −0.154139
$$100$$ 0 0
$$101$$ 914.669 0.901118 0.450559 0.892747i $$-0.351225\pi$$
0.450559 + 0.892747i $$0.351225\pi$$
$$102$$ 0 0
$$103$$ −469.098 −0.448753 −0.224377 0.974503i $$-0.572035\pi$$
−0.224377 + 0.974503i $$0.572035\pi$$
$$104$$ 0 0
$$105$$ −804.823 290.763i −0.748025 0.270244i
$$106$$ 0 0
$$107$$ −1553.58 −1.40364 −0.701822 0.712352i $$-0.747630\pi$$
−0.701822 + 0.712352i $$0.747630\pi$$
$$108$$ 0 0
$$109$$ 1424.25i 1.25155i 0.780005 + 0.625773i $$0.215216\pi$$
−0.780005 + 0.625773i $$0.784784\pi$$
$$110$$ 0 0
$$111$$ 1255.49 1.07357
$$112$$ 0 0
$$113$$ 784.755 0.653305 0.326653 0.945144i $$-0.394079\pi$$
0.326653 + 0.945144i $$0.394079\pi$$
$$114$$ 0 0
$$115$$ 4.07597i 0.00330510i
$$116$$ 0 0
$$117$$ −81.9261 −0.0647356
$$118$$ 0 0
$$119$$ 1288.22 + 465.402i 0.992358 + 0.358516i
$$120$$ 0 0
$$121$$ −1046.39 −0.786170
$$122$$ 0 0
$$123$$ 493.131 0.361497
$$124$$ 0 0
$$125$$ −196.910 −0.140897
$$126$$ 0 0
$$127$$ 2509.27i 1.75324i −0.481182 0.876620i $$-0.659793\pi$$
0.481182 0.876620i $$-0.340207\pi$$
$$128$$ 0 0
$$129$$ 800.003i 0.546018i
$$130$$ 0 0
$$131$$ 2050.10i 1.36731i 0.729805 + 0.683655i $$0.239611\pi$$
−0.729805 + 0.683655i $$0.760389\pi$$
$$132$$ 0 0
$$133$$ 2634.73 + 951.868i 1.71775 + 0.620582i
$$134$$ 0 0
$$135$$ 415.848i 0.265115i
$$136$$ 0 0
$$137$$ −2516.47 −1.56932 −0.784658 0.619929i $$-0.787161\pi$$
−0.784658 + 0.619929i $$0.787161\pi$$
$$138$$ 0 0
$$139$$ 270.678i 0.165170i 0.996584 + 0.0825849i $$0.0263176\pi$$
−0.996584 + 0.0825849i $$0.973682\pi$$
$$140$$ 0 0
$$141$$ 833.157i 0.497620i
$$142$$ 0 0
$$143$$ 153.569 0.0898048
$$144$$ 0 0
$$145$$ 4311.35i 2.46923i
$$146$$ 0 0
$$147$$ 657.668 791.400i 0.369004 0.444038i
$$148$$ 0 0
$$149$$ 238.893i 0.131348i 0.997841 + 0.0656742i $$0.0209198\pi$$
−0.997841 + 0.0656742i $$0.979080\pi$$
$$150$$ 0 0
$$151$$ 2859.49i 1.54107i 0.637397 + 0.770535i $$0.280011\pi$$
−0.637397 + 0.770535i $$0.719989\pi$$
$$152$$ 0 0
$$153$$ 665.616i 0.351711i
$$154$$ 0 0
$$155$$ −2276.38 −1.17964
$$156$$ 0 0
$$157$$ −566.367 −0.287904 −0.143952 0.989585i $$-0.545981\pi$$
−0.143952 + 0.989585i $$0.545981\pi$$
$$158$$ 0 0
$$159$$ −830.555 −0.414260
$$160$$ 0 0
$$161$$ 4.60965 + 1.66536i 0.00225647 + 0.000815208i
$$162$$ 0 0
$$163$$ 1330.25 0.639222 0.319611 0.947549i $$-0.396448\pi$$
0.319611 + 0.947549i $$0.396448\pi$$
$$164$$ 0 0
$$165$$ 779.500i 0.367782i
$$166$$ 0 0
$$167$$ 2770.08 1.28356 0.641782 0.766887i $$-0.278195\pi$$
0.641782 + 0.766887i $$0.278195\pi$$
$$168$$ 0 0
$$169$$ −2114.14 −0.962284
$$170$$ 0 0
$$171$$ 1361.36i 0.608804i
$$172$$ 0 0
$$173$$ 1389.16 0.610498 0.305249 0.952273i $$-0.401260\pi$$
0.305249 + 0.952273i $$0.401260\pi$$
$$174$$ 0 0
$$175$$ −706.153 + 1954.61i −0.305029 + 0.844310i
$$176$$ 0 0
$$177$$ 636.024 0.270093
$$178$$ 0 0
$$179$$ 2337.71 0.976136 0.488068 0.872806i $$-0.337702\pi$$
0.488068 + 0.872806i $$0.337702\pi$$
$$180$$ 0 0
$$181$$ 3318.66 1.36284 0.681420 0.731893i $$-0.261363\pi$$
0.681420 + 0.731893i $$0.261363\pi$$
$$182$$ 0 0
$$183$$ 523.622i 0.211515i
$$184$$ 0 0
$$185$$ 6445.62i 2.56157i
$$186$$ 0 0
$$187$$ 1247.69i 0.487913i
$$188$$ 0 0
$$189$$ 470.296 + 169.907i 0.181000 + 0.0653911i
$$190$$ 0 0
$$191$$ 1614.06i 0.611463i −0.952118 0.305731i $$-0.901099\pi$$
0.952118 0.305731i $$-0.0989010\pi$$
$$192$$ 0 0
$$193$$ −1248.70 −0.465719 −0.232859 0.972510i $$-0.574808\pi$$
−0.232859 + 0.972510i $$0.574808\pi$$
$$194$$ 0 0
$$195$$ 420.603i 0.154461i
$$196$$ 0 0
$$197$$ 4151.12i 1.50129i −0.660703 0.750647i $$-0.729742\pi$$
0.660703 0.750647i $$-0.270258\pi$$
$$198$$ 0 0
$$199$$ 2928.99 1.04337 0.521685 0.853138i $$-0.325304\pi$$
0.521685 + 0.853138i $$0.325304\pi$$
$$200$$ 0 0
$$201$$ 952.504i 0.334251i
$$202$$ 0 0
$$203$$ 4875.85 + 1761.53i 1.68580 + 0.609040i
$$204$$ 0 0
$$205$$ 2531.70i 0.862545i
$$206$$ 0 0
$$207$$ 2.38178i 0.000799737i
$$208$$ 0 0
$$209$$ 2551.84i 0.844566i
$$210$$ 0 0
$$211$$ −3360.79 −1.09652 −0.548261 0.836307i $$-0.684710\pi$$
−0.548261 + 0.836307i $$0.684710\pi$$
$$212$$ 0 0
$$213$$ −318.280 −0.102386
$$214$$ 0 0
$$215$$ 4107.16 1.30282
$$216$$ 0 0
$$217$$ 930.083 2574.43i 0.290959 0.805364i
$$218$$ 0 0
$$219$$ 2265.35 0.698988
$$220$$ 0 0
$$221$$ 673.226i 0.204914i
$$222$$ 0 0
$$223$$ 2329.45 0.699515 0.349757 0.936840i $$-0.386264\pi$$
0.349757 + 0.936840i $$0.386264\pi$$
$$224$$ 0 0
$$225$$ −1009.94 −0.299240
$$226$$ 0 0
$$227$$ 832.888i 0.243528i 0.992559 + 0.121764i $$0.0388550\pi$$
−0.992559 + 0.121764i $$0.961145\pi$$
$$228$$ 0 0
$$229$$ 1434.36 0.413908 0.206954 0.978351i $$-0.433645\pi$$
0.206954 + 0.978351i $$0.433645\pi$$
$$230$$ 0 0
$$231$$ −881.562 318.488i −0.251093 0.0907140i
$$232$$ 0 0
$$233$$ 2388.42 0.671547 0.335773 0.941943i $$-0.391002\pi$$
0.335773 + 0.941943i $$0.391002\pi$$
$$234$$ 0 0
$$235$$ 4277.37 1.18734
$$236$$ 0 0
$$237$$ −582.606 −0.159681
$$238$$ 0 0
$$239$$ 4808.99i 1.30154i −0.759276 0.650769i $$-0.774447\pi$$
0.759276 0.650769i $$-0.225553\pi$$
$$240$$ 0 0
$$241$$ 2269.59i 0.606627i 0.952891 + 0.303313i $$0.0980929\pi$$
−0.952891 + 0.303313i $$0.901907\pi$$
$$242$$ 0 0
$$243$$ 243.000i 0.0641500i
$$244$$ 0 0
$$245$$ −4062.99 3376.42i −1.05949 0.880455i
$$246$$ 0 0
$$247$$ 1376.92i 0.354702i
$$248$$ 0 0
$$249$$ −2993.29 −0.761816
$$250$$ 0 0
$$251$$ 2242.07i 0.563818i −0.959441 0.281909i $$-0.909032\pi$$
0.959441 0.281909i $$-0.0909676\pi$$
$$252$$ 0 0
$$253$$ 4.46461i 0.00110944i
$$254$$ 0 0
$$255$$ 3417.23 0.839196
$$256$$ 0 0
$$257$$ 787.861i 0.191227i −0.995419 0.0956136i $$-0.969519\pi$$
0.995419 0.0956136i $$-0.0304813\pi$$
$$258$$ 0 0
$$259$$ 7289.56 + 2633.54i 1.74885 + 0.631817i
$$260$$ 0 0
$$261$$ 2519.33i 0.597481i
$$262$$ 0 0
$$263$$ 6696.97i 1.57016i 0.619392 + 0.785082i $$0.287379\pi$$
−0.619392 + 0.785082i $$0.712621\pi$$
$$264$$ 0 0
$$265$$ 4264.01i 0.988439i
$$266$$ 0 0
$$267$$ −2964.96 −0.679597
$$268$$ 0 0
$$269$$ 4374.92 0.991612 0.495806 0.868433i $$-0.334873\pi$$
0.495806 + 0.868433i $$0.334873\pi$$
$$270$$ 0 0
$$271$$ 8058.24 1.80629 0.903143 0.429340i $$-0.141254\pi$$
0.903143 + 0.429340i $$0.141254\pi$$
$$272$$ 0 0
$$273$$ −475.673 171.850i −0.105454 0.0380982i
$$274$$ 0 0
$$275$$ 1893.11 0.415122
$$276$$ 0 0
$$277$$ 4224.44i 0.916324i 0.888869 + 0.458162i $$0.151492\pi$$
−0.888869 + 0.458162i $$0.848508\pi$$
$$278$$ 0 0
$$279$$ 1330.20 0.285437
$$280$$ 0 0
$$281$$ 3763.77 0.799031 0.399516 0.916726i $$-0.369178\pi$$
0.399516 + 0.916726i $$0.369178\pi$$
$$282$$ 0 0
$$283$$ 1604.16i 0.336952i −0.985706 0.168476i $$-0.946115\pi$$
0.985706 0.168476i $$-0.0538846\pi$$
$$284$$ 0 0
$$285$$ 6989.10 1.45263
$$286$$ 0 0
$$287$$ 2863.18 + 1034.40i 0.588879 + 0.212748i
$$288$$ 0 0
$$289$$ −556.685 −0.113309
$$290$$ 0 0
$$291$$ 3065.33 0.617502
$$292$$ 0 0
$$293$$ −3124.58 −0.623004 −0.311502 0.950245i $$-0.600832\pi$$
−0.311502 + 0.950245i $$0.600832\pi$$
$$294$$ 0 0
$$295$$ 3265.30i 0.644452i
$$296$$ 0 0
$$297$$ 455.499i 0.0889924i
$$298$$ 0 0
$$299$$ 2.40902i 0.000465943i
$$300$$ 0 0
$$301$$ −1678.10 + 4644.92i −0.321342 + 0.889464i
$$302$$ 0 0
$$303$$ 2744.01i 0.520261i
$$304$$ 0 0
$$305$$ 2688.24 0.504683
$$306$$ 0 0
$$307$$ 9789.14i 1.81986i 0.414767 + 0.909928i $$0.363863\pi$$
−0.414767 + 0.909928i $$0.636137\pi$$
$$308$$ 0 0
$$309$$ 1407.29i 0.259088i
$$310$$ 0 0
$$311$$ −3916.61 −0.714117 −0.357059 0.934082i $$-0.616220\pi$$
−0.357059 + 0.934082i $$0.616220\pi$$
$$312$$ 0 0
$$313$$ 5571.72i 1.00617i −0.864236 0.503087i $$-0.832198\pi$$
0.864236 0.503087i $$-0.167802\pi$$
$$314$$ 0 0
$$315$$ 872.290 2414.47i 0.156025 0.431873i
$$316$$ 0 0
$$317$$ 10110.5i 1.79136i −0.444700 0.895680i $$-0.646690\pi$$
0.444700 0.895680i $$-0.353310\pi$$
$$318$$ 0 0
$$319$$ 4722.44i 0.828858i
$$320$$ 0 0
$$321$$ 4660.73i 0.810395i
$$322$$ 0 0
$$323$$ −11186.9 −1.92711
$$324$$ 0 0
$$325$$ 1021.48 0.174344
$$326$$ 0 0
$$327$$ −4272.75 −0.722580
$$328$$ 0 0
$$329$$ −1747.64 + 4837.41i −0.292859 + 0.810624i
$$330$$ 0 0
$$331$$ 396.980 0.0659214 0.0329607 0.999457i $$-0.489506\pi$$
0.0329607 + 0.999457i $$0.489506\pi$$
$$332$$ 0 0
$$333$$ 3766.48i 0.619825i
$$334$$ 0 0
$$335$$ −4890.09 −0.797535
$$336$$ 0 0
$$337$$ 7848.71 1.26868 0.634342 0.773053i $$-0.281271\pi$$
0.634342 + 0.773053i $$0.281271\pi$$
$$338$$ 0 0
$$339$$ 2354.26i 0.377186i
$$340$$ 0 0
$$341$$ −2493.43 −0.395974
$$342$$ 0 0
$$343$$ 5478.56 3215.44i 0.862432 0.506173i
$$344$$ 0 0
$$345$$ 12.2279 0.00190820
$$346$$ 0 0
$$347$$ −12522.0 −1.93722 −0.968609 0.248591i $$-0.920033\pi$$
−0.968609 + 0.248591i $$0.920033\pi$$
$$348$$ 0 0
$$349$$ −5091.86 −0.780978 −0.390489 0.920608i $$-0.627694\pi$$
−0.390489 + 0.920608i $$0.627694\pi$$
$$350$$ 0 0
$$351$$ 245.778i 0.0373751i
$$352$$ 0 0
$$353$$ 9690.22i 1.46107i −0.682874 0.730536i $$-0.739270\pi$$
0.682874 0.730536i $$-0.260730\pi$$
$$354$$ 0 0
$$355$$ 1634.03i 0.244296i
$$356$$ 0 0
$$357$$ −1396.21 + 3864.65i −0.206989 + 0.572938i
$$358$$ 0 0
$$359$$ 9222.74i 1.35587i −0.735122 0.677935i $$-0.762875\pi$$
0.735122 0.677935i $$-0.237125\pi$$
$$360$$ 0 0
$$361$$ −16021.1 −2.33578
$$362$$ 0 0
$$363$$ 3139.18i 0.453895i
$$364$$ 0 0
$$365$$ 11630.2i 1.66781i
$$366$$ 0 0
$$367$$ −2968.62 −0.422236 −0.211118 0.977461i $$-0.567711\pi$$
−0.211118 + 0.977461i $$0.567711\pi$$
$$368$$ 0 0
$$369$$ 1479.39i 0.208710i
$$370$$ 0 0
$$371$$ −4822.31 1742.19i −0.674830 0.243800i
$$372$$ 0 0
$$373$$ 2883.02i 0.400207i 0.979775 + 0.200103i $$0.0641278\pi$$
−0.979775 + 0.200103i $$0.935872\pi$$
$$374$$ 0 0
$$375$$ 590.730i 0.0813471i
$$376$$ 0 0
$$377$$ 2548.13i 0.348105i
$$378$$ 0 0
$$379$$ −2727.26 −0.369630 −0.184815 0.982773i $$-0.559169\pi$$
−0.184815 + 0.982773i $$0.559169\pi$$
$$380$$ 0 0
$$381$$ 7527.81 1.01223
$$382$$ 0 0
$$383$$ −10418.3 −1.38995 −0.694976 0.719033i $$-0.744585\pi$$
−0.694976 + 0.719033i $$0.744585\pi$$
$$384$$ 0 0
$$385$$ −1635.09 + 4525.88i −0.216447 + 0.599117i
$$386$$ 0 0
$$387$$ −2400.01 −0.315244
$$388$$ 0 0
$$389$$ 9095.84i 1.18555i 0.805369 + 0.592773i $$0.201967\pi$$
−0.805369 + 0.592773i $$0.798033\pi$$
$$390$$ 0 0
$$391$$ −19.5723 −0.00253149
$$392$$ 0 0
$$393$$ −6150.29 −0.789417
$$394$$ 0 0
$$395$$ 2991.06i 0.381004i
$$396$$ 0 0
$$397$$ 1349.74 0.170633 0.0853167 0.996354i $$-0.472810\pi$$
0.0853167 + 0.996354i $$0.472810\pi$$
$$398$$ 0 0
$$399$$ −2855.60 + 7904.20i −0.358293 + 0.991742i
$$400$$ 0 0
$$401$$ 1830.81 0.227996 0.113998 0.993481i $$-0.463634\pi$$
0.113998 + 0.993481i $$0.463634\pi$$
$$402$$ 0 0
$$403$$ −1345.41 −0.166301
$$404$$ 0 0
$$405$$ 1247.54 0.153064
$$406$$ 0 0
$$407$$ 7060.20i 0.859855i
$$408$$ 0 0
$$409$$ 14709.9i 1.77838i 0.457542 + 0.889188i $$0.348730\pi$$
−0.457542 + 0.889188i $$0.651270\pi$$
$$410$$ 0 0
$$411$$ 7549.40i 0.906045i
$$412$$ 0 0
$$413$$ 3692.84 + 1334.14i 0.439982 + 0.158955i
$$414$$ 0 0
$$415$$ 15367.3i 1.81772i
$$416$$ 0 0
$$417$$ −812.034 −0.0953608
$$418$$ 0 0
$$419$$ 6721.49i 0.783690i 0.920031 + 0.391845i $$0.128163\pi$$
−0.920031 + 0.391845i $$0.871837\pi$$
$$420$$ 0 0
$$421$$ 4541.66i 0.525765i −0.964828 0.262882i $$-0.915327\pi$$
0.964828 0.262882i $$-0.0846731\pi$$
$$422$$ 0 0
$$423$$ −2499.47 −0.287301
$$424$$ 0 0
$$425$$ 8299.13i 0.947216i
$$426$$ 0 0
$$427$$ −1098.36 + 3040.22i −0.124481 + 0.344558i
$$428$$ 0 0
$$429$$ 460.707i 0.0518488i
$$430$$ 0 0
$$431$$ 10747.7i 1.20116i −0.799564 0.600580i $$-0.794936\pi$$
0.799564 0.600580i $$-0.205064\pi$$
$$432$$ 0 0
$$433$$ 10058.7i 1.11638i 0.829714 + 0.558188i $$0.188503\pi$$
−0.829714 + 0.558188i $$0.811497\pi$$
$$434$$ 0 0
$$435$$ 12934.1 1.42561
$$436$$ 0 0
$$437$$ −40.0303 −0.00438194
$$438$$ 0 0
$$439$$ −2944.00 −0.320067 −0.160034 0.987112i $$-0.551160\pi$$
−0.160034 + 0.987112i $$0.551160\pi$$
$$440$$ 0 0
$$441$$ 2374.20 + 1973.00i 0.256365 + 0.213044i
$$442$$ 0 0
$$443$$ −8667.71 −0.929606 −0.464803 0.885414i $$-0.653875\pi$$
−0.464803 + 0.885414i $$0.653875\pi$$
$$444$$ 0 0
$$445$$ 15221.9i 1.62154i
$$446$$ 0 0
$$447$$ −716.680 −0.0758340
$$448$$ 0 0
$$449$$ 2980.91 0.313314 0.156657 0.987653i $$-0.449928\pi$$
0.156657 + 0.987653i $$0.449928\pi$$
$$450$$ 0 0
$$451$$ 2773.10i 0.289534i
$$452$$ 0 0
$$453$$ −8578.46 −0.889738
$$454$$ 0 0
$$455$$ −882.263 + 2442.07i −0.0909036 + 0.251618i
$$456$$ 0 0
$$457$$ 5915.60 0.605515 0.302757 0.953068i $$-0.402093\pi$$
0.302757 + 0.953068i $$0.402093\pi$$
$$458$$ 0 0
$$459$$ −1996.85 −0.203061
$$460$$ 0 0
$$461$$ 5755.48 0.581474 0.290737 0.956803i $$-0.406099\pi$$
0.290737 + 0.956803i $$0.406099\pi$$
$$462$$ 0 0
$$463$$ 6502.53i 0.652696i 0.945250 + 0.326348i $$0.105818\pi$$
−0.945250 + 0.326348i $$0.894182\pi$$
$$464$$ 0 0
$$465$$ 6829.15i 0.681063i
$$466$$ 0 0
$$467$$ 4507.81i 0.446674i 0.974741 + 0.223337i $$0.0716950\pi$$
−0.974741 + 0.223337i $$0.928305\pi$$
$$468$$ 0 0
$$469$$ 1997.99 5530.36i 0.196713 0.544495i
$$470$$ 0 0
$$471$$ 1699.10i 0.166222i
$$472$$ 0 0
$$473$$ 4498.77 0.437323
$$474$$ 0 0
$$475$$ 16973.9i 1.63961i
$$476$$ 0 0
$$477$$ 2491.67i 0.239173i
$$478$$ 0 0
$$479$$ 2320.76 0.221375 0.110687 0.993855i $$-0.464695\pi$$
0.110687 + 0.993855i $$0.464695\pi$$
$$480$$ 0 0
$$481$$ 3809.54i 0.361123i
$$482$$ 0 0
$$483$$ −4.99607 + 13.8289i −0.000470661 + 0.00130277i
$$484$$ 0 0
$$485$$ 15737.2i 1.47338i
$$486$$ 0 0
$$487$$ 8971.64i 0.834792i −0.908725 0.417396i $$-0.862943\pi$$
0.908725 0.417396i $$-0.137057\pi$$
$$488$$ 0 0
$$489$$ 3990.75i 0.369055i
$$490$$ 0 0
$$491$$ −11942.9 −1.09771 −0.548857 0.835916i $$-0.684937\pi$$
−0.548857 + 0.835916i $$0.684937\pi$$
$$492$$ 0 0
$$493$$ −20702.5 −1.89127
$$494$$ 0 0
$$495$$ −2338.50 −0.212339
$$496$$ 0 0
$$497$$ −1847.98 667.630i −0.166787 0.0602561i
$$498$$ 0 0
$$499$$ 4865.01 0.436448 0.218224 0.975899i $$-0.429974\pi$$
0.218224 + 0.975899i $$0.429974\pi$$
$$500$$ 0 0
$$501$$ 8310.24i 0.741066i
$$502$$ 0 0
$$503$$ 5302.73 0.470054 0.235027 0.971989i $$-0.424482\pi$$
0.235027 + 0.971989i $$0.424482\pi$$
$$504$$ 0 0
$$505$$ 14087.5 1.24136
$$506$$ 0 0
$$507$$ 6342.41i 0.555575i
$$508$$ 0 0
$$509$$ −13255.3 −1.15428 −0.577142 0.816644i $$-0.695832\pi$$
−0.577142 + 0.816644i $$0.695832\pi$$
$$510$$ 0 0
$$511$$ 13152.9 + 4751.85i 1.13865 + 0.411368i
$$512$$ 0 0
$$513$$ −4084.07 −0.351493
$$514$$ 0 0
$$515$$ −7224.95 −0.618193
$$516$$ 0 0
$$517$$ 4685.21 0.398560
$$518$$ 0 0
$$519$$ 4167.49i 0.352471i
$$520$$ 0 0
$$521$$ 17961.3i 1.51036i 0.655517 + 0.755181i $$0.272451\pi$$
−0.655517 + 0.755181i $$0.727549\pi$$
$$522$$ 0 0
$$523$$ 15183.8i 1.26948i −0.772724 0.634742i $$-0.781106\pi$$
0.772724 0.634742i $$-0.218894\pi$$
$$524$$ 0 0
$$525$$ −5863.82 2118.46i −0.487463 0.176109i
$$526$$ 0 0
$$527$$ 10930.9i 0.903523i
$$528$$ 0 0
$$529$$ 12166.9 0.999994
$$530$$ 0 0
$$531$$ 1908.07i 0.155938i
$$532$$ 0 0
$$533$$ 1496.31i 0.121599i
$$534$$ 0 0
$$535$$ −23927.9 −1.93363
$$536$$ 0 0
$$537$$ 7013.12i 0.563572i
$$538$$ 0 0
$$539$$ −4450.40 3698.36i −0.355644 0.295547i
$$540$$ 0 0
$$541$$ 1840.34i 0.146252i −0.997323 0.0731262i $$-0.976702\pi$$
0.997323 0.0731262i $$-0.0232976\pi$$
$$542$$ 0 0
$$543$$ 9955.98i 0.786836i
$$544$$ 0 0
$$545$$ 21936.0i 1.72410i
$$546$$ 0 0
$$547$$ 17887.3 1.39818 0.699091 0.715033i $$-0.253588\pi$$
0.699091 + 0.715033i $$0.253588\pi$$
$$548$$ 0 0
$$549$$ −1570.87 −0.122118
$$550$$ 0 0
$$551$$ −42342.0 −3.27374
$$552$$ 0 0
$$553$$ −3382.69 1222.09i −0.260120 0.0939753i
$$554$$ 0 0
$$555$$ 19336.8 1.47893
$$556$$ 0 0
$$557$$ 12246.4i 0.931590i −0.884893 0.465795i $$-0.845768\pi$$
0.884893 0.465795i $$-0.154232\pi$$
$$558$$ 0 0
$$559$$ 2427.45 0.183667
$$560$$ 0 0
$$561$$ 3743.06 0.281697
$$562$$ 0 0
$$563$$ 18024.0i 1.34924i 0.738165 + 0.674621i $$0.235693\pi$$
−0.738165 + 0.674621i $$0.764307\pi$$
$$564$$ 0 0
$$565$$ 12086.6 0.899979
$$566$$ 0 0
$$567$$ −509.721 + 1410.89i −0.0377536 + 0.104500i
$$568$$ 0 0
$$569$$ 21534.4 1.58659 0.793294 0.608839i $$-0.208364\pi$$
0.793294 + 0.608839i $$0.208364\pi$$
$$570$$ 0 0
$$571$$ 5542.36 0.406201 0.203100 0.979158i $$-0.434898\pi$$
0.203100 + 0.979158i $$0.434898\pi$$
$$572$$ 0 0
$$573$$ 4842.19 0.353028
$$574$$ 0 0
$$575$$ 29.6969i 0.00215382i
$$576$$ 0 0
$$577$$ 10857.0i 0.783334i 0.920107 + 0.391667i $$0.128102\pi$$
−0.920107 + 0.391667i $$0.871898\pi$$
$$578$$ 0 0
$$579$$ 3746.11i 0.268883i
$$580$$ 0 0
$$581$$ −17379.4 6278.78i −1.24100 0.448344i
$$582$$ 0 0
$$583$$ 4670.58i 0.331794i
$$584$$ 0 0
$$585$$ −1261.81 −0.0891784
$$586$$ 0 0
$$587$$ 2426.15i 0.170593i −0.996356 0.0852963i $$-0.972816\pi$$
0.996356 0.0852963i $$-0.0271837\pi$$
$$588$$ 0 0
$$589$$ 22356.5i 1.56398i
$$590$$ 0 0
$$591$$ 12453.4 0.866773
$$592$$ 0 0
$$593$$ 6562.03i 0.454418i 0.973846 + 0.227209i $$0.0729601\pi$$
−0.973846 + 0.227209i $$0.927040\pi$$
$$594$$ 0 0
$$595$$ 19840.8 + 7168.03i 1.36705 + 0.493883i
$$596$$ 0 0
$$597$$ 8786.97i 0.602390i
$$598$$ 0 0
$$599$$ 14414.2i 0.983222i −0.870815 0.491611i $$-0.836408\pi$$
0.870815 0.491611i $$-0.163592\pi$$
$$600$$ 0 0
$$601$$ 206.035i 0.0139839i −0.999976 0.00699196i $$-0.997774\pi$$
0.999976 0.00699196i $$-0.00222563\pi$$
$$602$$ 0 0
$$603$$ 2857.51 0.192980
$$604$$ 0 0
$$605$$ −16116.3 −1.08301
$$606$$ 0 0
$$607$$ −9273.66 −0.620109 −0.310055 0.950719i $$-0.600347\pi$$
−0.310055 + 0.950719i $$0.600347\pi$$
$$608$$ 0 0
$$609$$ −5284.59 + 14627.5i −0.351629 + 0.973297i
$$610$$ 0 0
$$611$$ 2528.05 0.167388
$$612$$ 0 0
$$613$$ 1780.49i 0.117314i −0.998278 0.0586568i $$-0.981318\pi$$
0.998278 0.0586568i $$-0.0186817\pi$$
$$614$$ 0 0
$$615$$ 7595.10 0.497990
$$616$$ 0 0
$$617$$ −10288.9 −0.671338 −0.335669 0.941980i $$-0.608962\pi$$
−0.335669 + 0.941980i $$0.608962\pi$$
$$618$$ 0 0
$$619$$ 28693.8i 1.86317i −0.363525 0.931585i $$-0.618427\pi$$
0.363525 0.931585i $$-0.381573\pi$$
$$620$$ 0 0
$$621$$ −7.14535 −0.000461728
$$622$$ 0 0
$$623$$ −17214.9 6219.35i −1.10706 0.399956i
$$624$$ 0 0
$$625$$ −17059.7 −1.09182
$$626$$ 0 0
$$627$$ 7655.51 0.487610
$$628$$ 0 0
$$629$$ −30951.0 −1.96200
$$630$$ 0 0
$$631$$ 22169.2i 1.39864i 0.714808 + 0.699320i $$0.246514\pi$$
−0.714808 + 0.699320i $$0.753486\pi$$
$$632$$ 0 0
$$633$$ 10082.4i 0.633077i
$$634$$ 0 0
$$635$$ 38647.2i 2.41523i
$$636$$ 0 0
$$637$$ −2401.34 1995.56i −0.149364 0.124124i
$$638$$ 0 0
$$639$$ 954.841i 0.0591125i
$$640$$ 0 0
$$641$$ 15310.8 0.943430 0.471715 0.881751i $$-0.343635\pi$$
0.471715 + 0.881751i $$0.343635\pi$$
$$642$$ 0 0
$$643$$ 9.01281i 0.000552769i 1.00000 0.000276385i $$8.79760e-5\pi$$
−1.00000 0.000276385i $$0.999912\pi$$
$$644$$ 0 0
$$645$$ 12321.5i 0.752182i
$$646$$ 0 0
$$647$$ 20077.1 1.21996 0.609979 0.792417i $$-0.291178\pi$$
0.609979 + 0.792417i $$0.291178\pi$$
$$648$$ 0 0
$$649$$ 3576.65i 0.216326i
$$650$$ 0 0
$$651$$ 7723.30 + 2790.25i 0.464977 + 0.167985i
$$652$$ 0 0
$$653$$ 1796.00i 0.107631i 0.998551 + 0.0538154i $$0.0171383\pi$$
−0.998551 + 0.0538154i $$0.982862\pi$$
$$654$$ 0 0
$$655$$ 31575.1i 1.88358i
$$656$$ 0 0
$$657$$ 6796.06i 0.403561i
$$658$$ 0 0
$$659$$ −12136.5 −0.717405 −0.358703 0.933452i $$-0.616781\pi$$
−0.358703 + 0.933452i $$0.616781\pi$$
$$660$$ 0 0
$$661$$ 18080.9 1.06394 0.531970 0.846763i $$-0.321452\pi$$
0.531970 + 0.846763i $$0.321452\pi$$
$$662$$ 0 0
$$663$$ 2019.68 0.118307
$$664$$ 0 0
$$665$$ 40579.6 + 14660.5i 2.36633 + 0.854900i
$$666$$ 0 0
$$667$$ −74.0802 −0.00430045
$$668$$ 0 0
$$669$$ 6988.36i 0.403865i
$$670$$ 0 0
$$671$$ 2944.56 0.169409
$$672$$ 0 0
$$673$$ −25019.4 −1.43303 −0.716513 0.697573i $$-0.754263\pi$$
−0.716513 + 0.697573i $$0.754263\pi$$
$$674$$ 0 0
$$675$$ 3029.81i 0.172766i
$$676$$ 0 0
$$677$$ 28258.5 1.60423 0.802114 0.597170i $$-0.203708\pi$$
0.802114 + 0.597170i $$0.203708\pi$$
$$678$$ 0 0
$$679$$ 17797.7 + 6429.89i 1.00591 + 0.363412i
$$680$$ 0 0
$$681$$ −2498.67 −0.140601
$$682$$ 0 0
$$683$$ −14966.8 −0.838491 −0.419245 0.907873i $$-0.637705\pi$$
−0.419245 + 0.907873i $$0.637705\pi$$
$$684$$ 0 0
$$685$$ −38758.1 −2.16185
$$686$$ 0 0
$$687$$ 4303.07i 0.238970i
$$688$$ 0 0
$$689$$ 2520.15i 0.139347i
$$690$$ 0 0
$$691$$ 11414.7i 0.628415i 0.949354 + 0.314208i $$0.101739\pi$$
−0.949354 + 0.314208i $$0.898261\pi$$
$$692$$ 0 0
$$693$$ 955.463 2644.69i 0.0523738 0.144969i
$$694$$ 0 0
$$695$$ 4168.92i 0.227534i
$$696$$ 0 0
$$697$$ −12156.9 −0.660653
$$698$$ 0 0
$$699$$ 7165.25i 0.387718i
$$700$$ 0 0
$$701$$ 26445.0i 1.42484i 0.701753 + 0.712420i $$0.252401\pi$$
−0.701753 + 0.712420i $$0.747599\pi$$
$$702$$ 0 0
$$703$$ −63302.7 −3.39617
$$704$$ 0 0
$$705$$ 12832.1i 0.685511i
$$706$$ 0 0
$$707$$ −5755.88 + 15932.1i −0.306184 + 0.847506i
$$708$$ 0 0
$$709$$ 4251.03i 0.225177i 0.993642 + 0.112589i $$0.0359143\pi$$
−0.993642 + 0.112589i $$0.964086\pi$$
$$710$$ 0 0
$$711$$ 1747.82i 0.0921918i
$$712$$ 0 0
$$713$$ 39.1142i 0.00205447i
$$714$$ 0 0
$$715$$ 2365.24 0.123713
$$716$$ 0 0
$$717$$ 14427.0 0.751443
$$718$$ 0 0
$$719$$ −14049.0 −0.728703 −0.364352 0.931261i $$-0.618709\pi$$
−0.364352 + 0.931261i $$0.618709\pi$$
$$720$$ 0 0
$$721$$ 2951.96 8170.92i 0.152478 0.422054i
$$722$$ 0 0
$$723$$ −6808.76 −0.350236
$$724$$ 0 0
$$725$$ 31411.9i 1.60911i
$$726$$ 0 0
$$727$$ −22710.8 −1.15859 −0.579295 0.815118i $$-0.696672\pi$$
−0.579295 + 0.815118i $$0.696672\pi$$
$$728$$ 0 0
$$729$$ −729.000 −0.0370370
$$730$$ 0 0
$$731$$ 19722.0i 0.997873i
$$732$$ 0 0
$$733$$ 34196.7 1.72317 0.861586 0.507611i $$-0.169471\pi$$
0.861586 + 0.507611i $$0.169471\pi$$
$$734$$ 0 0
$$735$$ 10129.3 12189.0i 0.508331 0.611697i
$$736$$ 0 0
$$737$$ −5356.35 −0.267712
$$738$$ 0 0
$$739$$ −33629.7 −1.67400 −0.837001 0.547201i $$-0.815693\pi$$
−0.837001 + 0.547201i $$0.815693\pi$$
$$740$$ 0 0
$$741$$ 4130.76 0.204787
$$742$$ 0 0
$$743$$ 12955.5i 0.639693i −0.947469 0.319846i $$-0.896369\pi$$
0.947469 0.319846i $$-0.103631\pi$$
$$744$$ 0 0
$$745$$ 3679.39i 0.180943i
$$746$$ 0 0
$$747$$ 8979.87i 0.439835i
$$748$$ 0 0
$$749$$ 9776.43 27060.8i 0.476933 1.32013i
$$750$$ 0 0
$$751$$ 13497.2i 0.655820i −0.944709 0.327910i $$-0.893656\pi$$
0.944709 0.327910i $$-0.106344\pi$$
$$752$$ 0 0
$$753$$ 6726.21 0.325520
$$754$$ 0 0
$$755$$ 44041.2i 2.12295i
$$756$$ 0 0
$$757$$ 35571.1i 1.70786i 0.520386 + 0.853931i $$0.325788\pi$$
−0.520386 + 0.853931i $$0.674212\pi$$
$$758$$ 0 0
$$759$$ 13.3938 0.000640534
$$760$$ 0 0
$$761$$ 16927.8i 0.806348i −0.915123 0.403174i $$-0.867907\pi$$
0.915123 0.403174i $$-0.132093\pi$$
$$762$$ 0 0
$$763$$ −24808.1 8962.60i −1.17708 0.425253i
$$764$$ 0 0
$$765$$ 10251.7i 0.484510i
$$766$$ 0 0
$$767$$ 1929.89i 0.0908529i
$$768$$ 0 0
$$769$$ 15208.9i 0.713197i 0.934258 + 0.356599i $$0.116064\pi$$
−0.934258 + 0.356599i $$0.883936\pi$$
$$770$$ 0 0
$$771$$ 2363.58 0.110405
$$772$$ 0 0
$$773$$ −10234.0 −0.476187 −0.238093 0.971242i $$-0.576522\pi$$
−0.238093 + 0.971242i $$0.576522\pi$$
$$774$$ 0 0
$$775$$ −16585.4 −0.768728
$$776$$ 0 0
$$777$$ −7900.63 + 21868.7i −0.364780 + 1.00970i
$$778$$ 0 0
$$779$$ −24864.0 −1.14357
$$780$$ 0 0
$$781$$ 1789.83i 0.0820041i
$$782$$ 0 0
$$783$$ −7557.99 −0.344956
$$784$$ 0 0
$$785$$ −8723.06 −0.396611
$$786$$ 0 0
$$787$$ 26421.8i 1.19674i −0.801220 0.598370i $$-0.795815\pi$$
0.801220 0.598370i $$-0.204185\pi$$
$$788$$ 0 0
$$789$$ −20090.9 −0.906534
$$790$$ 0 0
$$791$$ −4938.34 + 13669.2i −0.221981 + 0.614437i
$$792$$ 0 0
$$793$$ 1588.83 0.0711486
$$794$$ 0 0
$$795$$ −12792.0 −0.570675
$$796$$ 0 0
$$797$$ 4607.96 0.204796 0.102398 0.994744i $$-0.467348\pi$$
0.102398 + 0.994744i $$0.467348\pi$$
$$798$$ 0 0
$$799$$ 20539.3i 0.909424i
$$800$$ 0 0
$$801$$ 8894.88i 0.392366i
$$802$$