# Properties

 Label 1344.4.p.c.223.16 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 223.16 Character $$\chi$$ $$=$$ 1344.223 Dual form 1344.4.p.c.223.15

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+3.00000i q^{3} +1.64166 q^{5} +(15.2747 - 10.4729i) q^{7} -9.00000 q^{9} +O(q^{10})$$ $$q+3.00000i q^{3} +1.64166 q^{5} +(15.2747 - 10.4729i) q^{7} -9.00000 q^{9} -20.3470 q^{11} +13.0999 q^{13} +4.92497i q^{15} +23.9396i q^{17} +87.7589i q^{19} +(31.4188 + 45.8242i) q^{21} -73.6175i q^{23} -122.305 q^{25} -27.0000i q^{27} -58.9537i q^{29} -124.909 q^{31} -61.0410i q^{33} +(25.0759 - 17.1930i) q^{35} +56.5972i q^{37} +39.2998i q^{39} +135.651i q^{41} -259.929 q^{43} -14.7749 q^{45} +217.682 q^{47} +(123.635 - 319.943i) q^{49} -71.8188 q^{51} +529.342i q^{53} -33.4028 q^{55} -263.277 q^{57} +685.329i q^{59} +149.916 q^{61} +(-137.473 + 94.2565i) q^{63} +21.5056 q^{65} +409.156 q^{67} +220.853 q^{69} +885.869i q^{71} -269.426i q^{73} -366.915i q^{75} +(-310.795 + 213.093i) q^{77} +902.587i q^{79} +81.0000 q^{81} +623.963i q^{83} +39.3006i q^{85} +176.861 q^{87} -986.131i q^{89} +(200.098 - 137.195i) q^{91} -374.726i q^{93} +144.070i q^{95} -179.437i q^{97} +183.123 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$32q - 288q^{9} + O(q^{10})$$ $$32q - 288q^{9} - 224q^{13} - 72q^{21} + 1120q^{25} - 752q^{49} - 672q^{57} - 544q^{61} + 1536q^{65} - 144q^{69} - 1632q^{77} + 2592q^{81} + O(q^{100})$$

## 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
$$5$$ 1.64166 0.146834 0.0734171 0.997301i $$-0.476610\pi$$
0.0734171 + 0.997301i $$0.476610\pi$$
$$6$$ 0 0
$$7$$ 15.2747 10.4729i 0.824758 0.565486i
$$8$$ 0 0
$$9$$ −9.00000 −0.333333
$$10$$ 0 0
$$11$$ −20.3470 −0.557714 −0.278857 0.960333i $$-0.589956\pi$$
−0.278857 + 0.960333i $$0.589956\pi$$
$$12$$ 0 0
$$13$$ 13.0999 0.279482 0.139741 0.990188i $$-0.455373\pi$$
0.139741 + 0.990188i $$0.455373\pi$$
$$14$$ 0 0
$$15$$ 4.92497i 0.0847748i
$$16$$ 0 0
$$17$$ 23.9396i 0.341542i 0.985311 + 0.170771i $$0.0546258\pi$$
−0.985311 + 0.170771i $$0.945374\pi$$
$$18$$ 0 0
$$19$$ 87.7589i 1.05965i 0.848108 + 0.529823i $$0.177742\pi$$
−0.848108 + 0.529823i $$0.822258\pi$$
$$20$$ 0 0
$$21$$ 31.4188 + 45.8242i 0.326483 + 0.476174i
$$22$$ 0 0
$$23$$ 73.6175i 0.667405i −0.942678 0.333703i $$-0.891702\pi$$
0.942678 0.333703i $$-0.108298\pi$$
$$24$$ 0 0
$$25$$ −122.305 −0.978440
$$26$$ 0 0
$$27$$ 27.0000i 0.192450i
$$28$$ 0 0
$$29$$ 58.9537i 0.377498i −0.982025 0.188749i $$-0.939557\pi$$
0.982025 0.188749i $$-0.0604432\pi$$
$$30$$ 0 0
$$31$$ −124.909 −0.723686 −0.361843 0.932239i $$-0.617852\pi$$
−0.361843 + 0.932239i $$0.617852\pi$$
$$32$$ 0 0
$$33$$ 61.0410i 0.321996i
$$34$$ 0 0
$$35$$ 25.0759 17.1930i 0.121103 0.0830327i
$$36$$ 0 0
$$37$$ 56.5972i 0.251474i 0.992064 + 0.125737i $$0.0401295\pi$$
−0.992064 + 0.125737i $$0.959871\pi$$
$$38$$ 0 0
$$39$$ 39.2998i 0.161359i
$$40$$ 0 0
$$41$$ 135.651i 0.516711i 0.966050 + 0.258356i $$0.0831806\pi$$
−0.966050 + 0.258356i $$0.916819\pi$$
$$42$$ 0 0
$$43$$ −259.929 −0.921833 −0.460917 0.887443i $$-0.652479\pi$$
−0.460917 + 0.887443i $$0.652479\pi$$
$$44$$ 0 0
$$45$$ −14.7749 −0.0489448
$$46$$ 0 0
$$47$$ 217.682 0.675580 0.337790 0.941222i $$-0.390321\pi$$
0.337790 + 0.941222i $$0.390321\pi$$
$$48$$ 0 0
$$49$$ 123.635 319.943i 0.360452 0.932778i
$$50$$ 0 0
$$51$$ −71.8188 −0.197189
$$52$$ 0 0
$$53$$ 529.342i 1.37190i 0.727649 + 0.685950i $$0.240613\pi$$
−0.727649 + 0.685950i $$0.759387\pi$$
$$54$$ 0 0
$$55$$ −33.4028 −0.0818916
$$56$$ 0 0
$$57$$ −263.277 −0.611787
$$58$$ 0 0
$$59$$ 685.329i 1.51224i 0.654433 + 0.756120i $$0.272908\pi$$
−0.654433 + 0.756120i $$0.727092\pi$$
$$60$$ 0 0
$$61$$ 149.916 0.314668 0.157334 0.987545i $$-0.449710\pi$$
0.157334 + 0.987545i $$0.449710\pi$$
$$62$$ 0 0
$$63$$ −137.473 + 94.2565i −0.274919 + 0.188495i
$$64$$ 0 0
$$65$$ 21.5056 0.0410376
$$66$$ 0 0
$$67$$ 409.156 0.746066 0.373033 0.927818i $$-0.378318\pi$$
0.373033 + 0.927818i $$0.378318\pi$$
$$68$$ 0 0
$$69$$ 220.853 0.385326
$$70$$ 0 0
$$71$$ 885.869i 1.48075i 0.672194 + 0.740375i $$0.265352\pi$$
−0.672194 + 0.740375i $$0.734648\pi$$
$$72$$ 0 0
$$73$$ 269.426i 0.431971i −0.976397 0.215986i $$-0.930704\pi$$
0.976397 0.215986i $$-0.0692964\pi$$
$$74$$ 0 0
$$75$$ 366.915i 0.564902i
$$76$$ 0 0
$$77$$ −310.795 + 213.093i −0.459979 + 0.315379i
$$78$$ 0 0
$$79$$ 902.587i 1.28543i 0.766105 + 0.642715i $$0.222192\pi$$
−0.766105 + 0.642715i $$0.777808\pi$$
$$80$$ 0 0
$$81$$ 81.0000 0.111111
$$82$$ 0 0
$$83$$ 623.963i 0.825166i 0.910920 + 0.412583i $$0.135373\pi$$
−0.910920 + 0.412583i $$0.864627\pi$$
$$84$$ 0 0
$$85$$ 39.3006i 0.0501500i
$$86$$ 0 0
$$87$$ 176.861 0.217948
$$88$$ 0 0
$$89$$ 986.131i 1.17449i −0.809409 0.587245i $$-0.800212\pi$$
0.809409 0.587245i $$-0.199788\pi$$
$$90$$ 0 0
$$91$$ 200.098 137.195i 0.230505 0.158043i
$$92$$ 0 0
$$93$$ 374.726i 0.417821i
$$94$$ 0 0
$$95$$ 144.070i 0.155592i
$$96$$ 0 0
$$97$$ 179.437i 0.187825i −0.995580 0.0939127i $$-0.970063\pi$$
0.995580 0.0939127i $$-0.0299375\pi$$
$$98$$ 0 0
$$99$$ 183.123 0.185905
$$100$$ 0 0
$$101$$ −266.959 −0.263004 −0.131502 0.991316i $$-0.541980\pi$$
−0.131502 + 0.991316i $$0.541980\pi$$
$$102$$ 0 0
$$103$$ −988.258 −0.945398 −0.472699 0.881224i $$-0.656720\pi$$
−0.472699 + 0.881224i $$0.656720\pi$$
$$104$$ 0 0
$$105$$ 51.5789 + 75.2276i 0.0479389 + 0.0699187i
$$106$$ 0 0
$$107$$ 1115.52 1.00787 0.503934 0.863742i $$-0.331886\pi$$
0.503934 + 0.863742i $$0.331886\pi$$
$$108$$ 0 0
$$109$$ 286.196i 0.251492i −0.992062 0.125746i $$-0.959868\pi$$
0.992062 0.125746i $$-0.0401324\pi$$
$$110$$ 0 0
$$111$$ −169.792 −0.145188
$$112$$ 0 0
$$113$$ −728.322 −0.606326 −0.303163 0.952939i $$-0.598043\pi$$
−0.303163 + 0.952939i $$0.598043\pi$$
$$114$$ 0 0
$$115$$ 120.855i 0.0979979i
$$116$$ 0 0
$$117$$ −117.899 −0.0931607
$$118$$ 0 0
$$119$$ 250.718 + 365.671i 0.193137 + 0.281689i
$$120$$ 0 0
$$121$$ −916.999 −0.688955
$$122$$ 0 0
$$123$$ −406.953 −0.298323
$$124$$ 0 0
$$125$$ −405.990 −0.290503
$$126$$ 0 0
$$127$$ 159.234i 0.111258i −0.998452 0.0556288i $$-0.982284\pi$$
0.998452 0.0556288i $$-0.0177163\pi$$
$$128$$ 0 0
$$129$$ 779.787i 0.532221i
$$130$$ 0 0
$$131$$ 748.323i 0.499094i 0.968363 + 0.249547i $$0.0802817\pi$$
−0.968363 + 0.249547i $$0.919718\pi$$
$$132$$ 0 0
$$133$$ 919.093 + 1340.49i 0.599214 + 0.873951i
$$134$$ 0 0
$$135$$ 44.3247i 0.0282583i
$$136$$ 0 0
$$137$$ −1189.48 −0.741780 −0.370890 0.928677i $$-0.620947\pi$$
−0.370890 + 0.928677i $$0.620947\pi$$
$$138$$ 0 0
$$139$$ 546.158i 0.333270i 0.986019 + 0.166635i $$0.0532901\pi$$
−0.986019 + 0.166635i $$0.946710\pi$$
$$140$$ 0 0
$$141$$ 653.047i 0.390046i
$$142$$ 0 0
$$143$$ −266.545 −0.155871
$$144$$ 0 0
$$145$$ 96.7818i 0.0554296i
$$146$$ 0 0
$$147$$ 959.828 + 370.905i 0.538539 + 0.208107i
$$148$$ 0 0
$$149$$ 2169.41i 1.19279i 0.802693 + 0.596393i $$0.203400\pi$$
−0.802693 + 0.596393i $$0.796600\pi$$
$$150$$ 0 0
$$151$$ 1873.28i 1.00957i 0.863244 + 0.504786i $$0.168429\pi$$
−0.863244 + 0.504786i $$0.831571\pi$$
$$152$$ 0 0
$$153$$ 215.457i 0.113847i
$$154$$ 0 0
$$155$$ −205.057 −0.106262
$$156$$ 0 0
$$157$$ −2457.07 −1.24902 −0.624508 0.781018i $$-0.714701\pi$$
−0.624508 + 0.781018i $$0.714701\pi$$
$$158$$ 0 0
$$159$$ −1588.02 −0.792066
$$160$$ 0 0
$$161$$ −770.992 1124.49i −0.377408 0.550448i
$$162$$ 0 0
$$163$$ 1184.76 0.569308 0.284654 0.958630i $$-0.408121\pi$$
0.284654 + 0.958630i $$0.408121\pi$$
$$164$$ 0 0
$$165$$ 100.208i 0.0472801i
$$166$$ 0 0
$$167$$ −2493.54 −1.15543 −0.577713 0.816240i $$-0.696055\pi$$
−0.577713 + 0.816240i $$0.696055\pi$$
$$168$$ 0 0
$$169$$ −2025.39 −0.921890
$$170$$ 0 0
$$171$$ 789.830i 0.353215i
$$172$$ 0 0
$$173$$ 336.961 0.148085 0.0740424 0.997255i $$-0.476410\pi$$
0.0740424 + 0.997255i $$0.476410\pi$$
$$174$$ 0 0
$$175$$ −1868.18 + 1280.89i −0.806976 + 0.553294i
$$176$$ 0 0
$$177$$ −2055.99 −0.873092
$$178$$ 0 0
$$179$$ −403.536 −0.168501 −0.0842506 0.996445i $$-0.526850\pi$$
−0.0842506 + 0.996445i $$0.526850\pi$$
$$180$$ 0 0
$$181$$ −626.262 −0.257180 −0.128590 0.991698i $$-0.541045\pi$$
−0.128590 + 0.991698i $$0.541045\pi$$
$$182$$ 0 0
$$183$$ 449.747i 0.181674i
$$184$$ 0 0
$$185$$ 92.9132i 0.0369249i
$$186$$ 0 0
$$187$$ 487.100i 0.190483i
$$188$$ 0 0
$$189$$ −282.769 412.418i −0.108828 0.158725i
$$190$$ 0 0
$$191$$ 696.358i 0.263805i 0.991263 + 0.131902i $$0.0421085\pi$$
−0.991263 + 0.131902i $$0.957891\pi$$
$$192$$ 0 0
$$193$$ −3330.70 −1.24222 −0.621111 0.783723i $$-0.713318\pi$$
−0.621111 + 0.783723i $$0.713318\pi$$
$$194$$ 0 0
$$195$$ 64.5168i 0.0236930i
$$196$$ 0 0
$$197$$ 841.118i 0.304199i 0.988365 + 0.152099i $$0.0486034\pi$$
−0.988365 + 0.152099i $$0.951397\pi$$
$$198$$ 0 0
$$199$$ 719.574 0.256328 0.128164 0.991753i $$-0.459092\pi$$
0.128164 + 0.991753i $$0.459092\pi$$
$$200$$ 0 0
$$201$$ 1227.47i 0.430741i
$$202$$ 0 0
$$203$$ −617.419 900.503i −0.213470 0.311344i
$$204$$ 0 0
$$205$$ 222.693i 0.0758709i
$$206$$ 0 0
$$207$$ 662.558i 0.222468i
$$208$$ 0 0
$$209$$ 1785.63i 0.590979i
$$210$$ 0 0
$$211$$ 4957.51 1.61748 0.808742 0.588163i $$-0.200149\pi$$
0.808742 + 0.588163i $$0.200149\pi$$
$$212$$ 0 0
$$213$$ −2657.61 −0.854912
$$214$$ 0 0
$$215$$ −426.715 −0.135357
$$216$$ 0 0
$$217$$ −1907.95 + 1308.16i −0.596866 + 0.409234i
$$218$$ 0 0
$$219$$ 808.277 0.249399
$$220$$ 0 0
$$221$$ 313.607i 0.0954548i
$$222$$ 0 0
$$223$$ −3947.42 −1.18538 −0.592688 0.805432i $$-0.701933\pi$$
−0.592688 + 0.805432i $$0.701933\pi$$
$$224$$ 0 0
$$225$$ 1100.74 0.326147
$$226$$ 0 0
$$227$$ 2044.37i 0.597751i 0.954292 + 0.298876i $$0.0966115\pi$$
−0.954292 + 0.298876i $$0.903388\pi$$
$$228$$ 0 0
$$229$$ −4391.90 −1.26736 −0.633679 0.773596i $$-0.718456\pi$$
−0.633679 + 0.773596i $$0.718456\pi$$
$$230$$ 0 0
$$231$$ −639.279 932.386i −0.182084 0.265569i
$$232$$ 0 0
$$233$$ −1970.16 −0.553946 −0.276973 0.960878i $$-0.589331\pi$$
−0.276973 + 0.960878i $$0.589331\pi$$
$$234$$ 0 0
$$235$$ 357.360 0.0991983
$$236$$ 0 0
$$237$$ −2707.76 −0.742144
$$238$$ 0 0
$$239$$ 2964.89i 0.802437i 0.915982 + 0.401219i $$0.131413\pi$$
−0.915982 + 0.401219i $$0.868587\pi$$
$$240$$ 0 0
$$241$$ 3658.31i 0.977810i −0.872337 0.488905i $$-0.837396\pi$$
0.872337 0.488905i $$-0.162604\pi$$
$$242$$ 0 0
$$243$$ 243.000i 0.0641500i
$$244$$ 0 0
$$245$$ 202.966 525.236i 0.0529267 0.136964i
$$246$$ 0 0
$$247$$ 1149.64i 0.296152i
$$248$$ 0 0
$$249$$ −1871.89 −0.476410
$$250$$ 0 0
$$251$$ 2719.35i 0.683840i 0.939729 + 0.341920i $$0.111077\pi$$
−0.939729 + 0.341920i $$0.888923\pi$$
$$252$$ 0 0
$$253$$ 1497.90i 0.372221i
$$254$$ 0 0
$$255$$ −117.902 −0.0289541
$$256$$ 0 0
$$257$$ 6798.11i 1.65002i −0.565120 0.825009i $$-0.691170\pi$$
0.565120 0.825009i $$-0.308830\pi$$
$$258$$ 0 0
$$259$$ 592.739 + 864.507i 0.142205 + 0.207405i
$$260$$ 0 0
$$261$$ 530.584i 0.125833i
$$262$$ 0 0
$$263$$ 7965.94i 1.86768i 0.357686 + 0.933842i $$0.383566\pi$$
−0.357686 + 0.933842i $$0.616434\pi$$
$$264$$ 0 0
$$265$$ 868.997i 0.201442i
$$266$$ 0 0
$$267$$ 2958.39 0.678092
$$268$$ 0 0
$$269$$ 5718.64 1.29618 0.648089 0.761565i $$-0.275569\pi$$
0.648089 + 0.761565i $$0.275569\pi$$
$$270$$ 0 0
$$271$$ 1289.85 0.289124 0.144562 0.989496i $$-0.453823\pi$$
0.144562 + 0.989496i $$0.453823\pi$$
$$272$$ 0 0
$$273$$ 411.584 + 600.294i 0.0912462 + 0.133082i
$$274$$ 0 0
$$275$$ 2488.54 0.545690
$$276$$ 0 0
$$277$$ 4121.16i 0.893922i −0.894553 0.446961i $$-0.852506\pi$$
0.894553 0.446961i $$-0.147494\pi$$
$$278$$ 0 0
$$279$$ 1124.18 0.241229
$$280$$ 0 0
$$281$$ −2432.92 −0.516497 −0.258248 0.966079i $$-0.583145\pi$$
−0.258248 + 0.966079i $$0.583145\pi$$
$$282$$ 0 0
$$283$$ 0.386542i 8.11927e-5i −1.00000 4.05963e-5i $$-0.999987\pi$$
1.00000 4.05963e-5i $$-1.29222e-5\pi$$
$$284$$ 0 0
$$285$$ −432.210 −0.0898312
$$286$$ 0 0
$$287$$ 1420.67 + 2072.04i 0.292193 + 0.426162i
$$288$$ 0 0
$$289$$ 4339.89 0.883349
$$290$$ 0 0
$$291$$ 538.311 0.108441
$$292$$ 0 0
$$293$$ 3394.41 0.676805 0.338402 0.941002i $$-0.390114\pi$$
0.338402 + 0.941002i $$0.390114\pi$$
$$294$$ 0 0
$$295$$ 1125.07i 0.222049i
$$296$$ 0 0
$$297$$ 549.369i 0.107332i
$$298$$ 0 0
$$299$$ 964.385i 0.186528i
$$300$$ 0 0
$$301$$ −3970.35 + 2722.22i −0.760289 + 0.521283i
$$302$$ 0 0
$$303$$ 800.877i 0.151845i
$$304$$ 0 0
$$305$$ 246.110 0.0462040
$$306$$ 0 0
$$307$$ 1720.47i 0.319844i −0.987130 0.159922i $$-0.948876\pi$$
0.987130 0.159922i $$-0.0511243\pi$$
$$308$$ 0 0
$$309$$ 2964.77i 0.545826i
$$310$$ 0 0
$$311$$ −4721.33 −0.860843 −0.430422 0.902628i $$-0.641635\pi$$
−0.430422 + 0.902628i $$0.641635\pi$$
$$312$$ 0 0
$$313$$ 483.679i 0.0873455i −0.999046 0.0436728i $$-0.986094\pi$$
0.999046 0.0436728i $$-0.0139059\pi$$
$$314$$ 0 0
$$315$$ −225.683 + 154.737i −0.0403676 + 0.0276776i
$$316$$ 0 0
$$317$$ 6443.81i 1.14170i 0.821053 + 0.570852i $$0.193387\pi$$
−0.821053 + 0.570852i $$0.806613\pi$$
$$318$$ 0 0
$$319$$ 1199.53i 0.210536i
$$320$$ 0 0
$$321$$ 3346.57i 0.581893i
$$322$$ 0 0
$$323$$ −2100.91 −0.361913
$$324$$ 0 0
$$325$$ −1602.19 −0.273456
$$326$$ 0 0
$$327$$ 858.588 0.145199
$$328$$ 0 0
$$329$$ 3325.04 2279.78i 0.557190 0.382031i
$$330$$ 0 0
$$331$$ 2784.85 0.462444 0.231222 0.972901i $$-0.425728\pi$$
0.231222 + 0.972901i $$0.425728\pi$$
$$332$$ 0 0
$$333$$ 509.375i 0.0838245i
$$334$$ 0 0
$$335$$ 671.694 0.109548
$$336$$ 0 0
$$337$$ −4181.48 −0.675904 −0.337952 0.941163i $$-0.609734\pi$$
−0.337952 + 0.941163i $$0.609734\pi$$
$$338$$ 0 0
$$339$$ 2184.97i 0.350062i
$$340$$ 0 0
$$341$$ 2541.52 0.403610
$$342$$ 0 0
$$343$$ −1462.25 6181.86i −0.230187 0.973146i
$$344$$ 0 0
$$345$$ 362.564 0.0565791
$$346$$ 0 0
$$347$$ −9524.25 −1.47345 −0.736727 0.676190i $$-0.763630\pi$$
−0.736727 + 0.676190i $$0.763630\pi$$
$$348$$ 0 0
$$349$$ 1248.33 0.191465 0.0957327 0.995407i $$-0.469481\pi$$
0.0957327 + 0.995407i $$0.469481\pi$$
$$350$$ 0 0
$$351$$ 353.698i 0.0537864i
$$352$$ 0 0
$$353$$ 605.680i 0.0913233i −0.998957 0.0456616i $$-0.985460\pi$$
0.998957 0.0456616i $$-0.0145396\pi$$
$$354$$ 0 0
$$355$$ 1454.29i 0.217425i
$$356$$ 0 0
$$357$$ −1097.01 + 752.154i −0.162633 + 0.111508i
$$358$$ 0 0
$$359$$ 83.1817i 0.0122289i −0.999981 0.00611443i $$-0.998054\pi$$
0.999981 0.00611443i $$-0.00194630\pi$$
$$360$$ 0 0
$$361$$ −842.618 −0.122849
$$362$$ 0 0
$$363$$ 2751.00i 0.397768i
$$364$$ 0 0
$$365$$ 442.305i 0.0634282i
$$366$$ 0 0
$$367$$ −4636.32 −0.659439 −0.329719 0.944079i $$-0.606954\pi$$
−0.329719 + 0.944079i $$0.606954\pi$$
$$368$$ 0 0
$$369$$ 1220.86i 0.172237i
$$370$$ 0 0
$$371$$ 5543.76 + 8085.55i 0.775789 + 1.13148i
$$372$$ 0 0
$$373$$ 2555.59i 0.354754i 0.984143 + 0.177377i $$0.0567612\pi$$
−0.984143 + 0.177377i $$0.943239\pi$$
$$374$$ 0 0
$$375$$ 1217.97i 0.167722i
$$376$$ 0 0
$$377$$ 772.290i 0.105504i
$$378$$ 0 0
$$379$$ −8981.28 −1.21725 −0.608624 0.793459i $$-0.708278\pi$$
−0.608624 + 0.793459i $$0.708278\pi$$
$$380$$ 0 0
$$381$$ 477.701 0.0642346
$$382$$ 0 0
$$383$$ 12164.5 1.62291 0.811456 0.584413i $$-0.198675\pi$$
0.811456 + 0.584413i $$0.198675\pi$$
$$384$$ 0 0
$$385$$ −510.219 + 349.826i −0.0675407 + 0.0463085i
$$386$$ 0 0
$$387$$ 2339.36 0.307278
$$388$$ 0 0
$$389$$ 3569.55i 0.465252i 0.972566 + 0.232626i $$0.0747319\pi$$
−0.972566 + 0.232626i $$0.925268\pi$$
$$390$$ 0 0
$$391$$ 1762.38 0.227947
$$392$$ 0 0
$$393$$ −2244.97 −0.288152
$$394$$ 0 0
$$395$$ 1481.74i 0.188745i
$$396$$ 0 0
$$397$$ −984.957 −0.124518 −0.0622589 0.998060i $$-0.519830\pi$$
−0.0622589 + 0.998060i $$0.519830\pi$$
$$398$$ 0 0
$$399$$ −4021.48 + 2757.28i −0.504576 + 0.345957i
$$400$$ 0 0
$$401$$ 1700.17 0.211727 0.105863 0.994381i $$-0.466239\pi$$
0.105863 + 0.994381i $$0.466239\pi$$
$$402$$ 0 0
$$403$$ −1636.30 −0.202257
$$404$$ 0 0
$$405$$ 132.974 0.0163149
$$406$$ 0 0
$$407$$ 1151.58i 0.140250i
$$408$$ 0 0
$$409$$ 2739.61i 0.331210i 0.986192 + 0.165605i $$0.0529577\pi$$
−0.986192 + 0.165605i $$0.947042\pi$$
$$410$$ 0 0
$$411$$ 3568.43i 0.428267i
$$412$$ 0 0
$$413$$ 7177.41 + 10468.2i 0.855150 + 1.24723i
$$414$$ 0 0
$$415$$ 1024.33i 0.121163i
$$416$$ 0 0
$$417$$ −1638.47 −0.192413
$$418$$ 0 0
$$419$$ 13461.7i 1.56957i 0.619770 + 0.784783i $$0.287226\pi$$
−0.619770 + 0.784783i $$0.712774\pi$$
$$420$$ 0 0
$$421$$ 5618.17i 0.650387i −0.945647 0.325194i $$-0.894571\pi$$
0.945647 0.325194i $$-0.105429\pi$$
$$422$$ 0 0
$$423$$ −1959.14 −0.225193
$$424$$ 0 0
$$425$$ 2927.93i 0.334178i
$$426$$ 0 0
$$427$$ 2289.92 1570.06i 0.259525 0.177940i
$$428$$ 0 0
$$429$$ 799.634i 0.0899923i
$$430$$ 0 0
$$431$$ 7137.27i 0.797657i −0.917026 0.398828i $$-0.869417\pi$$
0.917026 0.398828i $$-0.130583\pi$$
$$432$$ 0 0
$$433$$ 1458.21i 0.161841i 0.996721 + 0.0809203i $$0.0257859\pi$$
−0.996721 + 0.0809203i $$0.974214\pi$$
$$434$$ 0 0
$$435$$ 290.346 0.0320023
$$436$$ 0 0
$$437$$ 6460.59 0.707213
$$438$$ 0 0
$$439$$ 3231.27 0.351299 0.175650 0.984453i $$-0.443797\pi$$
0.175650 + 0.984453i $$0.443797\pi$$
$$440$$ 0 0
$$441$$ −1112.72 + 2879.48i −0.120151 + 0.310926i
$$442$$ 0 0
$$443$$ −17504.9 −1.87739 −0.938694 0.344751i $$-0.887963\pi$$
−0.938694 + 0.344751i $$0.887963\pi$$
$$444$$ 0 0
$$445$$ 1618.89i 0.172455i
$$446$$ 0 0
$$447$$ −6508.23 −0.688655
$$448$$ 0 0
$$449$$ 9069.04 0.953217 0.476608 0.879116i $$-0.341866\pi$$
0.476608 + 0.879116i $$0.341866\pi$$
$$450$$ 0 0
$$451$$ 2760.10i 0.288177i
$$452$$ 0 0
$$453$$ −5619.84 −0.582877
$$454$$ 0 0
$$455$$ 328.492 225.227i 0.0338461 0.0232062i
$$456$$ 0 0
$$457$$ −1722.16 −0.176279 −0.0881394 0.996108i $$-0.528092\pi$$
−0.0881394 + 0.996108i $$0.528092\pi$$
$$458$$ 0 0
$$459$$ 646.370 0.0657297
$$460$$ 0 0
$$461$$ 14064.0 1.42088 0.710442 0.703755i $$-0.248495\pi$$
0.710442 + 0.703755i $$0.248495\pi$$
$$462$$ 0 0
$$463$$ 7092.58i 0.711923i −0.934501 0.355961i $$-0.884153\pi$$
0.934501 0.355961i $$-0.115847\pi$$
$$464$$ 0 0
$$465$$ 615.172i 0.0613504i
$$466$$ 0 0
$$467$$ 8397.55i 0.832103i 0.909341 + 0.416052i $$0.136586\pi$$
−0.909341 + 0.416052i $$0.863414\pi$$
$$468$$ 0 0
$$469$$ 6249.76 4285.07i 0.615324 0.421889i
$$470$$ 0 0
$$471$$ 7371.21i 0.721120i
$$472$$ 0 0
$$473$$ 5288.78 0.514119
$$474$$ 0 0
$$475$$ 10733.3i 1.03680i
$$476$$ 0 0
$$477$$ 4764.07i 0.457300i
$$478$$ 0 0
$$479$$ 20229.8 1.92970 0.964849 0.262807i $$-0.0846482\pi$$
0.964849 + 0.262807i $$0.0846482\pi$$
$$480$$ 0 0
$$481$$ 741.419i 0.0702824i
$$482$$ 0 0
$$483$$ 3373.46 2312.98i 0.317801 0.217897i
$$484$$ 0 0
$$485$$ 294.574i 0.0275792i
$$486$$ 0 0
$$487$$ 1879.06i 0.174843i −0.996171 0.0874213i $$-0.972137\pi$$
0.996171 0.0874213i $$-0.0278626\pi$$
$$488$$ 0 0
$$489$$ 3554.27i 0.328690i
$$490$$ 0 0
$$491$$ −9249.10 −0.850114 −0.425057 0.905167i $$-0.639746\pi$$
−0.425057 + 0.905167i $$0.639746\pi$$
$$492$$ 0 0
$$493$$ 1411.33 0.128931
$$494$$ 0 0
$$495$$ 300.625 0.0272972
$$496$$ 0 0
$$497$$ 9277.65 + 13531.4i 0.837343 + 1.22126i
$$498$$ 0 0
$$499$$ 18142.9 1.62763 0.813813 0.581126i $$-0.197388\pi$$
0.813813 + 0.581126i $$0.197388\pi$$
$$500$$ 0 0
$$501$$ 7480.63i 0.667086i
$$502$$ 0 0
$$503$$ 7981.16 0.707480 0.353740 0.935344i $$-0.384910\pi$$
0.353740 + 0.935344i $$0.384910\pi$$
$$504$$ 0 0
$$505$$ −438.255 −0.0386180
$$506$$ 0 0
$$507$$ 6076.18i 0.532253i
$$508$$ 0 0
$$509$$ −9093.08 −0.791834 −0.395917 0.918286i $$-0.629573\pi$$
−0.395917 + 0.918286i $$0.629573\pi$$
$$510$$ 0 0
$$511$$ −2821.68 4115.41i −0.244274 0.356272i
$$512$$ 0 0
$$513$$ 2369.49 0.203929
$$514$$ 0 0
$$515$$ −1622.38 −0.138817
$$516$$ 0 0
$$517$$ −4429.19 −0.376780
$$518$$ 0 0
$$519$$ 1010.88i 0.0854968i
$$520$$ 0 0
$$521$$ 10886.0i 0.915399i −0.889107 0.457699i $$-0.848674\pi$$
0.889107 0.457699i $$-0.151326\pi$$
$$522$$ 0 0
$$523$$ 16709.0i 1.39701i −0.715607 0.698503i $$-0.753850\pi$$
0.715607 0.698503i $$-0.246150\pi$$
$$524$$ 0 0
$$525$$ −3842.68 5604.53i −0.319444 0.465908i
$$526$$ 0 0
$$527$$ 2990.27i 0.247169i
$$528$$ 0 0
$$529$$ 6747.46 0.554570
$$530$$ 0 0
$$531$$ 6167.96i 0.504080i
$$532$$ 0 0
$$533$$ 1777.02i 0.144411i
$$534$$ 0 0
$$535$$ 1831.31 0.147990
$$536$$ 0 0
$$537$$ 1210.61i 0.0972842i
$$538$$ 0 0
$$539$$ −2515.60 + 6509.88i −0.201029 + 0.520223i
$$540$$ 0 0
$$541$$ 9846.26i 0.782484i −0.920288 0.391242i $$-0.872046\pi$$
0.920288 0.391242i $$-0.127954\pi$$
$$542$$ 0 0
$$543$$ 1878.78i 0.148483i
$$544$$ 0 0
$$545$$ 469.836i 0.0369276i
$$546$$ 0 0
$$547$$ 3956.47 0.309262 0.154631 0.987972i $$-0.450581\pi$$
0.154631 + 0.987972i $$0.450581\pi$$
$$548$$ 0 0
$$549$$ −1349.24 −0.104889
$$550$$ 0 0
$$551$$ 5173.71 0.400014
$$552$$ 0 0
$$553$$ 9452.74 + 13786.8i 0.726892 + 1.06017i
$$554$$ 0 0
$$555$$ −278.740 −0.0213186
$$556$$ 0 0
$$557$$ 10754.5i 0.818106i −0.912511 0.409053i $$-0.865859\pi$$
0.912511 0.409053i $$-0.134141\pi$$
$$558$$ 0 0
$$559$$ −3405.05 −0.257636
$$560$$ 0 0
$$561$$ 1461.30 0.109975
$$562$$ 0 0
$$563$$ 9499.10i 0.711082i 0.934661 + 0.355541i $$0.115703\pi$$
−0.934661 + 0.355541i $$0.884297\pi$$
$$564$$ 0 0
$$565$$ −1195.66 −0.0890294
$$566$$ 0 0
$$567$$ 1237.25 848.308i 0.0916398 0.0628317i
$$568$$ 0 0
$$569$$ 21157.1 1.55879 0.779395 0.626533i $$-0.215526\pi$$
0.779395 + 0.626533i $$0.215526\pi$$
$$570$$ 0 0
$$571$$ −21995.3 −1.61204 −0.806021 0.591887i $$-0.798383\pi$$
−0.806021 + 0.591887i $$0.798383\pi$$
$$572$$ 0 0
$$573$$ −2089.07 −0.152308
$$574$$ 0 0
$$575$$ 9003.79i 0.653016i
$$576$$ 0 0
$$577$$ 7582.38i 0.547068i 0.961862 + 0.273534i $$0.0881927\pi$$
−0.961862 + 0.273534i $$0.911807\pi$$
$$578$$ 0 0
$$579$$ 9992.09i 0.717197i
$$580$$ 0 0
$$581$$ 6534.72 + 9530.86i 0.466620 + 0.680563i
$$582$$ 0 0
$$583$$ 10770.5i 0.765128i
$$584$$ 0 0
$$585$$ −193.550 −0.0136792
$$586$$ 0 0
$$587$$ 2177.57i 0.153114i 0.997065 + 0.0765569i $$0.0243927\pi$$
−0.997065 + 0.0765569i $$0.975607\pi$$
$$588$$ 0 0
$$589$$ 10961.9i 0.766851i
$$590$$ 0 0
$$591$$ −2523.35 −0.175629
$$592$$ 0 0
$$593$$ 181.962i 0.0126008i 0.999980 + 0.00630042i $$0.00200550\pi$$
−0.999980 + 0.00630042i $$0.997995\pi$$
$$594$$ 0 0
$$595$$ 411.593 + 600.307i 0.0283591 + 0.0413616i
$$596$$ 0 0
$$597$$ 2158.72i 0.147991i
$$598$$ 0 0
$$599$$ 255.073i 0.0173990i −0.999962 0.00869949i $$-0.997231\pi$$
0.999962 0.00869949i $$-0.00276917\pi$$
$$600$$ 0 0
$$601$$ 21122.3i 1.43361i 0.697275 + 0.716804i $$0.254396\pi$$
−0.697275 + 0.716804i $$0.745604\pi$$
$$602$$ 0 0
$$603$$ −3682.41 −0.248689
$$604$$ 0 0
$$605$$ −1505.40 −0.101162
$$606$$ 0 0
$$607$$ 20997.8 1.40408 0.702038 0.712139i $$-0.252273\pi$$
0.702038 + 0.712139i $$0.252273\pi$$
$$608$$ 0 0
$$609$$ 2701.51 1852.26i 0.179755 0.123247i
$$610$$ 0 0
$$611$$ 2851.63 0.188813
$$612$$ 0 0
$$613$$ 13781.4i 0.908032i −0.890993 0.454016i $$-0.849991\pi$$
0.890993 0.454016i $$-0.150009\pi$$
$$614$$ 0 0
$$615$$ −668.078 −0.0438041
$$616$$ 0 0
$$617$$ 15885.1 1.03648 0.518242 0.855234i $$-0.326586\pi$$
0.518242 + 0.855234i $$0.326586\pi$$
$$618$$ 0 0
$$619$$ 26764.3i 1.73788i −0.494917 0.868940i $$-0.664802\pi$$
0.494917 0.868940i $$-0.335198\pi$$
$$620$$ 0 0
$$621$$ −1987.67 −0.128442
$$622$$ 0 0
$$623$$ −10327.7 15062.9i −0.664157 0.968671i
$$624$$ 0 0
$$625$$ 14621.6 0.935784
$$626$$ 0 0
$$627$$ 5356.89 0.341202
$$628$$ 0 0
$$629$$ −1354.91 −0.0858887
$$630$$ 0 0
$$631$$ 12538.1i 0.791022i −0.918461 0.395511i $$-0.870568\pi$$
0.918461 0.395511i $$-0.129432\pi$$
$$632$$ 0 0
$$633$$ 14872.5i 0.933855i
$$634$$ 0 0
$$635$$ 261.407i 0.0163364i
$$636$$ 0 0
$$637$$ 1619.61 4191.23i 0.100740 0.260695i
$$638$$ 0 0
$$639$$ 7972.82i 0.493584i
$$640$$ 0 0
$$641$$ −10139.1 −0.624761 −0.312380 0.949957i $$-0.601126\pi$$
−0.312380 + 0.949957i $$0.601126\pi$$
$$642$$ 0 0
$$643$$ 14901.0i 0.913902i 0.889492 + 0.456951i $$0.151059\pi$$
−0.889492 + 0.456951i $$0.848941\pi$$
$$644$$ 0 0
$$645$$ 1280.14i 0.0781482i
$$646$$ 0 0
$$647$$ 23608.6 1.43454 0.717271 0.696794i $$-0.245391\pi$$
0.717271 + 0.696794i $$0.245391\pi$$
$$648$$ 0 0
$$649$$ 13944.4i 0.843398i
$$650$$ 0 0
$$651$$ −3924.49 5723.85i −0.236272 0.344601i
$$652$$ 0 0
$$653$$ 1066.91i 0.0639380i 0.999489 + 0.0319690i $$0.0101778\pi$$
−0.999489 + 0.0319690i $$0.989822\pi$$
$$654$$ 0 0
$$655$$ 1228.49i 0.0732841i
$$656$$ 0 0
$$657$$ 2424.83i 0.143990i
$$658$$ 0 0
$$659$$ −1256.55 −0.0742766 −0.0371383 0.999310i $$-0.511824\pi$$
−0.0371383 + 0.999310i $$0.511824\pi$$
$$660$$ 0 0
$$661$$ −11557.5 −0.680080 −0.340040 0.940411i $$-0.610441\pi$$
−0.340040 + 0.940411i $$0.610441\pi$$
$$662$$ 0 0
$$663$$ −940.822 −0.0551109
$$664$$ 0 0
$$665$$ 1508.84 + 2200.63i 0.0879852 + 0.128326i
$$666$$ 0 0
$$667$$ −4340.03 −0.251944
$$668$$ 0 0
$$669$$ 11842.3i 0.684377i
$$670$$ 0 0
$$671$$ −3050.34 −0.175495
$$672$$ 0 0
$$673$$ 4626.18 0.264972 0.132486 0.991185i $$-0.457704\pi$$
0.132486 + 0.991185i $$0.457704\pi$$
$$674$$ 0 0
$$675$$ 3302.23i 0.188301i
$$676$$ 0 0
$$677$$ 33749.5 1.91595 0.957975 0.286850i $$-0.0926082\pi$$
0.957975 + 0.286850i $$0.0926082\pi$$
$$678$$ 0 0
$$679$$ −1879.23 2740.85i −0.106213 0.154911i
$$680$$ 0 0
$$681$$ −6133.11 −0.345112
$$682$$ 0 0
$$683$$ −22799.7 −1.27732 −0.638658 0.769491i $$-0.720510\pi$$
−0.638658 + 0.769491i $$0.720510\pi$$
$$684$$ 0 0
$$685$$ −1952.71 −0.108919
$$686$$ 0 0
$$687$$ 13175.7i 0.731709i
$$688$$ 0 0
$$689$$ 6934.34i 0.383421i
$$690$$ 0 0
$$691$$ 22334.8i 1.22960i −0.788682 0.614802i $$-0.789236\pi$$
0.788682 0.614802i $$-0.210764\pi$$
$$692$$ 0 0
$$693$$ 2797.16 1917.84i 0.153326 0.105126i
$$694$$ 0 0
$$695$$ 896.603i 0.0489354i
$$696$$ 0 0
$$697$$ −3247.44 −0.176478
$$698$$ 0 0
$$699$$ 5910.48i 0.319821i
$$700$$ 0 0
$$701$$ 8429.88i 0.454197i 0.973872 + 0.227099i $$0.0729240\pi$$
−0.973872 + 0.227099i $$0.927076\pi$$
$$702$$ 0 0
$$703$$ −4966.91 −0.266473
$$704$$ 0 0
$$705$$ 1072.08i 0.0572722i
$$706$$ 0 0
$$707$$ −4077.73 + 2795.85i −0.216915 + 0.148725i
$$708$$ 0 0
$$709$$ 6186.00i 0.327673i −0.986488 0.163837i $$-0.947613\pi$$
0.986488 0.163837i $$-0.0523870\pi$$
$$710$$ 0 0
$$711$$ 8123.29i 0.428477i
$$712$$ 0 0
$$713$$ 9195.48i 0.482992i
$$714$$ 0 0
$$715$$ −437.575 −0.0228872
$$716$$ 0 0
$$717$$ −8894.66 −0.463287
$$718$$ 0 0
$$719$$ 17866.0 0.926688 0.463344 0.886178i $$-0.346649\pi$$
0.463344 + 0.886178i $$0.346649\pi$$
$$720$$ 0 0
$$721$$ −15095.4 + 10350.0i −0.779725 + 0.534609i
$$722$$ 0 0
$$723$$ 10974.9 0.564539
$$724$$ 0 0
$$725$$ 7210.34i 0.369359i
$$726$$ 0 0
$$727$$ −27651.7 −1.41065 −0.705326 0.708883i $$-0.749199\pi$$
−0.705326 + 0.708883i $$0.749199\pi$$
$$728$$ 0 0
$$729$$ −729.000 −0.0370370
$$730$$ 0 0
$$731$$ 6222.60i 0.314844i
$$732$$ 0 0
$$733$$ −26895.7 −1.35527 −0.677636 0.735397i $$-0.736996\pi$$
−0.677636 + 0.735397i $$0.736996\pi$$
$$734$$ 0 0
$$735$$ 1575.71 + 608.899i 0.0790761 + 0.0305573i
$$736$$ 0 0
$$737$$ −8325.11 −0.416091
$$738$$ 0 0
$$739$$ 22507.8 1.12038 0.560191 0.828364i $$-0.310728\pi$$
0.560191 + 0.828364i $$0.310728\pi$$
$$740$$ 0 0
$$741$$ −3448.91 −0.170983
$$742$$ 0 0
$$743$$ 19387.3i 0.957268i −0.878014 0.478634i $$-0.841132\pi$$
0.878014 0.478634i $$-0.158868\pi$$
$$744$$ 0 0
$$745$$ 3561.43i 0.175142i
$$746$$ 0 0
$$747$$ 5615.66i 0.275055i
$$748$$ 0 0
$$749$$ 17039.3 11682.8i 0.831247 0.569935i
$$750$$ 0 0
$$751$$ 34865.6i 1.69409i −0.531518 0.847047i $$-0.678378\pi$$
0.531518 0.847047i $$-0.321622\pi$$
$$752$$ 0 0
$$753$$ −8158.04 −0.394815
$$754$$ 0 0
$$755$$ 3075.29i 0.148240i
$$756$$ 0 0
$$757$$ 19477.5i 0.935165i 0.883949 + 0.467583i $$0.154875\pi$$
−0.883949 + 0.467583i $$0.845125\pi$$
$$758$$ 0 0
$$759$$ −4493.69 −0.214902
$$760$$ 0 0
$$761$$ 33587.3i 1.59992i −0.600053 0.799960i $$-0.704854\pi$$
0.600053 0.799960i $$-0.295146\pi$$
$$762$$ 0 0
$$763$$ −2997.31 4371.57i −0.142215 0.207420i
$$764$$ 0 0
$$765$$ 353.706i 0.0167167i
$$766$$ 0 0
$$767$$ 8977.76i 0.422644i
$$768$$ 0 0
$$769$$ 30658.2i 1.43766i 0.695185 + 0.718831i $$0.255323\pi$$
−0.695185 + 0.718831i $$0.744677\pi$$
$$770$$ 0 0
$$771$$ 20394.3 0.952638
$$772$$ 0 0
$$773$$ 12029.2 0.559714 0.279857 0.960042i $$-0.409713\pi$$
0.279857 + 0.960042i $$0.409713\pi$$
$$774$$ 0 0
$$775$$ 15277.0 0.708084
$$776$$ 0 0
$$777$$ −2593.52 + 1778.22i −0.119745 + 0.0821019i
$$778$$ 0 0
$$779$$ −11904.6 −0.547530
$$780$$ 0 0
$$781$$ 18024.8i 0.825836i
$$782$$ 0 0
$$783$$ −1591.75 −0.0726495
$$784$$ 0 0
$$785$$ −4033.67 −0.183398
$$786$$ 0 0
$$787$$ 33352.6i 1.51066i 0.655342 + 0.755332i $$0.272524\pi$$
−0.655342 + 0.755332i $$0.727476\pi$$
$$788$$ 0 0
$$789$$ −23897.8 −1.07831
$$790$$ 0 0
$$791$$ −11124.9 + 7627.68i −0.500072 + 0.342868i
$$792$$ 0 0
$$793$$ 1963.89 0.0879440
$$794$$ 0 0
$$795$$ −2606.99 −0.116302
$$796$$ 0 0
$$797$$ 44570.0 1.98087 0.990434 0.137989i $$-0.0440638\pi$$
0.990434 + 0.137989i $$0.0440638\pi$$
$$798$$ 0 0
$$799$$ 5211.23i 0.230739i
$$800$$ 0 0
$$801$$ 8875.18i 0.391497i