# Properties

 Label 7600.2.a.r.1.1 Level $7600$ Weight $2$ Character 7600.1 Self dual yes Analytic conductor $60.686$ Analytic rank $1$ Dimension $1$ CM no Inner twists $1$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$7600 = 2^{4} \cdot 5^{2} \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 7600.a (trivial)

## Newform invariants

 Self dual: yes Analytic conductor: $$60.6863055362$$ Analytic rank: $$1$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 380) Fricke sign: $$1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

 Embedding label 1.1 Character $$\chi$$ $$=$$ 7600.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+2.00000 q^{3} +2.00000 q^{7} +1.00000 q^{9} +O(q^{10})$$ $$q+2.00000 q^{3} +2.00000 q^{7} +1.00000 q^{9} -6.00000 q^{13} -2.00000 q^{17} +1.00000 q^{19} +4.00000 q^{21} -2.00000 q^{23} -4.00000 q^{27} -2.00000 q^{29} -4.00000 q^{31} +10.0000 q^{37} -12.0000 q^{39} -10.0000 q^{41} +6.00000 q^{43} -6.00000 q^{47} -3.00000 q^{49} -4.00000 q^{51} -6.00000 q^{53} +2.00000 q^{57} +4.00000 q^{59} +2.00000 q^{61} +2.00000 q^{63} -2.00000 q^{67} -4.00000 q^{69} -12.0000 q^{71} +6.00000 q^{73} -8.00000 q^{79} -11.0000 q^{81} -2.00000 q^{83} -4.00000 q^{87} +2.00000 q^{89} -12.0000 q^{91} -8.00000 q^{93} +18.0000 q^{97} +O(q^{100})$$

## 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
$$3$$ 2.00000 1.15470 0.577350 0.816497i $$-0.304087\pi$$
0.577350 + 0.816497i $$0.304087\pi$$
$$4$$ 0 0
$$5$$ 0 0
$$6$$ 0 0
$$7$$ 2.00000 0.755929 0.377964 0.925820i $$-0.376624\pi$$
0.377964 + 0.925820i $$0.376624\pi$$
$$8$$ 0 0
$$9$$ 1.00000 0.333333
$$10$$ 0 0
$$11$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$12$$ 0 0
$$13$$ −6.00000 −1.66410 −0.832050 0.554700i $$-0.812833\pi$$
−0.832050 + 0.554700i $$0.812833\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ −2.00000 −0.485071 −0.242536 0.970143i $$-0.577979\pi$$
−0.242536 + 0.970143i $$0.577979\pi$$
$$18$$ 0 0
$$19$$ 1.00000 0.229416
$$20$$ 0 0
$$21$$ 4.00000 0.872872
$$22$$ 0 0
$$23$$ −2.00000 −0.417029 −0.208514 0.978019i $$-0.566863\pi$$
−0.208514 + 0.978019i $$0.566863\pi$$
$$24$$ 0 0
$$25$$ 0 0
$$26$$ 0 0
$$27$$ −4.00000 −0.769800
$$28$$ 0 0
$$29$$ −2.00000 −0.371391 −0.185695 0.982607i $$-0.559454\pi$$
−0.185695 + 0.982607i $$0.559454\pi$$
$$30$$ 0 0
$$31$$ −4.00000 −0.718421 −0.359211 0.933257i $$-0.616954\pi$$
−0.359211 + 0.933257i $$0.616954\pi$$
$$32$$ 0 0
$$33$$ 0 0
$$34$$ 0 0
$$35$$ 0 0
$$36$$ 0 0
$$37$$ 10.0000 1.64399 0.821995 0.569495i $$-0.192861\pi$$
0.821995 + 0.569495i $$0.192861\pi$$
$$38$$ 0 0
$$39$$ −12.0000 −1.92154
$$40$$ 0 0
$$41$$ −10.0000 −1.56174 −0.780869 0.624695i $$-0.785223\pi$$
−0.780869 + 0.624695i $$0.785223\pi$$
$$42$$ 0 0
$$43$$ 6.00000 0.914991 0.457496 0.889212i $$-0.348747\pi$$
0.457496 + 0.889212i $$0.348747\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ −6.00000 −0.875190 −0.437595 0.899172i $$-0.644170\pi$$
−0.437595 + 0.899172i $$0.644170\pi$$
$$48$$ 0 0
$$49$$ −3.00000 −0.428571
$$50$$ 0 0
$$51$$ −4.00000 −0.560112
$$52$$ 0 0
$$53$$ −6.00000 −0.824163 −0.412082 0.911147i $$-0.635198\pi$$
−0.412082 + 0.911147i $$0.635198\pi$$
$$54$$ 0 0
$$55$$ 0 0
$$56$$ 0 0
$$57$$ 2.00000 0.264906
$$58$$ 0 0
$$59$$ 4.00000 0.520756 0.260378 0.965507i $$-0.416153\pi$$
0.260378 + 0.965507i $$0.416153\pi$$
$$60$$ 0 0
$$61$$ 2.00000 0.256074 0.128037 0.991769i $$-0.459132\pi$$
0.128037 + 0.991769i $$0.459132\pi$$
$$62$$ 0 0
$$63$$ 2.00000 0.251976
$$64$$ 0 0
$$65$$ 0 0
$$66$$ 0 0
$$67$$ −2.00000 −0.244339 −0.122169 0.992509i $$-0.538985\pi$$
−0.122169 + 0.992509i $$0.538985\pi$$
$$68$$ 0 0
$$69$$ −4.00000 −0.481543
$$70$$ 0 0
$$71$$ −12.0000 −1.42414 −0.712069 0.702109i $$-0.752242\pi$$
−0.712069 + 0.702109i $$0.752242\pi$$
$$72$$ 0 0
$$73$$ 6.00000 0.702247 0.351123 0.936329i $$-0.385800\pi$$
0.351123 + 0.936329i $$0.385800\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 0 0
$$77$$ 0 0
$$78$$ 0 0
$$79$$ −8.00000 −0.900070 −0.450035 0.893011i $$-0.648589\pi$$
−0.450035 + 0.893011i $$0.648589\pi$$
$$80$$ 0 0
$$81$$ −11.0000 −1.22222
$$82$$ 0 0
$$83$$ −2.00000 −0.219529 −0.109764 0.993958i $$-0.535010\pi$$
−0.109764 + 0.993958i $$0.535010\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ 0 0
$$87$$ −4.00000 −0.428845
$$88$$ 0 0
$$89$$ 2.00000 0.212000 0.106000 0.994366i $$-0.466196\pi$$
0.106000 + 0.994366i $$0.466196\pi$$
$$90$$ 0 0
$$91$$ −12.0000 −1.25794
$$92$$ 0 0
$$93$$ −8.00000 −0.829561
$$94$$ 0 0
$$95$$ 0 0
$$96$$ 0 0
$$97$$ 18.0000 1.82762 0.913812 0.406138i $$-0.133125\pi$$
0.913812 + 0.406138i $$0.133125\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ 0 0
$$101$$ −10.0000 −0.995037 −0.497519 0.867453i $$-0.665755\pi$$
−0.497519 + 0.867453i $$0.665755\pi$$
$$102$$ 0 0
$$103$$ −6.00000 −0.591198 −0.295599 0.955312i $$-0.595519\pi$$
−0.295599 + 0.955312i $$0.595519\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ −18.0000 −1.74013 −0.870063 0.492941i $$-0.835922\pi$$
−0.870063 + 0.492941i $$0.835922\pi$$
$$108$$ 0 0
$$109$$ 10.0000 0.957826 0.478913 0.877862i $$-0.341031\pi$$
0.478913 + 0.877862i $$0.341031\pi$$
$$110$$ 0 0
$$111$$ 20.0000 1.89832
$$112$$ 0 0
$$113$$ 10.0000 0.940721 0.470360 0.882474i $$-0.344124\pi$$
0.470360 + 0.882474i $$0.344124\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ 0 0
$$117$$ −6.00000 −0.554700
$$118$$ 0 0
$$119$$ −4.00000 −0.366679
$$120$$ 0 0
$$121$$ −11.0000 −1.00000
$$122$$ 0 0
$$123$$ −20.0000 −1.80334
$$124$$ 0 0
$$125$$ 0 0
$$126$$ 0 0
$$127$$ 6.00000 0.532414 0.266207 0.963916i $$-0.414230\pi$$
0.266207 + 0.963916i $$0.414230\pi$$
$$128$$ 0 0
$$129$$ 12.0000 1.05654
$$130$$ 0 0
$$131$$ −16.0000 −1.39793 −0.698963 0.715158i $$-0.746355\pi$$
−0.698963 + 0.715158i $$0.746355\pi$$
$$132$$ 0 0
$$133$$ 2.00000 0.173422
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ 6.00000 0.512615 0.256307 0.966595i $$-0.417494\pi$$
0.256307 + 0.966595i $$0.417494\pi$$
$$138$$ 0 0
$$139$$ −12.0000 −1.01783 −0.508913 0.860818i $$-0.669953\pi$$
−0.508913 + 0.860818i $$0.669953\pi$$
$$140$$ 0 0
$$141$$ −12.0000 −1.01058
$$142$$ 0 0
$$143$$ 0 0
$$144$$ 0 0
$$145$$ 0 0
$$146$$ 0 0
$$147$$ −6.00000 −0.494872
$$148$$ 0 0
$$149$$ 10.0000 0.819232 0.409616 0.912258i $$-0.365663\pi$$
0.409616 + 0.912258i $$0.365663\pi$$
$$150$$ 0 0
$$151$$ −12.0000 −0.976546 −0.488273 0.872691i $$-0.662373\pi$$
−0.488273 + 0.872691i $$0.662373\pi$$
$$152$$ 0 0
$$153$$ −2.00000 −0.161690
$$154$$ 0 0
$$155$$ 0 0
$$156$$ 0 0
$$157$$ −18.0000 −1.43656 −0.718278 0.695756i $$-0.755069\pi$$
−0.718278 + 0.695756i $$0.755069\pi$$
$$158$$ 0 0
$$159$$ −12.0000 −0.951662
$$160$$ 0 0
$$161$$ −4.00000 −0.315244
$$162$$ 0 0
$$163$$ 6.00000 0.469956 0.234978 0.972001i $$-0.424498\pi$$
0.234978 + 0.972001i $$0.424498\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ 14.0000 1.08335 0.541676 0.840587i $$-0.317790\pi$$
0.541676 + 0.840587i $$0.317790\pi$$
$$168$$ 0 0
$$169$$ 23.0000 1.76923
$$170$$ 0 0
$$171$$ 1.00000 0.0764719
$$172$$ 0 0
$$173$$ −6.00000 −0.456172 −0.228086 0.973641i $$-0.573247\pi$$
−0.228086 + 0.973641i $$0.573247\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 0 0
$$177$$ 8.00000 0.601317
$$178$$ 0 0
$$179$$ 12.0000 0.896922 0.448461 0.893802i $$-0.351972\pi$$
0.448461 + 0.893802i $$0.351972\pi$$
$$180$$ 0 0
$$181$$ −10.0000 −0.743294 −0.371647 0.928374i $$-0.621207\pi$$
−0.371647 + 0.928374i $$0.621207\pi$$
$$182$$ 0 0
$$183$$ 4.00000 0.295689
$$184$$ 0 0
$$185$$ 0 0
$$186$$ 0 0
$$187$$ 0 0
$$188$$ 0 0
$$189$$ −8.00000 −0.581914
$$190$$ 0 0
$$191$$ −20.0000 −1.44715 −0.723575 0.690246i $$-0.757502\pi$$
−0.723575 + 0.690246i $$0.757502\pi$$
$$192$$ 0 0
$$193$$ −22.0000 −1.58359 −0.791797 0.610784i $$-0.790854\pi$$
−0.791797 + 0.610784i $$0.790854\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ −2.00000 −0.142494 −0.0712470 0.997459i $$-0.522698\pi$$
−0.0712470 + 0.997459i $$0.522698\pi$$
$$198$$ 0 0
$$199$$ −8.00000 −0.567105 −0.283552 0.958957i $$-0.591513\pi$$
−0.283552 + 0.958957i $$0.591513\pi$$
$$200$$ 0 0
$$201$$ −4.00000 −0.282138
$$202$$ 0 0
$$203$$ −4.00000 −0.280745
$$204$$ 0 0
$$205$$ 0 0
$$206$$ 0 0
$$207$$ −2.00000 −0.139010
$$208$$ 0 0
$$209$$ 0 0
$$210$$ 0 0
$$211$$ −8.00000 −0.550743 −0.275371 0.961338i $$-0.588801\pi$$
−0.275371 + 0.961338i $$0.588801\pi$$
$$212$$ 0 0
$$213$$ −24.0000 −1.64445
$$214$$ 0 0
$$215$$ 0 0
$$216$$ 0 0
$$217$$ −8.00000 −0.543075
$$218$$ 0 0
$$219$$ 12.0000 0.810885
$$220$$ 0 0
$$221$$ 12.0000 0.807207
$$222$$ 0 0
$$223$$ 2.00000 0.133930 0.0669650 0.997755i $$-0.478668\pi$$
0.0669650 + 0.997755i $$0.478668\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ 14.0000 0.929213 0.464606 0.885517i $$-0.346196\pi$$
0.464606 + 0.885517i $$0.346196\pi$$
$$228$$ 0 0
$$229$$ −18.0000 −1.18947 −0.594737 0.803921i $$-0.702744\pi$$
−0.594737 + 0.803921i $$0.702744\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ 22.0000 1.44127 0.720634 0.693316i $$-0.243851\pi$$
0.720634 + 0.693316i $$0.243851\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ 0 0
$$237$$ −16.0000 −1.03931
$$238$$ 0 0
$$239$$ 24.0000 1.55243 0.776215 0.630468i $$-0.217137\pi$$
0.776215 + 0.630468i $$0.217137\pi$$
$$240$$ 0 0
$$241$$ 14.0000 0.901819 0.450910 0.892570i $$-0.351100\pi$$
0.450910 + 0.892570i $$0.351100\pi$$
$$242$$ 0 0
$$243$$ −10.0000 −0.641500
$$244$$ 0 0
$$245$$ 0 0
$$246$$ 0 0
$$247$$ −6.00000 −0.381771
$$248$$ 0 0
$$249$$ −4.00000 −0.253490
$$250$$ 0 0
$$251$$ −16.0000 −1.00991 −0.504956 0.863145i $$-0.668491\pi$$
−0.504956 + 0.863145i $$0.668491\pi$$
$$252$$ 0 0
$$253$$ 0 0
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ 18.0000 1.12281 0.561405 0.827541i $$-0.310261\pi$$
0.561405 + 0.827541i $$0.310261\pi$$
$$258$$ 0 0
$$259$$ 20.0000 1.24274
$$260$$ 0 0
$$261$$ −2.00000 −0.123797
$$262$$ 0 0
$$263$$ −26.0000 −1.60323 −0.801614 0.597841i $$-0.796025\pi$$
−0.801614 + 0.597841i $$0.796025\pi$$
$$264$$ 0 0
$$265$$ 0 0
$$266$$ 0 0
$$267$$ 4.00000 0.244796
$$268$$ 0 0
$$269$$ 26.0000 1.58525 0.792624 0.609711i $$-0.208714\pi$$
0.792624 + 0.609711i $$0.208714\pi$$
$$270$$ 0 0
$$271$$ 28.0000 1.70088 0.850439 0.526073i $$-0.176336\pi$$
0.850439 + 0.526073i $$0.176336\pi$$
$$272$$ 0 0
$$273$$ −24.0000 −1.45255
$$274$$ 0 0
$$275$$ 0 0
$$276$$ 0 0
$$277$$ 14.0000 0.841178 0.420589 0.907251i $$-0.361823\pi$$
0.420589 + 0.907251i $$0.361823\pi$$
$$278$$ 0 0
$$279$$ −4.00000 −0.239474
$$280$$ 0 0
$$281$$ 22.0000 1.31241 0.656205 0.754583i $$-0.272161\pi$$
0.656205 + 0.754583i $$0.272161\pi$$
$$282$$ 0 0
$$283$$ 22.0000 1.30776 0.653882 0.756596i $$-0.273139\pi$$
0.653882 + 0.756596i $$0.273139\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ −20.0000 −1.18056
$$288$$ 0 0
$$289$$ −13.0000 −0.764706
$$290$$ 0 0
$$291$$ 36.0000 2.11036
$$292$$ 0 0
$$293$$ 2.00000 0.116841 0.0584206 0.998292i $$-0.481394\pi$$
0.0584206 + 0.998292i $$0.481394\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ 0 0
$$297$$ 0 0
$$298$$ 0 0
$$299$$ 12.0000 0.693978
$$300$$ 0 0
$$301$$ 12.0000 0.691669
$$302$$ 0 0
$$303$$ −20.0000 −1.14897
$$304$$ 0 0
$$305$$ 0 0
$$306$$ 0 0
$$307$$ 22.0000 1.25561 0.627803 0.778372i $$-0.283954\pi$$
0.627803 + 0.778372i $$0.283954\pi$$
$$308$$ 0 0
$$309$$ −12.0000 −0.682656
$$310$$ 0 0
$$311$$ −12.0000 −0.680458 −0.340229 0.940343i $$-0.610505\pi$$
−0.340229 + 0.940343i $$0.610505\pi$$
$$312$$ 0 0
$$313$$ −10.0000 −0.565233 −0.282617 0.959233i $$-0.591202\pi$$
−0.282617 + 0.959233i $$0.591202\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ −30.0000 −1.68497 −0.842484 0.538721i $$-0.818908\pi$$
−0.842484 + 0.538721i $$0.818908\pi$$
$$318$$ 0 0
$$319$$ 0 0
$$320$$ 0 0
$$321$$ −36.0000 −2.00932
$$322$$ 0 0
$$323$$ −2.00000 −0.111283
$$324$$ 0 0
$$325$$ 0 0
$$326$$ 0 0
$$327$$ 20.0000 1.10600
$$328$$ 0 0
$$329$$ −12.0000 −0.661581
$$330$$ 0 0
$$331$$ −16.0000 −0.879440 −0.439720 0.898135i $$-0.644922\pi$$
−0.439720 + 0.898135i $$0.644922\pi$$
$$332$$ 0 0
$$333$$ 10.0000 0.547997
$$334$$ 0 0
$$335$$ 0 0
$$336$$ 0 0
$$337$$ 2.00000 0.108947 0.0544735 0.998515i $$-0.482652\pi$$
0.0544735 + 0.998515i $$0.482652\pi$$
$$338$$ 0 0
$$339$$ 20.0000 1.08625
$$340$$ 0 0
$$341$$ 0 0
$$342$$ 0 0
$$343$$ −20.0000 −1.07990
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ −6.00000 −0.322097 −0.161048 0.986947i $$-0.551488\pi$$
−0.161048 + 0.986947i $$0.551488\pi$$
$$348$$ 0 0
$$349$$ −26.0000 −1.39175 −0.695874 0.718164i $$-0.744983\pi$$
−0.695874 + 0.718164i $$0.744983\pi$$
$$350$$ 0 0
$$351$$ 24.0000 1.28103
$$352$$ 0 0
$$353$$ 6.00000 0.319348 0.159674 0.987170i $$-0.448956\pi$$
0.159674 + 0.987170i $$0.448956\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ 0 0
$$357$$ −8.00000 −0.423405
$$358$$ 0 0
$$359$$ 24.0000 1.26667 0.633336 0.773877i $$-0.281685\pi$$
0.633336 + 0.773877i $$0.281685\pi$$
$$360$$ 0 0
$$361$$ 1.00000 0.0526316
$$362$$ 0 0
$$363$$ −22.0000 −1.15470
$$364$$ 0 0
$$365$$ 0 0
$$366$$ 0 0
$$367$$ 26.0000 1.35719 0.678594 0.734513i $$-0.262589\pi$$
0.678594 + 0.734513i $$0.262589\pi$$
$$368$$ 0 0
$$369$$ −10.0000 −0.520579
$$370$$ 0 0
$$371$$ −12.0000 −0.623009
$$372$$ 0 0
$$373$$ −6.00000 −0.310668 −0.155334 0.987862i $$-0.549645\pi$$
−0.155334 + 0.987862i $$0.549645\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ 12.0000 0.618031
$$378$$ 0 0
$$379$$ −20.0000 −1.02733 −0.513665 0.857991i $$-0.671713\pi$$
−0.513665 + 0.857991i $$0.671713\pi$$
$$380$$ 0 0
$$381$$ 12.0000 0.614779
$$382$$ 0 0
$$383$$ −6.00000 −0.306586 −0.153293 0.988181i $$-0.548988\pi$$
−0.153293 + 0.988181i $$0.548988\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 0 0
$$387$$ 6.00000 0.304997
$$388$$ 0 0
$$389$$ −6.00000 −0.304212 −0.152106 0.988364i $$-0.548606\pi$$
−0.152106 + 0.988364i $$0.548606\pi$$
$$390$$ 0 0
$$391$$ 4.00000 0.202289
$$392$$ 0 0
$$393$$ −32.0000 −1.61419
$$394$$ 0 0
$$395$$ 0 0
$$396$$ 0 0
$$397$$ −10.0000 −0.501886 −0.250943 0.968002i $$-0.580741\pi$$
−0.250943 + 0.968002i $$0.580741\pi$$
$$398$$ 0 0
$$399$$ 4.00000 0.200250
$$400$$ 0 0
$$401$$ 18.0000 0.898877 0.449439 0.893311i $$-0.351624\pi$$
0.449439 + 0.893311i $$0.351624\pi$$
$$402$$ 0 0
$$403$$ 24.0000 1.19553
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 0 0
$$408$$ 0 0
$$409$$ −10.0000 −0.494468 −0.247234 0.968956i $$-0.579522\pi$$
−0.247234 + 0.968956i $$0.579522\pi$$
$$410$$ 0 0
$$411$$ 12.0000 0.591916
$$412$$ 0 0
$$413$$ 8.00000 0.393654
$$414$$ 0 0
$$415$$ 0 0
$$416$$ 0 0
$$417$$ −24.0000 −1.17529
$$418$$ 0 0
$$419$$ −4.00000 −0.195413 −0.0977064 0.995215i $$-0.531151\pi$$
−0.0977064 + 0.995215i $$0.531151\pi$$
$$420$$ 0 0
$$421$$ 10.0000 0.487370 0.243685 0.969854i $$-0.421644\pi$$
0.243685 + 0.969854i $$0.421644\pi$$
$$422$$ 0 0
$$423$$ −6.00000 −0.291730
$$424$$ 0 0
$$425$$ 0 0
$$426$$ 0 0
$$427$$ 4.00000 0.193574
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 36.0000 1.73406 0.867029 0.498257i $$-0.166026\pi$$
0.867029 + 0.498257i $$0.166026\pi$$
$$432$$ 0 0
$$433$$ 18.0000 0.865025 0.432512 0.901628i $$-0.357627\pi$$
0.432512 + 0.901628i $$0.357627\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ −2.00000 −0.0956730
$$438$$ 0 0
$$439$$ 8.00000 0.381819 0.190910 0.981608i $$-0.438856\pi$$
0.190910 + 0.981608i $$0.438856\pi$$
$$440$$ 0 0
$$441$$ −3.00000 −0.142857
$$442$$ 0 0
$$443$$ 30.0000 1.42534 0.712672 0.701498i $$-0.247485\pi$$
0.712672 + 0.701498i $$0.247485\pi$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ 0 0
$$447$$ 20.0000 0.945968
$$448$$ 0 0
$$449$$ −34.0000 −1.60456 −0.802280 0.596948i $$-0.796380\pi$$
−0.802280 + 0.596948i $$0.796380\pi$$
$$450$$ 0 0
$$451$$ 0 0
$$452$$ 0 0
$$453$$ −24.0000 −1.12762
$$454$$ 0 0
$$455$$ 0 0
$$456$$ 0 0
$$457$$ 38.0000 1.77757 0.888783 0.458329i $$-0.151552\pi$$
0.888783 + 0.458329i $$0.151552\pi$$
$$458$$ 0 0
$$459$$ 8.00000 0.373408
$$460$$ 0 0
$$461$$ −34.0000 −1.58354 −0.791769 0.610821i $$-0.790840\pi$$
−0.791769 + 0.610821i $$0.790840\pi$$
$$462$$ 0 0
$$463$$ −26.0000 −1.20832 −0.604161 0.796862i $$-0.706492\pi$$
−0.604161 + 0.796862i $$0.706492\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ 10.0000 0.462745 0.231372 0.972865i $$-0.425678\pi$$
0.231372 + 0.972865i $$0.425678\pi$$
$$468$$ 0 0
$$469$$ −4.00000 −0.184703
$$470$$ 0 0
$$471$$ −36.0000 −1.65879
$$472$$ 0 0
$$473$$ 0 0
$$474$$ 0 0
$$475$$ 0 0
$$476$$ 0 0
$$477$$ −6.00000 −0.274721
$$478$$ 0 0
$$479$$ −24.0000 −1.09659 −0.548294 0.836286i $$-0.684723\pi$$
−0.548294 + 0.836286i $$0.684723\pi$$
$$480$$ 0 0
$$481$$ −60.0000 −2.73576
$$482$$ 0 0
$$483$$ −8.00000 −0.364013
$$484$$ 0 0
$$485$$ 0 0
$$486$$ 0 0
$$487$$ −26.0000 −1.17817 −0.589086 0.808070i $$-0.700512\pi$$
−0.589086 + 0.808070i $$0.700512\pi$$
$$488$$ 0 0
$$489$$ 12.0000 0.542659
$$490$$ 0 0
$$491$$ −32.0000 −1.44414 −0.722070 0.691820i $$-0.756809\pi$$
−0.722070 + 0.691820i $$0.756809\pi$$
$$492$$ 0 0
$$493$$ 4.00000 0.180151
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ −24.0000 −1.07655
$$498$$ 0 0
$$499$$ 36.0000 1.61158 0.805791 0.592200i $$-0.201741\pi$$
0.805791 + 0.592200i $$0.201741\pi$$
$$500$$ 0 0
$$501$$ 28.0000 1.25095
$$502$$ 0 0
$$503$$ −26.0000 −1.15928 −0.579641 0.814872i $$-0.696807\pi$$
−0.579641 + 0.814872i $$0.696807\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ 0 0
$$507$$ 46.0000 2.04293
$$508$$ 0 0
$$509$$ 30.0000 1.32973 0.664863 0.746965i $$-0.268490\pi$$
0.664863 + 0.746965i $$0.268490\pi$$
$$510$$ 0 0
$$511$$ 12.0000 0.530849
$$512$$ 0 0
$$513$$ −4.00000 −0.176604
$$514$$ 0 0
$$515$$ 0 0
$$516$$ 0 0
$$517$$ 0 0
$$518$$ 0 0
$$519$$ −12.0000 −0.526742
$$520$$ 0 0
$$521$$ 42.0000 1.84005 0.920027 0.391856i $$-0.128167\pi$$
0.920027 + 0.391856i $$0.128167\pi$$
$$522$$ 0 0
$$523$$ 26.0000 1.13690 0.568450 0.822718i $$-0.307543\pi$$
0.568450 + 0.822718i $$0.307543\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ 8.00000 0.348485
$$528$$ 0 0
$$529$$ −19.0000 −0.826087
$$530$$ 0 0
$$531$$ 4.00000 0.173585
$$532$$ 0 0
$$533$$ 60.0000 2.59889
$$534$$ 0 0
$$535$$ 0 0
$$536$$ 0 0
$$537$$ 24.0000 1.03568
$$538$$ 0 0
$$539$$ 0 0
$$540$$ 0 0
$$541$$ −34.0000 −1.46177 −0.730887 0.682498i $$-0.760893\pi$$
−0.730887 + 0.682498i $$0.760893\pi$$
$$542$$ 0 0
$$543$$ −20.0000 −0.858282
$$544$$ 0 0
$$545$$ 0 0
$$546$$ 0 0
$$547$$ −2.00000 −0.0855138 −0.0427569 0.999086i $$-0.513614\pi$$
−0.0427569 + 0.999086i $$0.513614\pi$$
$$548$$ 0 0
$$549$$ 2.00000 0.0853579
$$550$$ 0 0
$$551$$ −2.00000 −0.0852029
$$552$$ 0 0
$$553$$ −16.0000 −0.680389
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ −26.0000 −1.10166 −0.550828 0.834619i $$-0.685688\pi$$
−0.550828 + 0.834619i $$0.685688\pi$$
$$558$$ 0 0
$$559$$ −36.0000 −1.52264
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ −38.0000 −1.60151 −0.800755 0.598993i $$-0.795568\pi$$
−0.800755 + 0.598993i $$0.795568\pi$$
$$564$$ 0 0
$$565$$ 0 0
$$566$$ 0 0
$$567$$ −22.0000 −0.923913
$$568$$ 0 0
$$569$$ 22.0000 0.922288 0.461144 0.887325i $$-0.347439\pi$$
0.461144 + 0.887325i $$0.347439\pi$$
$$570$$ 0 0
$$571$$ −40.0000 −1.67395 −0.836974 0.547243i $$-0.815677\pi$$
−0.836974 + 0.547243i $$0.815677\pi$$
$$572$$ 0 0
$$573$$ −40.0000 −1.67102
$$574$$ 0 0
$$575$$ 0 0
$$576$$ 0 0
$$577$$ 38.0000 1.58196 0.790980 0.611842i $$-0.209571\pi$$
0.790980 + 0.611842i $$0.209571\pi$$
$$578$$ 0 0
$$579$$ −44.0000 −1.82858
$$580$$ 0 0
$$581$$ −4.00000 −0.165948
$$582$$ 0 0
$$583$$ 0 0
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ 18.0000 0.742940 0.371470 0.928445i $$-0.378854\pi$$
0.371470 + 0.928445i $$0.378854\pi$$
$$588$$ 0 0
$$589$$ −4.00000 −0.164817
$$590$$ 0 0
$$591$$ −4.00000 −0.164538
$$592$$ 0 0
$$593$$ −2.00000 −0.0821302 −0.0410651 0.999156i $$-0.513075\pi$$
−0.0410651 + 0.999156i $$0.513075\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 0 0
$$597$$ −16.0000 −0.654836
$$598$$ 0 0
$$599$$ −48.0000 −1.96123 −0.980613 0.195952i $$-0.937220\pi$$
−0.980613 + 0.195952i $$0.937220\pi$$
$$600$$ 0 0
$$601$$ −10.0000 −0.407909 −0.203954 0.978980i $$-0.565379\pi$$
−0.203954 + 0.978980i $$0.565379\pi$$
$$602$$ 0 0
$$603$$ −2.00000 −0.0814463
$$604$$ 0 0
$$605$$ 0 0
$$606$$ 0 0
$$607$$ 22.0000 0.892952 0.446476 0.894795i $$-0.352679\pi$$
0.446476 + 0.894795i $$0.352679\pi$$
$$608$$ 0 0
$$609$$ −8.00000 −0.324176
$$610$$ 0 0
$$611$$ 36.0000 1.45640
$$612$$ 0 0
$$613$$ 22.0000 0.888572 0.444286 0.895885i $$-0.353457\pi$$
0.444286 + 0.895885i $$0.353457\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ −34.0000 −1.36879 −0.684394 0.729112i $$-0.739933\pi$$
−0.684394 + 0.729112i $$0.739933\pi$$
$$618$$ 0 0
$$619$$ −4.00000 −0.160774 −0.0803868 0.996764i $$-0.525616\pi$$
−0.0803868 + 0.996764i $$0.525616\pi$$
$$620$$ 0 0
$$621$$ 8.00000 0.321029
$$622$$ 0 0
$$623$$ 4.00000 0.160257
$$624$$ 0 0
$$625$$ 0 0
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 0 0
$$629$$ −20.0000 −0.797452
$$630$$ 0 0
$$631$$ 12.0000 0.477712 0.238856 0.971055i $$-0.423228\pi$$
0.238856 + 0.971055i $$0.423228\pi$$
$$632$$ 0 0
$$633$$ −16.0000 −0.635943
$$634$$ 0 0
$$635$$ 0 0
$$636$$ 0 0
$$637$$ 18.0000 0.713186
$$638$$ 0 0
$$639$$ −12.0000 −0.474713
$$640$$ 0 0
$$641$$ 30.0000 1.18493 0.592464 0.805597i $$-0.298155\pi$$
0.592464 + 0.805597i $$0.298155\pi$$
$$642$$ 0 0
$$643$$ −26.0000 −1.02534 −0.512670 0.858586i $$-0.671344\pi$$
−0.512670 + 0.858586i $$0.671344\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 18.0000 0.707653 0.353827 0.935311i $$-0.384880\pi$$
0.353827 + 0.935311i $$0.384880\pi$$
$$648$$ 0 0
$$649$$ 0 0
$$650$$ 0 0
$$651$$ −16.0000 −0.627089
$$652$$ 0 0
$$653$$ −18.0000 −0.704394 −0.352197 0.935926i $$-0.614565\pi$$
−0.352197 + 0.935926i $$0.614565\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ 0 0
$$657$$ 6.00000 0.234082
$$658$$ 0 0
$$659$$ −36.0000 −1.40236 −0.701180 0.712984i $$-0.747343\pi$$
−0.701180 + 0.712984i $$0.747343\pi$$
$$660$$ 0 0
$$661$$ 26.0000 1.01128 0.505641 0.862744i $$-0.331256\pi$$
0.505641 + 0.862744i $$0.331256\pi$$
$$662$$ 0 0
$$663$$ 24.0000 0.932083
$$664$$ 0 0
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 4.00000 0.154881
$$668$$ 0 0
$$669$$ 4.00000 0.154649
$$670$$ 0 0
$$671$$ 0 0
$$672$$ 0 0
$$673$$ 10.0000 0.385472 0.192736 0.981251i $$-0.438264\pi$$
0.192736 + 0.981251i $$0.438264\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ 2.00000 0.0768662 0.0384331 0.999261i $$-0.487763\pi$$
0.0384331 + 0.999261i $$0.487763\pi$$
$$678$$ 0 0
$$679$$ 36.0000 1.38155
$$680$$ 0 0
$$681$$ 28.0000 1.07296
$$682$$ 0 0
$$683$$ −30.0000 −1.14792 −0.573959 0.818884i $$-0.694593\pi$$
−0.573959 + 0.818884i $$0.694593\pi$$
$$684$$ 0 0
$$685$$ 0 0
$$686$$ 0 0
$$687$$ −36.0000 −1.37349
$$688$$ 0 0
$$689$$ 36.0000 1.37149
$$690$$ 0 0
$$691$$ 8.00000 0.304334 0.152167 0.988355i $$-0.451375\pi$$
0.152167 + 0.988355i $$0.451375\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ 0 0
$$696$$ 0 0
$$697$$ 20.0000 0.757554
$$698$$ 0 0
$$699$$ 44.0000 1.66423
$$700$$ 0 0
$$701$$ −30.0000 −1.13308 −0.566542 0.824033i $$-0.691719\pi$$
−0.566542 + 0.824033i $$0.691719\pi$$
$$702$$ 0 0
$$703$$ 10.0000 0.377157
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ −20.0000 −0.752177
$$708$$ 0 0
$$709$$ 14.0000 0.525781 0.262891 0.964826i $$-0.415324\pi$$
0.262891 + 0.964826i $$0.415324\pi$$
$$710$$ 0 0
$$711$$ −8.00000 −0.300023
$$712$$ 0 0
$$713$$ 8.00000 0.299602
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 0 0
$$717$$ 48.0000 1.79259
$$718$$ 0 0
$$719$$ −8.00000 −0.298350 −0.149175 0.988811i $$-0.547662\pi$$
−0.149175 + 0.988811i $$0.547662\pi$$
$$720$$ 0 0
$$721$$ −12.0000 −0.446903
$$722$$ 0 0
$$723$$ 28.0000 1.04133
$$724$$ 0 0
$$725$$ 0 0
$$726$$ 0 0
$$727$$ 2.00000 0.0741759 0.0370879 0.999312i $$-0.488192\pi$$
0.0370879 + 0.999312i $$0.488192\pi$$
$$728$$ 0 0
$$729$$ 13.0000 0.481481
$$730$$ 0 0
$$731$$ −12.0000 −0.443836
$$732$$ 0 0
$$733$$ 6.00000 0.221615 0.110808 0.993842i $$-0.464656\pi$$
0.110808 + 0.993842i $$0.464656\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 0 0
$$738$$ 0 0
$$739$$ 28.0000 1.03000 0.514998 0.857191i $$-0.327793\pi$$
0.514998 + 0.857191i $$0.327793\pi$$
$$740$$ 0 0
$$741$$ −12.0000 −0.440831
$$742$$ 0 0
$$743$$ 10.0000 0.366864 0.183432 0.983032i $$-0.441279\pi$$
0.183432 + 0.983032i $$0.441279\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ 0 0
$$747$$ −2.00000 −0.0731762
$$748$$ 0 0
$$749$$ −36.0000 −1.31541
$$750$$ 0 0
$$751$$ −4.00000 −0.145962 −0.0729810 0.997333i $$-0.523251\pi$$
−0.0729810 + 0.997333i $$0.523251\pi$$
$$752$$ 0 0
$$753$$ −32.0000 −1.16614
$$754$$ 0 0
$$755$$ 0 0
$$756$$ 0 0
$$757$$ −10.0000 −0.363456 −0.181728 0.983349i $$-0.558169\pi$$
−0.181728 + 0.983349i $$0.558169\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ −6.00000 −0.217500 −0.108750 0.994069i $$-0.534685\pi$$
−0.108750 + 0.994069i $$0.534685\pi$$
$$762$$ 0 0
$$763$$ 20.0000 0.724049
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ −24.0000 −0.866590
$$768$$ 0 0
$$769$$ −14.0000 −0.504853 −0.252426 0.967616i $$-0.581229\pi$$
−0.252426 + 0.967616i $$0.581229\pi$$
$$770$$ 0 0
$$771$$ 36.0000 1.29651
$$772$$ 0 0
$$773$$ 42.0000 1.51064 0.755318 0.655359i $$-0.227483\pi$$
0.755318 + 0.655359i $$0.227483\pi$$
$$774$$ 0 0
$$775$$ 0 0
$$776$$ 0 0
$$777$$ 40.0000 1.43499
$$778$$ 0 0
$$779$$ −10.0000 −0.358287
$$780$$ 0 0
$$781$$ 0 0
$$782$$ 0 0
$$783$$ 8.00000 0.285897
$$784$$ 0 0
$$785$$ 0 0
$$786$$ 0 0
$$787$$ 14.0000 0.499046 0.249523 0.968369i $$-0.419726\pi$$
0.249523 + 0.968369i $$0.419726\pi$$
$$788$$ 0 0
$$789$$ −52.0000 −1.85125
$$790$$ 0 0
$$791$$ 20.0000 0.711118
$$792$$ 0 0
$$793$$ −12.0000 −0.426132
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ −38.0000 −1.34603 −0.673015 0.739629i $$-0.735001\pi$$
−0.673015 + 0.739629i $$0.735001\pi$$
$$798$$ 0 0
$$799$$ 12.0000 0.424529
$$800$$ 0 0
$$801$$ 2.00000 0.0706665
$$802$$ 0 0
$$803$$ 0 0
$$804$$ 0 0
$$805$$ 0 0
$$806$$ 0 0
$$807$$ 52.0000 1.83049
$$808$$ 0 0
$$809$$ −6.00000 −0.210949 −0.105474 0.994422i $$-0.533636\pi$$
−0.105474 + 0.994422i $$0.533636\pi$$
$$810$$ 0 0
$$811$$ 40.0000 1.40459 0.702295 0.711886i $$-0.252159\pi$$
0.702295 + 0.711886i $$0.252159\pi$$
$$812$$ 0 0
$$813$$ 56.0000 1.96401
$$814$$ 0 0
$$815$$ 0 0
$$816$$ 0 0
$$817$$ 6.00000 0.209913
$$818$$ 0 0
$$819$$ −12.0000 −0.419314
$$820$$ 0 0
$$821$$ 10.0000 0.349002 0.174501 0.984657i $$-0.444169\pi$$
0.174501 + 0.984657i $$0.444169\pi$$
$$822$$ 0 0
$$823$$ 38.0000 1.32460 0.662298 0.749240i $$-0.269581\pi$$
0.662298 + 0.749240i $$0.269581\pi$$
$$824$$ 0 0
$$825$$ 0 0
$$826$$ 0 0
$$827$$ −18.0000 −0.625921 −0.312961 0.949766i $$-0.601321\pi$$
−0.312961 + 0.949766i $$0.601321\pi$$
$$828$$ 0 0
$$829$$ 42.0000 1.45872 0.729360 0.684130i $$-0.239818\pi$$
0.729360 + 0.684130i $$0.239818\pi$$
$$830$$ 0 0
$$831$$ 28.0000 0.971309
$$832$$ 0 0
$$833$$ 6.00000 0.207888
$$834$$ 0 0
$$835$$ 0 0
$$836$$ 0 0
$$837$$ 16.0000 0.553041
$$838$$ 0 0
$$839$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$840$$ 0 0
$$841$$ −25.0000 −0.862069
$$842$$ 0 0
$$843$$ 44.0000 1.51544
$$844$$ 0 0
$$845$$ 0 0
$$846$$ 0 0
$$847$$ −22.0000 −0.755929
$$848$$ 0 0
$$849$$ 44.0000 1.51008
$$850$$ 0 0
$$851$$ −20.0000 −0.685591
$$852$$ 0 0
$$853$$ −2.00000 −0.0684787 −0.0342393 0.999414i $$-0.510901\pi$$
−0.0342393 + 0.999414i $$0.510901\pi$$
$$854$$ 0 0
$$855$$ 0 0
$$856$$ 0 0
$$857$$ 42.0000 1.43469 0.717346 0.696717i $$-0.245357\pi$$
0.717346 + 0.696717i $$0.245357\pi$$
$$858$$ 0 0
$$859$$ 4.00000 0.136478 0.0682391 0.997669i $$-0.478262\pi$$
0.0682391 + 0.997669i $$0.478262\pi$$
$$860$$ 0 0
$$861$$ −40.0000 −1.36320
$$862$$ 0 0
$$863$$ −54.0000 −1.83818 −0.919091 0.394046i $$-0.871075\pi$$
−0.919091 + 0.394046i $$0.871075\pi$$
$$864$$ 0 0
$$865$$ 0 0
$$866$$ 0 0
$$867$$ −26.0000 −0.883006
$$868$$ 0 0
$$869$$ 0 0
$$870$$ 0 0
$$871$$ 12.0000 0.406604
$$872$$ 0 0
$$873$$ 18.0000 0.609208
$$874$$ 0 0
$$875$$ 0 0
$$876$$ 0 0
$$877$$ 26.0000 0.877958 0.438979 0.898497i $$-0.355340\pi$$
0.438979 + 0.898497i $$0.355340\pi$$
$$878$$ 0 0
$$879$$ 4.00000 0.134917
$$880$$ 0 0
$$881$$ 14.0000 0.471672 0.235836 0.971793i $$-0.424217\pi$$
0.235836 + 0.971793i $$0.424217\pi$$
$$882$$ 0 0
$$883$$ −34.0000 −1.14419 −0.572096 0.820187i $$-0.693869\pi$$
−0.572096 + 0.820187i $$0.693869\pi$$
$$884$$ 0 0
$$885$$ 0 0
$$886$$ 0 0
$$887$$ 22.0000 0.738688 0.369344 0.929293i $$-0.379582\pi$$
0.369344 + 0.929293i $$0.379582\pi$$
$$888$$ 0 0
$$889$$ 12.0000 0.402467
$$890$$ 0 0
$$891$$ 0 0
$$892$$ 0 0
$$893$$ −6.00000 −0.200782
$$894$$ 0 0
$$895$$ 0 0
$$896$$ 0 0
$$897$$ 24.0000 0.801337
$$898$$ 0 0
$$899$$ 8.00000 0.266815
$$900$$ 0 0
$$901$$ 12.0000 0.399778
$$902$$ 0 0
$$903$$ 24.0000 0.798670
$$904$$ 0 0
$$905$$ 0 0
$$906$$ 0 0
$$907$$ −10.0000 −0.332045 −0.166022 0.986122i $$-0.553092\pi$$
−0.166022 + 0.986122i $$0.553092\pi$$
$$908$$ 0 0
$$909$$ −10.0000 −0.331679
$$910$$ 0 0
$$911$$ −52.0000 −1.72284 −0.861418 0.507896i $$-0.830423\pi$$
−0.861418 + 0.507896i $$0.830423\pi$$
$$912$$ 0 0
$$913$$ 0 0
$$914$$ 0 0
$$915$$ 0 0
$$916$$ 0 0
$$917$$ −32.0000 −1.05673
$$918$$ 0 0
$$919$$ −32.0000 −1.05558 −0.527791 0.849374i $$-0.676980\pi$$
−0.527791 + 0.849374i $$0.676980\pi$$
$$920$$ 0 0
$$921$$ 44.0000 1.44985
$$922$$ 0 0
$$923$$ 72.0000 2.36991
$$924$$ 0 0
$$925$$ 0 0
$$926$$ 0 0
$$927$$ −6.00000 −0.197066
$$928$$ 0 0
$$929$$ 54.0000 1.77168 0.885841 0.463988i $$-0.153582\pi$$
0.885841 + 0.463988i $$0.153582\pi$$
$$930$$ 0 0
$$931$$ −3.00000 −0.0983210
$$932$$ 0 0
$$933$$ −24.0000 −0.785725
$$934$$ 0 0
$$935$$ 0 0
$$936$$ 0 0
$$937$$ 46.0000 1.50275 0.751377 0.659873i $$-0.229390\pi$$
0.751377 + 0.659873i $$0.229390\pi$$
$$938$$ 0 0
$$939$$ −20.0000 −0.652675
$$940$$ 0 0
$$941$$ 14.0000 0.456387 0.228193 0.973616i $$-0.426718\pi$$
0.228193 + 0.973616i $$0.426718\pi$$
$$942$$ 0 0
$$943$$ 20.0000 0.651290
$$944$$ 0 0
$$945$$ 0 0
$$946$$ 0 0
$$947$$ −22.0000 −0.714904 −0.357452 0.933932i $$-0.616354\pi$$
−0.357452 + 0.933932i $$0.616354\pi$$
$$948$$ 0 0
$$949$$ −36.0000 −1.16861
$$950$$ 0 0
$$951$$ −60.0000 −1.94563
$$952$$ 0 0
$$953$$ −14.0000 −0.453504 −0.226752 0.973952i $$-0.572811\pi$$
−0.226752 + 0.973952i $$0.572811\pi$$
$$954$$ 0 0
$$955$$ 0 0
$$956$$ 0 0
$$957$$ 0 0
$$958$$ 0 0
$$959$$ 12.0000 0.387500
$$960$$ 0 0
$$961$$ −15.0000 −0.483871
$$962$$ 0 0
$$963$$ −18.0000 −0.580042
$$964$$ 0 0
$$965$$ 0 0
$$966$$ 0 0
$$967$$ 18.0000 0.578841 0.289420 0.957202i $$-0.406537\pi$$
0.289420 + 0.957202i $$0.406537\pi$$
$$968$$ 0 0
$$969$$ −4.00000 −0.128499
$$970$$ 0 0
$$971$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$972$$ 0 0
$$973$$ −24.0000 −0.769405
$$974$$ 0 0
$$975$$ 0 0
$$976$$ 0 0
$$977$$ −6.00000 −0.191957 −0.0959785 0.995383i $$-0.530598\pi$$
−0.0959785 + 0.995383i $$0.530598\pi$$
$$978$$ 0 0
$$979$$ 0 0
$$980$$ 0 0
$$981$$ 10.0000 0.319275
$$982$$ 0 0
$$983$$ 18.0000 0.574111 0.287055 0.957914i $$-0.407324\pi$$
0.287055 + 0.957914i $$0.407324\pi$$
$$984$$ 0 0
$$985$$ 0 0
$$986$$ 0 0
$$987$$ −24.0000 −0.763928
$$988$$ 0 0
$$989$$ −12.0000 −0.381578
$$990$$ 0 0
$$991$$ 28.0000 0.889449 0.444725 0.895667i $$-0.353302\pi$$
0.444725 + 0.895667i $$0.353302\pi$$
$$992$$ 0 0
$$993$$ −32.0000 −1.01549
$$994$$ 0 0
$$995$$ 0 0
$$996$$ 0 0
$$997$$ −2.00000 −0.0633406 −0.0316703 0.999498i $$-0.510083\pi$$
−0.0316703 + 0.999498i $$0.510083\pi$$
$$998$$ 0 0
$$999$$ −40.0000 −1.26554
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 7600.2.a.r.1.1 1
4.3 odd 2 1900.2.a.a.1.1 1
5.4 even 2 1520.2.a.b.1.1 1
20.3 even 4 1900.2.c.a.1749.1 2
20.7 even 4 1900.2.c.a.1749.2 2
20.19 odd 2 380.2.a.b.1.1 1
40.19 odd 2 6080.2.a.f.1.1 1
40.29 even 2 6080.2.a.v.1.1 1
60.59 even 2 3420.2.a.f.1.1 1
380.379 even 2 7220.2.a.b.1.1 1

By twisted newform
Twist Min Dim Char Parity Ord Type
380.2.a.b.1.1 1 20.19 odd 2
1520.2.a.b.1.1 1 5.4 even 2
1900.2.a.a.1.1 1 4.3 odd 2
1900.2.c.a.1749.1 2 20.3 even 4
1900.2.c.a.1749.2 2 20.7 even 4
3420.2.a.f.1.1 1 60.59 even 2
6080.2.a.f.1.1 1 40.19 odd 2
6080.2.a.v.1.1 1 40.29 even 2
7220.2.a.b.1.1 1 380.379 even 2
7600.2.a.r.1.1 1 1.1 even 1 trivial