# Properties

 Label 35.5.c.a.34.1 Level $35$ Weight $5$ Character 35.34 Self dual yes Analytic conductor $3.618$ Analytic rank $0$ Dimension $1$ CM discriminant -35 Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$35 = 5 \cdot 7$$ Weight: $$k$$ $$=$$ $$5$$ Character orbit: $$[\chi]$$ $$=$$ 35.c (of order $$2$$, degree $$1$$, minimal)

## Newform invariants

 Self dual: yes Analytic conductor: $$3.61794870793$$ Analytic rank: $$0$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: yes Sato-Tate group: $\mathrm{U}(1)[D_{2}]$

## Embedding invariants

 Embedding label 34.1 Character $$\chi$$ $$=$$ 35.34

## $q$-expansion

 $$f(q)$$ $$=$$ $$q-17.0000 q^{3} +16.0000 q^{4} +25.0000 q^{5} +49.0000 q^{7} +208.000 q^{9} +O(q^{10})$$ $$q-17.0000 q^{3} +16.0000 q^{4} +25.0000 q^{5} +49.0000 q^{7} +208.000 q^{9} -73.0000 q^{11} -272.000 q^{12} +23.0000 q^{13} -425.000 q^{15} +256.000 q^{16} +263.000 q^{17} +400.000 q^{20} -833.000 q^{21} +625.000 q^{25} -2159.00 q^{27} +784.000 q^{28} -1153.00 q^{29} +1241.00 q^{33} +1225.00 q^{35} +3328.00 q^{36} -391.000 q^{39} -1168.00 q^{44} +5200.00 q^{45} -3457.00 q^{47} -4352.00 q^{48} +2401.00 q^{49} -4471.00 q^{51} +368.000 q^{52} -1825.00 q^{55} -6800.00 q^{60} +10192.0 q^{63} +4096.00 q^{64} +575.000 q^{65} +4208.00 q^{68} -10078.0 q^{71} -9502.00 q^{73} -10625.0 q^{75} -3577.00 q^{77} +12167.0 q^{79} +6400.00 q^{80} +19855.0 q^{81} -6382.00 q^{83} -13328.0 q^{84} +6575.00 q^{85} +19601.0 q^{87} +1127.00 q^{91} +3383.00 q^{97} -15184.0 q^{99} +O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/35\mathbb{Z}\right)^\times$$.

 $$n$$ $$22$$ $$31$$ $$\chi(n)$$ $$-1$$ $$-1$$

## Coefficient data

For each $$n$$ we display the coefficients of the $$q$$-expansion $$a_n$$, the Satake parameters $$\alpha_p$$, and the Satake angles $$\theta_p = \textrm{Arg}(\alpha_p)$$.

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$3$$ −17.0000 −1.88889 −0.944444 0.328671i $$-0.893399\pi$$
−0.944444 + 0.328671i $$0.893399\pi$$
$$4$$ 16.0000 1.00000
$$5$$ 25.0000 1.00000
$$6$$ 0 0
$$7$$ 49.0000 1.00000
$$8$$ 0 0
$$9$$ 208.000 2.56790
$$10$$ 0 0
$$11$$ −73.0000 −0.603306 −0.301653 0.953418i $$-0.597538\pi$$
−0.301653 + 0.953418i $$0.597538\pi$$
$$12$$ −272.000 −1.88889
$$13$$ 23.0000 0.136095 0.0680473 0.997682i $$-0.478323\pi$$
0.0680473 + 0.997682i $$0.478323\pi$$
$$14$$ 0 0
$$15$$ −425.000 −1.88889
$$16$$ 256.000 1.00000
$$17$$ 263.000 0.910035 0.455017 0.890483i $$-0.349633\pi$$
0.455017 + 0.890483i $$0.349633\pi$$
$$18$$ 0 0
$$19$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$20$$ 400.000 1.00000
$$21$$ −833.000 −1.88889
$$22$$ 0 0
$$23$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$24$$ 0 0
$$25$$ 625.000 1.00000
$$26$$ 0 0
$$27$$ −2159.00 −2.96159
$$28$$ 784.000 1.00000
$$29$$ −1153.00 −1.37099 −0.685493 0.728079i $$-0.740413\pi$$
−0.685493 + 0.728079i $$0.740413\pi$$
$$30$$ 0 0
$$31$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$32$$ 0 0
$$33$$ 1241.00 1.13958
$$34$$ 0 0
$$35$$ 1225.00 1.00000
$$36$$ 3328.00 2.56790
$$37$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$38$$ 0 0
$$39$$ −391.000 −0.257068
$$40$$ 0 0
$$41$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$42$$ 0 0
$$43$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$44$$ −1168.00 −0.603306
$$45$$ 5200.00 2.56790
$$46$$ 0 0
$$47$$ −3457.00 −1.56496 −0.782481 0.622675i $$-0.786046\pi$$
−0.782481 + 0.622675i $$0.786046\pi$$
$$48$$ −4352.00 −1.88889
$$49$$ 2401.00 1.00000
$$50$$ 0 0
$$51$$ −4471.00 −1.71895
$$52$$ 368.000 0.136095
$$53$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$54$$ 0 0
$$55$$ −1825.00 −0.603306
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 0 0
$$59$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$60$$ −6800.00 −1.88889
$$61$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$62$$ 0 0
$$63$$ 10192.0 2.56790
$$64$$ 4096.00 1.00000
$$65$$ 575.000 0.136095
$$66$$ 0 0
$$67$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$68$$ 4208.00 0.910035
$$69$$ 0 0
$$70$$ 0 0
$$71$$ −10078.0 −1.99921 −0.999603 0.0281662i $$-0.991033\pi$$
−0.999603 + 0.0281662i $$0.991033\pi$$
$$72$$ 0 0
$$73$$ −9502.00 −1.78307 −0.891537 0.452948i $$-0.850372\pi$$
−0.891537 + 0.452948i $$0.850372\pi$$
$$74$$ 0 0
$$75$$ −10625.0 −1.88889
$$76$$ 0 0
$$77$$ −3577.00 −0.603306
$$78$$ 0 0
$$79$$ 12167.0 1.94953 0.974764 0.223239i $$-0.0716632\pi$$
0.974764 + 0.223239i $$0.0716632\pi$$
$$80$$ 6400.00 1.00000
$$81$$ 19855.0 3.02622
$$82$$ 0 0
$$83$$ −6382.00 −0.926404 −0.463202 0.886253i $$-0.653300\pi$$
−0.463202 + 0.886253i $$0.653300\pi$$
$$84$$ −13328.0 −1.88889
$$85$$ 6575.00 0.910035
$$86$$ 0 0
$$87$$ 19601.0 2.58964
$$88$$ 0 0
$$89$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$90$$ 0 0
$$91$$ 1127.00 0.136095
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 0 0
$$95$$ 0 0
$$96$$ 0 0
$$97$$ 3383.00 0.359549 0.179775 0.983708i $$-0.442463\pi$$
0.179775 + 0.983708i $$0.442463\pi$$
$$98$$ 0 0
$$99$$ −15184.0 −1.54923
$$100$$ 10000.0 1.00000
$$101$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$102$$ 0 0
$$103$$ 18383.0 1.73277 0.866387 0.499373i $$-0.166436\pi$$
0.866387 + 0.499373i $$0.166436\pi$$
$$104$$ 0 0
$$105$$ −20825.0 −1.88889
$$106$$ 0 0
$$107$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$108$$ −34544.0 −2.96159
$$109$$ −14353.0 −1.20806 −0.604032 0.796960i $$-0.706440\pi$$
−0.604032 + 0.796960i $$0.706440\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 12544.0 1.00000
$$113$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ −18448.0 −1.37099
$$117$$ 4784.00 0.349478
$$118$$ 0 0
$$119$$ 12887.0 0.910035
$$120$$ 0 0
$$121$$ −9312.00 −0.636022
$$122$$ 0 0
$$123$$ 0 0
$$124$$ 0 0
$$125$$ 15625.0 1.00000
$$126$$ 0 0
$$127$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$128$$ 0 0
$$129$$ 0 0
$$130$$ 0 0
$$131$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$132$$ 19856.0 1.13958
$$133$$ 0 0
$$134$$ 0 0
$$135$$ −53975.0 −2.96159
$$136$$ 0 0
$$137$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$138$$ 0 0
$$139$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$140$$ 19600.0 1.00000
$$141$$ 58769.0 2.95604
$$142$$ 0 0
$$143$$ −1679.00 −0.0821067
$$144$$ 53248.0 2.56790
$$145$$ −28825.0 −1.37099
$$146$$ 0 0
$$147$$ −40817.0 −1.88889
$$148$$ 0 0
$$149$$ 24242.0 1.09193 0.545966 0.837807i $$-0.316163\pi$$
0.545966 + 0.837807i $$0.316163\pi$$
$$150$$ 0 0
$$151$$ −45433.0 −1.99259 −0.996294 0.0860129i $$-0.972587\pi$$
−0.996294 + 0.0860129i $$0.972587\pi$$
$$152$$ 0 0
$$153$$ 54704.0 2.33688
$$154$$ 0 0
$$155$$ 0 0
$$156$$ −6256.00 −0.257068
$$157$$ −31342.0 −1.27153 −0.635766 0.771882i $$-0.719316\pi$$
−0.635766 + 0.771882i $$0.719316\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 0 0
$$161$$ 0 0
$$162$$ 0 0
$$163$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$164$$ 0 0
$$165$$ 31025.0 1.13958
$$166$$ 0 0
$$167$$ 17663.0 0.633332 0.316666 0.948537i $$-0.397437\pi$$
0.316666 + 0.948537i $$0.397437\pi$$
$$168$$ 0 0
$$169$$ −28032.0 −0.981478
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 0 0
$$173$$ −11017.0 −0.368105 −0.184052 0.982916i $$-0.558922\pi$$
−0.184052 + 0.982916i $$0.558922\pi$$
$$174$$ 0 0
$$175$$ 30625.0 1.00000
$$176$$ −18688.0 −0.603306
$$177$$ 0 0
$$178$$ 0 0
$$179$$ −16558.0 −0.516775 −0.258388 0.966041i $$-0.583191\pi$$
−0.258388 + 0.966041i $$0.583191\pi$$
$$180$$ 83200.0 2.56790
$$181$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 0 0
$$185$$ 0 0
$$186$$ 0 0
$$187$$ −19199.0 −0.549029
$$188$$ −55312.0 −1.56496
$$189$$ −105791. −2.96159
$$190$$ 0 0
$$191$$ 47447.0 1.30059 0.650297 0.759680i $$-0.274644\pi$$
0.650297 + 0.759680i $$0.274644\pi$$
$$192$$ −69632.0 −1.88889
$$193$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$194$$ 0 0
$$195$$ −9775.00 −0.257068
$$196$$ 38416.0 1.00000
$$197$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$198$$ 0 0
$$199$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ 0 0
$$203$$ −56497.0 −1.37099
$$204$$ −71536.0 −1.71895
$$205$$ 0 0
$$206$$ 0 0
$$207$$ 0 0
$$208$$ 5888.00 0.136095
$$209$$ 0 0
$$210$$ 0 0
$$211$$ −77593.0 −1.74284 −0.871420 0.490537i $$-0.836801\pi$$
−0.871420 + 0.490537i $$0.836801\pi$$
$$212$$ 0 0
$$213$$ 171326. 3.77628
$$214$$ 0 0
$$215$$ 0 0
$$216$$ 0 0
$$217$$ 0 0
$$218$$ 0 0
$$219$$ 161534. 3.36803
$$220$$ −29200.0 −0.603306
$$221$$ 6049.00 0.123851
$$222$$ 0 0
$$223$$ 61343.0 1.23355 0.616773 0.787141i $$-0.288440\pi$$
0.616773 + 0.787141i $$0.288440\pi$$
$$224$$ 0 0
$$225$$ 130000. 2.56790
$$226$$ 0 0
$$227$$ 49823.0 0.966892 0.483446 0.875374i $$-0.339385\pi$$
0.483446 + 0.875374i $$0.339385\pi$$
$$228$$ 0 0
$$229$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$230$$ 0 0
$$231$$ 60809.0 1.13958
$$232$$ 0 0
$$233$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$234$$ 0 0
$$235$$ −86425.0 −1.56496
$$236$$ 0 0
$$237$$ −206839. −3.68244
$$238$$ 0 0
$$239$$ 43367.0 0.759213 0.379606 0.925148i $$-0.376059\pi$$
0.379606 + 0.925148i $$0.376059\pi$$
$$240$$ −108800. −1.88889
$$241$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$242$$ 0 0
$$243$$ −162656. −2.75459
$$244$$ 0 0
$$245$$ 60025.0 1.00000
$$246$$ 0 0
$$247$$ 0 0
$$248$$ 0 0
$$249$$ 108494. 1.74988
$$250$$ 0 0
$$251$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$252$$ 163072. 2.56790
$$253$$ 0 0
$$254$$ 0 0
$$255$$ −111775. −1.71895
$$256$$ 65536.0 1.00000
$$257$$ 111938. 1.69477 0.847386 0.530977i $$-0.178175\pi$$
0.847386 + 0.530977i $$0.178175\pi$$
$$258$$ 0 0
$$259$$ 0 0
$$260$$ 9200.00 0.136095
$$261$$ −239824. −3.52056
$$262$$ 0 0
$$263$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$264$$ 0 0
$$265$$ 0 0
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 0 0
$$269$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$270$$ 0 0
$$271$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$272$$ 67328.0 0.910035
$$273$$ −19159.0 −0.257068
$$274$$ 0 0
$$275$$ −45625.0 −0.603306
$$276$$ 0 0
$$277$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$278$$ 0 0
$$279$$ 0 0
$$280$$ 0 0
$$281$$ 119807. 1.51729 0.758647 0.651502i $$-0.225861\pi$$
0.758647 + 0.651502i $$0.225861\pi$$
$$282$$ 0 0
$$283$$ 152303. 1.90167 0.950836 0.309695i $$-0.100227\pi$$
0.950836 + 0.309695i $$0.100227\pi$$
$$284$$ −161248. −1.99921
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 0 0
$$288$$ 0 0
$$289$$ −14352.0 −0.171837
$$290$$ 0 0
$$291$$ −57511.0 −0.679149
$$292$$ −152032. −1.78307
$$293$$ −171337. −1.99579 −0.997897 0.0648123i $$-0.979355\pi$$
−0.997897 + 0.0648123i $$0.979355\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ 0 0
$$297$$ 157607. 1.78675
$$298$$ 0 0
$$299$$ 0 0
$$300$$ −170000. −1.88889
$$301$$ 0 0
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 0 0
$$305$$ 0 0
$$306$$ 0 0
$$307$$ 135263. 1.43517 0.717583 0.696473i $$-0.245248\pi$$
0.717583 + 0.696473i $$0.245248\pi$$
$$308$$ −57232.0 −0.603306
$$309$$ −312511. −3.27302
$$310$$ 0 0
$$311$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$312$$ 0 0
$$313$$ −147097. −1.50146 −0.750732 0.660606i $$-0.770299\pi$$
−0.750732 + 0.660606i $$0.770299\pi$$
$$314$$ 0 0
$$315$$ 254800. 2.56790
$$316$$ 194672. 1.94953
$$317$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$318$$ 0 0
$$319$$ 84169.0 0.827124
$$320$$ 102400. 1.00000
$$321$$ 0 0
$$322$$ 0 0
$$323$$ 0 0
$$324$$ 317680. 3.02622
$$325$$ 14375.0 0.136095
$$326$$ 0 0
$$327$$ 244001. 2.28190
$$328$$ 0 0
$$329$$ −169393. −1.56496
$$330$$ 0 0
$$331$$ 138482. 1.26397 0.631986 0.774980i $$-0.282240\pi$$
0.631986 + 0.774980i $$0.282240\pi$$
$$332$$ −102112. −0.926404
$$333$$ 0 0
$$334$$ 0 0
$$335$$ 0 0
$$336$$ −213248. −1.88889
$$337$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$338$$ 0 0
$$339$$ 0 0
$$340$$ 105200. 0.910035
$$341$$ 0 0
$$342$$ 0 0
$$343$$ 117649. 1.00000
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$348$$ 313616. 2.58964
$$349$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$350$$ 0 0
$$351$$ −49657.0 −0.403057
$$352$$ 0 0
$$353$$ −229897. −1.84495 −0.922473 0.386060i $$-0.873836\pi$$
−0.922473 + 0.386060i $$0.873836\pi$$
$$354$$ 0 0
$$355$$ −251950. −1.99921
$$356$$ 0 0
$$357$$ −219079. −1.71895
$$358$$ 0 0
$$359$$ 76322.0 0.592190 0.296095 0.955159i $$-0.404316\pi$$
0.296095 + 0.955159i $$0.404316\pi$$
$$360$$ 0 0
$$361$$ 130321. 1.00000
$$362$$ 0 0
$$363$$ 158304. 1.20138
$$364$$ 18032.0 0.136095
$$365$$ −237550. −1.78307
$$366$$ 0 0
$$367$$ −116497. −0.864933 −0.432467 0.901650i $$-0.642357\pi$$
−0.432467 + 0.901650i $$0.642357\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 0 0
$$371$$ 0 0
$$372$$ 0 0
$$373$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$374$$ 0 0
$$375$$ −265625. −1.88889
$$376$$ 0 0
$$377$$ −26519.0 −0.186584
$$378$$ 0 0
$$379$$ −35278.0 −0.245598 −0.122799 0.992432i $$-0.539187\pi$$
−0.122799 + 0.992432i $$0.539187\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 0 0
$$383$$ −29182.0 −0.198938 −0.0994689 0.995041i $$-0.531714\pi$$
−0.0994689 + 0.995041i $$0.531714\pi$$
$$384$$ 0 0
$$385$$ −89425.0 −0.603306
$$386$$ 0 0
$$387$$ 0 0
$$388$$ 54128.0 0.359549
$$389$$ 249407. 1.64820 0.824099 0.566446i $$-0.191682\pi$$
0.824099 + 0.566446i $$0.191682\pi$$
$$390$$ 0 0
$$391$$ 0 0
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 0 0
$$395$$ 304175. 1.94953
$$396$$ −242944. −1.54923
$$397$$ −163897. −1.03990 −0.519948 0.854198i $$-0.674049\pi$$
−0.519948 + 0.854198i $$0.674049\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 160000. 1.00000
$$401$$ −316273. −1.96686 −0.983430 0.181289i $$-0.941973\pi$$
−0.983430 + 0.181289i $$0.941973\pi$$
$$402$$ 0 0
$$403$$ 0 0
$$404$$ 0 0
$$405$$ 496375. 3.02622
$$406$$ 0 0
$$407$$ 0 0
$$408$$ 0 0
$$409$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 294128. 1.73277
$$413$$ 0 0
$$414$$ 0 0
$$415$$ −159550. −0.926404
$$416$$ 0 0
$$417$$ 0 0
$$418$$ 0 0
$$419$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$420$$ −333200. −1.88889
$$421$$ −76753.0 −0.433043 −0.216522 0.976278i $$-0.569471\pi$$
−0.216522 + 0.976278i $$0.569471\pi$$
$$422$$ 0 0
$$423$$ −719056. −4.01867
$$424$$ 0 0
$$425$$ 164375. 0.910035
$$426$$ 0 0
$$427$$ 0 0
$$428$$ 0 0
$$429$$ 28543.0 0.155090
$$430$$ 0 0
$$431$$ 356087. 1.91691 0.958455 0.285245i $$-0.0920749\pi$$
0.958455 + 0.285245i $$0.0920749\pi$$
$$432$$ −552704. −2.96159
$$433$$ 193538. 1.03226 0.516132 0.856509i $$-0.327372\pi$$
0.516132 + 0.856509i $$0.327372\pi$$
$$434$$ 0 0
$$435$$ 490025. 2.58964
$$436$$ −229648. −1.20806
$$437$$ 0 0
$$438$$ 0 0
$$439$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$440$$ 0 0
$$441$$ 499408. 2.56790
$$442$$ 0 0
$$443$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ 0 0
$$447$$ −412114. −2.06254
$$448$$ 200704. 1.00000
$$449$$ 264287. 1.31094 0.655470 0.755221i $$-0.272470\pi$$
0.655470 + 0.755221i $$0.272470\pi$$
$$450$$ 0 0
$$451$$ 0 0
$$452$$ 0 0
$$453$$ 772361. 3.76378
$$454$$ 0 0
$$455$$ 28175.0 0.136095
$$456$$ 0 0
$$457$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$458$$ 0 0
$$459$$ −567817. −2.69515
$$460$$ 0 0
$$461$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$462$$ 0 0
$$463$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$464$$ −295168. −1.37099
$$465$$ 0 0
$$466$$ 0 0
$$467$$ 322463. 1.47858 0.739292 0.673385i $$-0.235160\pi$$
0.739292 + 0.673385i $$0.235160\pi$$
$$468$$ 76544.0 0.349478
$$469$$ 0 0
$$470$$ 0 0
$$471$$ 532814. 2.40178
$$472$$ 0 0
$$473$$ 0 0
$$474$$ 0 0
$$475$$ 0 0
$$476$$ 206192. 0.910035
$$477$$ 0 0
$$478$$ 0 0
$$479$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$480$$ 0 0
$$481$$ 0 0
$$482$$ 0 0
$$483$$ 0 0
$$484$$ −148992. −0.636022
$$485$$ 84575.0 0.359549
$$486$$ 0 0
$$487$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$488$$ 0 0
$$489$$ 0 0
$$490$$ 0 0
$$491$$ −470713. −1.95251 −0.976255 0.216625i $$-0.930495\pi$$
−0.976255 + 0.216625i $$0.930495\pi$$
$$492$$ 0 0
$$493$$ −303239. −1.24765
$$494$$ 0 0
$$495$$ −379600. −1.54923
$$496$$ 0 0
$$497$$ −493822. −1.99921
$$498$$ 0 0
$$499$$ −31513.0 −0.126558 −0.0632789 0.997996i $$-0.520156\pi$$
−0.0632789 + 0.997996i $$0.520156\pi$$
$$500$$ 250000. 1.00000
$$501$$ −300271. −1.19629
$$502$$ 0 0
$$503$$ −313297. −1.23828 −0.619142 0.785279i $$-0.712519\pi$$
−0.619142 + 0.785279i $$0.712519\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ 0 0
$$507$$ 476544. 1.85390
$$508$$ 0 0
$$509$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$510$$ 0 0
$$511$$ −465598. −1.78307
$$512$$ 0 0
$$513$$ 0 0
$$514$$ 0 0
$$515$$ 459575. 1.73277
$$516$$ 0 0
$$517$$ 252361. 0.944150
$$518$$ 0 0
$$519$$ 187289. 0.695309
$$520$$ 0 0
$$521$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$522$$ 0 0
$$523$$ −440782. −1.61146 −0.805732 0.592281i $$-0.798228\pi$$
−0.805732 + 0.592281i $$0.798228\pi$$
$$524$$ 0 0
$$525$$ −520625. −1.88889
$$526$$ 0 0
$$527$$ 0 0
$$528$$ 317696. 1.13958
$$529$$ 279841. 1.00000
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 0 0
$$533$$ 0 0
$$534$$ 0 0
$$535$$ 0 0
$$536$$ 0 0
$$537$$ 281486. 0.976131
$$538$$ 0 0
$$539$$ −175273. −0.603306
$$540$$ −863600. −2.96159
$$541$$ 2927.00 0.0100006 0.00500032 0.999987i $$-0.498408\pi$$
0.00500032 + 0.999987i $$0.498408\pi$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ 0 0
$$545$$ −358825. −1.20806
$$546$$ 0 0
$$547$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$548$$ 0 0
$$549$$ 0 0
$$550$$ 0 0
$$551$$ 0 0
$$552$$ 0 0
$$553$$ 596183. 1.94953
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$558$$ 0 0
$$559$$ 0 0
$$560$$ 313600. 1.00000
$$561$$ 326383. 1.03706
$$562$$ 0 0
$$563$$ 129938. 0.409939 0.204970 0.978768i $$-0.434290\pi$$
0.204970 + 0.978768i $$0.434290\pi$$
$$564$$ 940304. 2.95604
$$565$$ 0 0
$$566$$ 0 0
$$567$$ 972895. 3.02622
$$568$$ 0 0
$$569$$ 566882. 1.75093 0.875464 0.483284i $$-0.160556\pi$$
0.875464 + 0.483284i $$0.160556\pi$$
$$570$$ 0 0
$$571$$ −638158. −1.95729 −0.978647 0.205549i $$-0.934102\pi$$
−0.978647 + 0.205549i $$0.934102\pi$$
$$572$$ −26864.0 −0.0821067
$$573$$ −806599. −2.45668
$$574$$ 0 0
$$575$$ 0 0
$$576$$ 851968. 2.56790
$$577$$ −665017. −1.99747 −0.998737 0.0502441i $$-0.984000\pi$$
−0.998737 + 0.0502441i $$0.984000\pi$$
$$578$$ 0 0
$$579$$ 0 0
$$580$$ −461200. −1.37099
$$581$$ −312718. −0.926404
$$582$$ 0 0
$$583$$ 0 0
$$584$$ 0 0
$$585$$ 119600. 0.349478
$$586$$ 0 0
$$587$$ 507698. 1.47343 0.736715 0.676204i $$-0.236376\pi$$
0.736715 + 0.676204i $$0.236376\pi$$
$$588$$ −653072. −1.88889
$$589$$ 0 0
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 0 0
$$593$$ −320137. −0.910388 −0.455194 0.890392i $$-0.650430\pi$$
−0.455194 + 0.890392i $$0.650430\pi$$
$$594$$ 0 0
$$595$$ 322175. 0.910035
$$596$$ 387872. 1.09193
$$597$$ 0 0
$$598$$ 0 0
$$599$$ −613273. −1.70923 −0.854614 0.519263i $$-0.826206\pi$$
−0.854614 + 0.519263i $$0.826206\pi$$
$$600$$ 0 0
$$601$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ −726928. −1.99259
$$605$$ −232800. −0.636022
$$606$$ 0 0
$$607$$ −82417.0 −0.223686 −0.111843 0.993726i $$-0.535675\pi$$
−0.111843 + 0.993726i $$0.535675\pi$$
$$608$$ 0 0
$$609$$ 960449. 2.58964
$$610$$ 0 0
$$611$$ −79511.0 −0.212983
$$612$$ 875264. 2.33688
$$613$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$618$$ 0 0
$$619$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ 0 0
$$624$$ −100096. −0.257068
$$625$$ 390625. 1.00000
$$626$$ 0 0
$$627$$ 0 0
$$628$$ −501472. −1.27153
$$629$$ 0 0
$$630$$ 0 0
$$631$$ 100487. 0.252378 0.126189 0.992006i $$-0.459725\pi$$
0.126189 + 0.992006i $$0.459725\pi$$
$$632$$ 0 0
$$633$$ 1.31908e6 3.29203
$$634$$ 0 0
$$635$$ 0 0
$$636$$ 0 0
$$637$$ 55223.0 0.136095
$$638$$ 0 0
$$639$$ −2.09622e6 −5.13376
$$640$$ 0 0
$$641$$ 96002.0 0.233649 0.116825 0.993153i $$-0.462728\pi$$
0.116825 + 0.993153i $$0.462728\pi$$
$$642$$ 0 0
$$643$$ 713183. 1.72496 0.862480 0.506091i $$-0.168910\pi$$
0.862480 + 0.506091i $$0.168910\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 111458. 0.266258 0.133129 0.991099i $$-0.457498\pi$$
0.133129 + 0.991099i $$0.457498\pi$$
$$648$$ 0 0
$$649$$ 0 0
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ 0 0
$$657$$ −1.97642e6 −4.57876
$$658$$ 0 0
$$659$$ 777527. 1.79038 0.895189 0.445687i $$-0.147041\pi$$
0.895189 + 0.445687i $$0.147041\pi$$
$$660$$ 496400. 1.13958
$$661$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$662$$ 0 0
$$663$$ −102833. −0.233941
$$664$$ 0 0
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 0 0
$$668$$ 282608. 0.633332
$$669$$ −1.04283e6 −2.33003
$$670$$ 0 0
$$671$$ 0 0
$$672$$ 0 0
$$673$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$674$$ 0 0
$$675$$ −1.34938e6 −2.96159
$$676$$ −448512. −0.981478
$$677$$ 750023. 1.63643 0.818215 0.574913i $$-0.194964\pi$$
0.818215 + 0.574913i $$0.194964\pi$$
$$678$$ 0 0
$$679$$ 165767. 0.359549
$$680$$ 0 0
$$681$$ −846991. −1.82635
$$682$$ 0 0
$$683$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$684$$ 0 0
$$685$$ 0 0
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 0 0
$$689$$ 0 0
$$690$$ 0 0
$$691$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$692$$ −176272. −0.368105
$$693$$ −744016. −1.54923
$$694$$ 0 0
$$695$$ 0 0
$$696$$ 0 0
$$697$$ 0 0
$$698$$ 0 0
$$699$$ 0 0
$$700$$ 490000. 1.00000
$$701$$ −884833. −1.80063 −0.900317 0.435235i $$-0.856665\pi$$
−0.900317 + 0.435235i $$0.856665\pi$$
$$702$$ 0 0
$$703$$ 0 0
$$704$$ −299008. −0.603306
$$705$$ 1.46922e6 2.95604
$$706$$ 0 0
$$707$$ 0 0
$$708$$ 0 0
$$709$$ 1.00253e6 1.99436 0.997180 0.0750454i $$-0.0239102\pi$$
0.997180 + 0.0750454i $$0.0239102\pi$$
$$710$$ 0 0
$$711$$ 2.53074e6 5.00619
$$712$$ 0 0
$$713$$ 0 0
$$714$$ 0 0
$$715$$ −41975.0 −0.0821067
$$716$$ −264928. −0.516775
$$717$$ −737239. −1.43407
$$718$$ 0 0
$$719$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$720$$ 1.33120e6 2.56790
$$721$$ 900767. 1.73277
$$722$$ 0 0
$$723$$ 0 0
$$724$$ 0 0
$$725$$ −720625. −1.37099
$$726$$ 0 0
$$727$$ 976418. 1.84743 0.923713 0.383086i $$-0.125139\pi$$
0.923713 + 0.383086i $$0.125139\pi$$
$$728$$ 0 0
$$729$$ 1.15690e6 2.17691
$$730$$ 0 0
$$731$$ 0 0
$$732$$ 0 0
$$733$$ 51143.0 0.0951871 0.0475936 0.998867i $$-0.484845\pi$$
0.0475936 + 0.998867i $$0.484845\pi$$
$$734$$ 0 0
$$735$$ −1.02042e6 −1.88889
$$736$$ 0 0
$$737$$ 0 0
$$738$$ 0 0
$$739$$ 749207. 1.37187 0.685935 0.727663i $$-0.259393\pi$$
0.685935 + 0.727663i $$0.259393\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$744$$ 0 0
$$745$$ 606050. 1.09193
$$746$$ 0 0
$$747$$ −1.32746e6 −2.37892
$$748$$ −307184. −0.549029
$$749$$ 0 0
$$750$$ 0 0
$$751$$ 648887. 1.15051 0.575253 0.817975i $$-0.304903\pi$$
0.575253 + 0.817975i $$0.304903\pi$$
$$752$$ −884992. −1.56496
$$753$$ 0 0
$$754$$ 0 0
$$755$$ −1.13582e6 −1.99259
$$756$$ −1.69266e6 −2.96159
$$757$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$762$$ 0 0
$$763$$ −703297. −1.20806
$$764$$ 759152. 1.30059
$$765$$ 1.36760e6 2.33688
$$766$$ 0 0
$$767$$ 0 0
$$768$$ −1.11411e6 −1.88889
$$769$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$770$$ 0 0
$$771$$ −1.90295e6 −3.20124
$$772$$ 0 0
$$773$$ 1.17962e6 1.97417 0.987084 0.160202i $$-0.0512144\pi$$
0.987084 + 0.160202i $$0.0512144\pi$$
$$774$$ 0 0
$$775$$ 0 0
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ 0 0
$$780$$ −156400. −0.257068
$$781$$ 735694. 1.20613
$$782$$ 0 0
$$783$$ 2.48933e6 4.06030
$$784$$ 614656. 1.00000
$$785$$ −783550. −1.27153
$$786$$ 0 0
$$787$$ −1.03714e6 −1.67451 −0.837253 0.546816i $$-0.815840\pi$$
−0.837253 + 0.546816i $$0.815840\pi$$
$$788$$ 0 0
$$789$$ 0 0
$$790$$ 0 0
$$791$$ 0 0
$$792$$ 0 0
$$793$$ 0 0
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ 1.07354e6 1.69006 0.845031 0.534717i $$-0.179582\pi$$
0.845031 + 0.534717i $$0.179582\pi$$
$$798$$ 0 0
$$799$$ −909191. −1.42417
$$800$$ 0 0
$$801$$ 0 0
$$802$$ 0 0
$$803$$ 693646. 1.07574
$$804$$ 0 0
$$805$$ 0 0
$$806$$ 0 0
$$807$$ 0 0
$$808$$ 0 0
$$809$$ −1.29955e6 −1.98562 −0.992812 0.119685i $$-0.961811\pi$$
−0.992812 + 0.119685i $$0.961811\pi$$
$$810$$ 0 0
$$811$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$812$$ −903952. −1.37099
$$813$$ 0 0
$$814$$ 0 0
$$815$$ 0 0
$$816$$ −1.14458e6 −1.71895
$$817$$ 0 0
$$818$$ 0 0
$$819$$ 234416. 0.349478
$$820$$ 0 0
$$821$$ 1.23437e6 1.83129 0.915647 0.401984i $$-0.131679\pi$$
0.915647 + 0.401984i $$0.131679\pi$$
$$822$$ 0 0
$$823$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$824$$ 0 0
$$825$$ 775625. 1.13958
$$826$$ 0 0
$$827$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$828$$ 0 0
$$829$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$830$$ 0 0
$$831$$ 0 0
$$832$$ 94208.0 0.136095
$$833$$ 631463. 0.910035
$$834$$ 0 0
$$835$$ 441575. 0.633332
$$836$$ 0 0
$$837$$ 0 0
$$838$$ 0 0
$$839$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$840$$ 0 0
$$841$$ 622128. 0.879605
$$842$$ 0 0
$$843$$ −2.03672e6 −2.86600
$$844$$ −1.24149e6 −1.74284
$$845$$ −700800. −0.981478
$$846$$ 0 0
$$847$$ −456288. −0.636022
$$848$$ 0 0
$$849$$ −2.58915e6 −3.59205
$$850$$ 0 0
$$851$$ 0 0
$$852$$ 2.74122e6 3.77628
$$853$$ −1.44782e6 −1.98984 −0.994918 0.100692i $$-0.967894\pi$$
−0.994918 + 0.100692i $$0.967894\pi$$
$$854$$ 0 0
$$855$$ 0 0
$$856$$ 0 0
$$857$$ −970462. −1.32135 −0.660674 0.750673i $$-0.729729\pi$$
−0.660674 + 0.750673i $$0.729729\pi$$
$$858$$ 0 0
$$859$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$860$$ 0 0
$$861$$ 0 0
$$862$$ 0 0
$$863$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$864$$ 0 0
$$865$$ −275425. −0.368105
$$866$$ 0 0
$$867$$ 243984. 0.324581
$$868$$ 0 0
$$869$$ −888191. −1.17616
$$870$$ 0 0
$$871$$ 0 0
$$872$$ 0 0
$$873$$ 703664. 0.923287
$$874$$ 0 0
$$875$$ 765625. 1.00000
$$876$$ 2.58454e6 3.36803
$$877$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$878$$ 0 0
$$879$$ 2.91273e6 3.76983
$$880$$ −467200. −0.603306
$$881$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$882$$ 0 0
$$883$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$884$$ 96784.0 0.123851
$$885$$ 0 0
$$886$$ 0 0
$$887$$ −1.32950e6 −1.68983 −0.844913 0.534904i $$-0.820348\pi$$
−0.844913 + 0.534904i $$0.820348\pi$$
$$888$$ 0 0
$$889$$ 0 0
$$890$$ 0 0
$$891$$ −1.44942e6 −1.82573
$$892$$ 981488. 1.23355
$$893$$ 0 0
$$894$$ 0 0
$$895$$ −413950. −0.516775
$$896$$ 0 0
$$897$$ 0 0
$$898$$ 0 0
$$899$$ 0 0
$$900$$ 2.08000e6 2.56790
$$901$$ 0 0
$$902$$ 0 0
$$903$$ 0 0
$$904$$ 0 0
$$905$$ 0 0
$$906$$ 0 0
$$907$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$908$$ 797168. 0.966892
$$909$$ 0 0
$$910$$ 0 0
$$911$$ 1.15584e6 1.39271 0.696357 0.717696i $$-0.254803\pi$$
0.696357 + 0.717696i $$0.254803\pi$$
$$912$$ 0 0
$$913$$ 465886. 0.558905
$$914$$ 0 0
$$915$$ 0 0
$$916$$ 0 0
$$917$$ 0 0
$$918$$ 0 0
$$919$$ −695113. −0.823047 −0.411523 0.911399i $$-0.635003\pi$$
−0.411523 + 0.911399i $$0.635003\pi$$
$$920$$ 0 0
$$921$$ −2.29947e6 −2.71087
$$922$$ 0 0
$$923$$ −231794. −0.272081
$$924$$ 972944. 1.13958
$$925$$ 0 0
$$926$$ 0 0
$$927$$ 3.82366e6 4.44959
$$928$$ 0 0
$$929$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$930$$ 0 0
$$931$$ 0 0
$$932$$ 0 0
$$933$$ 0 0
$$934$$ 0 0
$$935$$ −479975. −0.549029
$$936$$ 0 0
$$937$$ 1.58930e6 1.81020 0.905102 0.425195i $$-0.139794\pi$$
0.905102 + 0.425195i $$0.139794\pi$$
$$938$$ 0 0
$$939$$ 2.50065e6 2.83610
$$940$$ −1.38280e6 −1.56496
$$941$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$942$$ 0 0
$$943$$ 0 0
$$944$$ 0 0
$$945$$ −2.64478e6 −2.96159
$$946$$ 0 0
$$947$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$948$$ −3.30942e6 −3.68244
$$949$$ −218546. −0.242667
$$950$$ 0 0
$$951$$ 0 0
$$952$$ 0 0
$$953$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$954$$ 0 0
$$955$$ 1.18618e6 1.30059
$$956$$ 693872. 0.759213
$$957$$ −1.43087e6 −1.56235
$$958$$ 0 0
$$959$$ 0 0
$$960$$ −1.74080e6 −1.88889
$$961$$ 923521. 1.00000
$$962$$ 0 0
$$963$$ 0 0
$$964$$ 0 0
$$965$$ 0 0
$$966$$ 0 0
$$967$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$968$$ 0 0
$$969$$ 0 0
$$970$$ 0 0
$$971$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$972$$ −2.60250e6 −2.75459
$$973$$ 0 0
$$974$$ 0 0
$$975$$ −244375. −0.257068
$$976$$ 0 0
$$977$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$978$$ 0 0
$$979$$ 0 0
$$980$$ 960400. 1.00000
$$981$$ −2.98542e6 −3.10219
$$982$$ 0 0
$$983$$ −675937. −0.699518 −0.349759 0.936840i $$-0.613737\pi$$
−0.349759 + 0.936840i $$0.613737\pi$$
$$984$$ 0 0
$$985$$ 0 0
$$986$$ 0 0
$$987$$ 2.87968e6 2.95604
$$988$$ 0 0
$$989$$ 0 0
$$990$$ 0 0
$$991$$ −1.44288e6 −1.46920 −0.734602 0.678498i $$-0.762631\pi$$
−0.734602 + 0.678498i $$0.762631\pi$$
$$992$$ 0 0
$$993$$ −2.35419e6 −2.38750
$$994$$ 0 0
$$995$$ 0 0
$$996$$ 1.73590e6 1.74988
$$997$$ 737783. 0.742230 0.371115 0.928587i $$-0.378976\pi$$
0.371115 + 0.928587i $$0.378976\pi$$
$$998$$ 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 35.5.c.a.34.1 1
3.2 odd 2 315.5.e.a.244.1 1
4.3 odd 2 560.5.p.b.209.1 1
5.2 odd 4 175.5.d.c.76.2 2
5.3 odd 4 175.5.d.c.76.1 2
5.4 even 2 35.5.c.b.34.1 yes 1
7.6 odd 2 35.5.c.b.34.1 yes 1
15.14 odd 2 315.5.e.b.244.1 1
20.19 odd 2 560.5.p.a.209.1 1
21.20 even 2 315.5.e.b.244.1 1
28.27 even 2 560.5.p.a.209.1 1
35.13 even 4 175.5.d.c.76.2 2
35.27 even 4 175.5.d.c.76.1 2
35.34 odd 2 CM 35.5.c.a.34.1 1
105.104 even 2 315.5.e.a.244.1 1
140.139 even 2 560.5.p.b.209.1 1

By twisted newform
Twist Min Dim Char Parity Ord Type
35.5.c.a.34.1 1 1.1 even 1 trivial
35.5.c.a.34.1 1 35.34 odd 2 CM
35.5.c.b.34.1 yes 1 5.4 even 2
35.5.c.b.34.1 yes 1 7.6 odd 2
175.5.d.c.76.1 2 5.3 odd 4
175.5.d.c.76.1 2 35.27 even 4
175.5.d.c.76.2 2 5.2 odd 4
175.5.d.c.76.2 2 35.13 even 4
315.5.e.a.244.1 1 3.2 odd 2
315.5.e.a.244.1 1 105.104 even 2
315.5.e.b.244.1 1 15.14 odd 2
315.5.e.b.244.1 1 21.20 even 2
560.5.p.a.209.1 1 20.19 odd 2
560.5.p.a.209.1 1 28.27 even 2
560.5.p.b.209.1 1 4.3 odd 2
560.5.p.b.209.1 1 140.139 even 2