# Properties

 Label 720.4.a.x.1.1 Level $720$ Weight $4$ Character 720.1 Self dual yes Analytic conductor $42.481$ Analytic rank $1$ Dimension $1$ CM no Inner twists $1$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$720 = 2^{4} \cdot 3^{2} \cdot 5$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 720.a (trivial)

## Newform invariants

 Self dual: yes Analytic conductor: $$42.4813752041$$ Analytic rank: $$1$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 360) Fricke sign: $$-1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

 Embedding label 1.1 Character $$\chi$$ $$=$$ 720.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+5.00000 q^{5} -2.00000 q^{7} +O(q^{10})$$ $$q+5.00000 q^{5} -2.00000 q^{7} +34.0000 q^{11} -68.0000 q^{13} -38.0000 q^{17} -4.00000 q^{19} -152.000 q^{23} +25.0000 q^{25} -46.0000 q^{29} +260.000 q^{31} -10.0000 q^{35} -312.000 q^{37} +48.0000 q^{41} +200.000 q^{43} -104.000 q^{47} -339.000 q^{49} -414.000 q^{53} +170.000 q^{55} +2.00000 q^{59} -38.0000 q^{61} -340.000 q^{65} +244.000 q^{67} -708.000 q^{71} -378.000 q^{73} -68.0000 q^{77} +852.000 q^{79} -844.000 q^{83} -190.000 q^{85} -1380.00 q^{89} +136.000 q^{91} -20.0000 q^{95} +514.000 q^{97} +O(q^{100})$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0 0
$$3$$ 0 0
$$4$$ 0 0
$$5$$ 5.00000 0.447214
$$6$$ 0 0
$$7$$ −2.00000 −0.107990 −0.0539949 0.998541i $$-0.517195\pi$$
−0.0539949 + 0.998541i $$0.517195\pi$$
$$8$$ 0 0
$$9$$ 0 0
$$10$$ 0 0
$$11$$ 34.0000 0.931944 0.465972 0.884799i $$-0.345705\pi$$
0.465972 + 0.884799i $$0.345705\pi$$
$$12$$ 0 0
$$13$$ −68.0000 −1.45075 −0.725377 0.688352i $$-0.758335\pi$$
−0.725377 + 0.688352i $$0.758335\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ −38.0000 −0.542138 −0.271069 0.962560i $$-0.587377\pi$$
−0.271069 + 0.962560i $$0.587377\pi$$
$$18$$ 0 0
$$19$$ −4.00000 −0.0482980 −0.0241490 0.999708i $$-0.507688\pi$$
−0.0241490 + 0.999708i $$0.507688\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 0 0
$$23$$ −152.000 −1.37801 −0.689004 0.724757i $$-0.741952\pi$$
−0.689004 + 0.724757i $$0.741952\pi$$
$$24$$ 0 0
$$25$$ 25.0000 0.200000
$$26$$ 0 0
$$27$$ 0 0
$$28$$ 0 0
$$29$$ −46.0000 −0.294551 −0.147276 0.989095i $$-0.547050\pi$$
−0.147276 + 0.989095i $$0.547050\pi$$
$$30$$ 0 0
$$31$$ 260.000 1.50637 0.753184 0.657810i $$-0.228517\pi$$
0.753184 + 0.657810i $$0.228517\pi$$
$$32$$ 0 0
$$33$$ 0 0
$$34$$ 0 0
$$35$$ −10.0000 −0.0482945
$$36$$ 0 0
$$37$$ −312.000 −1.38628 −0.693142 0.720801i $$-0.743774\pi$$
−0.693142 + 0.720801i $$0.743774\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 0 0
$$41$$ 48.0000 0.182838 0.0914188 0.995813i $$-0.470860\pi$$
0.0914188 + 0.995813i $$0.470860\pi$$
$$42$$ 0 0
$$43$$ 200.000 0.709296 0.354648 0.935000i $$-0.384601\pi$$
0.354648 + 0.935000i $$0.384601\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ −104.000 −0.322765 −0.161383 0.986892i $$-0.551595\pi$$
−0.161383 + 0.986892i $$0.551595\pi$$
$$48$$ 0 0
$$49$$ −339.000 −0.988338
$$50$$ 0 0
$$51$$ 0 0
$$52$$ 0 0
$$53$$ −414.000 −1.07297 −0.536484 0.843911i $$-0.680248\pi$$
−0.536484 + 0.843911i $$0.680248\pi$$
$$54$$ 0 0
$$55$$ 170.000 0.416778
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 0 0
$$59$$ 2.00000 0.00441318 0.00220659 0.999998i $$-0.499298\pi$$
0.00220659 + 0.999998i $$0.499298\pi$$
$$60$$ 0 0
$$61$$ −38.0000 −0.0797607 −0.0398803 0.999204i $$-0.512698\pi$$
−0.0398803 + 0.999204i $$0.512698\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 0 0
$$65$$ −340.000 −0.648797
$$66$$ 0 0
$$67$$ 244.000 0.444916 0.222458 0.974942i $$-0.428592\pi$$
0.222458 + 0.974942i $$0.428592\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ 0 0
$$71$$ −708.000 −1.18344 −0.591719 0.806144i $$-0.701551\pi$$
−0.591719 + 0.806144i $$0.701551\pi$$
$$72$$ 0 0
$$73$$ −378.000 −0.606049 −0.303024 0.952983i $$-0.597996\pi$$
−0.303024 + 0.952983i $$0.597996\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 0 0
$$77$$ −68.0000 −0.100641
$$78$$ 0 0
$$79$$ 852.000 1.21339 0.606693 0.794936i $$-0.292496\pi$$
0.606693 + 0.794936i $$0.292496\pi$$
$$80$$ 0 0
$$81$$ 0 0
$$82$$ 0 0
$$83$$ −844.000 −1.11616 −0.558079 0.829788i $$-0.688461\pi$$
−0.558079 + 0.829788i $$0.688461\pi$$
$$84$$ 0 0
$$85$$ −190.000 −0.242452
$$86$$ 0 0
$$87$$ 0 0
$$88$$ 0 0
$$89$$ −1380.00 −1.64359 −0.821796 0.569782i $$-0.807028\pi$$
−0.821796 + 0.569782i $$0.807028\pi$$
$$90$$ 0 0
$$91$$ 136.000 0.156667
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 0 0
$$95$$ −20.0000 −0.0215995
$$96$$ 0 0
$$97$$ 514.000 0.538029 0.269014 0.963136i $$-0.413302\pi$$
0.269014 + 0.963136i $$0.413302\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ 0 0
$$101$$ −702.000 −0.691600 −0.345800 0.938308i $$-0.612392\pi$$
−0.345800 + 0.938308i $$0.612392\pi$$
$$102$$ 0 0
$$103$$ −898.000 −0.859054 −0.429527 0.903054i $$-0.641320\pi$$
−0.429527 + 0.903054i $$0.641320\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ −876.000 −0.791459 −0.395730 0.918367i $$-0.629508\pi$$
−0.395730 + 0.918367i $$0.629508\pi$$
$$108$$ 0 0
$$109$$ 602.000 0.529001 0.264501 0.964386i $$-0.414793\pi$$
0.264501 + 0.964386i $$0.414793\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 0 0
$$113$$ 1350.00 1.12387 0.561935 0.827181i $$-0.310057\pi$$
0.561935 + 0.827181i $$0.310057\pi$$
$$114$$ 0 0
$$115$$ −760.000 −0.616264
$$116$$ 0 0
$$117$$ 0 0
$$118$$ 0 0
$$119$$ 76.0000 0.0585455
$$120$$ 0 0
$$121$$ −175.000 −0.131480
$$122$$ 0 0
$$123$$ 0 0
$$124$$ 0 0
$$125$$ 125.000 0.0894427
$$126$$ 0 0
$$127$$ 366.000 0.255726 0.127863 0.991792i $$-0.459188\pi$$
0.127863 + 0.991792i $$0.459188\pi$$
$$128$$ 0 0
$$129$$ 0 0
$$130$$ 0 0
$$131$$ −498.000 −0.332141 −0.166070 0.986114i $$-0.553108\pi$$
−0.166070 + 0.986114i $$0.553108\pi$$
$$132$$ 0 0
$$133$$ 8.00000 0.00521570
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ −2026.00 −1.26345 −0.631726 0.775192i $$-0.717653\pi$$
−0.631726 + 0.775192i $$0.717653\pi$$
$$138$$ 0 0
$$139$$ −2460.00 −1.50111 −0.750556 0.660807i $$-0.770214\pi$$
−0.750556 + 0.660807i $$0.770214\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ −2312.00 −1.35202
$$144$$ 0 0
$$145$$ −230.000 −0.131727
$$146$$ 0 0
$$147$$ 0 0
$$148$$ 0 0
$$149$$ −3362.00 −1.84850 −0.924248 0.381794i $$-0.875306\pi$$
−0.924248 + 0.381794i $$0.875306\pi$$
$$150$$ 0 0
$$151$$ −2096.00 −1.12960 −0.564802 0.825227i $$-0.691047\pi$$
−0.564802 + 0.825227i $$0.691047\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0 0
$$155$$ 1300.00 0.673668
$$156$$ 0 0
$$157$$ 2092.00 1.06344 0.531719 0.846921i $$-0.321546\pi$$
0.531719 + 0.846921i $$0.321546\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 0 0
$$161$$ 304.000 0.148811
$$162$$ 0 0
$$163$$ −244.000 −0.117249 −0.0586244 0.998280i $$-0.518671\pi$$
−0.0586244 + 0.998280i $$0.518671\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ −2064.00 −0.956390 −0.478195 0.878254i $$-0.658709\pi$$
−0.478195 + 0.878254i $$0.658709\pi$$
$$168$$ 0 0
$$169$$ 2427.00 1.10469
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 0 0
$$173$$ 1258.00 0.552855 0.276428 0.961035i $$-0.410849\pi$$
0.276428 + 0.961035i $$0.410849\pi$$
$$174$$ 0 0
$$175$$ −50.0000 −0.0215980
$$176$$ 0 0
$$177$$ 0 0
$$178$$ 0 0
$$179$$ 3986.00 1.66440 0.832200 0.554475i $$-0.187081\pi$$
0.832200 + 0.554475i $$0.187081\pi$$
$$180$$ 0 0
$$181$$ 2570.00 1.05540 0.527698 0.849432i $$-0.323055\pi$$
0.527698 + 0.849432i $$0.323055\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 0 0
$$185$$ −1560.00 −0.619965
$$186$$ 0 0
$$187$$ −1292.00 −0.505243
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ −4684.00 −1.77446 −0.887231 0.461325i $$-0.847374\pi$$
−0.887231 + 0.461325i $$0.847374\pi$$
$$192$$ 0 0
$$193$$ 214.000 0.0798138 0.0399069 0.999203i $$-0.487294\pi$$
0.0399069 + 0.999203i $$0.487294\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ 3014.00 1.09004 0.545022 0.838422i $$-0.316521\pi$$
0.545022 + 0.838422i $$0.316521\pi$$
$$198$$ 0 0
$$199$$ 1792.00 0.638349 0.319175 0.947696i $$-0.396594\pi$$
0.319175 + 0.947696i $$0.396594\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ 0 0
$$203$$ 92.0000 0.0318085
$$204$$ 0 0
$$205$$ 240.000 0.0817674
$$206$$ 0 0
$$207$$ 0 0
$$208$$ 0 0
$$209$$ −136.000 −0.0450111
$$210$$ 0 0
$$211$$ 4540.00 1.48126 0.740631 0.671911i $$-0.234526\pi$$
0.740631 + 0.671911i $$0.234526\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 0 0
$$215$$ 1000.00 0.317207
$$216$$ 0 0
$$217$$ −520.000 −0.162672
$$218$$ 0 0
$$219$$ 0 0
$$220$$ 0 0
$$221$$ 2584.00 0.786510
$$222$$ 0 0
$$223$$ −6506.00 −1.95369 −0.976847 0.213937i $$-0.931371\pi$$
−0.976847 + 0.213937i $$0.931371\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ 3696.00 1.08067 0.540335 0.841450i $$-0.318297\pi$$
0.540335 + 0.841450i $$0.318297\pi$$
$$228$$ 0 0
$$229$$ −3386.00 −0.977088 −0.488544 0.872539i $$-0.662472\pi$$
−0.488544 + 0.872539i $$0.662472\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ 3306.00 0.929542 0.464771 0.885431i $$-0.346137\pi$$
0.464771 + 0.885431i $$0.346137\pi$$
$$234$$ 0 0
$$235$$ −520.000 −0.144345
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 0 0
$$239$$ 4188.00 1.13347 0.566735 0.823900i $$-0.308206\pi$$
0.566735 + 0.823900i $$0.308206\pi$$
$$240$$ 0 0
$$241$$ 5462.00 1.45991 0.729955 0.683495i $$-0.239541\pi$$
0.729955 + 0.683495i $$0.239541\pi$$
$$242$$ 0 0
$$243$$ 0 0
$$244$$ 0 0
$$245$$ −1695.00 −0.441998
$$246$$ 0 0
$$247$$ 272.000 0.0700686
$$248$$ 0 0
$$249$$ 0 0
$$250$$ 0 0
$$251$$ 3366.00 0.846454 0.423227 0.906024i $$-0.360897\pi$$
0.423227 + 0.906024i $$0.360897\pi$$
$$252$$ 0 0
$$253$$ −5168.00 −1.28423
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ 1158.00 0.281066 0.140533 0.990076i $$-0.455118\pi$$
0.140533 + 0.990076i $$0.455118\pi$$
$$258$$ 0 0
$$259$$ 624.000 0.149705
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 0 0
$$263$$ −8304.00 −1.94695 −0.973473 0.228804i $$-0.926519\pi$$
−0.973473 + 0.228804i $$0.926519\pi$$
$$264$$ 0 0
$$265$$ −2070.00 −0.479846
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 0 0
$$269$$ −7478.00 −1.69495 −0.847475 0.530835i $$-0.821878\pi$$
−0.847475 + 0.530835i $$0.821878\pi$$
$$270$$ 0 0
$$271$$ 6792.00 1.52245 0.761226 0.648486i $$-0.224598\pi$$
0.761226 + 0.648486i $$0.224598\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ 850.000 0.186389
$$276$$ 0 0
$$277$$ −2296.00 −0.498026 −0.249013 0.968500i $$-0.580106\pi$$
−0.249013 + 0.968500i $$0.580106\pi$$
$$278$$ 0 0
$$279$$ 0 0
$$280$$ 0 0
$$281$$ 3980.00 0.844936 0.422468 0.906378i $$-0.361164\pi$$
0.422468 + 0.906378i $$0.361164\pi$$
$$282$$ 0 0
$$283$$ 1972.00 0.414216 0.207108 0.978318i $$-0.433595\pi$$
0.207108 + 0.978318i $$0.433595\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ −96.0000 −0.0197446
$$288$$ 0 0
$$289$$ −3469.00 −0.706086
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 0 0
$$293$$ 9254.00 1.84513 0.922567 0.385836i $$-0.126087\pi$$
0.922567 + 0.385836i $$0.126087\pi$$
$$294$$ 0 0
$$295$$ 10.0000 0.00197364
$$296$$ 0 0
$$297$$ 0 0
$$298$$ 0 0
$$299$$ 10336.0 1.99915
$$300$$ 0 0
$$301$$ −400.000 −0.0765967
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 0 0
$$305$$ −190.000 −0.0356701
$$306$$ 0 0
$$307$$ 5888.00 1.09461 0.547306 0.836933i $$-0.315653\pi$$
0.547306 + 0.836933i $$0.315653\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 0 0
$$311$$ 4604.00 0.839450 0.419725 0.907651i $$-0.362127\pi$$
0.419725 + 0.907651i $$0.362127\pi$$
$$312$$ 0 0
$$313$$ −8026.00 −1.44938 −0.724691 0.689074i $$-0.758017\pi$$
−0.724691 + 0.689074i $$0.758017\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ 2838.00 0.502833 0.251416 0.967879i $$-0.419104\pi$$
0.251416 + 0.967879i $$0.419104\pi$$
$$318$$ 0 0
$$319$$ −1564.00 −0.274505
$$320$$ 0 0
$$321$$ 0 0
$$322$$ 0 0
$$323$$ 152.000 0.0261842
$$324$$ 0 0
$$325$$ −1700.00 −0.290151
$$326$$ 0 0
$$327$$ 0 0
$$328$$ 0 0
$$329$$ 208.000 0.0348554
$$330$$ 0 0
$$331$$ 1020.00 0.169378 0.0846892 0.996407i $$-0.473010\pi$$
0.0846892 + 0.996407i $$0.473010\pi$$
$$332$$ 0 0
$$333$$ 0 0
$$334$$ 0 0
$$335$$ 1220.00 0.198972
$$336$$ 0 0
$$337$$ 814.000 0.131577 0.0657884 0.997834i $$-0.479044\pi$$
0.0657884 + 0.997834i $$0.479044\pi$$
$$338$$ 0 0
$$339$$ 0 0
$$340$$ 0 0
$$341$$ 8840.00 1.40385
$$342$$ 0 0
$$343$$ 1364.00 0.214720
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ 4544.00 0.702982 0.351491 0.936191i $$-0.385675\pi$$
0.351491 + 0.936191i $$0.385675\pi$$
$$348$$ 0 0
$$349$$ 6978.00 1.07027 0.535134 0.844767i $$-0.320261\pi$$
0.535134 + 0.844767i $$0.320261\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0 0
$$353$$ 2818.00 0.424892 0.212446 0.977173i $$-0.431857\pi$$
0.212446 + 0.977173i $$0.431857\pi$$
$$354$$ 0 0
$$355$$ −3540.00 −0.529250
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ −744.000 −0.109378 −0.0546892 0.998503i $$-0.517417\pi$$
−0.0546892 + 0.998503i $$0.517417\pi$$
$$360$$ 0 0
$$361$$ −6843.00 −0.997667
$$362$$ 0 0
$$363$$ 0 0
$$364$$ 0 0
$$365$$ −1890.00 −0.271033
$$366$$ 0 0
$$367$$ 6454.00 0.917973 0.458986 0.888443i $$-0.348213\pi$$
0.458986 + 0.888443i $$0.348213\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 0 0
$$371$$ 828.000 0.115870
$$372$$ 0 0
$$373$$ −5900.00 −0.819009 −0.409505 0.912308i $$-0.634298\pi$$
−0.409505 + 0.912308i $$0.634298\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ 3128.00 0.427321
$$378$$ 0 0
$$379$$ 11876.0 1.60958 0.804788 0.593563i $$-0.202279\pi$$
0.804788 + 0.593563i $$0.202279\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 0 0
$$383$$ 552.000 0.0736446 0.0368223 0.999322i $$-0.488276\pi$$
0.0368223 + 0.999322i $$0.488276\pi$$
$$384$$ 0 0
$$385$$ −340.000 −0.0450078
$$386$$ 0 0
$$387$$ 0 0
$$388$$ 0 0
$$389$$ −1722.00 −0.224444 −0.112222 0.993683i $$-0.535797\pi$$
−0.112222 + 0.993683i $$0.535797\pi$$
$$390$$ 0 0
$$391$$ 5776.00 0.747071
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 0 0
$$395$$ 4260.00 0.542643
$$396$$ 0 0
$$397$$ 4576.00 0.578496 0.289248 0.957254i $$-0.406595\pi$$
0.289248 + 0.957254i $$0.406595\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0 0
$$401$$ 2892.00 0.360149 0.180074 0.983653i $$-0.442366\pi$$
0.180074 + 0.983653i $$0.442366\pi$$
$$402$$ 0 0
$$403$$ −17680.0 −2.18537
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ −10608.0 −1.29194
$$408$$ 0 0
$$409$$ −230.000 −0.0278063 −0.0139031 0.999903i $$-0.504426\pi$$
−0.0139031 + 0.999903i $$0.504426\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 0 0
$$413$$ −4.00000 −0.000476579 0
$$414$$ 0 0
$$415$$ −4220.00 −0.499161
$$416$$ 0 0
$$417$$ 0 0
$$418$$ 0 0
$$419$$ 15438.0 1.79999 0.899995 0.435901i $$-0.143570\pi$$
0.899995 + 0.435901i $$0.143570\pi$$
$$420$$ 0 0
$$421$$ 12294.0 1.42321 0.711607 0.702578i $$-0.247968\pi$$
0.711607 + 0.702578i $$0.247968\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ 0 0
$$425$$ −950.000 −0.108428
$$426$$ 0 0
$$427$$ 76.0000 0.00861334
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ −17488.0 −1.95445 −0.977224 0.212209i $$-0.931934\pi$$
−0.977224 + 0.212209i $$0.931934\pi$$
$$432$$ 0 0
$$433$$ −8698.00 −0.965356 −0.482678 0.875798i $$-0.660336\pi$$
−0.482678 + 0.875798i $$0.660336\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ 608.000 0.0665551
$$438$$ 0 0
$$439$$ −8536.00 −0.928021 −0.464010 0.885830i $$-0.653590\pi$$
−0.464010 + 0.885830i $$0.653590\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 0 0
$$443$$ 8712.00 0.934356 0.467178 0.884163i $$-0.345271\pi$$
0.467178 + 0.884163i $$0.345271\pi$$
$$444$$ 0 0
$$445$$ −6900.00 −0.735037
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 0 0
$$449$$ −5484.00 −0.576405 −0.288203 0.957569i $$-0.593058\pi$$
−0.288203 + 0.957569i $$0.593058\pi$$
$$450$$ 0 0
$$451$$ 1632.00 0.170394
$$452$$ 0 0
$$453$$ 0 0
$$454$$ 0 0
$$455$$ 680.000 0.0700635
$$456$$ 0 0
$$457$$ 19402.0 1.98597 0.992984 0.118250i $$-0.0377283\pi$$
0.992984 + 0.118250i $$0.0377283\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 0 0
$$461$$ −13578.0 −1.37178 −0.685890 0.727705i $$-0.740587\pi$$
−0.685890 + 0.727705i $$0.740587\pi$$
$$462$$ 0 0
$$463$$ −6222.00 −0.624537 −0.312269 0.949994i $$-0.601089\pi$$
−0.312269 + 0.949994i $$0.601089\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ 15260.0 1.51210 0.756048 0.654516i $$-0.227128\pi$$
0.756048 + 0.654516i $$0.227128\pi$$
$$468$$ 0 0
$$469$$ −488.000 −0.0480464
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0 0
$$473$$ 6800.00 0.661024
$$474$$ 0 0
$$475$$ −100.000 −0.00965961
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 0 0
$$479$$ −9812.00 −0.935953 −0.467977 0.883741i $$-0.655017\pi$$
−0.467977 + 0.883741i $$0.655017\pi$$
$$480$$ 0 0
$$481$$ 21216.0 2.01116
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 0 0
$$485$$ 2570.00 0.240614
$$486$$ 0 0
$$487$$ 7226.00 0.672364 0.336182 0.941797i $$-0.390864\pi$$
0.336182 + 0.941797i $$0.390864\pi$$
$$488$$ 0 0
$$489$$ 0 0
$$490$$ 0 0
$$491$$ 6750.00 0.620414 0.310207 0.950669i $$-0.399602\pi$$
0.310207 + 0.950669i $$0.399602\pi$$
$$492$$ 0 0
$$493$$ 1748.00 0.159688
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ 1416.00 0.127799
$$498$$ 0 0
$$499$$ 4156.00 0.372842 0.186421 0.982470i $$-0.440311\pi$$
0.186421 + 0.982470i $$0.440311\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 0 0
$$503$$ −14088.0 −1.24881 −0.624406 0.781100i $$-0.714659\pi$$
−0.624406 + 0.781100i $$0.714659\pi$$
$$504$$ 0 0
$$505$$ −3510.00 −0.309293
$$506$$ 0 0
$$507$$ 0 0
$$508$$ 0 0
$$509$$ 16970.0 1.47776 0.738882 0.673835i $$-0.235354\pi$$
0.738882 + 0.673835i $$0.235354\pi$$
$$510$$ 0 0
$$511$$ 756.000 0.0654471
$$512$$ 0 0
$$513$$ 0 0
$$514$$ 0 0
$$515$$ −4490.00 −0.384181
$$516$$ 0 0
$$517$$ −3536.00 −0.300799
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ −8500.00 −0.714763 −0.357382 0.933958i $$-0.616330\pi$$
−0.357382 + 0.933958i $$0.616330\pi$$
$$522$$ 0 0
$$523$$ −20620.0 −1.72400 −0.861998 0.506912i $$-0.830787\pi$$
−0.861998 + 0.506912i $$0.830787\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ −9880.00 −0.816660
$$528$$ 0 0
$$529$$ 10937.0 0.898907
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 0 0
$$533$$ −3264.00 −0.265252
$$534$$ 0 0
$$535$$ −4380.00 −0.353951
$$536$$ 0 0
$$537$$ 0 0
$$538$$ 0 0
$$539$$ −11526.0 −0.921076
$$540$$ 0 0
$$541$$ 5314.00 0.422304 0.211152 0.977453i $$-0.432278\pi$$
0.211152 + 0.977453i $$0.432278\pi$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ 0 0
$$545$$ 3010.00 0.236577
$$546$$ 0 0
$$547$$ −24104.0 −1.88412 −0.942059 0.335447i $$-0.891113\pi$$
−0.942059 + 0.335447i $$0.891113\pi$$
$$548$$ 0 0
$$549$$ 0 0
$$550$$ 0 0
$$551$$ 184.000 0.0142262
$$552$$ 0 0
$$553$$ −1704.00 −0.131033
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ −23582.0 −1.79390 −0.896949 0.442134i $$-0.854222\pi$$
−0.896949 + 0.442134i $$0.854222\pi$$
$$558$$ 0 0
$$559$$ −13600.0 −1.02901
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ 2680.00 0.200619 0.100310 0.994956i $$-0.468017\pi$$
0.100310 + 0.994956i $$0.468017\pi$$
$$564$$ 0 0
$$565$$ 6750.00 0.502610
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 0 0
$$569$$ −25004.0 −1.84222 −0.921109 0.389304i $$-0.872715\pi$$
−0.921109 + 0.389304i $$0.872715\pi$$
$$570$$ 0 0
$$571$$ 11180.0 0.819384 0.409692 0.912224i $$-0.365636\pi$$
0.409692 + 0.912224i $$0.365636\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ −3800.00 −0.275602
$$576$$ 0 0
$$577$$ −15862.0 −1.14444 −0.572222 0.820099i $$-0.693918\pi$$
−0.572222 + 0.820099i $$0.693918\pi$$
$$578$$ 0 0
$$579$$ 0 0
$$580$$ 0 0
$$581$$ 1688.00 0.120534
$$582$$ 0 0
$$583$$ −14076.0 −0.999946
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ −15036.0 −1.05724 −0.528622 0.848857i $$-0.677291\pi$$
−0.528622 + 0.848857i $$0.677291\pi$$
$$588$$ 0 0
$$589$$ −1040.00 −0.0727546
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 0 0
$$593$$ −12786.0 −0.885427 −0.442713 0.896663i $$-0.645984\pi$$
−0.442713 + 0.896663i $$0.645984\pi$$
$$594$$ 0 0
$$595$$ 380.000 0.0261823
$$596$$ 0 0
$$597$$ 0 0
$$598$$ 0 0
$$599$$ −13464.0 −0.918404 −0.459202 0.888332i $$-0.651865\pi$$
−0.459202 + 0.888332i $$0.651865\pi$$
$$600$$ 0 0
$$601$$ 8518.00 0.578131 0.289065 0.957309i $$-0.406656\pi$$
0.289065 + 0.957309i $$0.406656\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ 0 0
$$605$$ −875.000 −0.0587997
$$606$$ 0 0
$$607$$ 11082.0 0.741029 0.370514 0.928827i $$-0.379181\pi$$
0.370514 + 0.928827i $$0.379181\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 7072.00 0.468253
$$612$$ 0 0
$$613$$ −26568.0 −1.75052 −0.875262 0.483649i $$-0.839311\pi$$
−0.875262 + 0.483649i $$0.839311\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 3282.00 0.214146 0.107073 0.994251i $$-0.465852\pi$$
0.107073 + 0.994251i $$0.465852\pi$$
$$618$$ 0 0
$$619$$ 2308.00 0.149865 0.0749324 0.997189i $$-0.476126\pi$$
0.0749324 + 0.997189i $$0.476126\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ 2760.00 0.177491
$$624$$ 0 0
$$625$$ 625.000 0.0400000
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 0 0
$$629$$ 11856.0 0.751558
$$630$$ 0 0
$$631$$ 24572.0 1.55023 0.775116 0.631819i $$-0.217692\pi$$
0.775116 + 0.631819i $$0.217692\pi$$
$$632$$ 0 0
$$633$$ 0 0
$$634$$ 0 0
$$635$$ 1830.00 0.114364
$$636$$ 0 0
$$637$$ 23052.0 1.43384
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ 2136.00 0.131618 0.0658088 0.997832i $$-0.479037\pi$$
0.0658088 + 0.997832i $$0.479037\pi$$
$$642$$ 0 0
$$643$$ 5508.00 0.337814 0.168907 0.985632i $$-0.445976\pi$$
0.168907 + 0.985632i $$0.445976\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 4536.00 0.275624 0.137812 0.990458i $$-0.455993\pi$$
0.137812 + 0.990458i $$0.455993\pi$$
$$648$$ 0 0
$$649$$ 68.0000 0.00411284
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ −27914.0 −1.67283 −0.836416 0.548095i $$-0.815353\pi$$
−0.836416 + 0.548095i $$0.815353\pi$$
$$654$$ 0 0
$$655$$ −2490.00 −0.148538
$$656$$ 0 0
$$657$$ 0 0
$$658$$ 0 0
$$659$$ −22842.0 −1.35022 −0.675112 0.737715i $$-0.735905\pi$$
−0.675112 + 0.737715i $$0.735905\pi$$
$$660$$ 0 0
$$661$$ 16458.0 0.968445 0.484222 0.874945i $$-0.339103\pi$$
0.484222 + 0.874945i $$0.339103\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ 40.0000 0.00233253
$$666$$ 0 0
$$667$$ 6992.00 0.405894
$$668$$ 0 0
$$669$$ 0 0
$$670$$ 0 0
$$671$$ −1292.00 −0.0743325
$$672$$ 0 0
$$673$$ −16050.0 −0.919290 −0.459645 0.888103i $$-0.652023\pi$$
−0.459645 + 0.888103i $$0.652023\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ −5314.00 −0.301674 −0.150837 0.988559i $$-0.548197\pi$$
−0.150837 + 0.988559i $$0.548197\pi$$
$$678$$ 0 0
$$679$$ −1028.00 −0.0581016
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 0 0
$$683$$ 15876.0 0.889426 0.444713 0.895673i $$-0.353306\pi$$
0.444713 + 0.895673i $$0.353306\pi$$
$$684$$ 0 0
$$685$$ −10130.0 −0.565033
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 0 0
$$689$$ 28152.0 1.55661
$$690$$ 0 0
$$691$$ 13372.0 0.736172 0.368086 0.929792i $$-0.380013\pi$$
0.368086 + 0.929792i $$0.380013\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ −12300.0 −0.671317
$$696$$ 0 0
$$697$$ −1824.00 −0.0991233
$$698$$ 0 0
$$699$$ 0 0
$$700$$ 0 0
$$701$$ −3230.00 −0.174031 −0.0870153 0.996207i $$-0.527733\pi$$
−0.0870153 + 0.996207i $$0.527733\pi$$
$$702$$ 0 0
$$703$$ 1248.00 0.0669548
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ 1404.00 0.0746858
$$708$$ 0 0
$$709$$ −6154.00 −0.325978 −0.162989 0.986628i $$-0.552113\pi$$
−0.162989 + 0.986628i $$0.552113\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 0 0
$$713$$ −39520.0 −2.07579
$$714$$ 0 0
$$715$$ −11560.0 −0.604643
$$716$$ 0 0
$$717$$ 0 0
$$718$$ 0 0
$$719$$ −20264.0 −1.05107 −0.525535 0.850772i $$-0.676135\pi$$
−0.525535 + 0.850772i $$0.676135\pi$$
$$720$$ 0 0
$$721$$ 1796.00 0.0927691
$$722$$ 0 0
$$723$$ 0 0
$$724$$ 0 0
$$725$$ −1150.00 −0.0589102
$$726$$ 0 0
$$727$$ 25354.0 1.29344 0.646718 0.762729i $$-0.276141\pi$$
0.646718 + 0.762729i $$0.276141\pi$$
$$728$$ 0 0
$$729$$ 0 0
$$730$$ 0 0
$$731$$ −7600.00 −0.384536
$$732$$ 0 0
$$733$$ −13344.0 −0.672404 −0.336202 0.941790i $$-0.609142\pi$$
−0.336202 + 0.941790i $$0.609142\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 8296.00 0.414636
$$738$$ 0 0
$$739$$ 28452.0 1.41627 0.708135 0.706077i $$-0.249537\pi$$
0.708135 + 0.706077i $$0.249537\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ 5784.00 0.285591 0.142796 0.989752i $$-0.454391\pi$$
0.142796 + 0.989752i $$0.454391\pi$$
$$744$$ 0 0
$$745$$ −16810.0 −0.826672
$$746$$ 0 0
$$747$$ 0 0
$$748$$ 0 0
$$749$$ 1752.00 0.0854695
$$750$$ 0 0
$$751$$ −852.000 −0.0413980 −0.0206990 0.999786i $$-0.506589\pi$$
−0.0206990 + 0.999786i $$0.506589\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 0 0
$$755$$ −10480.0 −0.505174
$$756$$ 0 0
$$757$$ −5704.00 −0.273864 −0.136932 0.990580i $$-0.543724\pi$$
−0.136932 + 0.990580i $$0.543724\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ −24828.0 −1.18267 −0.591337 0.806425i $$-0.701400\pi$$
−0.591337 + 0.806425i $$0.701400\pi$$
$$762$$ 0 0
$$763$$ −1204.00 −0.0571268
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ −136.000 −0.00640245
$$768$$ 0 0
$$769$$ −13298.0 −0.623587 −0.311793 0.950150i $$-0.600930\pi$$
−0.311793 + 0.950150i $$0.600930\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 0 0
$$773$$ −642.000 −0.0298721 −0.0149361 0.999888i $$-0.504754\pi$$
−0.0149361 + 0.999888i $$0.504754\pi$$
$$774$$ 0 0
$$775$$ 6500.00 0.301273
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ −192.000 −0.00883070
$$780$$ 0 0
$$781$$ −24072.0 −1.10290
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 0 0
$$785$$ 10460.0 0.475584
$$786$$ 0 0
$$787$$ 20236.0 0.916564 0.458282 0.888807i $$-0.348465\pi$$
0.458282 + 0.888807i $$0.348465\pi$$
$$788$$ 0 0
$$789$$ 0 0
$$790$$ 0 0
$$791$$ −2700.00 −0.121367
$$792$$ 0 0
$$793$$ 2584.00 0.115713
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ 11562.0 0.513861 0.256930 0.966430i $$-0.417289\pi$$
0.256930 + 0.966430i $$0.417289\pi$$
$$798$$ 0 0
$$799$$ 3952.00 0.174983
$$800$$ 0 0
$$801$$ 0 0
$$802$$ 0 0
$$803$$ −12852.0 −0.564804
$$804$$ 0 0
$$805$$ 1520.00 0.0665503
$$806$$ 0 0
$$807$$ 0 0
$$808$$ 0 0
$$809$$ 18984.0 0.825021 0.412510 0.910953i $$-0.364652\pi$$
0.412510 + 0.910953i $$0.364652\pi$$
$$810$$ 0 0
$$811$$ 2332.00 0.100971 0.0504856 0.998725i $$-0.483923\pi$$
0.0504856 + 0.998725i $$0.483923\pi$$
$$812$$ 0 0
$$813$$ 0 0
$$814$$ 0 0
$$815$$ −1220.00 −0.0524353
$$816$$ 0 0
$$817$$ −800.000 −0.0342576
$$818$$ 0 0
$$819$$ 0 0
$$820$$ 0 0
$$821$$ −19126.0 −0.813035 −0.406518 0.913643i $$-0.633257\pi$$
−0.406518 + 0.913643i $$0.633257\pi$$
$$822$$ 0 0
$$823$$ −37102.0 −1.57144 −0.785720 0.618583i $$-0.787707\pi$$
−0.785720 + 0.618583i $$0.787707\pi$$
$$824$$ 0 0
$$825$$ 0 0
$$826$$ 0 0
$$827$$ 11304.0 0.475307 0.237653 0.971350i $$-0.423622\pi$$
0.237653 + 0.971350i $$0.423622\pi$$
$$828$$ 0 0
$$829$$ −974.000 −0.0408063 −0.0204031 0.999792i $$-0.506495\pi$$
−0.0204031 + 0.999792i $$0.506495\pi$$
$$830$$ 0 0
$$831$$ 0 0
$$832$$ 0 0
$$833$$ 12882.0 0.535816
$$834$$ 0 0
$$835$$ −10320.0 −0.427711
$$836$$ 0 0
$$837$$ 0 0
$$838$$ 0 0
$$839$$ −16480.0 −0.678132 −0.339066 0.940763i $$-0.610111\pi$$
−0.339066 + 0.940763i $$0.610111\pi$$
$$840$$ 0 0
$$841$$ −22273.0 −0.913240
$$842$$ 0 0
$$843$$ 0 0
$$844$$ 0 0
$$845$$ 12135.0 0.494032
$$846$$ 0 0
$$847$$ 350.000 0.0141985
$$848$$ 0 0
$$849$$ 0 0
$$850$$ 0 0
$$851$$ 47424.0 1.91031
$$852$$ 0 0
$$853$$ 11192.0 0.449246 0.224623 0.974446i $$-0.427885\pi$$
0.224623 + 0.974446i $$0.427885\pi$$
$$854$$ 0 0
$$855$$ 0 0
$$856$$ 0 0
$$857$$ −34278.0 −1.36629 −0.683147 0.730281i $$-0.739389\pi$$
−0.683147 + 0.730281i $$0.739389\pi$$
$$858$$ 0 0
$$859$$ 14020.0 0.556876 0.278438 0.960454i $$-0.410183\pi$$
0.278438 + 0.960454i $$0.410183\pi$$
$$860$$ 0 0
$$861$$ 0 0
$$862$$ 0 0
$$863$$ 30528.0 1.20415 0.602077 0.798438i $$-0.294340\pi$$
0.602077 + 0.798438i $$0.294340\pi$$
$$864$$ 0 0
$$865$$ 6290.00 0.247244
$$866$$ 0 0
$$867$$ 0 0
$$868$$ 0 0
$$869$$ 28968.0 1.13081
$$870$$ 0 0
$$871$$ −16592.0 −0.645463
$$872$$ 0 0
$$873$$ 0 0
$$874$$ 0 0
$$875$$ −250.000 −0.00965891
$$876$$ 0 0
$$877$$ 2932.00 0.112892 0.0564462 0.998406i $$-0.482023\pi$$
0.0564462 + 0.998406i $$0.482023\pi$$
$$878$$ 0 0
$$879$$ 0 0
$$880$$ 0 0
$$881$$ 7116.00 0.272127 0.136064 0.990700i $$-0.456555\pi$$
0.136064 + 0.990700i $$0.456555\pi$$
$$882$$ 0 0
$$883$$ 35140.0 1.33925 0.669624 0.742701i $$-0.266455\pi$$
0.669624 + 0.742701i $$0.266455\pi$$
$$884$$ 0 0
$$885$$ 0 0
$$886$$ 0 0
$$887$$ 20296.0 0.768290 0.384145 0.923273i $$-0.374496\pi$$
0.384145 + 0.923273i $$0.374496\pi$$
$$888$$ 0 0
$$889$$ −732.000 −0.0276159
$$890$$ 0 0
$$891$$ 0 0
$$892$$ 0 0
$$893$$ 416.000 0.0155889
$$894$$ 0 0
$$895$$ 19930.0 0.744342
$$896$$ 0 0
$$897$$ 0 0
$$898$$ 0 0
$$899$$ −11960.0 −0.443702
$$900$$ 0 0
$$901$$ 15732.0 0.581697
$$902$$ 0 0
$$903$$ 0 0
$$904$$ 0 0
$$905$$ 12850.0 0.471987
$$906$$ 0 0
$$907$$ −19512.0 −0.714317 −0.357158 0.934044i $$-0.616254\pi$$
−0.357158 + 0.934044i $$0.616254\pi$$
$$908$$ 0 0
$$909$$ 0 0
$$910$$ 0 0
$$911$$ 16720.0 0.608077 0.304039 0.952660i $$-0.401665\pi$$
0.304039 + 0.952660i $$0.401665\pi$$
$$912$$ 0 0
$$913$$ −28696.0 −1.04020
$$914$$ 0 0
$$915$$ 0 0
$$916$$ 0 0
$$917$$ 996.000 0.0358678
$$918$$ 0 0
$$919$$ −7340.00 −0.263465 −0.131732 0.991285i $$-0.542054\pi$$
−0.131732 + 0.991285i $$0.542054\pi$$
$$920$$ 0 0
$$921$$ 0 0
$$922$$ 0 0
$$923$$ 48144.0 1.71688
$$924$$ 0 0
$$925$$ −7800.00 −0.277257
$$926$$ 0 0
$$927$$ 0 0
$$928$$ 0 0
$$929$$ 48932.0 1.72810 0.864051 0.503404i $$-0.167919\pi$$
0.864051 + 0.503404i $$0.167919\pi$$
$$930$$ 0 0
$$931$$ 1356.00 0.0477348
$$932$$ 0 0
$$933$$ 0 0
$$934$$ 0 0
$$935$$ −6460.00 −0.225951
$$936$$ 0 0
$$937$$ 30298.0 1.05634 0.528171 0.849138i $$-0.322878\pi$$
0.528171 + 0.849138i $$0.322878\pi$$
$$938$$ 0 0
$$939$$ 0 0
$$940$$ 0 0
$$941$$ 8414.00 0.291486 0.145743 0.989322i $$-0.453443\pi$$
0.145743 + 0.989322i $$0.453443\pi$$
$$942$$ 0 0
$$943$$ −7296.00 −0.251952
$$944$$ 0 0
$$945$$ 0 0
$$946$$ 0 0
$$947$$ −23912.0 −0.820523 −0.410262 0.911968i $$-0.634563\pi$$
−0.410262 + 0.911968i $$0.634563\pi$$
$$948$$ 0 0
$$949$$ 25704.0 0.879228
$$950$$ 0 0
$$951$$ 0 0
$$952$$ 0 0
$$953$$ −22866.0 −0.777232 −0.388616 0.921400i $$-0.627047\pi$$
−0.388616 + 0.921400i $$0.627047\pi$$
$$954$$ 0 0
$$955$$ −23420.0 −0.793564
$$956$$ 0 0
$$957$$ 0 0
$$958$$ 0 0
$$959$$ 4052.00 0.136440
$$960$$ 0 0
$$961$$ 37809.0 1.26914
$$962$$ 0 0
$$963$$ 0 0
$$964$$ 0 0
$$965$$ 1070.00 0.0356938
$$966$$ 0 0
$$967$$ −738.000 −0.0245424 −0.0122712 0.999925i $$-0.503906\pi$$
−0.0122712 + 0.999925i $$0.503906\pi$$
$$968$$ 0 0
$$969$$ 0 0
$$970$$ 0 0
$$971$$ −44098.0 −1.45744 −0.728719 0.684813i $$-0.759884\pi$$
−0.728719 + 0.684813i $$0.759884\pi$$
$$972$$ 0 0
$$973$$ 4920.00 0.162105
$$974$$ 0 0
$$975$$ 0 0
$$976$$ 0 0
$$977$$ 34426.0 1.12731 0.563657 0.826009i $$-0.309394\pi$$
0.563657 + 0.826009i $$0.309394\pi$$
$$978$$ 0 0
$$979$$ −46920.0 −1.53174
$$980$$ 0 0
$$981$$ 0 0
$$982$$ 0 0
$$983$$ 30216.0 0.980408 0.490204 0.871608i $$-0.336922\pi$$
0.490204 + 0.871608i $$0.336922\pi$$
$$984$$ 0 0
$$985$$ 15070.0 0.487482
$$986$$ 0 0
$$987$$ 0 0
$$988$$ 0 0
$$989$$ −30400.0 −0.977415
$$990$$ 0 0
$$991$$ −4592.00 −0.147194 −0.0735972 0.997288i $$-0.523448\pi$$
−0.0735972 + 0.997288i $$0.523448\pi$$
$$992$$ 0 0
$$993$$ 0 0
$$994$$ 0 0
$$995$$ 8960.00 0.285478
$$996$$ 0 0
$$997$$ −24276.0 −0.771142 −0.385571 0.922678i $$-0.625996\pi$$
−0.385571 + 0.922678i $$0.625996\pi$$
$$998$$ 0 0
$$999$$ 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 720.4.a.x.1.1 1
3.2 odd 2 720.4.a.g.1.1 1
4.3 odd 2 360.4.a.k.1.1 yes 1
12.11 even 2 360.4.a.d.1.1 1
20.3 even 4 1800.4.f.f.649.1 2
20.7 even 4 1800.4.f.f.649.2 2
20.19 odd 2 1800.4.a.q.1.1 1
60.23 odd 4 1800.4.f.t.649.1 2
60.47 odd 4 1800.4.f.t.649.2 2
60.59 even 2 1800.4.a.r.1.1 1

By twisted newform
Twist Min Dim Char Parity Ord Type
360.4.a.d.1.1 1 12.11 even 2
360.4.a.k.1.1 yes 1 4.3 odd 2
720.4.a.g.1.1 1 3.2 odd 2
720.4.a.x.1.1 1 1.1 even 1 trivial
1800.4.a.q.1.1 1 20.19 odd 2
1800.4.a.r.1.1 1 60.59 even 2
1800.4.f.f.649.1 2 20.3 even 4
1800.4.f.f.649.2 2 20.7 even 4
1800.4.f.t.649.1 2 60.23 odd 4
1800.4.f.t.649.2 2 60.47 odd 4