# Properties

 Label 154.4.a.c.1.1 Level $154$ Weight $4$ Character 154.1 Self dual yes Analytic conductor $9.086$ Analytic rank $0$ Dimension $1$ CM no Inner twists $1$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$154 = 2 \cdot 7 \cdot 11$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 154.a (trivial)

## Newform invariants

 Self dual: yes Analytic conductor: $$9.08629414088$$ Analytic rank: $$0$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: yes Fricke sign: $$1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

 Embedding label 1.1 Character $$\chi$$ $$=$$ 154.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+2.00000 q^{2} -10.0000 q^{3} +4.00000 q^{4} -14.0000 q^{5} -20.0000 q^{6} +7.00000 q^{7} +8.00000 q^{8} +73.0000 q^{9} +O(q^{10})$$ $$q+2.00000 q^{2} -10.0000 q^{3} +4.00000 q^{4} -14.0000 q^{5} -20.0000 q^{6} +7.00000 q^{7} +8.00000 q^{8} +73.0000 q^{9} -28.0000 q^{10} -11.0000 q^{11} -40.0000 q^{12} -16.0000 q^{13} +14.0000 q^{14} +140.000 q^{15} +16.0000 q^{16} +108.000 q^{17} +146.000 q^{18} +116.000 q^{19} -56.0000 q^{20} -70.0000 q^{21} -22.0000 q^{22} +68.0000 q^{23} -80.0000 q^{24} +71.0000 q^{25} -32.0000 q^{26} -460.000 q^{27} +28.0000 q^{28} +122.000 q^{29} +280.000 q^{30} -262.000 q^{31} +32.0000 q^{32} +110.000 q^{33} +216.000 q^{34} -98.0000 q^{35} +292.000 q^{36} +130.000 q^{37} +232.000 q^{38} +160.000 q^{39} -112.000 q^{40} +204.000 q^{41} -140.000 q^{42} -396.000 q^{43} -44.0000 q^{44} -1022.00 q^{45} +136.000 q^{46} +166.000 q^{47} -160.000 q^{48} +49.0000 q^{49} +142.000 q^{50} -1080.00 q^{51} -64.0000 q^{52} +442.000 q^{53} -920.000 q^{54} +154.000 q^{55} +56.0000 q^{56} -1160.00 q^{57} +244.000 q^{58} +702.000 q^{59} +560.000 q^{60} +196.000 q^{61} -524.000 q^{62} +511.000 q^{63} +64.0000 q^{64} +224.000 q^{65} +220.000 q^{66} -416.000 q^{67} +432.000 q^{68} -680.000 q^{69} -196.000 q^{70} +492.000 q^{71} +584.000 q^{72} +408.000 q^{73} +260.000 q^{74} -710.000 q^{75} +464.000 q^{76} -77.0000 q^{77} +320.000 q^{78} +600.000 q^{79} -224.000 q^{80} +2629.00 q^{81} +408.000 q^{82} -1212.00 q^{83} -280.000 q^{84} -1512.00 q^{85} -792.000 q^{86} -1220.00 q^{87} -88.0000 q^{88} +1146.00 q^{89} -2044.00 q^{90} -112.000 q^{91} +272.000 q^{92} +2620.00 q^{93} +332.000 q^{94} -1624.00 q^{95} -320.000 q^{96} -482.000 q^{97} +98.0000 q^{98} -803.000 q^{99} +O(q^{100})$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 2.00000 0.707107
$$3$$ −10.0000 −1.92450 −0.962250 0.272166i $$-0.912260\pi$$
−0.962250 + 0.272166i $$0.912260\pi$$
$$4$$ 4.00000 0.500000
$$5$$ −14.0000 −1.25220 −0.626099 0.779744i $$-0.715349\pi$$
−0.626099 + 0.779744i $$0.715349\pi$$
$$6$$ −20.0000 −1.36083
$$7$$ 7.00000 0.377964
$$8$$ 8.00000 0.353553
$$9$$ 73.0000 2.70370
$$10$$ −28.0000 −0.885438
$$11$$ −11.0000 −0.301511
$$12$$ −40.0000 −0.962250
$$13$$ −16.0000 −0.341354 −0.170677 0.985327i $$-0.554595\pi$$
−0.170677 + 0.985327i $$0.554595\pi$$
$$14$$ 14.0000 0.267261
$$15$$ 140.000 2.40986
$$16$$ 16.0000 0.250000
$$17$$ 108.000 1.54081 0.770407 0.637552i $$-0.220053\pi$$
0.770407 + 0.637552i $$0.220053\pi$$
$$18$$ 146.000 1.91181
$$19$$ 116.000 1.40064 0.700322 0.713827i $$-0.253040\pi$$
0.700322 + 0.713827i $$0.253040\pi$$
$$20$$ −56.0000 −0.626099
$$21$$ −70.0000 −0.727393
$$22$$ −22.0000 −0.213201
$$23$$ 68.0000 0.616477 0.308239 0.951309i $$-0.400260\pi$$
0.308239 + 0.951309i $$0.400260\pi$$
$$24$$ −80.0000 −0.680414
$$25$$ 71.0000 0.568000
$$26$$ −32.0000 −0.241374
$$27$$ −460.000 −3.27878
$$28$$ 28.0000 0.188982
$$29$$ 122.000 0.781201 0.390601 0.920560i $$-0.372267\pi$$
0.390601 + 0.920560i $$0.372267\pi$$
$$30$$ 280.000 1.70403
$$31$$ −262.000 −1.51795 −0.758977 0.651117i $$-0.774301\pi$$
−0.758977 + 0.651117i $$0.774301\pi$$
$$32$$ 32.0000 0.176777
$$33$$ 110.000 0.580259
$$34$$ 216.000 1.08952
$$35$$ −98.0000 −0.473286
$$36$$ 292.000 1.35185
$$37$$ 130.000 0.577618 0.288809 0.957387i $$-0.406741\pi$$
0.288809 + 0.957387i $$0.406741\pi$$
$$38$$ 232.000 0.990404
$$39$$ 160.000 0.656936
$$40$$ −112.000 −0.442719
$$41$$ 204.000 0.777060 0.388530 0.921436i $$-0.372983\pi$$
0.388530 + 0.921436i $$0.372983\pi$$
$$42$$ −140.000 −0.514344
$$43$$ −396.000 −1.40441 −0.702203 0.711977i $$-0.747800\pi$$
−0.702203 + 0.711977i $$0.747800\pi$$
$$44$$ −44.0000 −0.150756
$$45$$ −1022.00 −3.38557
$$46$$ 136.000 0.435915
$$47$$ 166.000 0.515183 0.257591 0.966254i $$-0.417071\pi$$
0.257591 + 0.966254i $$0.417071\pi$$
$$48$$ −160.000 −0.481125
$$49$$ 49.0000 0.142857
$$50$$ 142.000 0.401637
$$51$$ −1080.00 −2.96530
$$52$$ −64.0000 −0.170677
$$53$$ 442.000 1.14554 0.572768 0.819718i $$-0.305870\pi$$
0.572768 + 0.819718i $$0.305870\pi$$
$$54$$ −920.000 −2.31845
$$55$$ 154.000 0.377552
$$56$$ 56.0000 0.133631
$$57$$ −1160.00 −2.69554
$$58$$ 244.000 0.552393
$$59$$ 702.000 1.54903 0.774514 0.632557i $$-0.217995\pi$$
0.774514 + 0.632557i $$0.217995\pi$$
$$60$$ 560.000 1.20493
$$61$$ 196.000 0.411397 0.205699 0.978615i $$-0.434053\pi$$
0.205699 + 0.978615i $$0.434053\pi$$
$$62$$ −524.000 −1.07336
$$63$$ 511.000 1.02190
$$64$$ 64.0000 0.125000
$$65$$ 224.000 0.427443
$$66$$ 220.000 0.410305
$$67$$ −416.000 −0.758545 −0.379272 0.925285i $$-0.623826\pi$$
−0.379272 + 0.925285i $$0.623826\pi$$
$$68$$ 432.000 0.770407
$$69$$ −680.000 −1.18641
$$70$$ −196.000 −0.334664
$$71$$ 492.000 0.822390 0.411195 0.911548i $$-0.365112\pi$$
0.411195 + 0.911548i $$0.365112\pi$$
$$72$$ 584.000 0.955904
$$73$$ 408.000 0.654148 0.327074 0.944999i $$-0.393937\pi$$
0.327074 + 0.944999i $$0.393937\pi$$
$$74$$ 260.000 0.408438
$$75$$ −710.000 −1.09312
$$76$$ 464.000 0.700322
$$77$$ −77.0000 −0.113961
$$78$$ 320.000 0.464524
$$79$$ 600.000 0.854497 0.427249 0.904134i $$-0.359483\pi$$
0.427249 + 0.904134i $$0.359483\pi$$
$$80$$ −224.000 −0.313050
$$81$$ 2629.00 3.60631
$$82$$ 408.000 0.549464
$$83$$ −1212.00 −1.60282 −0.801411 0.598114i $$-0.795917\pi$$
−0.801411 + 0.598114i $$0.795917\pi$$
$$84$$ −280.000 −0.363696
$$85$$ −1512.00 −1.92941
$$86$$ −792.000 −0.993065
$$87$$ −1220.00 −1.50342
$$88$$ −88.0000 −0.106600
$$89$$ 1146.00 1.36490 0.682448 0.730934i $$-0.260915\pi$$
0.682448 + 0.730934i $$0.260915\pi$$
$$90$$ −2044.00 −2.39396
$$91$$ −112.000 −0.129020
$$92$$ 272.000 0.308239
$$93$$ 2620.00 2.92130
$$94$$ 332.000 0.364289
$$95$$ −1624.00 −1.75388
$$96$$ −320.000 −0.340207
$$97$$ −482.000 −0.504533 −0.252266 0.967658i $$-0.581176\pi$$
−0.252266 + 0.967658i $$0.581176\pi$$
$$98$$ 98.0000 0.101015
$$99$$ −803.000 −0.815197
$$100$$ 284.000 0.284000
$$101$$ 1216.00 1.19799 0.598993 0.800754i $$-0.295568\pi$$
0.598993 + 0.800754i $$0.295568\pi$$
$$102$$ −2160.00 −2.09678
$$103$$ 1406.00 1.34502 0.672511 0.740087i $$-0.265216\pi$$
0.672511 + 0.740087i $$0.265216\pi$$
$$104$$ −128.000 −0.120687
$$105$$ 980.000 0.910840
$$106$$ 884.000 0.810016
$$107$$ −588.000 −0.531253 −0.265627 0.964076i $$-0.585579\pi$$
−0.265627 + 0.964076i $$0.585579\pi$$
$$108$$ −1840.00 −1.63939
$$109$$ 154.000 0.135326 0.0676630 0.997708i $$-0.478446\pi$$
0.0676630 + 0.997708i $$0.478446\pi$$
$$110$$ 308.000 0.266970
$$111$$ −1300.00 −1.11163
$$112$$ 112.000 0.0944911
$$113$$ −1902.00 −1.58341 −0.791704 0.610905i $$-0.790806\pi$$
−0.791704 + 0.610905i $$0.790806\pi$$
$$114$$ −2320.00 −1.90603
$$115$$ −952.000 −0.771952
$$116$$ 488.000 0.390601
$$117$$ −1168.00 −0.922920
$$118$$ 1404.00 1.09533
$$119$$ 756.000 0.582373
$$120$$ 1120.00 0.852013
$$121$$ 121.000 0.0909091
$$122$$ 392.000 0.290902
$$123$$ −2040.00 −1.49545
$$124$$ −1048.00 −0.758977
$$125$$ 756.000 0.540950
$$126$$ 1022.00 0.722595
$$127$$ 64.0000 0.0447172 0.0223586 0.999750i $$-0.492882\pi$$
0.0223586 + 0.999750i $$0.492882\pi$$
$$128$$ 128.000 0.0883883
$$129$$ 3960.00 2.70278
$$130$$ 448.000 0.302248
$$131$$ −1584.00 −1.05645 −0.528224 0.849105i $$-0.677142\pi$$
−0.528224 + 0.849105i $$0.677142\pi$$
$$132$$ 440.000 0.290129
$$133$$ 812.000 0.529393
$$134$$ −832.000 −0.536372
$$135$$ 6440.00 4.10568
$$136$$ 864.000 0.544760
$$137$$ 998.000 0.622371 0.311186 0.950349i $$-0.399274\pi$$
0.311186 + 0.950349i $$0.399274\pi$$
$$138$$ −1360.00 −0.838919
$$139$$ 276.000 0.168417 0.0842087 0.996448i $$-0.473164\pi$$
0.0842087 + 0.996448i $$0.473164\pi$$
$$140$$ −392.000 −0.236643
$$141$$ −1660.00 −0.991470
$$142$$ 984.000 0.581517
$$143$$ 176.000 0.102922
$$144$$ 1168.00 0.675926
$$145$$ −1708.00 −0.978218
$$146$$ 816.000 0.462552
$$147$$ −490.000 −0.274929
$$148$$ 520.000 0.288809
$$149$$ 1318.00 0.724663 0.362331 0.932049i $$-0.381981\pi$$
0.362331 + 0.932049i $$0.381981\pi$$
$$150$$ −1420.00 −0.772950
$$151$$ −984.000 −0.530310 −0.265155 0.964206i $$-0.585423\pi$$
−0.265155 + 0.964206i $$0.585423\pi$$
$$152$$ 928.000 0.495202
$$153$$ 7884.00 4.16591
$$154$$ −154.000 −0.0805823
$$155$$ 3668.00 1.90078
$$156$$ 640.000 0.328468
$$157$$ 1706.00 0.867221 0.433610 0.901101i $$-0.357239\pi$$
0.433610 + 0.901101i $$0.357239\pi$$
$$158$$ 1200.00 0.604221
$$159$$ −4420.00 −2.20458
$$160$$ −448.000 −0.221359
$$161$$ 476.000 0.233007
$$162$$ 5258.00 2.55005
$$163$$ 1168.00 0.561257 0.280628 0.959817i $$-0.409457\pi$$
0.280628 + 0.959817i $$0.409457\pi$$
$$164$$ 816.000 0.388530
$$165$$ −1540.00 −0.726599
$$166$$ −2424.00 −1.13337
$$167$$ 72.0000 0.0333624 0.0166812 0.999861i $$-0.494690\pi$$
0.0166812 + 0.999861i $$0.494690\pi$$
$$168$$ −560.000 −0.257172
$$169$$ −1941.00 −0.883477
$$170$$ −3024.00 −1.36430
$$171$$ 8468.00 3.78692
$$172$$ −1584.00 −0.702203
$$173$$ −4328.00 −1.90203 −0.951017 0.309140i $$-0.899959\pi$$
−0.951017 + 0.309140i $$0.899959\pi$$
$$174$$ −2440.00 −1.06308
$$175$$ 497.000 0.214684
$$176$$ −176.000 −0.0753778
$$177$$ −7020.00 −2.98110
$$178$$ 2292.00 0.965127
$$179$$ −1924.00 −0.803388 −0.401694 0.915774i $$-0.631579\pi$$
−0.401694 + 0.915774i $$0.631579\pi$$
$$180$$ −4088.00 −1.69279
$$181$$ 2230.00 0.915771 0.457886 0.889011i $$-0.348607\pi$$
0.457886 + 0.889011i $$0.348607\pi$$
$$182$$ −224.000 −0.0912307
$$183$$ −1960.00 −0.791734
$$184$$ 544.000 0.217958
$$185$$ −1820.00 −0.723292
$$186$$ 5240.00 2.06567
$$187$$ −1188.00 −0.464573
$$188$$ 664.000 0.257591
$$189$$ −3220.00 −1.23926
$$190$$ −3248.00 −1.24018
$$191$$ 2176.00 0.824345 0.412172 0.911106i $$-0.364770\pi$$
0.412172 + 0.911106i $$0.364770\pi$$
$$192$$ −640.000 −0.240563
$$193$$ −3126.00 −1.16588 −0.582939 0.812516i $$-0.698097\pi$$
−0.582939 + 0.812516i $$0.698097\pi$$
$$194$$ −964.000 −0.356759
$$195$$ −2240.00 −0.822614
$$196$$ 196.000 0.0714286
$$197$$ −1122.00 −0.405783 −0.202891 0.979201i $$-0.565034\pi$$
−0.202891 + 0.979201i $$0.565034\pi$$
$$198$$ −1606.00 −0.576432
$$199$$ −5586.00 −1.98985 −0.994927 0.100597i $$-0.967925\pi$$
−0.994927 + 0.100597i $$0.967925\pi$$
$$200$$ 568.000 0.200818
$$201$$ 4160.00 1.45982
$$202$$ 2432.00 0.847104
$$203$$ 854.000 0.295266
$$204$$ −4320.00 −1.48265
$$205$$ −2856.00 −0.973033
$$206$$ 2812.00 0.951074
$$207$$ 4964.00 1.66677
$$208$$ −256.000 −0.0853385
$$209$$ −1276.00 −0.422310
$$210$$ 1960.00 0.644061
$$211$$ 3372.00 1.10018 0.550090 0.835105i $$-0.314593\pi$$
0.550090 + 0.835105i $$0.314593\pi$$
$$212$$ 1768.00 0.572768
$$213$$ −4920.00 −1.58269
$$214$$ −1176.00 −0.375653
$$215$$ 5544.00 1.75859
$$216$$ −3680.00 −1.15922
$$217$$ −1834.00 −0.573733
$$218$$ 308.000 0.0956899
$$219$$ −4080.00 −1.25891
$$220$$ 616.000 0.188776
$$221$$ −1728.00 −0.525963
$$222$$ −2600.00 −0.786039
$$223$$ 606.000 0.181977 0.0909883 0.995852i $$-0.470997\pi$$
0.0909883 + 0.995852i $$0.470997\pi$$
$$224$$ 224.000 0.0668153
$$225$$ 5183.00 1.53570
$$226$$ −3804.00 −1.11964
$$227$$ 144.000 0.0421040 0.0210520 0.999778i $$-0.493298\pi$$
0.0210520 + 0.999778i $$0.493298\pi$$
$$228$$ −4640.00 −1.34777
$$229$$ −1010.00 −0.291453 −0.145726 0.989325i $$-0.546552\pi$$
−0.145726 + 0.989325i $$0.546552\pi$$
$$230$$ −1904.00 −0.545852
$$231$$ 770.000 0.219317
$$232$$ 976.000 0.276196
$$233$$ 3790.00 1.06563 0.532814 0.846233i $$-0.321135\pi$$
0.532814 + 0.846233i $$0.321135\pi$$
$$234$$ −2336.00 −0.652603
$$235$$ −2324.00 −0.645111
$$236$$ 2808.00 0.774514
$$237$$ −6000.00 −1.64448
$$238$$ 1512.00 0.411800
$$239$$ 2184.00 0.591093 0.295546 0.955328i $$-0.404498\pi$$
0.295546 + 0.955328i $$0.404498\pi$$
$$240$$ 2240.00 0.602464
$$241$$ −4268.00 −1.14077 −0.570386 0.821377i $$-0.693206\pi$$
−0.570386 + 0.821377i $$0.693206\pi$$
$$242$$ 242.000 0.0642824
$$243$$ −13870.0 −3.66157
$$244$$ 784.000 0.205699
$$245$$ −686.000 −0.178885
$$246$$ −4080.00 −1.05744
$$247$$ −1856.00 −0.478115
$$248$$ −2096.00 −0.536678
$$249$$ 12120.0 3.08463
$$250$$ 1512.00 0.382509
$$251$$ 7922.00 1.99216 0.996080 0.0884559i $$-0.0281932\pi$$
0.996080 + 0.0884559i $$0.0281932\pi$$
$$252$$ 2044.00 0.510952
$$253$$ −748.000 −0.185875
$$254$$ 128.000 0.0316198
$$255$$ 15120.0 3.71314
$$256$$ 256.000 0.0625000
$$257$$ 4002.00 0.971354 0.485677 0.874138i $$-0.338573\pi$$
0.485677 + 0.874138i $$0.338573\pi$$
$$258$$ 7920.00 1.91115
$$259$$ 910.000 0.218319
$$260$$ 896.000 0.213721
$$261$$ 8906.00 2.11214
$$262$$ −3168.00 −0.747022
$$263$$ −3960.00 −0.928457 −0.464228 0.885716i $$-0.653668\pi$$
−0.464228 + 0.885716i $$0.653668\pi$$
$$264$$ 880.000 0.205152
$$265$$ −6188.00 −1.43444
$$266$$ 1624.00 0.374338
$$267$$ −11460.0 −2.62674
$$268$$ −1664.00 −0.379272
$$269$$ 1878.00 0.425664 0.212832 0.977089i $$-0.431731\pi$$
0.212832 + 0.977089i $$0.431731\pi$$
$$270$$ 12880.0 2.90315
$$271$$ −4740.00 −1.06249 −0.531244 0.847219i $$-0.678275\pi$$
−0.531244 + 0.847219i $$0.678275\pi$$
$$272$$ 1728.00 0.385204
$$273$$ 1120.00 0.248298
$$274$$ 1996.00 0.440083
$$275$$ −781.000 −0.171258
$$276$$ −2720.00 −0.593206
$$277$$ 710.000 0.154006 0.0770032 0.997031i $$-0.475465\pi$$
0.0770032 + 0.997031i $$0.475465\pi$$
$$278$$ 552.000 0.119089
$$279$$ −19126.0 −4.10410
$$280$$ −784.000 −0.167332
$$281$$ −90.0000 −0.0191066 −0.00955329 0.999954i $$-0.503041\pi$$
−0.00955329 + 0.999954i $$0.503041\pi$$
$$282$$ −3320.00 −0.701075
$$283$$ −3448.00 −0.724248 −0.362124 0.932130i $$-0.617948\pi$$
−0.362124 + 0.932130i $$0.617948\pi$$
$$284$$ 1968.00 0.411195
$$285$$ 16240.0 3.37535
$$286$$ 352.000 0.0727769
$$287$$ 1428.00 0.293701
$$288$$ 2336.00 0.477952
$$289$$ 6751.00 1.37411
$$290$$ −3416.00 −0.691705
$$291$$ 4820.00 0.970974
$$292$$ 1632.00 0.327074
$$293$$ −2804.00 −0.559083 −0.279542 0.960134i $$-0.590183\pi$$
−0.279542 + 0.960134i $$0.590183\pi$$
$$294$$ −980.000 −0.194404
$$295$$ −9828.00 −1.93969
$$296$$ 1040.00 0.204219
$$297$$ 5060.00 0.988589
$$298$$ 2636.00 0.512414
$$299$$ −1088.00 −0.210437
$$300$$ −2840.00 −0.546558
$$301$$ −2772.00 −0.530815
$$302$$ −1968.00 −0.374986
$$303$$ −12160.0 −2.30552
$$304$$ 1856.00 0.350161
$$305$$ −2744.00 −0.515151
$$306$$ 15768.0 2.94574
$$307$$ 1320.00 0.245395 0.122698 0.992444i $$-0.460845\pi$$
0.122698 + 0.992444i $$0.460845\pi$$
$$308$$ −308.000 −0.0569803
$$309$$ −14060.0 −2.58850
$$310$$ 7336.00 1.34405
$$311$$ −1066.00 −0.194364 −0.0971822 0.995267i $$-0.530983\pi$$
−0.0971822 + 0.995267i $$0.530983\pi$$
$$312$$ 1280.00 0.232262
$$313$$ −9254.00 −1.67114 −0.835570 0.549384i $$-0.814863\pi$$
−0.835570 + 0.549384i $$0.814863\pi$$
$$314$$ 3412.00 0.613218
$$315$$ −7154.00 −1.27963
$$316$$ 2400.00 0.427249
$$317$$ −9722.00 −1.72253 −0.861265 0.508156i $$-0.830327\pi$$
−0.861265 + 0.508156i $$0.830327\pi$$
$$318$$ −8840.00 −1.55888
$$319$$ −1342.00 −0.235541
$$320$$ −896.000 −0.156525
$$321$$ 5880.00 1.02240
$$322$$ 952.000 0.164761
$$323$$ 12528.0 2.15813
$$324$$ 10516.0 1.80316
$$325$$ −1136.00 −0.193889
$$326$$ 2336.00 0.396868
$$327$$ −1540.00 −0.260435
$$328$$ 1632.00 0.274732
$$329$$ 1162.00 0.194721
$$330$$ −3080.00 −0.513783
$$331$$ 2620.00 0.435070 0.217535 0.976053i $$-0.430198\pi$$
0.217535 + 0.976053i $$0.430198\pi$$
$$332$$ −4848.00 −0.801411
$$333$$ 9490.00 1.56171
$$334$$ 144.000 0.0235908
$$335$$ 5824.00 0.949848
$$336$$ −1120.00 −0.181848
$$337$$ 2806.00 0.453568 0.226784 0.973945i $$-0.427179\pi$$
0.226784 + 0.973945i $$0.427179\pi$$
$$338$$ −3882.00 −0.624713
$$339$$ 19020.0 3.04727
$$340$$ −6048.00 −0.964703
$$341$$ 2882.00 0.457680
$$342$$ 16936.0 2.67776
$$343$$ 343.000 0.0539949
$$344$$ −3168.00 −0.496532
$$345$$ 9520.00 1.48562
$$346$$ −8656.00 −1.34494
$$347$$ 5564.00 0.860781 0.430391 0.902643i $$-0.358376\pi$$
0.430391 + 0.902643i $$0.358376\pi$$
$$348$$ −4880.00 −0.751711
$$349$$ 10060.0 1.54298 0.771489 0.636242i $$-0.219512\pi$$
0.771489 + 0.636242i $$0.219512\pi$$
$$350$$ 994.000 0.151804
$$351$$ 7360.00 1.11922
$$352$$ −352.000 −0.0533002
$$353$$ −5102.00 −0.769269 −0.384635 0.923069i $$-0.625673\pi$$
−0.384635 + 0.923069i $$0.625673\pi$$
$$354$$ −14040.0 −2.10796
$$355$$ −6888.00 −1.02979
$$356$$ 4584.00 0.682448
$$357$$ −7560.00 −1.12078
$$358$$ −3848.00 −0.568081
$$359$$ 7976.00 1.17258 0.586291 0.810100i $$-0.300587\pi$$
0.586291 + 0.810100i $$0.300587\pi$$
$$360$$ −8176.00 −1.19698
$$361$$ 6597.00 0.961802
$$362$$ 4460.00 0.647548
$$363$$ −1210.00 −0.174955
$$364$$ −448.000 −0.0645098
$$365$$ −5712.00 −0.819123
$$366$$ −3920.00 −0.559841
$$367$$ −1234.00 −0.175516 −0.0877579 0.996142i $$-0.527970\pi$$
−0.0877579 + 0.996142i $$0.527970\pi$$
$$368$$ 1088.00 0.154119
$$369$$ 14892.0 2.10094
$$370$$ −3640.00 −0.511445
$$371$$ 3094.00 0.432972
$$372$$ 10480.0 1.46065
$$373$$ 8030.00 1.11469 0.557343 0.830283i $$-0.311821\pi$$
0.557343 + 0.830283i $$0.311821\pi$$
$$374$$ −2376.00 −0.328503
$$375$$ −7560.00 −1.04106
$$376$$ 1328.00 0.182145
$$377$$ −1952.00 −0.266666
$$378$$ −6440.00 −0.876291
$$379$$ −5184.00 −0.702597 −0.351298 0.936264i $$-0.614260\pi$$
−0.351298 + 0.936264i $$0.614260\pi$$
$$380$$ −6496.00 −0.876941
$$381$$ −640.000 −0.0860583
$$382$$ 4352.00 0.582900
$$383$$ 7570.00 1.00994 0.504972 0.863135i $$-0.331503\pi$$
0.504972 + 0.863135i $$0.331503\pi$$
$$384$$ −1280.00 −0.170103
$$385$$ 1078.00 0.142701
$$386$$ −6252.00 −0.824400
$$387$$ −28908.0 −3.79710
$$388$$ −1928.00 −0.252266
$$389$$ −5370.00 −0.699922 −0.349961 0.936764i $$-0.613805\pi$$
−0.349961 + 0.936764i $$0.613805\pi$$
$$390$$ −4480.00 −0.581676
$$391$$ 7344.00 0.949877
$$392$$ 392.000 0.0505076
$$393$$ 15840.0 2.03314
$$394$$ −2244.00 −0.286932
$$395$$ −8400.00 −1.07000
$$396$$ −3212.00 −0.407599
$$397$$ 11442.0 1.44649 0.723246 0.690590i $$-0.242649\pi$$
0.723246 + 0.690590i $$0.242649\pi$$
$$398$$ −11172.0 −1.40704
$$399$$ −8120.00 −1.01882
$$400$$ 1136.00 0.142000
$$401$$ 2362.00 0.294146 0.147073 0.989126i $$-0.453015\pi$$
0.147073 + 0.989126i $$0.453015\pi$$
$$402$$ 8320.00 1.03225
$$403$$ 4192.00 0.518160
$$404$$ 4864.00 0.598993
$$405$$ −36806.0 −4.51581
$$406$$ 1708.00 0.208785
$$407$$ −1430.00 −0.174158
$$408$$ −8640.00 −1.04839
$$409$$ −16.0000 −0.00193435 −0.000967175 1.00000i $$-0.500308\pi$$
−0.000967175 1.00000i $$0.500308\pi$$
$$410$$ −5712.00 −0.688038
$$411$$ −9980.00 −1.19775
$$412$$ 5624.00 0.672511
$$413$$ 4914.00 0.585477
$$414$$ 9928.00 1.17859
$$415$$ 16968.0 2.00705
$$416$$ −512.000 −0.0603434
$$417$$ −2760.00 −0.324119
$$418$$ −2552.00 −0.298618
$$419$$ 9462.00 1.10322 0.551610 0.834102i $$-0.314014\pi$$
0.551610 + 0.834102i $$0.314014\pi$$
$$420$$ 3920.00 0.455420
$$421$$ −6302.00 −0.729550 −0.364775 0.931096i $$-0.618854\pi$$
−0.364775 + 0.931096i $$0.618854\pi$$
$$422$$ 6744.00 0.777945
$$423$$ 12118.0 1.39290
$$424$$ 3536.00 0.405008
$$425$$ 7668.00 0.875183
$$426$$ −9840.00 −1.11913
$$427$$ 1372.00 0.155494
$$428$$ −2352.00 −0.265627
$$429$$ −1760.00 −0.198074
$$430$$ 11088.0 1.24351
$$431$$ 7816.00 0.873512 0.436756 0.899580i $$-0.356127\pi$$
0.436756 + 0.899580i $$0.356127\pi$$
$$432$$ −7360.00 −0.819695
$$433$$ −9506.00 −1.05503 −0.527516 0.849545i $$-0.676877\pi$$
−0.527516 + 0.849545i $$0.676877\pi$$
$$434$$ −3668.00 −0.405690
$$435$$ 17080.0 1.88258
$$436$$ 616.000 0.0676630
$$437$$ 7888.00 0.863465
$$438$$ −8160.00 −0.890182
$$439$$ −8228.00 −0.894535 −0.447268 0.894400i $$-0.647603\pi$$
−0.447268 + 0.894400i $$0.647603\pi$$
$$440$$ 1232.00 0.133485
$$441$$ 3577.00 0.386243
$$442$$ −3456.00 −0.371912
$$443$$ 7668.00 0.822388 0.411194 0.911548i $$-0.365112\pi$$
0.411194 + 0.911548i $$0.365112\pi$$
$$444$$ −5200.00 −0.555813
$$445$$ −16044.0 −1.70912
$$446$$ 1212.00 0.128677
$$447$$ −13180.0 −1.39461
$$448$$ 448.000 0.0472456
$$449$$ −922.000 −0.0969084 −0.0484542 0.998825i $$-0.515429\pi$$
−0.0484542 + 0.998825i $$0.515429\pi$$
$$450$$ 10366.0 1.08591
$$451$$ −2244.00 −0.234292
$$452$$ −7608.00 −0.791704
$$453$$ 9840.00 1.02058
$$454$$ 288.000 0.0297720
$$455$$ 1568.00 0.161558
$$456$$ −9280.00 −0.953017
$$457$$ 3386.00 0.346587 0.173294 0.984870i $$-0.444559\pi$$
0.173294 + 0.984870i $$0.444559\pi$$
$$458$$ −2020.00 −0.206088
$$459$$ −49680.0 −5.05199
$$460$$ −3808.00 −0.385976
$$461$$ −3300.00 −0.333398 −0.166699 0.986008i $$-0.553311\pi$$
−0.166699 + 0.986008i $$0.553311\pi$$
$$462$$ 1540.00 0.155081
$$463$$ 14236.0 1.42895 0.714474 0.699662i $$-0.246666\pi$$
0.714474 + 0.699662i $$0.246666\pi$$
$$464$$ 1952.00 0.195300
$$465$$ −36680.0 −3.65805
$$466$$ 7580.00 0.753512
$$467$$ 3770.00 0.373565 0.186782 0.982401i $$-0.440194\pi$$
0.186782 + 0.982401i $$0.440194\pi$$
$$468$$ −4672.00 −0.461460
$$469$$ −2912.00 −0.286703
$$470$$ −4648.00 −0.456162
$$471$$ −17060.0 −1.66897
$$472$$ 5616.00 0.547664
$$473$$ 4356.00 0.423444
$$474$$ −12000.0 −1.16282
$$475$$ 8236.00 0.795565
$$476$$ 3024.00 0.291187
$$477$$ 32266.0 3.09719
$$478$$ 4368.00 0.417966
$$479$$ 17796.0 1.69754 0.848768 0.528765i $$-0.177345\pi$$
0.848768 + 0.528765i $$0.177345\pi$$
$$480$$ 4480.00 0.426006
$$481$$ −2080.00 −0.197172
$$482$$ −8536.00 −0.806648
$$483$$ −4760.00 −0.448421
$$484$$ 484.000 0.0454545
$$485$$ 6748.00 0.631775
$$486$$ −27740.0 −2.58912
$$487$$ −3684.00 −0.342788 −0.171394 0.985203i $$-0.554827\pi$$
−0.171394 + 0.985203i $$0.554827\pi$$
$$488$$ 1568.00 0.145451
$$489$$ −11680.0 −1.08014
$$490$$ −1372.00 −0.126491
$$491$$ −17236.0 −1.58422 −0.792108 0.610381i $$-0.791016\pi$$
−0.792108 + 0.610381i $$0.791016\pi$$
$$492$$ −8160.00 −0.747726
$$493$$ 13176.0 1.20369
$$494$$ −3712.00 −0.338078
$$495$$ 11242.0 1.02079
$$496$$ −4192.00 −0.379489
$$497$$ 3444.00 0.310834
$$498$$ 24240.0 2.18117
$$499$$ 13176.0 1.18204 0.591021 0.806656i $$-0.298725\pi$$
0.591021 + 0.806656i $$0.298725\pi$$
$$500$$ 3024.00 0.270475
$$501$$ −720.000 −0.0642060
$$502$$ 15844.0 1.40867
$$503$$ 15428.0 1.36760 0.683798 0.729672i $$-0.260327\pi$$
0.683798 + 0.729672i $$0.260327\pi$$
$$504$$ 4088.00 0.361298
$$505$$ −17024.0 −1.50011
$$506$$ −1496.00 −0.131433
$$507$$ 19410.0 1.70025
$$508$$ 256.000 0.0223586
$$509$$ −7842.00 −0.682889 −0.341445 0.939902i $$-0.610916\pi$$
−0.341445 + 0.939902i $$0.610916\pi$$
$$510$$ 30240.0 2.62559
$$511$$ 2856.00 0.247245
$$512$$ 512.000 0.0441942
$$513$$ −53360.0 −4.59240
$$514$$ 8004.00 0.686851
$$515$$ −19684.0 −1.68423
$$516$$ 15840.0 1.35139
$$517$$ −1826.00 −0.155333
$$518$$ 1820.00 0.154375
$$519$$ 43280.0 3.66046
$$520$$ 1792.00 0.151124
$$521$$ −17250.0 −1.45055 −0.725275 0.688460i $$-0.758287\pi$$
−0.725275 + 0.688460i $$0.758287\pi$$
$$522$$ 17812.0 1.49351
$$523$$ 1032.00 0.0862834 0.0431417 0.999069i $$-0.486263\pi$$
0.0431417 + 0.999069i $$0.486263\pi$$
$$524$$ −6336.00 −0.528224
$$525$$ −4970.00 −0.413159
$$526$$ −7920.00 −0.656518
$$527$$ −28296.0 −2.33889
$$528$$ 1760.00 0.145065
$$529$$ −7543.00 −0.619956
$$530$$ −12376.0 −1.01430
$$531$$ 51246.0 4.18811
$$532$$ 3248.00 0.264697
$$533$$ −3264.00 −0.265252
$$534$$ −22920.0 −1.85739
$$535$$ 8232.00 0.665234
$$536$$ −3328.00 −0.268186
$$537$$ 19240.0 1.54612
$$538$$ 3756.00 0.300990
$$539$$ −539.000 −0.0430730
$$540$$ 25760.0 2.05284
$$541$$ 94.0000 0.00747020 0.00373510 0.999993i $$-0.498811\pi$$
0.00373510 + 0.999993i $$0.498811\pi$$
$$542$$ −9480.00 −0.751293
$$543$$ −22300.0 −1.76240
$$544$$ 3456.00 0.272380
$$545$$ −2156.00 −0.169455
$$546$$ 2240.00 0.175574
$$547$$ −11676.0 −0.912669 −0.456334 0.889808i $$-0.650838\pi$$
−0.456334 + 0.889808i $$0.650838\pi$$
$$548$$ 3992.00 0.311186
$$549$$ 14308.0 1.11230
$$550$$ −1562.00 −0.121098
$$551$$ 14152.0 1.09418
$$552$$ −5440.00 −0.419460
$$553$$ 4200.00 0.322970
$$554$$ 1420.00 0.108899
$$555$$ 18200.0 1.39198
$$556$$ 1104.00 0.0842087
$$557$$ −1858.00 −0.141339 −0.0706696 0.997500i $$-0.522514\pi$$
−0.0706696 + 0.997500i $$0.522514\pi$$
$$558$$ −38252.0 −2.90204
$$559$$ 6336.00 0.479399
$$560$$ −1568.00 −0.118322
$$561$$ 11880.0 0.894071
$$562$$ −180.000 −0.0135104
$$563$$ −23028.0 −1.72383 −0.861913 0.507056i $$-0.830734\pi$$
−0.861913 + 0.507056i $$0.830734\pi$$
$$564$$ −6640.00 −0.495735
$$565$$ 26628.0 1.98274
$$566$$ −6896.00 −0.512121
$$567$$ 18403.0 1.36306
$$568$$ 3936.00 0.290759
$$569$$ −17066.0 −1.25737 −0.628685 0.777660i $$-0.716407\pi$$
−0.628685 + 0.777660i $$0.716407\pi$$
$$570$$ 32480.0 2.38673
$$571$$ −10252.0 −0.751371 −0.375686 0.926747i $$-0.622593\pi$$
−0.375686 + 0.926747i $$0.622593\pi$$
$$572$$ 704.000 0.0514610
$$573$$ −21760.0 −1.58645
$$574$$ 2856.00 0.207678
$$575$$ 4828.00 0.350159
$$576$$ 4672.00 0.337963
$$577$$ 2142.00 0.154545 0.0772726 0.997010i $$-0.475379\pi$$
0.0772726 + 0.997010i $$0.475379\pi$$
$$578$$ 13502.0 0.971642
$$579$$ 31260.0 2.24373
$$580$$ −6832.00 −0.489109
$$581$$ −8484.00 −0.605810
$$582$$ 9640.00 0.686582
$$583$$ −4862.00 −0.345392
$$584$$ 3264.00 0.231276
$$585$$ 16352.0 1.15568
$$586$$ −5608.00 −0.395332
$$587$$ 3474.00 0.244271 0.122136 0.992513i $$-0.461026\pi$$
0.122136 + 0.992513i $$0.461026\pi$$
$$588$$ −1960.00 −0.137464
$$589$$ −30392.0 −2.12611
$$590$$ −19656.0 −1.37157
$$591$$ 11220.0 0.780929
$$592$$ 2080.00 0.144405
$$593$$ −17424.0 −1.20661 −0.603303 0.797512i $$-0.706149\pi$$
−0.603303 + 0.797512i $$0.706149\pi$$
$$594$$ 10120.0 0.699038
$$595$$ −10584.0 −0.729247
$$596$$ 5272.00 0.362331
$$597$$ 55860.0 3.82948
$$598$$ −2176.00 −0.148801
$$599$$ 6916.00 0.471753 0.235877 0.971783i $$-0.424204\pi$$
0.235877 + 0.971783i $$0.424204\pi$$
$$600$$ −5680.00 −0.386475
$$601$$ 16468.0 1.11771 0.558855 0.829265i $$-0.311241\pi$$
0.558855 + 0.829265i $$0.311241\pi$$
$$602$$ −5544.00 −0.375343
$$603$$ −30368.0 −2.05088
$$604$$ −3936.00 −0.265155
$$605$$ −1694.00 −0.113836
$$606$$ −24320.0 −1.63025
$$607$$ −17176.0 −1.14852 −0.574261 0.818673i $$-0.694710\pi$$
−0.574261 + 0.818673i $$0.694710\pi$$
$$608$$ 3712.00 0.247601
$$609$$ −8540.00 −0.568240
$$610$$ −5488.00 −0.364267
$$611$$ −2656.00 −0.175860
$$612$$ 31536.0 2.08295
$$613$$ 11402.0 0.751260 0.375630 0.926770i $$-0.377426\pi$$
0.375630 + 0.926770i $$0.377426\pi$$
$$614$$ 2640.00 0.173521
$$615$$ 28560.0 1.87260
$$616$$ −616.000 −0.0402911
$$617$$ 3654.00 0.238419 0.119209 0.992869i $$-0.461964\pi$$
0.119209 + 0.992869i $$0.461964\pi$$
$$618$$ −28120.0 −1.83034
$$619$$ −11318.0 −0.734909 −0.367455 0.930041i $$-0.619771\pi$$
−0.367455 + 0.930041i $$0.619771\pi$$
$$620$$ 14672.0 0.950390
$$621$$ −31280.0 −2.02129
$$622$$ −2132.00 −0.137436
$$623$$ 8022.00 0.515882
$$624$$ 2560.00 0.164234
$$625$$ −19459.0 −1.24538
$$626$$ −18508.0 −1.18167
$$627$$ 12760.0 0.812736
$$628$$ 6824.00 0.433610
$$629$$ 14040.0 0.890002
$$630$$ −14308.0 −0.904832
$$631$$ −23872.0 −1.50607 −0.753034 0.657981i $$-0.771411\pi$$
−0.753034 + 0.657981i $$0.771411\pi$$
$$632$$ 4800.00 0.302110
$$633$$ −33720.0 −2.11730
$$634$$ −19444.0 −1.21801
$$635$$ −896.000 −0.0559948
$$636$$ −17680.0 −1.10229
$$637$$ −784.000 −0.0487649
$$638$$ −2684.00 −0.166553
$$639$$ 35916.0 2.22350
$$640$$ −1792.00 −0.110680
$$641$$ −27026.0 −1.66531 −0.832654 0.553793i $$-0.813180\pi$$
−0.832654 + 0.553793i $$0.813180\pi$$
$$642$$ 11760.0 0.722944
$$643$$ 6498.00 0.398532 0.199266 0.979945i $$-0.436144\pi$$
0.199266 + 0.979945i $$0.436144\pi$$
$$644$$ 1904.00 0.116503
$$645$$ −55440.0 −3.38442
$$646$$ 25056.0 1.52603
$$647$$ −6422.00 −0.390224 −0.195112 0.980781i $$-0.562507\pi$$
−0.195112 + 0.980781i $$0.562507\pi$$
$$648$$ 21032.0 1.27502
$$649$$ −7722.00 −0.467049
$$650$$ −2272.00 −0.137100
$$651$$ 18340.0 1.10415
$$652$$ 4672.00 0.280628
$$653$$ 23670.0 1.41850 0.709249 0.704958i $$-0.249034\pi$$
0.709249 + 0.704958i $$0.249034\pi$$
$$654$$ −3080.00 −0.184155
$$655$$ 22176.0 1.32288
$$656$$ 3264.00 0.194265
$$657$$ 29784.0 1.76862
$$658$$ 2324.00 0.137688
$$659$$ −9812.00 −0.580002 −0.290001 0.957026i $$-0.593656\pi$$
−0.290001 + 0.957026i $$0.593656\pi$$
$$660$$ −6160.00 −0.363300
$$661$$ −5190.00 −0.305397 −0.152699 0.988273i $$-0.548796\pi$$
−0.152699 + 0.988273i $$0.548796\pi$$
$$662$$ 5240.00 0.307641
$$663$$ 17280.0 1.01222
$$664$$ −9696.00 −0.566683
$$665$$ −11368.0 −0.662905
$$666$$ 18980.0 1.10429
$$667$$ 8296.00 0.481593
$$668$$ 288.000 0.0166812
$$669$$ −6060.00 −0.350214
$$670$$ 11648.0 0.671644
$$671$$ −2156.00 −0.124041
$$672$$ −2240.00 −0.128586
$$673$$ 94.0000 0.00538400 0.00269200 0.999996i $$-0.499143\pi$$
0.00269200 + 0.999996i $$0.499143\pi$$
$$674$$ 5612.00 0.320721
$$675$$ −32660.0 −1.86235
$$676$$ −7764.00 −0.441739
$$677$$ −12432.0 −0.705762 −0.352881 0.935668i $$-0.614798\pi$$
−0.352881 + 0.935668i $$0.614798\pi$$
$$678$$ 38040.0 2.15475
$$679$$ −3374.00 −0.190695
$$680$$ −12096.0 −0.682148
$$681$$ −1440.00 −0.0810293
$$682$$ 5764.00 0.323629
$$683$$ −2308.00 −0.129302 −0.0646509 0.997908i $$-0.520593\pi$$
−0.0646509 + 0.997908i $$0.520593\pi$$
$$684$$ 33872.0 1.89346
$$685$$ −13972.0 −0.779332
$$686$$ 686.000 0.0381802
$$687$$ 10100.0 0.560901
$$688$$ −6336.00 −0.351101
$$689$$ −7072.00 −0.391033
$$690$$ 19040.0 1.05049
$$691$$ 26446.0 1.45594 0.727969 0.685610i $$-0.240464\pi$$
0.727969 + 0.685610i $$0.240464\pi$$
$$692$$ −17312.0 −0.951017
$$693$$ −5621.00 −0.308116
$$694$$ 11128.0 0.608664
$$695$$ −3864.00 −0.210892
$$696$$ −9760.00 −0.531540
$$697$$ 22032.0 1.19730
$$698$$ 20120.0 1.09105
$$699$$ −37900.0 −2.05080
$$700$$ 1988.00 0.107342
$$701$$ 26450.0 1.42511 0.712555 0.701616i $$-0.247538\pi$$
0.712555 + 0.701616i $$0.247538\pi$$
$$702$$ 14720.0 0.791411
$$703$$ 15080.0 0.809037
$$704$$ −704.000 −0.0376889
$$705$$ 23240.0 1.24152
$$706$$ −10204.0 −0.543956
$$707$$ 8512.00 0.452796
$$708$$ −28080.0 −1.49055
$$709$$ 17102.0 0.905894 0.452947 0.891537i $$-0.350373\pi$$
0.452947 + 0.891537i $$0.350373\pi$$
$$710$$ −13776.0 −0.728175
$$711$$ 43800.0 2.31031
$$712$$ 9168.00 0.482564
$$713$$ −17816.0 −0.935785
$$714$$ −15120.0 −0.792509
$$715$$ −2464.00 −0.128879
$$716$$ −7696.00 −0.401694
$$717$$ −21840.0 −1.13756
$$718$$ 15952.0 0.829141
$$719$$ −16854.0 −0.874198 −0.437099 0.899413i $$-0.643994\pi$$
−0.437099 + 0.899413i $$0.643994\pi$$
$$720$$ −16352.0 −0.846393
$$721$$ 9842.00 0.508371
$$722$$ 13194.0 0.680097
$$723$$ 42680.0 2.19542
$$724$$ 8920.00 0.457886
$$725$$ 8662.00 0.443722
$$726$$ −2420.00 −0.123712
$$727$$ −34670.0 −1.76869 −0.884346 0.466832i $$-0.845395\pi$$
−0.884346 + 0.466832i $$0.845395\pi$$
$$728$$ −896.000 −0.0456153
$$729$$ 67717.0 3.44038
$$730$$ −11424.0 −0.579207
$$731$$ −42768.0 −2.16393
$$732$$ −7840.00 −0.395867
$$733$$ 11716.0 0.590369 0.295184 0.955440i $$-0.404619\pi$$
0.295184 + 0.955440i $$0.404619\pi$$
$$734$$ −2468.00 −0.124108
$$735$$ 6860.00 0.344265
$$736$$ 2176.00 0.108979
$$737$$ 4576.00 0.228710
$$738$$ 29784.0 1.48559
$$739$$ 29772.0 1.48198 0.740988 0.671518i $$-0.234357\pi$$
0.740988 + 0.671518i $$0.234357\pi$$
$$740$$ −7280.00 −0.361646
$$741$$ 18560.0 0.920133
$$742$$ 6188.00 0.306157
$$743$$ −24928.0 −1.23085 −0.615424 0.788196i $$-0.711015\pi$$
−0.615424 + 0.788196i $$0.711015\pi$$
$$744$$ 20960.0 1.03284
$$745$$ −18452.0 −0.907421
$$746$$ 16060.0 0.788202
$$747$$ −88476.0 −4.33356
$$748$$ −4752.00 −0.232287
$$749$$ −4116.00 −0.200795
$$750$$ −15120.0 −0.736139
$$751$$ −4652.00 −0.226037 −0.113019 0.993593i $$-0.536052\pi$$
−0.113019 + 0.993593i $$0.536052\pi$$
$$752$$ 2656.00 0.128796
$$753$$ −79220.0 −3.83391
$$754$$ −3904.00 −0.188561
$$755$$ 13776.0 0.664053
$$756$$ −12880.0 −0.619631
$$757$$ −1802.00 −0.0865189 −0.0432594 0.999064i $$-0.513774\pi$$
−0.0432594 + 0.999064i $$0.513774\pi$$
$$758$$ −10368.0 −0.496811
$$759$$ 7480.00 0.357716
$$760$$ −12992.0 −0.620091
$$761$$ −808.000 −0.0384888 −0.0192444 0.999815i $$-0.506126\pi$$
−0.0192444 + 0.999815i $$0.506126\pi$$
$$762$$ −1280.00 −0.0608524
$$763$$ 1078.00 0.0511484
$$764$$ 8704.00 0.412172
$$765$$ −110376. −5.21654
$$766$$ 15140.0 0.714139
$$767$$ −11232.0 −0.528767
$$768$$ −2560.00 −0.120281
$$769$$ 23144.0 1.08530 0.542649 0.839960i $$-0.317421\pi$$
0.542649 + 0.839960i $$0.317421\pi$$
$$770$$ 2156.00 0.100905
$$771$$ −40020.0 −1.86937
$$772$$ −12504.0 −0.582939
$$773$$ −27466.0 −1.27799 −0.638993 0.769212i $$-0.720649\pi$$
−0.638993 + 0.769212i $$0.720649\pi$$
$$774$$ −57816.0 −2.68495
$$775$$ −18602.0 −0.862198
$$776$$ −3856.00 −0.178379
$$777$$ −9100.00 −0.420155
$$778$$ −10740.0 −0.494920
$$779$$ 23664.0 1.08838
$$780$$ −8960.00 −0.411307
$$781$$ −5412.00 −0.247960
$$782$$ 14688.0 0.671665
$$783$$ −56120.0 −2.56139
$$784$$ 784.000 0.0357143
$$785$$ −23884.0 −1.08593
$$786$$ 31680.0 1.43764
$$787$$ 23604.0 1.06911 0.534556 0.845133i $$-0.320479\pi$$
0.534556 + 0.845133i $$0.320479\pi$$
$$788$$ −4488.00 −0.202891
$$789$$ 39600.0 1.78682
$$790$$ −16800.0 −0.756604
$$791$$ −13314.0 −0.598472
$$792$$ −6424.00 −0.288216
$$793$$ −3136.00 −0.140432
$$794$$ 22884.0 1.02282
$$795$$ 61880.0 2.76058
$$796$$ −22344.0 −0.994927
$$797$$ 4122.00 0.183198 0.0915990 0.995796i $$-0.470802\pi$$
0.0915990 + 0.995796i $$0.470802\pi$$
$$798$$ −16240.0 −0.720413
$$799$$ 17928.0 0.793801
$$800$$ 2272.00 0.100409
$$801$$ 83658.0 3.69027
$$802$$ 4724.00 0.207993
$$803$$ −4488.00 −0.197233
$$804$$ 16640.0 0.729910
$$805$$ −6664.00 −0.291770
$$806$$ 8384.00 0.366394
$$807$$ −18780.0 −0.819191
$$808$$ 9728.00 0.423552
$$809$$ −9110.00 −0.395909 −0.197955 0.980211i $$-0.563430\pi$$
−0.197955 + 0.980211i $$0.563430\pi$$
$$810$$ −73612.0 −3.19316
$$811$$ −28352.0 −1.22759 −0.613794 0.789466i $$-0.710357\pi$$
−0.613794 + 0.789466i $$0.710357\pi$$
$$812$$ 3416.00 0.147633
$$813$$ 47400.0 2.04476
$$814$$ −2860.00 −0.123149
$$815$$ −16352.0 −0.702804
$$816$$ −17280.0 −0.741325
$$817$$ −45936.0 −1.96707
$$818$$ −32.0000 −0.00136779
$$819$$ −8176.00 −0.348831
$$820$$ −11424.0 −0.486516
$$821$$ −14002.0 −0.595217 −0.297609 0.954688i $$-0.596189\pi$$
−0.297609 + 0.954688i $$0.596189\pi$$
$$822$$ −19960.0 −0.846940
$$823$$ −14848.0 −0.628881 −0.314440 0.949277i $$-0.601817\pi$$
−0.314440 + 0.949277i $$0.601817\pi$$
$$824$$ 11248.0 0.475537
$$825$$ 7810.00 0.329587
$$826$$ 9828.00 0.413995
$$827$$ 10500.0 0.441500 0.220750 0.975330i $$-0.429149\pi$$
0.220750 + 0.975330i $$0.429149\pi$$
$$828$$ 19856.0 0.833386
$$829$$ 23890.0 1.00089 0.500443 0.865770i $$-0.333171\pi$$
0.500443 + 0.865770i $$0.333171\pi$$
$$830$$ 33936.0 1.41920
$$831$$ −7100.00 −0.296385
$$832$$ −1024.00 −0.0426692
$$833$$ 5292.00 0.220116
$$834$$ −5520.00 −0.229187
$$835$$ −1008.00 −0.0417764
$$836$$ −5104.00 −0.211155
$$837$$ 120520. 4.97704
$$838$$ 18924.0 0.780094
$$839$$ −670.000 −0.0275697 −0.0137848 0.999905i $$-0.504388\pi$$
−0.0137848 + 0.999905i $$0.504388\pi$$
$$840$$ 7840.00 0.322031
$$841$$ −9505.00 −0.389725
$$842$$ −12604.0 −0.515870
$$843$$ 900.000 0.0367706
$$844$$ 13488.0 0.550090
$$845$$ 27174.0 1.10629
$$846$$ 24236.0 0.984930
$$847$$ 847.000 0.0343604
$$848$$ 7072.00 0.286384
$$849$$ 34480.0 1.39382
$$850$$ 15336.0 0.618848
$$851$$ 8840.00 0.356088
$$852$$ −19680.0 −0.791345
$$853$$ −4776.00 −0.191708 −0.0958541 0.995395i $$-0.530558\pi$$
−0.0958541 + 0.995395i $$0.530558\pi$$
$$854$$ 2744.00 0.109951
$$855$$ −118552. −4.74198
$$856$$ −4704.00 −0.187826
$$857$$ −13024.0 −0.519126 −0.259563 0.965726i $$-0.583579\pi$$
−0.259563 + 0.965726i $$0.583579\pi$$
$$858$$ −3520.00 −0.140059
$$859$$ −32998.0 −1.31068 −0.655342 0.755332i $$-0.727475\pi$$
−0.655342 + 0.755332i $$0.727475\pi$$
$$860$$ 22176.0 0.879297
$$861$$ −14280.0 −0.565228
$$862$$ 15632.0 0.617666
$$863$$ 22272.0 0.878503 0.439251 0.898364i $$-0.355244\pi$$
0.439251 + 0.898364i $$0.355244\pi$$
$$864$$ −14720.0 −0.579612
$$865$$ 60592.0 2.38172
$$866$$ −19012.0 −0.746021
$$867$$ −67510.0 −2.64447
$$868$$ −7336.00 −0.286866
$$869$$ −6600.00 −0.257641
$$870$$ 34160.0 1.33119
$$871$$ 6656.00 0.258932
$$872$$ 1232.00 0.0478449
$$873$$ −35186.0 −1.36411
$$874$$ 15776.0 0.610562
$$875$$ 5292.00 0.204460
$$876$$ −16320.0 −0.629454
$$877$$ −30398.0 −1.17043 −0.585215 0.810878i $$-0.698990\pi$$
−0.585215 + 0.810878i $$0.698990\pi$$
$$878$$ −16456.0 −0.632532
$$879$$ 28040.0 1.07596
$$880$$ 2464.00 0.0943880
$$881$$ 1630.00 0.0623338 0.0311669 0.999514i $$-0.490078\pi$$
0.0311669 + 0.999514i $$0.490078\pi$$
$$882$$ 7154.00 0.273115
$$883$$ −20228.0 −0.770925 −0.385462 0.922724i $$-0.625958\pi$$
−0.385462 + 0.922724i $$0.625958\pi$$
$$884$$ −6912.00 −0.262982
$$885$$ 98280.0 3.73293
$$886$$ 15336.0 0.581516
$$887$$ 38908.0 1.47283 0.736416 0.676528i $$-0.236516\pi$$
0.736416 + 0.676528i $$0.236516\pi$$
$$888$$ −10400.0 −0.393019
$$889$$ 448.000 0.0169015
$$890$$ −32088.0 −1.20853
$$891$$ −28919.0 −1.08734
$$892$$ 2424.00 0.0909883
$$893$$ 19256.0 0.721587
$$894$$ −26360.0 −0.986141
$$895$$ 26936.0 1.00600
$$896$$ 896.000 0.0334077
$$897$$ 10880.0 0.404986
$$898$$ −1844.00 −0.0685246
$$899$$ −31964.0 −1.18583
$$900$$ 20732.0 0.767852
$$901$$ 47736.0 1.76506
$$902$$ −4488.00 −0.165670
$$903$$ 27720.0 1.02155
$$904$$ −15216.0 −0.559819
$$905$$ −31220.0 −1.14673
$$906$$ 19680.0 0.721660
$$907$$ −20936.0 −0.766448 −0.383224 0.923655i $$-0.625186\pi$$
−0.383224 + 0.923655i $$0.625186\pi$$
$$908$$ 576.000 0.0210520
$$909$$ 88768.0 3.23900
$$910$$ 3136.00 0.114239
$$911$$ 48204.0 1.75310 0.876548 0.481315i $$-0.159841\pi$$
0.876548 + 0.481315i $$0.159841\pi$$
$$912$$ −18560.0 −0.673885
$$913$$ 13332.0 0.483269
$$914$$ 6772.00 0.245074
$$915$$ 27440.0 0.991408
$$916$$ −4040.00 −0.145726
$$917$$ −11088.0 −0.399300
$$918$$ −99360.0 −3.57230
$$919$$ −27304.0 −0.980061 −0.490030 0.871705i $$-0.663014\pi$$
−0.490030 + 0.871705i $$0.663014\pi$$
$$920$$ −7616.00 −0.272926
$$921$$ −13200.0 −0.472264
$$922$$ −6600.00 −0.235748
$$923$$ −7872.00 −0.280726
$$924$$ 3080.00 0.109659
$$925$$ 9230.00 0.328087
$$926$$ 28472.0 1.01042
$$927$$ 102638. 3.63654
$$928$$ 3904.00 0.138098
$$929$$ 30.0000 0.00105949 0.000529746 1.00000i $$-0.499831\pi$$
0.000529746 1.00000i $$0.499831\pi$$
$$930$$ −73360.0 −2.58663
$$931$$ 5684.00 0.200092
$$932$$ 15160.0 0.532814
$$933$$ 10660.0 0.374054
$$934$$ 7540.00 0.264150
$$935$$ 16632.0 0.581737
$$936$$ −9344.00 −0.326301
$$937$$ 4736.00 0.165121 0.0825605 0.996586i $$-0.473690\pi$$
0.0825605 + 0.996586i $$0.473690\pi$$
$$938$$ −5824.00 −0.202730
$$939$$ 92540.0 3.21611
$$940$$ −9296.00 −0.322555
$$941$$ 19996.0 0.692722 0.346361 0.938101i $$-0.387417\pi$$
0.346361 + 0.938101i $$0.387417\pi$$
$$942$$ −34120.0 −1.18014
$$943$$ 13872.0 0.479040
$$944$$ 11232.0 0.387257
$$945$$ 45080.0 1.55180
$$946$$ 8712.00 0.299420
$$947$$ −1252.00 −0.0429615 −0.0214807 0.999769i $$-0.506838\pi$$
−0.0214807 + 0.999769i $$0.506838\pi$$
$$948$$ −24000.0 −0.822240
$$949$$ −6528.00 −0.223296
$$950$$ 16472.0 0.562550
$$951$$ 97220.0 3.31501
$$952$$ 6048.00 0.205900
$$953$$ 17986.0 0.611357 0.305679 0.952135i $$-0.401117\pi$$
0.305679 + 0.952135i $$0.401117\pi$$
$$954$$ 64532.0 2.19004
$$955$$ −30464.0 −1.03224
$$956$$ 8736.00 0.295546
$$957$$ 13420.0 0.453299
$$958$$ 35592.0 1.20034
$$959$$ 6986.00 0.235234
$$960$$ 8960.00 0.301232
$$961$$ 38853.0 1.30419
$$962$$ −4160.00 −0.139422
$$963$$ −42924.0 −1.43635
$$964$$ −17072.0 −0.570386
$$965$$ 43764.0 1.45991
$$966$$ −9520.00 −0.317082
$$967$$ 14256.0 0.474087 0.237043 0.971499i $$-0.423822\pi$$
0.237043 + 0.971499i $$0.423822\pi$$
$$968$$ 968.000 0.0321412
$$969$$ −125280. −4.15333
$$970$$ 13496.0 0.446732
$$971$$ −50214.0 −1.65957 −0.829786 0.558082i $$-0.811537\pi$$
−0.829786 + 0.558082i $$0.811537\pi$$
$$972$$ −55480.0 −1.83078
$$973$$ 1932.00 0.0636558
$$974$$ −7368.00 −0.242388
$$975$$ 11360.0 0.373140
$$976$$ 3136.00 0.102849
$$977$$ −35814.0 −1.17276 −0.586382 0.810034i $$-0.699448\pi$$
−0.586382 + 0.810034i $$0.699448\pi$$
$$978$$ −23360.0 −0.763773
$$979$$ −12606.0 −0.411532
$$980$$ −2744.00 −0.0894427
$$981$$ 11242.0 0.365881
$$982$$ −34472.0 −1.12021
$$983$$ −19274.0 −0.625377 −0.312688 0.949856i $$-0.601230\pi$$
−0.312688 + 0.949856i $$0.601230\pi$$
$$984$$ −16320.0 −0.528722
$$985$$ 15708.0 0.508120
$$986$$ 26352.0 0.851135
$$987$$ −11620.0 −0.374740
$$988$$ −7424.00 −0.239058
$$989$$ −26928.0 −0.865784
$$990$$ 22484.0 0.721806
$$991$$ 59996.0 1.92314 0.961572 0.274553i $$-0.0885298\pi$$
0.961572 + 0.274553i $$0.0885298\pi$$
$$992$$ −8384.00 −0.268339
$$993$$ −26200.0 −0.837293
$$994$$ 6888.00 0.219793
$$995$$ 78204.0 2.49169
$$996$$ 48480.0 1.54232
$$997$$ 24344.0 0.773302 0.386651 0.922226i $$-0.373632\pi$$
0.386651 + 0.922226i $$0.373632\pi$$
$$998$$ 26352.0 0.835830
$$999$$ −59800.0 −1.89388
Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000

## Twists

By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 154.4.a.c.1.1 1
3.2 odd 2 1386.4.a.g.1.1 1
4.3 odd 2 1232.4.a.i.1.1 1
7.6 odd 2 1078.4.a.h.1.1 1
11.10 odd 2 1694.4.a.a.1.1 1

By twisted newform
Twist Min Dim Char Parity Ord Type
154.4.a.c.1.1 1 1.1 even 1 trivial
1078.4.a.h.1.1 1 7.6 odd 2
1232.4.a.i.1.1 1 4.3 odd 2
1386.4.a.g.1.1 1 3.2 odd 2
1694.4.a.a.1.1 1 11.10 odd 2