Properties

 Label 72.6.a.e.1.1 Level $72$ Weight $6$ Character 72.1 Self dual yes Analytic conductor $11.548$ Analytic rank $1$ Dimension $1$ CM no Inner twists $1$

Related objects

Newspace parameters

 Level: $$N$$ $$=$$ $$72 = 2^{3} \cdot 3^{2}$$ Weight: $$k$$ $$=$$ $$6$$ Character orbit: $$[\chi]$$ $$=$$ 72.a (trivial)

Newform invariants

 Self dual: yes Analytic conductor: $$11.5476350265$$ Analytic rank: $$1$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 24) Fricke sign: $$1$$ Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

 Embedding label 1.1 Character $$\chi$$ $$=$$ 72.1

$q$-expansion

 $$f(q)$$ $$=$$ $$q+34.0000 q^{5} -240.000 q^{7} +O(q^{10})$$ $$q+34.0000 q^{5} -240.000 q^{7} +124.000 q^{11} +46.0000 q^{13} -1954.00 q^{17} -1924.00 q^{19} -2840.00 q^{23} -1969.00 q^{25} +8922.00 q^{29} -4648.00 q^{31} -8160.00 q^{35} -4362.00 q^{37} +2886.00 q^{41} +11332.0 q^{43} -7008.00 q^{47} +40793.0 q^{49} +22594.0 q^{53} +4216.00 q^{55} +28.0000 q^{59} -6386.00 q^{61} +1564.00 q^{65} -39076.0 q^{67} +54872.0 q^{71} +21034.0 q^{73} -29760.0 q^{77} +26632.0 q^{79} -56188.0 q^{83} -66436.0 q^{85} -64410.0 q^{89} -11040.0 q^{91} -65416.0 q^{95} -116158. q^{97} +O(q^{100})$$

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
$$5$$ 34.0000 0.608210 0.304105 0.952638i $$-0.401643\pi$$
0.304105 + 0.952638i $$0.401643\pi$$
$$6$$ 0 0
$$7$$ −240.000 −1.85125 −0.925627 0.378436i $$-0.876462\pi$$
−0.925627 + 0.378436i $$0.876462\pi$$
$$8$$ 0 0
$$9$$ 0 0
$$10$$ 0 0
$$11$$ 124.000 0.308987 0.154493 0.987994i $$-0.450625\pi$$
0.154493 + 0.987994i $$0.450625\pi$$
$$12$$ 0 0
$$13$$ 46.0000 0.0754917 0.0377459 0.999287i $$-0.487982\pi$$
0.0377459 + 0.999287i $$0.487982\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ −1954.00 −1.63984 −0.819921 0.572476i $$-0.805983\pi$$
−0.819921 + 0.572476i $$0.805983\pi$$
$$18$$ 0 0
$$19$$ −1924.00 −1.22270 −0.611352 0.791359i $$-0.709374\pi$$
−0.611352 + 0.791359i $$0.709374\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 0 0
$$23$$ −2840.00 −1.11943 −0.559717 0.828684i $$-0.689090\pi$$
−0.559717 + 0.828684i $$0.689090\pi$$
$$24$$ 0 0
$$25$$ −1969.00 −0.630080
$$26$$ 0 0
$$27$$ 0 0
$$28$$ 0 0
$$29$$ 8922.00 1.97000 0.985002 0.172541i $$-0.0551979\pi$$
0.985002 + 0.172541i $$0.0551979\pi$$
$$30$$ 0 0
$$31$$ −4648.00 −0.868684 −0.434342 0.900748i $$-0.643019\pi$$
−0.434342 + 0.900748i $$0.643019\pi$$
$$32$$ 0 0
$$33$$ 0 0
$$34$$ 0 0
$$35$$ −8160.00 −1.12595
$$36$$ 0 0
$$37$$ −4362.00 −0.523819 −0.261910 0.965092i $$-0.584352\pi$$
−0.261910 + 0.965092i $$0.584352\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 0 0
$$41$$ 2886.00 0.268125 0.134062 0.990973i $$-0.457198\pi$$
0.134062 + 0.990973i $$0.457198\pi$$
$$42$$ 0 0
$$43$$ 11332.0 0.934621 0.467310 0.884093i $$-0.345223\pi$$
0.467310 + 0.884093i $$0.345223\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ −7008.00 −0.462753 −0.231377 0.972864i $$-0.574323\pi$$
−0.231377 + 0.972864i $$0.574323\pi$$
$$48$$ 0 0
$$49$$ 40793.0 2.42714
$$50$$ 0 0
$$51$$ 0 0
$$52$$ 0 0
$$53$$ 22594.0 1.10485 0.552425 0.833562i $$-0.313703\pi$$
0.552425 + 0.833562i $$0.313703\pi$$
$$54$$ 0 0
$$55$$ 4216.00 0.187929
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 0 0
$$59$$ 28.0000 0.00104720 0.000523598 1.00000i $$-0.499833\pi$$
0.000523598 1.00000i $$0.499833\pi$$
$$60$$ 0 0
$$61$$ −6386.00 −0.219738 −0.109869 0.993946i $$-0.535043\pi$$
−0.109869 + 0.993946i $$0.535043\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 0 0
$$65$$ 1564.00 0.0459149
$$66$$ 0 0
$$67$$ −39076.0 −1.06346 −0.531732 0.846912i $$-0.678459\pi$$
−0.531732 + 0.846912i $$0.678459\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 54872.0 1.29183 0.645914 0.763410i $$-0.276476\pi$$
0.645914 + 0.763410i $$0.276476\pi$$
$$72$$ 0 0
$$73$$ 21034.0 0.461971 0.230986 0.972957i $$-0.425805\pi$$
0.230986 + 0.972957i $$0.425805\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 0 0
$$77$$ −29760.0 −0.572013
$$78$$ 0 0
$$79$$ 26632.0 0.480105 0.240052 0.970760i $$-0.422835\pi$$
0.240052 + 0.970760i $$0.422835\pi$$
$$80$$ 0 0
$$81$$ 0 0
$$82$$ 0 0
$$83$$ −56188.0 −0.895258 −0.447629 0.894219i $$-0.647732\pi$$
−0.447629 + 0.894219i $$0.647732\pi$$
$$84$$ 0 0
$$85$$ −66436.0 −0.997370
$$86$$ 0 0
$$87$$ 0 0
$$88$$ 0 0
$$89$$ −64410.0 −0.861942 −0.430971 0.902366i $$-0.641829\pi$$
−0.430971 + 0.902366i $$0.641829\pi$$
$$90$$ 0 0
$$91$$ −11040.0 −0.139754
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 0 0
$$95$$ −65416.0 −0.743661
$$96$$ 0 0
$$97$$ −116158. −1.25349 −0.626743 0.779226i $$-0.715613\pi$$
−0.626743 + 0.779226i $$0.715613\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ 0 0
$$101$$ 66834.0 0.651920 0.325960 0.945384i $$-0.394313\pi$$
0.325960 + 0.945384i $$0.394313\pi$$
$$102$$ 0 0
$$103$$ 64000.0 0.594411 0.297206 0.954814i $$-0.403945\pi$$
0.297206 + 0.954814i $$0.403945\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ 15084.0 0.127367 0.0636835 0.997970i $$-0.479715\pi$$
0.0636835 + 0.997970i $$0.479715\pi$$
$$108$$ 0 0
$$109$$ −39698.0 −0.320039 −0.160019 0.987114i $$-0.551156\pi$$
−0.160019 + 0.987114i $$0.551156\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 0 0
$$113$$ −155154. −1.14305 −0.571527 0.820583i $$-0.693649\pi$$
−0.571527 + 0.820583i $$0.693649\pi$$
$$114$$ 0 0
$$115$$ −96560.0 −0.680852
$$116$$ 0 0
$$117$$ 0 0
$$118$$ 0 0
$$119$$ 468960. 3.03577
$$120$$ 0 0
$$121$$ −145675. −0.904527
$$122$$ 0 0
$$123$$ 0 0
$$124$$ 0 0
$$125$$ −173196. −0.991432
$$126$$ 0 0
$$127$$ 52072.0 0.286480 0.143240 0.989688i $$-0.454248\pi$$
0.143240 + 0.989688i $$0.454248\pi$$
$$128$$ 0 0
$$129$$ 0 0
$$130$$ 0 0
$$131$$ −159964. −0.814412 −0.407206 0.913336i $$-0.633497\pi$$
−0.407206 + 0.913336i $$0.633497\pi$$
$$132$$ 0 0
$$133$$ 461760. 2.26353
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ 262278. 1.19388 0.596940 0.802286i $$-0.296383\pi$$
0.596940 + 0.802286i $$0.296383\pi$$
$$138$$ 0 0
$$139$$ 253524. 1.11297 0.556483 0.830859i $$-0.312150\pi$$
0.556483 + 0.830859i $$0.312150\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ 5704.00 0.0233260
$$144$$ 0 0
$$145$$ 303348. 1.19818
$$146$$ 0 0
$$147$$ 0 0
$$148$$ 0 0
$$149$$ −355630. −1.31230 −0.656149 0.754631i $$-0.727816\pi$$
−0.656149 + 0.754631i $$0.727816\pi$$
$$150$$ 0 0
$$151$$ −1024.00 −0.00365475 −0.00182737 0.999998i $$-0.500582\pi$$
−0.00182737 + 0.999998i $$0.500582\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0 0
$$155$$ −158032. −0.528343
$$156$$ 0 0
$$157$$ −59954.0 −0.194119 −0.0970597 0.995279i $$-0.530944\pi$$
−0.0970597 + 0.995279i $$0.530944\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 0 0
$$161$$ 681600. 2.07236
$$162$$ 0 0
$$163$$ −341556. −1.00692 −0.503458 0.864020i $$-0.667939\pi$$
−0.503458 + 0.864020i $$0.667939\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ −5016.00 −0.0139177 −0.00695883 0.999976i $$-0.502215\pi$$
−0.00695883 + 0.999976i $$0.502215\pi$$
$$168$$ 0 0
$$169$$ −369177. −0.994301
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 0 0
$$173$$ 228666. 0.580880 0.290440 0.956893i $$-0.406198\pi$$
0.290440 + 0.956893i $$0.406198\pi$$
$$174$$ 0 0
$$175$$ 472560. 1.16644
$$176$$ 0 0
$$177$$ 0 0
$$178$$ 0 0
$$179$$ −161388. −0.376477 −0.188239 0.982123i $$-0.560278\pi$$
−0.188239 + 0.982123i $$0.560278\pi$$
$$180$$ 0 0
$$181$$ −291690. −0.661797 −0.330899 0.943666i $$-0.607352\pi$$
−0.330899 + 0.943666i $$0.607352\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 0 0
$$185$$ −148308. −0.318592
$$186$$ 0 0
$$187$$ −242296. −0.506690
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ 55680.0 0.110437 0.0552187 0.998474i $$-0.482414\pi$$
0.0552187 + 0.998474i $$0.482414\pi$$
$$192$$ 0 0
$$193$$ −176254. −0.340601 −0.170300 0.985392i $$-0.554474\pi$$
−0.170300 + 0.985392i $$0.554474\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ 374610. 0.687723 0.343862 0.939020i $$-0.388265\pi$$
0.343862 + 0.939020i $$0.388265\pi$$
$$198$$ 0 0
$$199$$ −637760. −1.14163 −0.570814 0.821079i $$-0.693372\pi$$
−0.570814 + 0.821079i $$0.693372\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ 0 0
$$203$$ −2.14128e6 −3.64698
$$204$$ 0 0
$$205$$ 98124.0 0.163076
$$206$$ 0 0
$$207$$ 0 0
$$208$$ 0 0
$$209$$ −238576. −0.377799
$$210$$ 0 0
$$211$$ −904628. −1.39883 −0.699413 0.714717i $$-0.746555\pi$$
−0.699413 + 0.714717i $$0.746555\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 0 0
$$215$$ 385288. 0.568446
$$216$$ 0 0
$$217$$ 1.11552e6 1.60816
$$218$$ 0 0
$$219$$ 0 0
$$220$$ 0 0
$$221$$ −89884.0 −0.123795
$$222$$ 0 0
$$223$$ 619048. 0.833609 0.416804 0.908996i $$-0.363150\pi$$
0.416804 + 0.908996i $$0.363150\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ 1.46975e6 1.89312 0.946560 0.322527i $$-0.104532\pi$$
0.946560 + 0.322527i $$0.104532\pi$$
$$228$$ 0 0
$$229$$ −3290.00 −0.00414579 −0.00207289 0.999998i $$-0.500660\pi$$
−0.00207289 + 0.999998i $$0.500660\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ −935402. −1.12878 −0.564389 0.825509i $$-0.690888\pi$$
−0.564389 + 0.825509i $$0.690888\pi$$
$$234$$ 0 0
$$235$$ −238272. −0.281451
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 0 0
$$239$$ 875600. 0.991542 0.495771 0.868453i $$-0.334886\pi$$
0.495771 + 0.868453i $$0.334886\pi$$
$$240$$ 0 0
$$241$$ −959214. −1.06383 −0.531916 0.846797i $$-0.678528\pi$$
−0.531916 + 0.846797i $$0.678528\pi$$
$$242$$ 0 0
$$243$$ 0 0
$$244$$ 0 0
$$245$$ 1.38696e6 1.47621
$$246$$ 0 0
$$247$$ −88504.0 −0.0923040
$$248$$ 0 0
$$249$$ 0 0
$$250$$ 0 0
$$251$$ −318868. −0.319467 −0.159734 0.987160i $$-0.551064\pi$$
−0.159734 + 0.987160i $$0.551064\pi$$
$$252$$ 0 0
$$253$$ −352160. −0.345891
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ −1.71469e6 −1.61940 −0.809698 0.586847i $$-0.800369\pi$$
−0.809698 + 0.586847i $$0.800369\pi$$
$$258$$ 0 0
$$259$$ 1.04688e6 0.969723
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 0 0
$$263$$ 1.11028e6 0.989790 0.494895 0.868953i $$-0.335206\pi$$
0.494895 + 0.868953i $$0.335206\pi$$
$$264$$ 0 0
$$265$$ 768196. 0.671982
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 0 0
$$269$$ 398378. 0.335672 0.167836 0.985815i $$-0.446322\pi$$
0.167836 + 0.985815i $$0.446322\pi$$
$$270$$ 0 0
$$271$$ 1.44198e6 1.19271 0.596355 0.802721i $$-0.296615\pi$$
0.596355 + 0.802721i $$0.296615\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ −244156. −0.194686
$$276$$ 0 0
$$277$$ 117238. 0.0918056 0.0459028 0.998946i $$-0.485384\pi$$
0.0459028 + 0.998946i $$0.485384\pi$$
$$278$$ 0 0
$$279$$ 0 0
$$280$$ 0 0
$$281$$ 1.67514e6 1.26557 0.632784 0.774328i $$-0.281912\pi$$
0.632784 + 0.774328i $$0.281912\pi$$
$$282$$ 0 0
$$283$$ 1.92468e6 1.42854 0.714269 0.699872i $$-0.246760\pi$$
0.714269 + 0.699872i $$0.246760\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ −692640. −0.496367
$$288$$ 0 0
$$289$$ 2.39826e6 1.68908
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 0 0
$$293$$ −1.28062e6 −0.871469 −0.435734 0.900075i $$-0.643511\pi$$
−0.435734 + 0.900075i $$0.643511\pi$$
$$294$$ 0 0
$$295$$ 952.000 0.000636916 0
$$296$$ 0 0
$$297$$ 0 0
$$298$$ 0 0
$$299$$ −130640. −0.0845081
$$300$$ 0 0
$$301$$ −2.71968e6 −1.73022
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 0 0
$$305$$ −217124. −0.133647
$$306$$ 0 0
$$307$$ −2.26319e6 −1.37049 −0.685243 0.728314i $$-0.740304\pi$$
−0.685243 + 0.728314i $$0.740304\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 0 0
$$311$$ −247848. −0.145306 −0.0726532 0.997357i $$-0.523147\pi$$
−0.0726532 + 0.997357i $$0.523147\pi$$
$$312$$ 0 0
$$313$$ −1.82391e6 −1.05231 −0.526154 0.850390i $$-0.676366\pi$$
−0.526154 + 0.850390i $$0.676366\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ −2.85629e6 −1.59645 −0.798224 0.602361i $$-0.794227\pi$$
−0.798224 + 0.602361i $$0.794227\pi$$
$$318$$ 0 0
$$319$$ 1.10633e6 0.608705
$$320$$ 0 0
$$321$$ 0 0
$$322$$ 0 0
$$323$$ 3.75950e6 2.00504
$$324$$ 0 0
$$325$$ −90574.0 −0.0475658
$$326$$ 0 0
$$327$$ 0 0
$$328$$ 0 0
$$329$$ 1.68192e6 0.856674
$$330$$ 0 0
$$331$$ −147148. −0.0738218 −0.0369109 0.999319i $$-0.511752\pi$$
−0.0369109 + 0.999319i $$0.511752\pi$$
$$332$$ 0 0
$$333$$ 0 0
$$334$$ 0 0
$$335$$ −1.32858e6 −0.646810
$$336$$ 0 0
$$337$$ −3.24728e6 −1.55756 −0.778780 0.627297i $$-0.784161\pi$$
−0.778780 + 0.627297i $$0.784161\pi$$
$$338$$ 0 0
$$339$$ 0 0
$$340$$ 0 0
$$341$$ −576352. −0.268412
$$342$$ 0 0
$$343$$ −5.75664e6 −2.64201
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ 1.55675e6 0.694056 0.347028 0.937855i $$-0.387191\pi$$
0.347028 + 0.937855i $$0.387191\pi$$
$$348$$ 0 0
$$349$$ 4.03217e6 1.77205 0.886024 0.463639i $$-0.153456\pi$$
0.886024 + 0.463639i $$0.153456\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0 0
$$353$$ −1.79399e6 −0.766271 −0.383135 0.923692i $$-0.625156\pi$$
−0.383135 + 0.923692i $$0.625156\pi$$
$$354$$ 0 0
$$355$$ 1.86565e6 0.785704
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ −1.55278e6 −0.635876 −0.317938 0.948111i $$-0.602990\pi$$
−0.317938 + 0.948111i $$0.602990\pi$$
$$360$$ 0 0
$$361$$ 1.22568e6 0.495003
$$362$$ 0 0
$$363$$ 0 0
$$364$$ 0 0
$$365$$ 715156. 0.280976
$$366$$ 0 0
$$367$$ −3.11545e6 −1.20741 −0.603706 0.797207i $$-0.706310\pi$$
−0.603706 + 0.797207i $$0.706310\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 0 0
$$371$$ −5.42256e6 −2.04536
$$372$$ 0 0
$$373$$ −630682. −0.234714 −0.117357 0.993090i $$-0.537442\pi$$
−0.117357 + 0.993090i $$0.537442\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ 410412. 0.148719
$$378$$ 0 0
$$379$$ 48404.0 0.0173094 0.00865472 0.999963i $$-0.497245\pi$$
0.00865472 + 0.999963i $$0.497245\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 0 0
$$383$$ −1.74182e6 −0.606747 −0.303373 0.952872i $$-0.598113\pi$$
−0.303373 + 0.952872i $$0.598113\pi$$
$$384$$ 0 0
$$385$$ −1.01184e6 −0.347904
$$386$$ 0 0
$$387$$ 0 0
$$388$$ 0 0
$$389$$ 3.06819e6 1.02804 0.514019 0.857779i $$-0.328156\pi$$
0.514019 + 0.857779i $$0.328156\pi$$
$$390$$ 0 0
$$391$$ 5.54936e6 1.83570
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 0 0
$$395$$ 905488. 0.292005
$$396$$ 0 0
$$397$$ 5.35984e6 1.70677 0.853386 0.521280i $$-0.174545\pi$$
0.853386 + 0.521280i $$0.174545\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0 0
$$401$$ 2.76473e6 0.858603 0.429302 0.903161i $$-0.358760\pi$$
0.429302 + 0.903161i $$0.358760\pi$$
$$402$$ 0 0
$$403$$ −213808. −0.0655785
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ −540888. −0.161853
$$408$$ 0 0
$$409$$ −1.20893e6 −0.357350 −0.178675 0.983908i $$-0.557181\pi$$
−0.178675 + 0.983908i $$0.557181\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 0 0
$$413$$ −6720.00 −0.00193863
$$414$$ 0 0
$$415$$ −1.91039e6 −0.544505
$$416$$ 0 0
$$417$$ 0 0
$$418$$ 0 0
$$419$$ 4.38008e6 1.21884 0.609421 0.792847i $$-0.291402\pi$$
0.609421 + 0.792847i $$0.291402\pi$$
$$420$$ 0 0
$$421$$ −922810. −0.253751 −0.126875 0.991919i $$-0.540495\pi$$
−0.126875 + 0.991919i $$0.540495\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ 0 0
$$425$$ 3.84743e6 1.03323
$$426$$ 0 0
$$427$$ 1.53264e6 0.406790
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ −6.12678e6 −1.58869 −0.794345 0.607466i $$-0.792186\pi$$
−0.794345 + 0.607466i $$0.792186\pi$$
$$432$$ 0 0
$$433$$ −1.76315e6 −0.451928 −0.225964 0.974136i $$-0.572553\pi$$
−0.225964 + 0.974136i $$0.572553\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ 5.46416e6 1.36874
$$438$$ 0 0
$$439$$ 3.85906e6 0.955696 0.477848 0.878443i $$-0.341417\pi$$
0.477848 + 0.878443i $$0.341417\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 0 0
$$443$$ 4.39396e6 1.06377 0.531884 0.846817i $$-0.321484\pi$$
0.531884 + 0.846817i $$0.321484\pi$$
$$444$$ 0 0
$$445$$ −2.18994e6 −0.524242
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 0 0
$$449$$ 793390. 0.185725 0.0928626 0.995679i $$-0.470398\pi$$
0.0928626 + 0.995679i $$0.470398\pi$$
$$450$$ 0 0
$$451$$ 357864. 0.0828470
$$452$$ 0 0
$$453$$ 0 0
$$454$$ 0 0
$$455$$ −375360. −0.0850001
$$456$$ 0 0
$$457$$ 7.04302e6 1.57750 0.788748 0.614717i $$-0.210730\pi$$
0.788748 + 0.614717i $$0.210730\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 0 0
$$461$$ −7.43005e6 −1.62832 −0.814160 0.580641i $$-0.802802\pi$$
−0.814160 + 0.580641i $$0.802802\pi$$
$$462$$ 0 0
$$463$$ −4.10567e6 −0.890086 −0.445043 0.895509i $$-0.646812\pi$$
−0.445043 + 0.895509i $$0.646812\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ −3.39817e6 −0.721030 −0.360515 0.932753i $$-0.617399\pi$$
−0.360515 + 0.932753i $$0.617399\pi$$
$$468$$ 0 0
$$469$$ 9.37824e6 1.96874
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0 0
$$473$$ 1.40517e6 0.288786
$$474$$ 0 0
$$475$$ 3.78836e6 0.770401
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 0 0
$$479$$ −2.78133e6 −0.553877 −0.276939 0.960888i $$-0.589320\pi$$
−0.276939 + 0.960888i $$0.589320\pi$$
$$480$$ 0 0
$$481$$ −200652. −0.0395440
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 0 0
$$485$$ −3.94937e6 −0.762384
$$486$$ 0 0
$$487$$ −2.06734e6 −0.394994 −0.197497 0.980304i $$-0.563281\pi$$
−0.197497 + 0.980304i $$0.563281\pi$$
$$488$$ 0 0
$$489$$ 0 0
$$490$$ 0 0
$$491$$ 7.65976e6 1.43387 0.716937 0.697138i $$-0.245543\pi$$
0.716937 + 0.697138i $$0.245543\pi$$
$$492$$ 0 0
$$493$$ −1.74336e7 −3.23050
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ −1.31693e7 −2.39150
$$498$$ 0 0
$$499$$ −386580. −0.0695005 −0.0347503 0.999396i $$-0.511064\pi$$
−0.0347503 + 0.999396i $$0.511064\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 0 0
$$503$$ 2.57326e6 0.453485 0.226743 0.973955i $$-0.427192\pi$$
0.226743 + 0.973955i $$0.427192\pi$$
$$504$$ 0 0
$$505$$ 2.27236e6 0.396504
$$506$$ 0 0
$$507$$ 0 0
$$508$$ 0 0
$$509$$ −360678. −0.0617057 −0.0308528 0.999524i $$-0.509822\pi$$
−0.0308528 + 0.999524i $$0.509822\pi$$
$$510$$ 0 0
$$511$$ −5.04816e6 −0.855226
$$512$$ 0 0
$$513$$ 0 0
$$514$$ 0 0
$$515$$ 2.17600e6 0.361527
$$516$$ 0 0
$$517$$ −868992. −0.142985
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ 1.55908e6 0.251636 0.125818 0.992053i $$-0.459844\pi$$
0.125818 + 0.992053i $$0.459844\pi$$
$$522$$ 0 0
$$523$$ −9.18220e6 −1.46789 −0.733944 0.679210i $$-0.762322\pi$$
−0.733944 + 0.679210i $$0.762322\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ 9.08219e6 1.42451
$$528$$ 0 0
$$529$$ 1.62926e6 0.253134
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 0 0
$$533$$ 132756. 0.0202412
$$534$$ 0 0
$$535$$ 512856. 0.0774660
$$536$$ 0 0
$$537$$ 0 0
$$538$$ 0 0
$$539$$ 5.05833e6 0.749955
$$540$$ 0 0
$$541$$ −6.67773e6 −0.980925 −0.490462 0.871462i $$-0.663172\pi$$
−0.490462 + 0.871462i $$0.663172\pi$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ 0 0
$$545$$ −1.34973e6 −0.194651
$$546$$ 0 0
$$547$$ 8.89656e6 1.27132 0.635658 0.771971i $$-0.280729\pi$$
0.635658 + 0.771971i $$0.280729\pi$$
$$548$$ 0 0
$$549$$ 0 0
$$550$$ 0 0
$$551$$ −1.71659e7 −2.40873
$$552$$ 0 0
$$553$$ −6.39168e6 −0.888796
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ 4.46070e6 0.609207 0.304603 0.952479i $$-0.401476\pi$$
0.304603 + 0.952479i $$0.401476\pi$$
$$558$$ 0 0
$$559$$ 521272. 0.0705562
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ −6.37660e6 −0.847849 −0.423924 0.905698i $$-0.639348\pi$$
−0.423924 + 0.905698i $$0.639348\pi$$
$$564$$ 0 0
$$565$$ −5.27524e6 −0.695218
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 0 0
$$569$$ −5.51143e6 −0.713648 −0.356824 0.934172i $$-0.616140\pi$$
−0.356824 + 0.934172i $$0.616140\pi$$
$$570$$ 0 0
$$571$$ 1.35431e6 0.173831 0.0869155 0.996216i $$-0.472299\pi$$
0.0869155 + 0.996216i $$0.472299\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ 5.59196e6 0.705333
$$576$$ 0 0
$$577$$ −5.00736e6 −0.626137 −0.313068 0.949731i $$-0.601357\pi$$
−0.313068 + 0.949731i $$0.601357\pi$$
$$578$$ 0 0
$$579$$ 0 0
$$580$$ 0 0
$$581$$ 1.34851e7 1.65735
$$582$$ 0 0
$$583$$ 2.80166e6 0.341384
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ −2.69964e6 −0.323378 −0.161689 0.986842i $$-0.551694\pi$$
−0.161689 + 0.986842i $$0.551694\pi$$
$$588$$ 0 0
$$589$$ 8.94275e6 1.06214
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 0 0
$$593$$ −1.31035e7 −1.53021 −0.765103 0.643908i $$-0.777312\pi$$
−0.765103 + 0.643908i $$0.777312\pi$$
$$594$$ 0 0
$$595$$ 1.59446e7 1.84639
$$596$$ 0 0
$$597$$ 0 0
$$598$$ 0 0
$$599$$ 5.22804e6 0.595349 0.297675 0.954667i $$-0.403789\pi$$
0.297675 + 0.954667i $$0.403789\pi$$
$$600$$ 0 0
$$601$$ 1.02248e7 1.15470 0.577351 0.816496i $$-0.304087\pi$$
0.577351 + 0.816496i $$0.304087\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ 0 0
$$605$$ −4.95295e6 −0.550143
$$606$$ 0 0
$$607$$ 8.81684e6 0.971273 0.485636 0.874161i $$-0.338588\pi$$
0.485636 + 0.874161i $$0.338588\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ −322368. −0.0349340
$$612$$ 0 0
$$613$$ 1.13600e7 1.22103 0.610514 0.792006i $$-0.290963\pi$$
0.610514 + 0.792006i $$0.290963\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 4.77356e6 0.504812 0.252406 0.967621i $$-0.418778\pi$$
0.252406 + 0.967621i $$0.418778\pi$$
$$618$$ 0 0
$$619$$ −2.55931e6 −0.268470 −0.134235 0.990950i $$-0.542858\pi$$
−0.134235 + 0.990950i $$0.542858\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ 1.54584e7 1.59567
$$624$$ 0 0
$$625$$ 264461. 0.0270808
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 0 0
$$629$$ 8.52335e6 0.858981
$$630$$ 0 0
$$631$$ −8.41981e6 −0.841839 −0.420919 0.907098i $$-0.638292\pi$$
−0.420919 + 0.907098i $$0.638292\pi$$
$$632$$ 0 0
$$633$$ 0 0
$$634$$ 0 0
$$635$$ 1.77045e6 0.174240
$$636$$ 0 0
$$637$$ 1.87648e6 0.183229
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ 1.21494e7 1.16791 0.583957 0.811785i $$-0.301504\pi$$
0.583957 + 0.811785i $$0.301504\pi$$
$$642$$ 0 0
$$643$$ −1.08968e7 −1.03937 −0.519685 0.854358i $$-0.673951\pi$$
−0.519685 + 0.854358i $$0.673951\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ −1.32166e7 −1.24124 −0.620622 0.784110i $$-0.713120\pi$$
−0.620622 + 0.784110i $$0.713120\pi$$
$$648$$ 0 0
$$649$$ 3472.00 0.000323570 0
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ −1.65915e7 −1.52266 −0.761329 0.648365i $$-0.775453\pi$$
−0.761329 + 0.648365i $$0.775453\pi$$
$$654$$ 0 0
$$655$$ −5.43878e6 −0.495334
$$656$$ 0 0
$$657$$ 0 0
$$658$$ 0 0
$$659$$ 2.29372e6 0.205743 0.102872 0.994695i $$-0.467197\pi$$
0.102872 + 0.994695i $$0.467197\pi$$
$$660$$ 0 0
$$661$$ −719194. −0.0640239 −0.0320120 0.999487i $$-0.510191\pi$$
−0.0320120 + 0.999487i $$0.510191\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ 1.56998e7 1.37671
$$666$$ 0 0
$$667$$ −2.53385e7 −2.20529
$$668$$ 0 0
$$669$$ 0 0
$$670$$ 0 0
$$671$$ −791864. −0.0678960
$$672$$ 0 0
$$673$$ 8.64695e6 0.735911 0.367955 0.929843i $$-0.380058\pi$$
0.367955 + 0.929843i $$0.380058\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ 1.69592e7 1.42211 0.711056 0.703135i $$-0.248217\pi$$
0.711056 + 0.703135i $$0.248217\pi$$
$$678$$ 0 0
$$679$$ 2.78779e7 2.32052
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 0 0
$$683$$ −1.87105e7 −1.53473 −0.767367 0.641209i $$-0.778433\pi$$
−0.767367 + 0.641209i $$0.778433\pi$$
$$684$$ 0 0
$$685$$ 8.91745e6 0.726130
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 0 0
$$689$$ 1.03932e6 0.0834071
$$690$$ 0 0
$$691$$ −1.16204e7 −0.925820 −0.462910 0.886405i $$-0.653195\pi$$
−0.462910 + 0.886405i $$0.653195\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ 8.61982e6 0.676918
$$696$$ 0 0
$$697$$ −5.63924e6 −0.439682
$$698$$ 0 0
$$699$$ 0 0
$$700$$ 0 0
$$701$$ −2.23497e7 −1.71781 −0.858907 0.512132i $$-0.828856\pi$$
−0.858907 + 0.512132i $$0.828856\pi$$
$$702$$ 0 0
$$703$$ 8.39249e6 0.640475
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ −1.60402e7 −1.20687
$$708$$ 0 0
$$709$$ 1.02353e7 0.764687 0.382344 0.924020i $$-0.375117\pi$$
0.382344 + 0.924020i $$0.375117\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 0 0
$$713$$ 1.32003e7 0.972435
$$714$$ 0 0
$$715$$ 193936. 0.0141871
$$716$$ 0 0
$$717$$ 0 0
$$718$$ 0 0
$$719$$ 1.70339e7 1.22883 0.614416 0.788982i $$-0.289392\pi$$
0.614416 + 0.788982i $$0.289392\pi$$
$$720$$ 0 0
$$721$$ −1.53600e7 −1.10041
$$722$$ 0 0
$$723$$ 0 0
$$724$$ 0 0
$$725$$ −1.75674e7 −1.24126
$$726$$ 0 0
$$727$$ −1.62280e7 −1.13875 −0.569377 0.822077i $$-0.692815\pi$$
−0.569377 + 0.822077i $$0.692815\pi$$
$$728$$ 0 0
$$729$$ 0 0
$$730$$ 0 0
$$731$$ −2.21427e7 −1.53263
$$732$$ 0 0
$$733$$ −2.17495e7 −1.49517 −0.747583 0.664168i $$-0.768786\pi$$
−0.747583 + 0.664168i $$0.768786\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ −4.84542e6 −0.328597
$$738$$ 0 0
$$739$$ 1.96200e7 1.32156 0.660781 0.750578i $$-0.270225\pi$$
0.660781 + 0.750578i $$0.270225\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ −1.74018e7 −1.15644 −0.578218 0.815882i $$-0.696252\pi$$
−0.578218 + 0.815882i $$0.696252\pi$$
$$744$$ 0 0
$$745$$ −1.20914e7 −0.798154
$$746$$ 0 0
$$747$$ 0 0
$$748$$ 0 0
$$749$$ −3.62016e6 −0.235789
$$750$$ 0 0
$$751$$ −2.62693e7 −1.69961 −0.849803 0.527101i $$-0.823279\pi$$
−0.849803 + 0.527101i $$0.823279\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 0 0
$$755$$ −34816.0 −0.00222286
$$756$$ 0 0
$$757$$ −5.70356e6 −0.361748 −0.180874 0.983506i $$-0.557893\pi$$
−0.180874 + 0.983506i $$0.557893\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 2.13762e7 1.33804 0.669020 0.743244i $$-0.266714\pi$$
0.669020 + 0.743244i $$0.266714\pi$$
$$762$$ 0 0
$$763$$ 9.52752e6 0.592473
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ 1288.00 7.90547e−5 0
$$768$$ 0 0
$$769$$ −2.01523e6 −0.122888 −0.0614439 0.998111i $$-0.519571\pi$$
−0.0614439 + 0.998111i $$0.519571\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 0 0
$$773$$ 1.27674e7 0.768520 0.384260 0.923225i $$-0.374457\pi$$
0.384260 + 0.923225i $$0.374457\pi$$
$$774$$ 0 0
$$775$$ 9.15191e6 0.547340
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ −5.55266e6 −0.327837
$$780$$ 0 0
$$781$$ 6.80413e6 0.399158
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 0 0
$$785$$ −2.03844e6 −0.118065
$$786$$ 0 0
$$787$$ −2.72384e7 −1.56764 −0.783818 0.620990i $$-0.786731\pi$$
−0.783818 + 0.620990i $$0.786731\pi$$
$$788$$ 0 0
$$789$$ 0 0
$$790$$ 0 0
$$791$$ 3.72370e7 2.11608
$$792$$ 0 0
$$793$$ −293756. −0.0165884
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ 7.66724e6 0.427556 0.213778 0.976882i $$-0.431423\pi$$
0.213778 + 0.976882i $$0.431423\pi$$
$$798$$ 0 0
$$799$$ 1.36936e7 0.758843
$$800$$ 0 0
$$801$$ 0 0
$$802$$ 0 0
$$803$$ 2.60822e6 0.142743
$$804$$ 0 0
$$805$$ 2.31744e7 1.26043
$$806$$ 0 0
$$807$$ 0 0
$$808$$ 0 0
$$809$$ 1.05541e7 0.566956 0.283478 0.958979i $$-0.408512\pi$$
0.283478 + 0.958979i $$0.408512\pi$$
$$810$$ 0 0
$$811$$ −1.32883e6 −0.0709442 −0.0354721 0.999371i $$-0.511293\pi$$
−0.0354721 + 0.999371i $$0.511293\pi$$
$$812$$ 0 0
$$813$$ 0 0
$$814$$ 0 0
$$815$$ −1.16129e7 −0.612416
$$816$$ 0 0
$$817$$ −2.18028e7 −1.14276
$$818$$ 0 0
$$819$$ 0 0
$$820$$ 0 0
$$821$$ 6.15933e6 0.318915 0.159458 0.987205i $$-0.449025\pi$$
0.159458 + 0.987205i $$0.449025\pi$$
$$822$$ 0 0
$$823$$ 1.00734e7 0.518414 0.259207 0.965822i $$-0.416539\pi$$
0.259207 + 0.965822i $$0.416539\pi$$
$$824$$ 0 0
$$825$$ 0 0
$$826$$ 0 0
$$827$$ 6.49152e6 0.330052 0.165026 0.986289i $$-0.447229\pi$$
0.165026 + 0.986289i $$0.447229\pi$$
$$828$$ 0 0
$$829$$ −1.93536e7 −0.978082 −0.489041 0.872261i $$-0.662653\pi$$
−0.489041 + 0.872261i $$0.662653\pi$$
$$830$$ 0 0
$$831$$ 0 0
$$832$$ 0 0
$$833$$ −7.97095e7 −3.98013
$$834$$ 0 0
$$835$$ −170544. −0.00846487
$$836$$ 0 0
$$837$$ 0 0
$$838$$ 0 0
$$839$$ 2.78622e7 1.36650 0.683251 0.730183i $$-0.260565\pi$$
0.683251 + 0.730183i $$0.260565\pi$$
$$840$$ 0 0
$$841$$ 5.90909e7 2.88092
$$842$$ 0 0
$$843$$ 0 0
$$844$$ 0 0
$$845$$ −1.25520e7 −0.604744
$$846$$ 0 0
$$847$$ 3.49620e7 1.67451
$$848$$ 0 0
$$849$$ 0 0
$$850$$ 0 0
$$851$$ 1.23881e7 0.586381
$$852$$ 0 0
$$853$$ 1.07651e7 0.506577 0.253288 0.967391i $$-0.418488\pi$$
0.253288 + 0.967391i $$0.418488\pi$$
$$854$$ 0 0
$$855$$ 0 0
$$856$$ 0 0
$$857$$ −1.22439e7 −0.569465 −0.284733 0.958607i $$-0.591905\pi$$
−0.284733 + 0.958607i $$0.591905\pi$$
$$858$$ 0 0
$$859$$ −1.38664e6 −0.0641179 −0.0320590 0.999486i $$-0.510206\pi$$
−0.0320590 + 0.999486i $$0.510206\pi$$
$$860$$ 0 0
$$861$$ 0 0
$$862$$ 0 0
$$863$$ 1.09856e7 0.502109 0.251055 0.967973i $$-0.419223\pi$$
0.251055 + 0.967973i $$0.419223\pi$$
$$864$$ 0 0
$$865$$ 7.77464e6 0.353297
$$866$$ 0 0
$$867$$ 0 0
$$868$$ 0 0
$$869$$ 3.30237e6 0.148346
$$870$$ 0 0
$$871$$ −1.79750e6 −0.0802828
$$872$$ 0 0
$$873$$ 0 0
$$874$$ 0 0
$$875$$ 4.15670e7 1.83539
$$876$$ 0 0
$$877$$ 8.17798e6 0.359044 0.179522 0.983754i $$-0.442545\pi$$
0.179522 + 0.983754i $$0.442545\pi$$
$$878$$ 0 0
$$879$$ 0 0
$$880$$ 0 0
$$881$$ −4.66520e6 −0.202503 −0.101251 0.994861i $$-0.532285\pi$$
−0.101251 + 0.994861i $$0.532285\pi$$
$$882$$ 0 0
$$883$$ 3.82201e7 1.64964 0.824822 0.565393i $$-0.191276\pi$$
0.824822 + 0.565393i $$0.191276\pi$$
$$884$$ 0 0
$$885$$ 0 0
$$886$$ 0 0
$$887$$ 7.72172e6 0.329538 0.164769 0.986332i $$-0.447312\pi$$
0.164769 + 0.986332i $$0.447312\pi$$
$$888$$ 0 0
$$889$$ −1.24973e7 −0.530348
$$890$$ 0 0
$$891$$ 0 0
$$892$$ 0 0
$$893$$ 1.34834e7 0.565810
$$894$$ 0 0
$$895$$ −5.48719e6 −0.228977
$$896$$ 0 0
$$897$$ 0 0
$$898$$ 0 0
$$899$$ −4.14695e7 −1.71131
$$900$$ 0 0
$$901$$ −4.41487e7 −1.81178
$$902$$ 0 0
$$903$$ 0 0
$$904$$ 0 0
$$905$$ −9.91746e6 −0.402512
$$906$$ 0 0
$$907$$ 4.33137e7 1.74826 0.874131 0.485689i $$-0.161431\pi$$
0.874131 + 0.485689i $$0.161431\pi$$
$$908$$ 0 0
$$909$$ 0 0
$$910$$ 0 0
$$911$$ −3.44456e6 −0.137511 −0.0687556 0.997634i $$-0.521903\pi$$
−0.0687556 + 0.997634i $$0.521903\pi$$
$$912$$ 0 0
$$913$$ −6.96731e6 −0.276623
$$914$$ 0 0
$$915$$ 0 0
$$916$$ 0 0
$$917$$ 3.83914e7 1.50768
$$918$$ 0 0
$$919$$ −4.37073e7 −1.70712 −0.853562 0.520991i $$-0.825563\pi$$
−0.853562 + 0.520991i $$0.825563\pi$$
$$920$$ 0 0
$$921$$ 0 0
$$922$$ 0 0
$$923$$ 2.52411e6 0.0975224
$$924$$ 0 0
$$925$$ 8.58878e6 0.330048
$$926$$ 0 0
$$927$$ 0 0
$$928$$ 0 0
$$929$$ 4.13022e7 1.57012 0.785062 0.619418i $$-0.212631\pi$$
0.785062 + 0.619418i $$0.212631\pi$$
$$930$$ 0 0
$$931$$ −7.84857e7 −2.96768
$$932$$ 0 0
$$933$$ 0 0
$$934$$ 0 0
$$935$$ −8.23806e6 −0.308174
$$936$$ 0 0
$$937$$ 9.57460e6 0.356264 0.178132 0.984007i $$-0.442995\pi$$
0.178132 + 0.984007i $$0.442995\pi$$
$$938$$ 0 0
$$939$$ 0 0
$$940$$ 0 0
$$941$$ −8.71623e6 −0.320889 −0.160444 0.987045i $$-0.551293\pi$$
−0.160444 + 0.987045i $$0.551293\pi$$
$$942$$ 0 0
$$943$$ −8.19624e6 −0.300148
$$944$$ 0 0
$$945$$ 0 0
$$946$$ 0 0
$$947$$ 1.30605e7 0.473244 0.236622 0.971602i $$-0.423960\pi$$
0.236622 + 0.971602i $$0.423960\pi$$
$$948$$ 0 0
$$949$$ 967564. 0.0348750
$$950$$ 0 0
$$951$$ 0 0
$$952$$ 0 0
$$953$$ −1.13875e7 −0.406158 −0.203079 0.979162i $$-0.565095\pi$$
−0.203079 + 0.979162i $$0.565095\pi$$
$$954$$ 0 0
$$955$$ 1.89312e6 0.0671691
$$956$$ 0 0
$$957$$ 0 0
$$958$$ 0 0
$$959$$ −6.29467e7 −2.21017
$$960$$ 0 0
$$961$$ −7.02525e6 −0.245388
$$962$$ 0 0
$$963$$ 0 0
$$964$$ 0 0
$$965$$ −5.99264e6 −0.207157
$$966$$ 0 0
$$967$$ 4.62711e7 1.59127 0.795634 0.605778i $$-0.207138\pi$$
0.795634 + 0.605778i $$0.207138\pi$$
$$968$$ 0 0
$$969$$ 0 0
$$970$$ 0 0
$$971$$ −1.63206e7 −0.555506 −0.277753 0.960653i $$-0.589590\pi$$
−0.277753 + 0.960653i $$0.589590\pi$$
$$972$$ 0 0
$$973$$ −6.08458e7 −2.06038
$$974$$ 0 0
$$975$$ 0 0
$$976$$ 0 0
$$977$$ 1.95213e7 0.654294 0.327147 0.944973i $$-0.393913\pi$$
0.327147 + 0.944973i $$0.393913\pi$$
$$978$$ 0 0
$$979$$ −7.98684e6 −0.266329
$$980$$ 0 0
$$981$$ 0 0
$$982$$ 0 0
$$983$$ 4.33962e7 1.43241 0.716207 0.697888i $$-0.245877\pi$$
0.716207 + 0.697888i $$0.245877\pi$$
$$984$$ 0 0
$$985$$ 1.27367e7 0.418281
$$986$$ 0 0
$$987$$ 0 0
$$988$$ 0 0
$$989$$ −3.21829e7 −1.04625
$$990$$ 0 0
$$991$$ 3.83518e7 1.24051 0.620257 0.784399i $$-0.287028\pi$$
0.620257 + 0.784399i $$0.287028\pi$$
$$992$$ 0 0
$$993$$ 0 0
$$994$$ 0 0
$$995$$ −2.16838e7 −0.694350
$$996$$ 0 0
$$997$$ −7.82206e6 −0.249220 −0.124610 0.992206i $$-0.539768\pi$$
−0.124610 + 0.992206i $$0.539768\pi$$
$$998$$ 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 72.6.a.e.1.1 1
3.2 odd 2 24.6.a.a.1.1 1
4.3 odd 2 144.6.a.i.1.1 1
8.3 odd 2 576.6.a.l.1.1 1
8.5 even 2 576.6.a.k.1.1 1
12.11 even 2 48.6.a.d.1.1 1
15.2 even 4 600.6.f.f.49.2 2
15.8 even 4 600.6.f.f.49.1 2
15.14 odd 2 600.6.a.i.1.1 1
24.5 odd 2 192.6.a.n.1.1 1
24.11 even 2 192.6.a.f.1.1 1
48.5 odd 4 768.6.d.r.385.2 2
48.11 even 4 768.6.d.a.385.1 2
48.29 odd 4 768.6.d.r.385.1 2
48.35 even 4 768.6.d.a.385.2 2

By twisted newform
Twist Min Dim Char Parity Ord Type
24.6.a.a.1.1 1 3.2 odd 2
48.6.a.d.1.1 1 12.11 even 2
72.6.a.e.1.1 1 1.1 even 1 trivial
144.6.a.i.1.1 1 4.3 odd 2
192.6.a.f.1.1 1 24.11 even 2
192.6.a.n.1.1 1 24.5 odd 2
576.6.a.k.1.1 1 8.5 even 2
576.6.a.l.1.1 1 8.3 odd 2
600.6.a.i.1.1 1 15.14 odd 2
600.6.f.f.49.1 2 15.8 even 4
600.6.f.f.49.2 2 15.2 even 4
768.6.d.a.385.1 2 48.11 even 4
768.6.d.a.385.2 2 48.35 even 4
768.6.d.r.385.1 2 48.29 odd 4
768.6.d.r.385.2 2 48.5 odd 4