# Properties

 Label 1575.4.a.b.1.1 Level $1575$ Weight $4$ Character 1575.1 Self dual yes Analytic conductor $92.928$ Analytic rank $1$ Dimension $1$ CM no Inner twists $1$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$1575 = 3^{2} \cdot 5^{2} \cdot 7$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 1575.a (trivial)

## Newform invariants

 Self dual: yes Analytic conductor: $$92.9280082590$$ Analytic rank: $$1$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 21) Fricke sign: $$-1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

 Embedding label 1.1 Character $$\chi$$ $$=$$ 1575.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q-3.00000 q^{2} +1.00000 q^{4} -7.00000 q^{7} +21.0000 q^{8} +O(q^{10})$$ $$q-3.00000 q^{2} +1.00000 q^{4} -7.00000 q^{7} +21.0000 q^{8} +36.0000 q^{11} +34.0000 q^{13} +21.0000 q^{14} -71.0000 q^{16} +42.0000 q^{17} -124.000 q^{19} -108.000 q^{22} -102.000 q^{26} -7.00000 q^{28} -102.000 q^{29} -160.000 q^{31} +45.0000 q^{32} -126.000 q^{34} -398.000 q^{37} +372.000 q^{38} +318.000 q^{41} +268.000 q^{43} +36.0000 q^{44} +240.000 q^{47} +49.0000 q^{49} +34.0000 q^{52} -498.000 q^{53} -147.000 q^{56} +306.000 q^{58} +132.000 q^{59} +398.000 q^{61} +480.000 q^{62} +433.000 q^{64} -92.0000 q^{67} +42.0000 q^{68} +720.000 q^{71} +502.000 q^{73} +1194.00 q^{74} -124.000 q^{76} -252.000 q^{77} -1024.00 q^{79} -954.000 q^{82} -204.000 q^{83} -804.000 q^{86} +756.000 q^{88} -354.000 q^{89} -238.000 q^{91} -720.000 q^{94} +286.000 q^{97} -147.000 q^{98} +O(q^{100})$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −3.00000 −1.06066 −0.530330 0.847791i $$-0.677932\pi$$
−0.530330 + 0.847791i $$0.677932\pi$$
$$3$$ 0 0
$$4$$ 1.00000 0.125000
$$5$$ 0 0
$$6$$ 0 0
$$7$$ −7.00000 −0.377964
$$8$$ 21.0000 0.928078
$$9$$ 0 0
$$10$$ 0 0
$$11$$ 36.0000 0.986764 0.493382 0.869813i $$-0.335760\pi$$
0.493382 + 0.869813i $$0.335760\pi$$
$$12$$ 0 0
$$13$$ 34.0000 0.725377 0.362689 0.931910i $$-0.381859\pi$$
0.362689 + 0.931910i $$0.381859\pi$$
$$14$$ 21.0000 0.400892
$$15$$ 0 0
$$16$$ −71.0000 −1.10938
$$17$$ 42.0000 0.599206 0.299603 0.954064i $$-0.403146\pi$$
0.299603 + 0.954064i $$0.403146\pi$$
$$18$$ 0 0
$$19$$ −124.000 −1.49724 −0.748620 0.663000i $$-0.769283\pi$$
−0.748620 + 0.663000i $$0.769283\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ −108.000 −1.04662
$$23$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$24$$ 0 0
$$25$$ 0 0
$$26$$ −102.000 −0.769379
$$27$$ 0 0
$$28$$ −7.00000 −0.0472456
$$29$$ −102.000 −0.653135 −0.326568 0.945174i $$-0.605892\pi$$
−0.326568 + 0.945174i $$0.605892\pi$$
$$30$$ 0 0
$$31$$ −160.000 −0.926995 −0.463498 0.886098i $$-0.653406\pi$$
−0.463498 + 0.886098i $$0.653406\pi$$
$$32$$ 45.0000 0.248592
$$33$$ 0 0
$$34$$ −126.000 −0.635554
$$35$$ 0 0
$$36$$ 0 0
$$37$$ −398.000 −1.76840 −0.884200 0.467109i $$-0.845296\pi$$
−0.884200 + 0.467109i $$0.845296\pi$$
$$38$$ 372.000 1.58806
$$39$$ 0 0
$$40$$ 0 0
$$41$$ 318.000 1.21130 0.605649 0.795732i $$-0.292913\pi$$
0.605649 + 0.795732i $$0.292913\pi$$
$$42$$ 0 0
$$43$$ 268.000 0.950456 0.475228 0.879863i $$-0.342366\pi$$
0.475228 + 0.879863i $$0.342366\pi$$
$$44$$ 36.0000 0.123346
$$45$$ 0 0
$$46$$ 0 0
$$47$$ 240.000 0.744843 0.372421 0.928064i $$-0.378528\pi$$
0.372421 + 0.928064i $$0.378528\pi$$
$$48$$ 0 0
$$49$$ 49.0000 0.142857
$$50$$ 0 0
$$51$$ 0 0
$$52$$ 34.0000 0.0906721
$$53$$ −498.000 −1.29067 −0.645335 0.763899i $$-0.723282\pi$$
−0.645335 + 0.763899i $$0.723282\pi$$
$$54$$ 0 0
$$55$$ 0 0
$$56$$ −147.000 −0.350780
$$57$$ 0 0
$$58$$ 306.000 0.692755
$$59$$ 132.000 0.291270 0.145635 0.989338i $$-0.453477\pi$$
0.145635 + 0.989338i $$0.453477\pi$$
$$60$$ 0 0
$$61$$ 398.000 0.835388 0.417694 0.908588i $$-0.362838\pi$$
0.417694 + 0.908588i $$0.362838\pi$$
$$62$$ 480.000 0.983227
$$63$$ 0 0
$$64$$ 433.000 0.845703
$$65$$ 0 0
$$66$$ 0 0
$$67$$ −92.0000 −0.167755 −0.0838775 0.996476i $$-0.526730\pi$$
−0.0838775 + 0.996476i $$0.526730\pi$$
$$68$$ 42.0000 0.0749007
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 720.000 1.20350 0.601748 0.798686i $$-0.294471\pi$$
0.601748 + 0.798686i $$0.294471\pi$$
$$72$$ 0 0
$$73$$ 502.000 0.804858 0.402429 0.915451i $$-0.368166\pi$$
0.402429 + 0.915451i $$0.368166\pi$$
$$74$$ 1194.00 1.87567
$$75$$ 0 0
$$76$$ −124.000 −0.187155
$$77$$ −252.000 −0.372962
$$78$$ 0 0
$$79$$ −1024.00 −1.45834 −0.729171 0.684332i $$-0.760094\pi$$
−0.729171 + 0.684332i $$0.760094\pi$$
$$80$$ 0 0
$$81$$ 0 0
$$82$$ −954.000 −1.28478
$$83$$ −204.000 −0.269782 −0.134891 0.990860i $$-0.543068\pi$$
−0.134891 + 0.990860i $$0.543068\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ −804.000 −1.00811
$$87$$ 0 0
$$88$$ 756.000 0.915794
$$89$$ −354.000 −0.421617 −0.210809 0.977527i $$-0.567610\pi$$
−0.210809 + 0.977527i $$0.567610\pi$$
$$90$$ 0 0
$$91$$ −238.000 −0.274167
$$92$$ 0 0
$$93$$ 0 0
$$94$$ −720.000 −0.790025
$$95$$ 0 0
$$96$$ 0 0
$$97$$ 286.000 0.299370 0.149685 0.988734i $$-0.452174\pi$$
0.149685 + 0.988734i $$0.452174\pi$$
$$98$$ −147.000 −0.151523
$$99$$ 0 0
$$100$$ 0 0
$$101$$ −414.000 −0.407867 −0.203933 0.978985i $$-0.565373\pi$$
−0.203933 + 0.978985i $$0.565373\pi$$
$$102$$ 0 0
$$103$$ −56.0000 −0.0535713 −0.0267857 0.999641i $$-0.508527\pi$$
−0.0267857 + 0.999641i $$0.508527\pi$$
$$104$$ 714.000 0.673206
$$105$$ 0 0
$$106$$ 1494.00 1.36896
$$107$$ 12.0000 0.0108419 0.00542095 0.999985i $$-0.498274\pi$$
0.00542095 + 0.999985i $$0.498274\pi$$
$$108$$ 0 0
$$109$$ 1478.00 1.29878 0.649389 0.760457i $$-0.275025\pi$$
0.649389 + 0.760457i $$0.275025\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 497.000 0.419304
$$113$$ 402.000 0.334664 0.167332 0.985901i $$-0.446485\pi$$
0.167332 + 0.985901i $$0.446485\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ −102.000 −0.0816419
$$117$$ 0 0
$$118$$ −396.000 −0.308939
$$119$$ −294.000 −0.226478
$$120$$ 0 0
$$121$$ −35.0000 −0.0262960
$$122$$ −1194.00 −0.886063
$$123$$ 0 0
$$124$$ −160.000 −0.115874
$$125$$ 0 0
$$126$$ 0 0
$$127$$ −1280.00 −0.894344 −0.447172 0.894448i $$-0.647569\pi$$
−0.447172 + 0.894448i $$0.647569\pi$$
$$128$$ −1659.00 −1.14560
$$129$$ 0 0
$$130$$ 0 0
$$131$$ −1764.00 −1.17650 −0.588250 0.808679i $$-0.700183\pi$$
−0.588250 + 0.808679i $$0.700183\pi$$
$$132$$ 0 0
$$133$$ 868.000 0.565903
$$134$$ 276.000 0.177931
$$135$$ 0 0
$$136$$ 882.000 0.556109
$$137$$ −2358.00 −1.47049 −0.735246 0.677800i $$-0.762934\pi$$
−0.735246 + 0.677800i $$0.762934\pi$$
$$138$$ 0 0
$$139$$ −52.0000 −0.0317308 −0.0158654 0.999874i $$-0.505050\pi$$
−0.0158654 + 0.999874i $$0.505050\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ −2160.00 −1.27650
$$143$$ 1224.00 0.715776
$$144$$ 0 0
$$145$$ 0 0
$$146$$ −1506.00 −0.853681
$$147$$ 0 0
$$148$$ −398.000 −0.221050
$$149$$ 1746.00 0.959986 0.479993 0.877272i $$-0.340639\pi$$
0.479993 + 0.877272i $$0.340639\pi$$
$$150$$ 0 0
$$151$$ −232.000 −0.125032 −0.0625162 0.998044i $$-0.519913\pi$$
−0.0625162 + 0.998044i $$0.519913\pi$$
$$152$$ −2604.00 −1.38955
$$153$$ 0 0
$$154$$ 756.000 0.395586
$$155$$ 0 0
$$156$$ 0 0
$$157$$ −1694.00 −0.861120 −0.430560 0.902562i $$-0.641684\pi$$
−0.430560 + 0.902562i $$0.641684\pi$$
$$158$$ 3072.00 1.54681
$$159$$ 0 0
$$160$$ 0 0
$$161$$ 0 0
$$162$$ 0 0
$$163$$ 2932.00 1.40891 0.704454 0.709750i $$-0.251192\pi$$
0.704454 + 0.709750i $$0.251192\pi$$
$$164$$ 318.000 0.151412
$$165$$ 0 0
$$166$$ 612.000 0.286147
$$167$$ 1176.00 0.544920 0.272460 0.962167i $$-0.412163\pi$$
0.272460 + 0.962167i $$0.412163\pi$$
$$168$$ 0 0
$$169$$ −1041.00 −0.473828
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 268.000 0.118807
$$173$$ 870.000 0.382340 0.191170 0.981557i $$-0.438772\pi$$
0.191170 + 0.981557i $$0.438772\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ −2556.00 −1.09469
$$177$$ 0 0
$$178$$ 1062.00 0.447193
$$179$$ 2316.00 0.967072 0.483536 0.875324i $$-0.339352\pi$$
0.483536 + 0.875324i $$0.339352\pi$$
$$180$$ 0 0
$$181$$ −106.000 −0.0435299 −0.0217650 0.999763i $$-0.506929\pi$$
−0.0217650 + 0.999763i $$0.506929\pi$$
$$182$$ 714.000 0.290798
$$183$$ 0 0
$$184$$ 0 0
$$185$$ 0 0
$$186$$ 0 0
$$187$$ 1512.00 0.591275
$$188$$ 240.000 0.0931053
$$189$$ 0 0
$$190$$ 0 0
$$191$$ 1128.00 0.427326 0.213663 0.976907i $$-0.431461\pi$$
0.213663 + 0.976907i $$0.431461\pi$$
$$192$$ 0 0
$$193$$ −4034.00 −1.50453 −0.752263 0.658862i $$-0.771038\pi$$
−0.752263 + 0.658862i $$0.771038\pi$$
$$194$$ −858.000 −0.317530
$$195$$ 0 0
$$196$$ 49.0000 0.0178571
$$197$$ −1314.00 −0.475221 −0.237611 0.971360i $$-0.576364\pi$$
−0.237611 + 0.971360i $$0.576364\pi$$
$$198$$ 0 0
$$199$$ 5096.00 1.81531 0.907653 0.419722i $$-0.137872\pi$$
0.907653 + 0.419722i $$0.137872\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ 1242.00 0.432608
$$203$$ 714.000 0.246862
$$204$$ 0 0
$$205$$ 0 0
$$206$$ 168.000 0.0568209
$$207$$ 0 0
$$208$$ −2414.00 −0.804715
$$209$$ −4464.00 −1.47742
$$210$$ 0 0
$$211$$ −3076.00 −1.00360 −0.501802 0.864982i $$-0.667330\pi$$
−0.501802 + 0.864982i $$0.667330\pi$$
$$212$$ −498.000 −0.161334
$$213$$ 0 0
$$214$$ −36.0000 −0.0114996
$$215$$ 0 0
$$216$$ 0 0
$$217$$ 1120.00 0.350371
$$218$$ −4434.00 −1.37756
$$219$$ 0 0
$$220$$ 0 0
$$221$$ 1428.00 0.434650
$$222$$ 0 0
$$223$$ 1888.00 0.566950 0.283475 0.958980i $$-0.408513\pi$$
0.283475 + 0.958980i $$0.408513\pi$$
$$224$$ −315.000 −0.0939590
$$225$$ 0 0
$$226$$ −1206.00 −0.354964
$$227$$ −4716.00 −1.37891 −0.689454 0.724330i $$-0.742149\pi$$
−0.689454 + 0.724330i $$0.742149\pi$$
$$228$$ 0 0
$$229$$ −1690.00 −0.487678 −0.243839 0.969816i $$-0.578407\pi$$
−0.243839 + 0.969816i $$0.578407\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ −2142.00 −0.606160
$$233$$ 138.000 0.0388012 0.0194006 0.999812i $$-0.493824\pi$$
0.0194006 + 0.999812i $$0.493824\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ 132.000 0.0364088
$$237$$ 0 0
$$238$$ 882.000 0.240217
$$239$$ −1896.00 −0.513147 −0.256573 0.966525i $$-0.582594\pi$$
−0.256573 + 0.966525i $$0.582594\pi$$
$$240$$ 0 0
$$241$$ −3598.00 −0.961691 −0.480846 0.876805i $$-0.659670\pi$$
−0.480846 + 0.876805i $$0.659670\pi$$
$$242$$ 105.000 0.0278911
$$243$$ 0 0
$$244$$ 398.000 0.104424
$$245$$ 0 0
$$246$$ 0 0
$$247$$ −4216.00 −1.08606
$$248$$ −3360.00 −0.860323
$$249$$ 0 0
$$250$$ 0 0
$$251$$ 3060.00 0.769504 0.384752 0.923020i $$-0.374287\pi$$
0.384752 + 0.923020i $$0.374287\pi$$
$$252$$ 0 0
$$253$$ 0 0
$$254$$ 3840.00 0.948595
$$255$$ 0 0
$$256$$ 1513.00 0.369385
$$257$$ −6822.00 −1.65582 −0.827908 0.560864i $$-0.810469\pi$$
−0.827908 + 0.560864i $$0.810469\pi$$
$$258$$ 0 0
$$259$$ 2786.00 0.668392
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 5292.00 1.24787
$$263$$ 2592.00 0.607717 0.303858 0.952717i $$-0.401725\pi$$
0.303858 + 0.952717i $$0.401725\pi$$
$$264$$ 0 0
$$265$$ 0 0
$$266$$ −2604.00 −0.600231
$$267$$ 0 0
$$268$$ −92.0000 −0.0209694
$$269$$ −8214.00 −1.86177 −0.930886 0.365311i $$-0.880963\pi$$
−0.930886 + 0.365311i $$0.880963\pi$$
$$270$$ 0 0
$$271$$ −5344.00 −1.19788 −0.598939 0.800795i $$-0.704411\pi$$
−0.598939 + 0.800795i $$0.704411\pi$$
$$272$$ −2982.00 −0.664744
$$273$$ 0 0
$$274$$ 7074.00 1.55969
$$275$$ 0 0
$$276$$ 0 0
$$277$$ 6514.00 1.41295 0.706477 0.707736i $$-0.250283\pi$$
0.706477 + 0.707736i $$0.250283\pi$$
$$278$$ 156.000 0.0336556
$$279$$ 0 0
$$280$$ 0 0
$$281$$ −6618.00 −1.40497 −0.702485 0.711698i $$-0.747926\pi$$
−0.702485 + 0.711698i $$0.747926\pi$$
$$282$$ 0 0
$$283$$ −3260.00 −0.684759 −0.342380 0.939562i $$-0.611233\pi$$
−0.342380 + 0.939562i $$0.611233\pi$$
$$284$$ 720.000 0.150437
$$285$$ 0 0
$$286$$ −3672.00 −0.759195
$$287$$ −2226.00 −0.457828
$$288$$ 0 0
$$289$$ −3149.00 −0.640953
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 502.000 0.100607
$$293$$ 5118.00 1.02047 0.510233 0.860036i $$-0.329559\pi$$
0.510233 + 0.860036i $$0.329559\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ −8358.00 −1.64121
$$297$$ 0 0
$$298$$ −5238.00 −1.01822
$$299$$ 0 0
$$300$$ 0 0
$$301$$ −1876.00 −0.359239
$$302$$ 696.000 0.132617
$$303$$ 0 0
$$304$$ 8804.00 1.66100
$$305$$ 0 0
$$306$$ 0 0
$$307$$ −452.000 −0.0840293 −0.0420147 0.999117i $$-0.513378\pi$$
−0.0420147 + 0.999117i $$0.513378\pi$$
$$308$$ −252.000 −0.0466202
$$309$$ 0 0
$$310$$ 0 0
$$311$$ −5016.00 −0.914570 −0.457285 0.889320i $$-0.651178\pi$$
−0.457285 + 0.889320i $$0.651178\pi$$
$$312$$ 0 0
$$313$$ −5402.00 −0.975524 −0.487762 0.872977i $$-0.662187\pi$$
−0.487762 + 0.872977i $$0.662187\pi$$
$$314$$ 5082.00 0.913356
$$315$$ 0 0
$$316$$ −1024.00 −0.182293
$$317$$ 10086.0 1.78702 0.893511 0.449041i $$-0.148234\pi$$
0.893511 + 0.449041i $$0.148234\pi$$
$$318$$ 0 0
$$319$$ −3672.00 −0.644491
$$320$$ 0 0
$$321$$ 0 0
$$322$$ 0 0
$$323$$ −5208.00 −0.897154
$$324$$ 0 0
$$325$$ 0 0
$$326$$ −8796.00 −1.49437
$$327$$ 0 0
$$328$$ 6678.00 1.12418
$$329$$ −1680.00 −0.281524
$$330$$ 0 0
$$331$$ −8044.00 −1.33577 −0.667883 0.744267i $$-0.732799\pi$$
−0.667883 + 0.744267i $$0.732799\pi$$
$$332$$ −204.000 −0.0337228
$$333$$ 0 0
$$334$$ −3528.00 −0.577975
$$335$$ 0 0
$$336$$ 0 0
$$337$$ −4178.00 −0.675342 −0.337671 0.941264i $$-0.609639\pi$$
−0.337671 + 0.941264i $$0.609639\pi$$
$$338$$ 3123.00 0.502570
$$339$$ 0 0
$$340$$ 0 0
$$341$$ −5760.00 −0.914726
$$342$$ 0 0
$$343$$ −343.000 −0.0539949
$$344$$ 5628.00 0.882097
$$345$$ 0 0
$$346$$ −2610.00 −0.405533
$$347$$ 156.000 0.0241341 0.0120670 0.999927i $$-0.496159\pi$$
0.0120670 + 0.999927i $$0.496159\pi$$
$$348$$ 0 0
$$349$$ −12418.0 −1.90464 −0.952321 0.305097i $$-0.901311\pi$$
−0.952321 + 0.305097i $$0.901311\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 1620.00 0.245302
$$353$$ −7830.00 −1.18059 −0.590296 0.807187i $$-0.700989\pi$$
−0.590296 + 0.807187i $$0.700989\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ −354.000 −0.0527021
$$357$$ 0 0
$$358$$ −6948.00 −1.02574
$$359$$ 9312.00 1.36899 0.684497 0.729016i $$-0.260022\pi$$
0.684497 + 0.729016i $$0.260022\pi$$
$$360$$ 0 0
$$361$$ 8517.00 1.24173
$$362$$ 318.000 0.0461705
$$363$$ 0 0
$$364$$ −238.000 −0.0342709
$$365$$ 0 0
$$366$$ 0 0
$$367$$ 3760.00 0.534797 0.267398 0.963586i $$-0.413836\pi$$
0.267398 + 0.963586i $$0.413836\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 0 0
$$371$$ 3486.00 0.487828
$$372$$ 0 0
$$373$$ −5870.00 −0.814845 −0.407422 0.913240i $$-0.633572\pi$$
−0.407422 + 0.913240i $$0.633572\pi$$
$$374$$ −4536.00 −0.627142
$$375$$ 0 0
$$376$$ 5040.00 0.691272
$$377$$ −3468.00 −0.473769
$$378$$ 0 0
$$379$$ −1852.00 −0.251005 −0.125502 0.992093i $$-0.540054\pi$$
−0.125502 + 0.992093i $$0.540054\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ −3384.00 −0.453247
$$383$$ 2160.00 0.288175 0.144087 0.989565i $$-0.453975\pi$$
0.144087 + 0.989565i $$0.453975\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 12102.0 1.59579
$$387$$ 0 0
$$388$$ 286.000 0.0374213
$$389$$ 6786.00 0.884483 0.442241 0.896896i $$-0.354183\pi$$
0.442241 + 0.896896i $$0.354183\pi$$
$$390$$ 0 0
$$391$$ 0 0
$$392$$ 1029.00 0.132583
$$393$$ 0 0
$$394$$ 3942.00 0.504048
$$395$$ 0 0
$$396$$ 0 0
$$397$$ 6514.00 0.823497 0.411748 0.911298i $$-0.364918\pi$$
0.411748 + 0.911298i $$0.364918\pi$$
$$398$$ −15288.0 −1.92542
$$399$$ 0 0
$$400$$ 0 0
$$401$$ −3330.00 −0.414694 −0.207347 0.978267i $$-0.566483\pi$$
−0.207347 + 0.978267i $$0.566483\pi$$
$$402$$ 0 0
$$403$$ −5440.00 −0.672421
$$404$$ −414.000 −0.0509833
$$405$$ 0 0
$$406$$ −2142.00 −0.261837
$$407$$ −14328.0 −1.74499
$$408$$ 0 0
$$409$$ −5398.00 −0.652601 −0.326301 0.945266i $$-0.605802\pi$$
−0.326301 + 0.945266i $$0.605802\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ −56.0000 −0.00669641
$$413$$ −924.000 −0.110090
$$414$$ 0 0
$$415$$ 0 0
$$416$$ 1530.00 0.180323
$$417$$ 0 0
$$418$$ 13392.0 1.56704
$$419$$ −13092.0 −1.52646 −0.763229 0.646128i $$-0.776387\pi$$
−0.763229 + 0.646128i $$0.776387\pi$$
$$420$$ 0 0
$$421$$ −322.000 −0.0372763 −0.0186381 0.999826i $$-0.505933\pi$$
−0.0186381 + 0.999826i $$0.505933\pi$$
$$422$$ 9228.00 1.06448
$$423$$ 0 0
$$424$$ −10458.0 −1.19784
$$425$$ 0 0
$$426$$ 0 0
$$427$$ −2786.00 −0.315747
$$428$$ 12.0000 0.00135524
$$429$$ 0 0
$$430$$ 0 0
$$431$$ −2616.00 −0.292363 −0.146181 0.989258i $$-0.546698\pi$$
−0.146181 + 0.989258i $$0.546698\pi$$
$$432$$ 0 0
$$433$$ −4322.00 −0.479681 −0.239841 0.970812i $$-0.577095\pi$$
−0.239841 + 0.970812i $$0.577095\pi$$
$$434$$ −3360.00 −0.371625
$$435$$ 0 0
$$436$$ 1478.00 0.162347
$$437$$ 0 0
$$438$$ 0 0
$$439$$ −9016.00 −0.980205 −0.490103 0.871665i $$-0.663041\pi$$
−0.490103 + 0.871665i $$0.663041\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ −4284.00 −0.461016
$$443$$ −5268.00 −0.564989 −0.282495 0.959269i $$-0.591162\pi$$
−0.282495 + 0.959269i $$0.591162\pi$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ −5664.00 −0.601341
$$447$$ 0 0
$$448$$ −3031.00 −0.319646
$$449$$ 5310.00 0.558117 0.279058 0.960274i $$-0.409978\pi$$
0.279058 + 0.960274i $$0.409978\pi$$
$$450$$ 0 0
$$451$$ 11448.0 1.19527
$$452$$ 402.000 0.0418329
$$453$$ 0 0
$$454$$ 14148.0 1.46255
$$455$$ 0 0
$$456$$ 0 0
$$457$$ −15770.0 −1.61420 −0.807100 0.590415i $$-0.798964\pi$$
−0.807100 + 0.590415i $$0.798964\pi$$
$$458$$ 5070.00 0.517261
$$459$$ 0 0
$$460$$ 0 0
$$461$$ 5370.00 0.542529 0.271264 0.962505i $$-0.412558\pi$$
0.271264 + 0.962505i $$0.412558\pi$$
$$462$$ 0 0
$$463$$ 3328.00 0.334050 0.167025 0.985953i $$-0.446584\pi$$
0.167025 + 0.985953i $$0.446584\pi$$
$$464$$ 7242.00 0.724572
$$465$$ 0 0
$$466$$ −414.000 −0.0411549
$$467$$ 4548.00 0.450656 0.225328 0.974283i $$-0.427655\pi$$
0.225328 + 0.974283i $$0.427655\pi$$
$$468$$ 0 0
$$469$$ 644.000 0.0634055
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 2772.00 0.270321
$$473$$ 9648.00 0.937876
$$474$$ 0 0
$$475$$ 0 0
$$476$$ −294.000 −0.0283098
$$477$$ 0 0
$$478$$ 5688.00 0.544274
$$479$$ 8064.00 0.769214 0.384607 0.923080i $$-0.374337\pi$$
0.384607 + 0.923080i $$0.374337\pi$$
$$480$$ 0 0
$$481$$ −13532.0 −1.28276
$$482$$ 10794.0 1.02003
$$483$$ 0 0
$$484$$ −35.0000 −0.00328700
$$485$$ 0 0
$$486$$ 0 0
$$487$$ −16616.0 −1.54608 −0.773042 0.634355i $$-0.781266\pi$$
−0.773042 + 0.634355i $$0.781266\pi$$
$$488$$ 8358.00 0.775305
$$489$$ 0 0
$$490$$ 0 0
$$491$$ 7140.00 0.656260 0.328130 0.944633i $$-0.393582\pi$$
0.328130 + 0.944633i $$0.393582\pi$$
$$492$$ 0 0
$$493$$ −4284.00 −0.391362
$$494$$ 12648.0 1.15194
$$495$$ 0 0
$$496$$ 11360.0 1.02839
$$497$$ −5040.00 −0.454879
$$498$$ 0 0
$$499$$ −9124.00 −0.818530 −0.409265 0.912416i $$-0.634215\pi$$
−0.409265 + 0.912416i $$0.634215\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ −9180.00 −0.816182
$$503$$ −6552.00 −0.580794 −0.290397 0.956906i $$-0.593787\pi$$
−0.290397 + 0.956906i $$0.593787\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ 0 0
$$507$$ 0 0
$$508$$ −1280.00 −0.111793
$$509$$ −2790.00 −0.242956 −0.121478 0.992594i $$-0.538763\pi$$
−0.121478 + 0.992594i $$0.538763\pi$$
$$510$$ 0 0
$$511$$ −3514.00 −0.304208
$$512$$ 8733.00 0.753804
$$513$$ 0 0
$$514$$ 20466.0 1.75626
$$515$$ 0 0
$$516$$ 0 0
$$517$$ 8640.00 0.734984
$$518$$ −8358.00 −0.708937
$$519$$ 0 0
$$520$$ 0 0
$$521$$ 14862.0 1.24974 0.624871 0.780728i $$-0.285151\pi$$
0.624871 + 0.780728i $$0.285151\pi$$
$$522$$ 0 0
$$523$$ −17660.0 −1.47652 −0.738258 0.674518i $$-0.764351\pi$$
−0.738258 + 0.674518i $$0.764351\pi$$
$$524$$ −1764.00 −0.147062
$$525$$ 0 0
$$526$$ −7776.00 −0.644581
$$527$$ −6720.00 −0.555461
$$528$$ 0 0
$$529$$ −12167.0 −1.00000
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 868.000 0.0707379
$$533$$ 10812.0 0.878649
$$534$$ 0 0
$$535$$ 0 0
$$536$$ −1932.00 −0.155690
$$537$$ 0 0
$$538$$ 24642.0 1.97471
$$539$$ 1764.00 0.140966
$$540$$ 0 0
$$541$$ −19834.0 −1.57621 −0.788106 0.615540i $$-0.788938\pi$$
−0.788106 + 0.615540i $$0.788938\pi$$
$$542$$ 16032.0 1.27054
$$543$$ 0 0
$$544$$ 1890.00 0.148958
$$545$$ 0 0
$$546$$ 0 0
$$547$$ −20972.0 −1.63930 −0.819651 0.572863i $$-0.805833\pi$$
−0.819651 + 0.572863i $$0.805833\pi$$
$$548$$ −2358.00 −0.183812
$$549$$ 0 0
$$550$$ 0 0
$$551$$ 12648.0 0.977900
$$552$$ 0 0
$$553$$ 7168.00 0.551201
$$554$$ −19542.0 −1.49866
$$555$$ 0 0
$$556$$ −52.0000 −0.00396635
$$557$$ 21174.0 1.61072 0.805360 0.592786i $$-0.201972\pi$$
0.805360 + 0.592786i $$0.201972\pi$$
$$558$$ 0 0
$$559$$ 9112.00 0.689439
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 19854.0 1.49020
$$563$$ −17772.0 −1.33037 −0.665187 0.746677i $$-0.731648\pi$$
−0.665187 + 0.746677i $$0.731648\pi$$
$$564$$ 0 0
$$565$$ 0 0
$$566$$ 9780.00 0.726297
$$567$$ 0 0
$$568$$ 15120.0 1.11694
$$569$$ −8250.00 −0.607835 −0.303917 0.952698i $$-0.598295\pi$$
−0.303917 + 0.952698i $$0.598295\pi$$
$$570$$ 0 0
$$571$$ 20756.0 1.52121 0.760606 0.649214i $$-0.224902\pi$$
0.760606 + 0.649214i $$0.224902\pi$$
$$572$$ 1224.00 0.0894720
$$573$$ 0 0
$$574$$ 6678.00 0.485600
$$575$$ 0 0
$$576$$ 0 0
$$577$$ −2.00000 −0.000144300 0 −7.21500e−5 1.00000i $$-0.500023\pi$$
−7.21500e−5 1.00000i $$0.500023\pi$$
$$578$$ 9447.00 0.679833
$$579$$ 0 0
$$580$$ 0 0
$$581$$ 1428.00 0.101968
$$582$$ 0 0
$$583$$ −17928.0 −1.27359
$$584$$ 10542.0 0.746971
$$585$$ 0 0
$$586$$ −15354.0 −1.08237
$$587$$ 26364.0 1.85376 0.926881 0.375354i $$-0.122479\pi$$
0.926881 + 0.375354i $$0.122479\pi$$
$$588$$ 0 0
$$589$$ 19840.0 1.38793
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 28258.0 1.96182
$$593$$ 2298.00 0.159136 0.0795679 0.996829i $$-0.474646\pi$$
0.0795679 + 0.996829i $$0.474646\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 1746.00 0.119998
$$597$$ 0 0
$$598$$ 0 0
$$599$$ −3072.00 −0.209547 −0.104773 0.994496i $$-0.533412\pi$$
−0.104773 + 0.994496i $$0.533412\pi$$
$$600$$ 0 0
$$601$$ 24554.0 1.66652 0.833260 0.552881i $$-0.186472\pi$$
0.833260 + 0.552881i $$0.186472\pi$$
$$602$$ 5628.00 0.381030
$$603$$ 0 0
$$604$$ −232.000 −0.0156290
$$605$$ 0 0
$$606$$ 0 0
$$607$$ −16832.0 −1.12552 −0.562759 0.826621i $$-0.690260\pi$$
−0.562759 + 0.826621i $$0.690260\pi$$
$$608$$ −5580.00 −0.372202
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 8160.00 0.540292
$$612$$ 0 0
$$613$$ 2482.00 0.163535 0.0817676 0.996651i $$-0.473943\pi$$
0.0817676 + 0.996651i $$0.473943\pi$$
$$614$$ 1356.00 0.0891266
$$615$$ 0 0
$$616$$ −5292.00 −0.346138
$$617$$ −15798.0 −1.03080 −0.515400 0.856950i $$-0.672357\pi$$
−0.515400 + 0.856950i $$0.672357\pi$$
$$618$$ 0 0
$$619$$ −15460.0 −1.00386 −0.501930 0.864908i $$-0.667377\pi$$
−0.501930 + 0.864908i $$0.667377\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 15048.0 0.970048
$$623$$ 2478.00 0.159356
$$624$$ 0 0
$$625$$ 0 0
$$626$$ 16206.0 1.03470
$$627$$ 0 0
$$628$$ −1694.00 −0.107640
$$629$$ −16716.0 −1.05964
$$630$$ 0 0
$$631$$ −7720.00 −0.487050 −0.243525 0.969895i $$-0.578304\pi$$
−0.243525 + 0.969895i $$0.578304\pi$$
$$632$$ −21504.0 −1.35345
$$633$$ 0 0
$$634$$ −30258.0 −1.89542
$$635$$ 0 0
$$636$$ 0 0
$$637$$ 1666.00 0.103625
$$638$$ 11016.0 0.683586
$$639$$ 0 0
$$640$$ 0 0
$$641$$ 17262.0 1.06366 0.531832 0.846850i $$-0.321504\pi$$
0.531832 + 0.846850i $$0.321504\pi$$
$$642$$ 0 0
$$643$$ 12220.0 0.749471 0.374735 0.927132i $$-0.377734\pi$$
0.374735 + 0.927132i $$0.377734\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 15624.0 0.951576
$$647$$ 13560.0 0.823955 0.411977 0.911194i $$-0.364838\pi$$
0.411977 + 0.911194i $$0.364838\pi$$
$$648$$ 0 0
$$649$$ 4752.00 0.287415
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 2932.00 0.176113
$$653$$ 23094.0 1.38398 0.691989 0.721908i $$-0.256735\pi$$
0.691989 + 0.721908i $$0.256735\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ −22578.0 −1.34378
$$657$$ 0 0
$$658$$ 5040.00 0.298601
$$659$$ −22548.0 −1.33285 −0.666423 0.745574i $$-0.732175\pi$$
−0.666423 + 0.745574i $$0.732175\pi$$
$$660$$ 0 0
$$661$$ 17462.0 1.02752 0.513762 0.857933i $$-0.328252\pi$$
0.513762 + 0.857933i $$0.328252\pi$$
$$662$$ 24132.0 1.41679
$$663$$ 0 0
$$664$$ −4284.00 −0.250379
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 0 0
$$668$$ 1176.00 0.0681150
$$669$$ 0 0
$$670$$ 0 0
$$671$$ 14328.0 0.824331
$$672$$ 0 0
$$673$$ 22462.0 1.28655 0.643274 0.765636i $$-0.277576\pi$$
0.643274 + 0.765636i $$0.277576\pi$$
$$674$$ 12534.0 0.716308
$$675$$ 0 0
$$676$$ −1041.00 −0.0592285
$$677$$ −25554.0 −1.45069 −0.725347 0.688383i $$-0.758321\pi$$
−0.725347 + 0.688383i $$0.758321\pi$$
$$678$$ 0 0
$$679$$ −2002.00 −0.113151
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 17280.0 0.970213
$$683$$ 9276.00 0.519672 0.259836 0.965653i $$-0.416331\pi$$
0.259836 + 0.965653i $$0.416331\pi$$
$$684$$ 0 0
$$685$$ 0 0
$$686$$ 1029.00 0.0572703
$$687$$ 0 0
$$688$$ −19028.0 −1.05441
$$689$$ −16932.0 −0.936223
$$690$$ 0 0
$$691$$ 27380.0 1.50736 0.753679 0.657243i $$-0.228277\pi$$
0.753679 + 0.657243i $$0.228277\pi$$
$$692$$ 870.000 0.0477925
$$693$$ 0 0
$$694$$ −468.000 −0.0255980
$$695$$ 0 0
$$696$$ 0 0
$$697$$ 13356.0 0.725817
$$698$$ 37254.0 2.02018
$$699$$ 0 0
$$700$$ 0 0
$$701$$ −25830.0 −1.39171 −0.695853 0.718184i $$-0.744973\pi$$
−0.695853 + 0.718184i $$0.744973\pi$$
$$702$$ 0 0
$$703$$ 49352.0 2.64772
$$704$$ 15588.0 0.834510
$$705$$ 0 0
$$706$$ 23490.0 1.25221
$$707$$ 2898.00 0.154159
$$708$$ 0 0
$$709$$ −6226.00 −0.329792 −0.164896 0.986311i $$-0.552729\pi$$
−0.164896 + 0.986311i $$0.552729\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ −7434.00 −0.391293
$$713$$ 0 0
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 2316.00 0.120884
$$717$$ 0 0
$$718$$ −27936.0 −1.45204
$$719$$ 15072.0 0.781767 0.390884 0.920440i $$-0.372169\pi$$
0.390884 + 0.920440i $$0.372169\pi$$
$$720$$ 0 0
$$721$$ 392.000 0.0202480
$$722$$ −25551.0 −1.31705
$$723$$ 0 0
$$724$$ −106.000 −0.00544124
$$725$$ 0 0
$$726$$ 0 0
$$727$$ 32920.0 1.67942 0.839708 0.543038i $$-0.182726\pi$$
0.839708 + 0.543038i $$0.182726\pi$$
$$728$$ −4998.00 −0.254448
$$729$$ 0 0
$$730$$ 0 0
$$731$$ 11256.0 0.569519
$$732$$ 0 0
$$733$$ 6946.00 0.350009 0.175004 0.984568i $$-0.444006\pi$$
0.175004 + 0.984568i $$0.444006\pi$$
$$734$$ −11280.0 −0.567238
$$735$$ 0 0
$$736$$ 0 0
$$737$$ −3312.00 −0.165535
$$738$$ 0 0
$$739$$ −2356.00 −0.117276 −0.0586379 0.998279i $$-0.518676\pi$$
−0.0586379 + 0.998279i $$0.518676\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ −10458.0 −0.517419
$$743$$ −23520.0 −1.16133 −0.580663 0.814144i $$-0.697207\pi$$
−0.580663 + 0.814144i $$0.697207\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ 17610.0 0.864273
$$747$$ 0 0
$$748$$ 1512.00 0.0739094
$$749$$ −84.0000 −0.00409785
$$750$$ 0 0
$$751$$ 3008.00 0.146156 0.0730782 0.997326i $$-0.476718\pi$$
0.0730782 + 0.997326i $$0.476718\pi$$
$$752$$ −17040.0 −0.826310
$$753$$ 0 0
$$754$$ 10404.0 0.502508
$$755$$ 0 0
$$756$$ 0 0
$$757$$ 20770.0 0.997224 0.498612 0.866825i $$-0.333843\pi$$
0.498612 + 0.866825i $$0.333843\pi$$
$$758$$ 5556.00 0.266231
$$759$$ 0 0
$$760$$ 0 0
$$761$$ −11538.0 −0.549609 −0.274804 0.961500i $$-0.588613\pi$$
−0.274804 + 0.961500i $$0.588613\pi$$
$$762$$ 0 0
$$763$$ −10346.0 −0.490892
$$764$$ 1128.00 0.0534157
$$765$$ 0 0
$$766$$ −6480.00 −0.305655
$$767$$ 4488.00 0.211281
$$768$$ 0 0
$$769$$ 8498.00 0.398499 0.199249 0.979949i $$-0.436150\pi$$
0.199249 + 0.979949i $$0.436150\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ −4034.00 −0.188066
$$773$$ −32322.0 −1.50393 −0.751967 0.659200i $$-0.770895\pi$$
−0.751967 + 0.659200i $$0.770895\pi$$
$$774$$ 0 0
$$775$$ 0 0
$$776$$ 6006.00 0.277839
$$777$$ 0 0
$$778$$ −20358.0 −0.938136
$$779$$ −39432.0 −1.81360
$$780$$ 0 0
$$781$$ 25920.0 1.18757
$$782$$ 0 0
$$783$$ 0 0
$$784$$ −3479.00 −0.158482
$$785$$ 0 0
$$786$$ 0 0
$$787$$ −26228.0 −1.18796 −0.593982 0.804479i $$-0.702445\pi$$
−0.593982 + 0.804479i $$0.702445\pi$$
$$788$$ −1314.00 −0.0594027
$$789$$ 0 0
$$790$$ 0 0
$$791$$ −2814.00 −0.126491
$$792$$ 0 0
$$793$$ 13532.0 0.605972
$$794$$ −19542.0 −0.873450
$$795$$ 0 0
$$796$$ 5096.00 0.226913
$$797$$ −43338.0 −1.92611 −0.963056 0.269302i $$-0.913207\pi$$
−0.963056 + 0.269302i $$0.913207\pi$$
$$798$$ 0 0
$$799$$ 10080.0 0.446314
$$800$$ 0 0
$$801$$ 0 0
$$802$$ 9990.00 0.439849
$$803$$ 18072.0 0.794206
$$804$$ 0 0
$$805$$ 0 0
$$806$$ 16320.0 0.713210
$$807$$ 0 0
$$808$$ −8694.00 −0.378532
$$809$$ 28902.0 1.25604 0.628022 0.778195i $$-0.283865\pi$$
0.628022 + 0.778195i $$0.283865\pi$$
$$810$$ 0 0
$$811$$ 27164.0 1.17615 0.588075 0.808807i $$-0.299886\pi$$
0.588075 + 0.808807i $$0.299886\pi$$
$$812$$ 714.000 0.0308577
$$813$$ 0 0
$$814$$ 42984.0 1.85085
$$815$$ 0 0
$$816$$ 0 0
$$817$$ −33232.0 −1.42306
$$818$$ 16194.0 0.692188
$$819$$ 0 0
$$820$$ 0 0
$$821$$ 17202.0 0.731247 0.365624 0.930763i $$-0.380856\pi$$
0.365624 + 0.930763i $$0.380856\pi$$
$$822$$ 0 0
$$823$$ 5992.00 0.253789 0.126894 0.991916i $$-0.459499\pi$$
0.126894 + 0.991916i $$0.459499\pi$$
$$824$$ −1176.00 −0.0497183
$$825$$ 0 0
$$826$$ 2772.00 0.116768
$$827$$ 25884.0 1.08836 0.544181 0.838968i $$-0.316841\pi$$
0.544181 + 0.838968i $$0.316841\pi$$
$$828$$ 0 0
$$829$$ −1474.00 −0.0617541 −0.0308770 0.999523i $$-0.509830\pi$$
−0.0308770 + 0.999523i $$0.509830\pi$$
$$830$$ 0 0
$$831$$ 0 0
$$832$$ 14722.0 0.613454
$$833$$ 2058.00 0.0856008
$$834$$ 0 0
$$835$$ 0 0
$$836$$ −4464.00 −0.184678
$$837$$ 0 0
$$838$$ 39276.0 1.61905
$$839$$ −33528.0 −1.37964 −0.689818 0.723983i $$-0.742310\pi$$
−0.689818 + 0.723983i $$0.742310\pi$$
$$840$$ 0 0
$$841$$ −13985.0 −0.573414
$$842$$ 966.000 0.0395375
$$843$$ 0 0
$$844$$ −3076.00 −0.125451
$$845$$ 0 0
$$846$$ 0 0
$$847$$ 245.000 0.00993896
$$848$$ 35358.0 1.43184
$$849$$ 0 0
$$850$$ 0 0
$$851$$ 0 0
$$852$$ 0 0
$$853$$ −1190.00 −0.0477665 −0.0238832 0.999715i $$-0.507603\pi$$
−0.0238832 + 0.999715i $$0.507603\pi$$
$$854$$ 8358.00 0.334900
$$855$$ 0 0
$$856$$ 252.000 0.0100621
$$857$$ 34578.0 1.37825 0.689126 0.724642i $$-0.257995\pi$$
0.689126 + 0.724642i $$0.257995\pi$$
$$858$$ 0 0
$$859$$ −44404.0 −1.76373 −0.881865 0.471501i $$-0.843712\pi$$
−0.881865 + 0.471501i $$0.843712\pi$$
$$860$$ 0 0
$$861$$ 0 0
$$862$$ 7848.00 0.310097
$$863$$ −38328.0 −1.51182 −0.755910 0.654676i $$-0.772805\pi$$
−0.755910 + 0.654676i $$0.772805\pi$$
$$864$$ 0 0
$$865$$ 0 0
$$866$$ 12966.0 0.508779
$$867$$ 0 0
$$868$$ 1120.00 0.0437964
$$869$$ −36864.0 −1.43904
$$870$$ 0 0
$$871$$ −3128.00 −0.121686
$$872$$ 31038.0 1.20537
$$873$$ 0 0
$$874$$ 0 0
$$875$$ 0 0
$$876$$ 0 0
$$877$$ 38842.0 1.49555 0.747777 0.663950i $$-0.231121\pi$$
0.747777 + 0.663950i $$0.231121\pi$$
$$878$$ 27048.0 1.03966
$$879$$ 0 0
$$880$$ 0 0
$$881$$ 35046.0 1.34022 0.670108 0.742264i $$-0.266248\pi$$
0.670108 + 0.742264i $$0.266248\pi$$
$$882$$ 0 0
$$883$$ −14204.0 −0.541339 −0.270670 0.962672i $$-0.587245\pi$$
−0.270670 + 0.962672i $$0.587245\pi$$
$$884$$ 1428.00 0.0543313
$$885$$ 0 0
$$886$$ 15804.0 0.599262
$$887$$ −26136.0 −0.989359 −0.494679 0.869076i $$-0.664714\pi$$
−0.494679 + 0.869076i $$0.664714\pi$$
$$888$$ 0 0
$$889$$ 8960.00 0.338030
$$890$$ 0 0
$$891$$ 0 0
$$892$$ 1888.00 0.0708687
$$893$$ −29760.0 −1.11521
$$894$$ 0 0
$$895$$ 0 0
$$896$$ 11613.0 0.432995
$$897$$ 0 0
$$898$$ −15930.0 −0.591972
$$899$$ 16320.0 0.605453
$$900$$ 0 0
$$901$$ −20916.0 −0.773377
$$902$$ −34344.0 −1.26777
$$903$$ 0 0
$$904$$ 8442.00 0.310594
$$905$$ 0 0
$$906$$ 0 0
$$907$$ 9052.00 0.331386 0.165693 0.986177i $$-0.447014\pi$$
0.165693 + 0.986177i $$0.447014\pi$$
$$908$$ −4716.00 −0.172363
$$909$$ 0 0
$$910$$ 0 0
$$911$$ −5016.00 −0.182423 −0.0912116 0.995832i $$-0.529074\pi$$
−0.0912116 + 0.995832i $$0.529074\pi$$
$$912$$ 0 0
$$913$$ −7344.00 −0.266211
$$914$$ 47310.0 1.71212
$$915$$ 0 0
$$916$$ −1690.00 −0.0609598
$$917$$ 12348.0 0.444675
$$918$$ 0 0
$$919$$ 44552.0 1.59917 0.799584 0.600555i $$-0.205054\pi$$
0.799584 + 0.600555i $$0.205054\pi$$
$$920$$ 0 0
$$921$$ 0 0
$$922$$ −16110.0 −0.575439
$$923$$ 24480.0 0.872989
$$924$$ 0 0
$$925$$ 0 0
$$926$$ −9984.00 −0.354314
$$927$$ 0 0
$$928$$ −4590.00 −0.162364
$$929$$ −24234.0 −0.855858 −0.427929 0.903812i $$-0.640757\pi$$
−0.427929 + 0.903812i $$0.640757\pi$$
$$930$$ 0 0
$$931$$ −6076.00 −0.213891
$$932$$ 138.000 0.00485015
$$933$$ 0 0
$$934$$ −13644.0 −0.477993
$$935$$ 0 0
$$936$$ 0 0
$$937$$ 13894.0 0.484415 0.242208 0.970224i $$-0.422128\pi$$
0.242208 + 0.970224i $$0.422128\pi$$
$$938$$ −1932.00 −0.0672516
$$939$$ 0 0
$$940$$ 0 0
$$941$$ −46758.0 −1.61984 −0.809919 0.586542i $$-0.800489\pi$$
−0.809919 + 0.586542i $$0.800489\pi$$
$$942$$ 0 0
$$943$$ 0 0
$$944$$ −9372.00 −0.323128
$$945$$ 0 0
$$946$$ −28944.0 −0.994768
$$947$$ 13812.0 0.473949 0.236974 0.971516i $$-0.423844\pi$$
0.236974 + 0.971516i $$0.423844\pi$$
$$948$$ 0 0
$$949$$ 17068.0 0.583826
$$950$$ 0 0
$$951$$ 0 0
$$952$$ −6174.00 −0.210190
$$953$$ −58518.0 −1.98907 −0.994535 0.104402i $$-0.966707\pi$$
−0.994535 + 0.104402i $$0.966707\pi$$
$$954$$ 0 0
$$955$$ 0 0
$$956$$ −1896.00 −0.0641433
$$957$$ 0 0
$$958$$ −24192.0 −0.815875
$$959$$ 16506.0 0.555794
$$960$$ 0 0
$$961$$ −4191.00 −0.140680
$$962$$ 40596.0 1.36057
$$963$$ 0 0
$$964$$ −3598.00 −0.120211
$$965$$ 0 0
$$966$$ 0 0
$$967$$ −19640.0 −0.653133 −0.326567 0.945174i $$-0.605892\pi$$
−0.326567 + 0.945174i $$0.605892\pi$$
$$968$$ −735.000 −0.0244047
$$969$$ 0 0
$$970$$ 0 0
$$971$$ 58308.0 1.92708 0.963539 0.267568i $$-0.0862200\pi$$
0.963539 + 0.267568i $$0.0862200\pi$$
$$972$$ 0 0
$$973$$ 364.000 0.0119931
$$974$$ 49848.0 1.63987
$$975$$ 0 0
$$976$$ −28258.0 −0.926759
$$977$$ −23550.0 −0.771168 −0.385584 0.922673i $$-0.626000\pi$$
−0.385584 + 0.922673i $$0.626000\pi$$
$$978$$ 0 0
$$979$$ −12744.0 −0.416037
$$980$$ 0 0
$$981$$ 0 0
$$982$$ −21420.0 −0.696069
$$983$$ 15768.0 0.511619 0.255809 0.966727i $$-0.417658\pi$$
0.255809 + 0.966727i $$0.417658\pi$$
$$984$$ 0 0
$$985$$ 0 0
$$986$$ 12852.0 0.415102
$$987$$ 0 0
$$988$$ −4216.00 −0.135758
$$989$$ 0 0
$$990$$ 0 0
$$991$$ 35264.0 1.13037 0.565186 0.824964i $$-0.308805\pi$$
0.565186 + 0.824964i $$0.308805\pi$$
$$992$$ −7200.00 −0.230444
$$993$$ 0 0
$$994$$ 15120.0 0.482472
$$995$$ 0 0
$$996$$ 0 0
$$997$$ 29338.0 0.931940 0.465970 0.884801i $$-0.345706\pi$$
0.465970 + 0.884801i $$0.345706\pi$$
$$998$$ 27372.0 0.868182
$$999$$ 0 0
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 1575.4.a.b.1.1 1
3.2 odd 2 525.4.a.g.1.1 1
5.4 even 2 63.4.a.c.1.1 1
15.2 even 4 525.4.d.c.274.2 2
15.8 even 4 525.4.d.c.274.1 2
15.14 odd 2 21.4.a.a.1.1 1
20.19 odd 2 1008.4.a.v.1.1 1
35.4 even 6 441.4.e.b.226.1 2
35.9 even 6 441.4.e.b.361.1 2
35.19 odd 6 441.4.e.d.361.1 2
35.24 odd 6 441.4.e.d.226.1 2
35.34 odd 2 441.4.a.j.1.1 1
60.59 even 2 336.4.a.f.1.1 1
105.44 odd 6 147.4.e.i.67.1 2
105.59 even 6 147.4.e.g.79.1 2
105.74 odd 6 147.4.e.i.79.1 2
105.89 even 6 147.4.e.g.67.1 2
105.104 even 2 147.4.a.c.1.1 1
120.29 odd 2 1344.4.a.ba.1.1 1
120.59 even 2 1344.4.a.n.1.1 1
420.419 odd 2 2352.4.a.r.1.1 1

By twisted newform
Twist Min Dim Char Parity Ord Type
21.4.a.a.1.1 1 15.14 odd 2
63.4.a.c.1.1 1 5.4 even 2
147.4.a.c.1.1 1 105.104 even 2
147.4.e.g.67.1 2 105.89 even 6
147.4.e.g.79.1 2 105.59 even 6
147.4.e.i.67.1 2 105.44 odd 6
147.4.e.i.79.1 2 105.74 odd 6
336.4.a.f.1.1 1 60.59 even 2
441.4.a.j.1.1 1 35.34 odd 2
441.4.e.b.226.1 2 35.4 even 6
441.4.e.b.361.1 2 35.9 even 6
441.4.e.d.226.1 2 35.24 odd 6
441.4.e.d.361.1 2 35.19 odd 6
525.4.a.g.1.1 1 3.2 odd 2
525.4.d.c.274.1 2 15.8 even 4
525.4.d.c.274.2 2 15.2 even 4
1008.4.a.v.1.1 1 20.19 odd 2
1344.4.a.n.1.1 1 120.59 even 2
1344.4.a.ba.1.1 1 120.29 odd 2
1575.4.a.b.1.1 1 1.1 even 1 trivial
2352.4.a.r.1.1 1 420.419 odd 2