# Properties

 Label 7650.2.a.be.1.1 Level $7650$ Weight $2$ Character 7650.1 Self dual yes Analytic conductor $61.086$ Analytic rank $1$ Dimension $1$ CM no Inner twists $1$

# Related objects

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [7650,2,Mod(1,7650)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7650, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("7650.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$7650 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 17$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 7650.a (trivial)

## Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

 Self dual: yes Analytic conductor: $$61.0855575463$$ Analytic rank: $$1$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 2550) Fricke sign: $$1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

 Embedding label 1.1 Character $$\chi$$ $$=$$ 7650.1

## $q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q-1.00000 q^{2} +1.00000 q^{4} +3.00000 q^{7} -1.00000 q^{8} +O(q^{10})$$ $$q-1.00000 q^{2} +1.00000 q^{4} +3.00000 q^{7} -1.00000 q^{8} +5.00000 q^{11} -2.00000 q^{13} -3.00000 q^{14} +1.00000 q^{16} -1.00000 q^{17} +1.00000 q^{19} -5.00000 q^{22} -6.00000 q^{23} +2.00000 q^{26} +3.00000 q^{28} -10.0000 q^{29} +5.00000 q^{31} -1.00000 q^{32} +1.00000 q^{34} -3.00000 q^{37} -1.00000 q^{38} -6.00000 q^{41} -1.00000 q^{43} +5.00000 q^{44} +6.00000 q^{46} -3.00000 q^{47} +2.00000 q^{49} -2.00000 q^{52} +1.00000 q^{53} -3.00000 q^{56} +10.0000 q^{58} -8.00000 q^{59} -2.00000 q^{61} -5.00000 q^{62} +1.00000 q^{64} -11.0000 q^{67} -1.00000 q^{68} -6.00000 q^{71} -12.0000 q^{73} +3.00000 q^{74} +1.00000 q^{76} +15.0000 q^{77} +5.00000 q^{79} +6.00000 q^{82} -18.0000 q^{83} +1.00000 q^{86} -5.00000 q^{88} -12.0000 q^{89} -6.00000 q^{91} -6.00000 q^{92} +3.00000 q^{94} -14.0000 q^{97} -2.00000 q^{98} +O(q^{100})$$

## Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −1.00000 −0.707107
$$3$$ 0 0
$$4$$ 1.00000 0.500000
$$5$$ 0 0
$$6$$ 0 0
$$7$$ 3.00000 1.13389 0.566947 0.823754i $$-0.308125\pi$$
0.566947 + 0.823754i $$0.308125\pi$$
$$8$$ −1.00000 −0.353553
$$9$$ 0 0
$$10$$ 0 0
$$11$$ 5.00000 1.50756 0.753778 0.657129i $$-0.228229\pi$$
0.753778 + 0.657129i $$0.228229\pi$$
$$12$$ 0 0
$$13$$ −2.00000 −0.554700 −0.277350 0.960769i $$-0.589456\pi$$
−0.277350 + 0.960769i $$0.589456\pi$$
$$14$$ −3.00000 −0.801784
$$15$$ 0 0
$$16$$ 1.00000 0.250000
$$17$$ −1.00000 −0.242536
$$18$$ 0 0
$$19$$ 1.00000 0.229416 0.114708 0.993399i $$-0.463407\pi$$
0.114708 + 0.993399i $$0.463407\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ −5.00000 −1.06600
$$23$$ −6.00000 −1.25109 −0.625543 0.780189i $$-0.715123\pi$$
−0.625543 + 0.780189i $$0.715123\pi$$
$$24$$ 0 0
$$25$$ 0 0
$$26$$ 2.00000 0.392232
$$27$$ 0 0
$$28$$ 3.00000 0.566947
$$29$$ −10.0000 −1.85695 −0.928477 0.371391i $$-0.878881\pi$$
−0.928477 + 0.371391i $$0.878881\pi$$
$$30$$ 0 0
$$31$$ 5.00000 0.898027 0.449013 0.893525i $$-0.351776\pi$$
0.449013 + 0.893525i $$0.351776\pi$$
$$32$$ −1.00000 −0.176777
$$33$$ 0 0
$$34$$ 1.00000 0.171499
$$35$$ 0 0
$$36$$ 0 0
$$37$$ −3.00000 −0.493197 −0.246598 0.969118i $$-0.579313\pi$$
−0.246598 + 0.969118i $$0.579313\pi$$
$$38$$ −1.00000 −0.162221
$$39$$ 0 0
$$40$$ 0 0
$$41$$ −6.00000 −0.937043 −0.468521 0.883452i $$-0.655213\pi$$
−0.468521 + 0.883452i $$0.655213\pi$$
$$42$$ 0 0
$$43$$ −1.00000 −0.152499 −0.0762493 0.997089i $$-0.524294\pi$$
−0.0762493 + 0.997089i $$0.524294\pi$$
$$44$$ 5.00000 0.753778
$$45$$ 0 0
$$46$$ 6.00000 0.884652
$$47$$ −3.00000 −0.437595 −0.218797 0.975770i $$-0.570213\pi$$
−0.218797 + 0.975770i $$0.570213\pi$$
$$48$$ 0 0
$$49$$ 2.00000 0.285714
$$50$$ 0 0
$$51$$ 0 0
$$52$$ −2.00000 −0.277350
$$53$$ 1.00000 0.137361 0.0686803 0.997639i $$-0.478121\pi$$
0.0686803 + 0.997639i $$0.478121\pi$$
$$54$$ 0 0
$$55$$ 0 0
$$56$$ −3.00000 −0.400892
$$57$$ 0 0
$$58$$ 10.0000 1.31306
$$59$$ −8.00000 −1.04151 −0.520756 0.853706i $$-0.674350\pi$$
−0.520756 + 0.853706i $$0.674350\pi$$
$$60$$ 0 0
$$61$$ −2.00000 −0.256074 −0.128037 0.991769i $$-0.540868\pi$$
−0.128037 + 0.991769i $$0.540868\pi$$
$$62$$ −5.00000 −0.635001
$$63$$ 0 0
$$64$$ 1.00000 0.125000
$$65$$ 0 0
$$66$$ 0 0
$$67$$ −11.0000 −1.34386 −0.671932 0.740613i $$-0.734535\pi$$
−0.671932 + 0.740613i $$0.734535\pi$$
$$68$$ −1.00000 −0.121268
$$69$$ 0 0
$$70$$ 0 0
$$71$$ −6.00000 −0.712069 −0.356034 0.934473i $$-0.615871\pi$$
−0.356034 + 0.934473i $$0.615871\pi$$
$$72$$ 0 0
$$73$$ −12.0000 −1.40449 −0.702247 0.711934i $$-0.747820\pi$$
−0.702247 + 0.711934i $$0.747820\pi$$
$$74$$ 3.00000 0.348743
$$75$$ 0 0
$$76$$ 1.00000 0.114708
$$77$$ 15.0000 1.70941
$$78$$ 0 0
$$79$$ 5.00000 0.562544 0.281272 0.959628i $$-0.409244\pi$$
0.281272 + 0.959628i $$0.409244\pi$$
$$80$$ 0 0
$$81$$ 0 0
$$82$$ 6.00000 0.662589
$$83$$ −18.0000 −1.97576 −0.987878 0.155230i $$-0.950388\pi$$
−0.987878 + 0.155230i $$0.950388\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ 1.00000 0.107833
$$87$$ 0 0
$$88$$ −5.00000 −0.533002
$$89$$ −12.0000 −1.27200 −0.635999 0.771690i $$-0.719412\pi$$
−0.635999 + 0.771690i $$0.719412\pi$$
$$90$$ 0 0
$$91$$ −6.00000 −0.628971
$$92$$ −6.00000 −0.625543
$$93$$ 0 0
$$94$$ 3.00000 0.309426
$$95$$ 0 0
$$96$$ 0 0
$$97$$ −14.0000 −1.42148 −0.710742 0.703452i $$-0.751641\pi$$
−0.710742 + 0.703452i $$0.751641\pi$$
$$98$$ −2.00000 −0.202031
$$99$$ 0 0
$$100$$ 0 0
$$101$$ −11.0000 −1.09454 −0.547270 0.836956i $$-0.684333\pi$$
−0.547270 + 0.836956i $$0.684333\pi$$
$$102$$ 0 0
$$103$$ 4.00000 0.394132 0.197066 0.980390i $$-0.436859\pi$$
0.197066 + 0.980390i $$0.436859\pi$$
$$104$$ 2.00000 0.196116
$$105$$ 0 0
$$106$$ −1.00000 −0.0971286
$$107$$ 5.00000 0.483368 0.241684 0.970355i $$-0.422300\pi$$
0.241684 + 0.970355i $$0.422300\pi$$
$$108$$ 0 0
$$109$$ 5.00000 0.478913 0.239457 0.970907i $$-0.423031\pi$$
0.239457 + 0.970907i $$0.423031\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 3.00000 0.283473
$$113$$ −1.00000 −0.0940721 −0.0470360 0.998893i $$-0.514978\pi$$
−0.0470360 + 0.998893i $$0.514978\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ −10.0000 −0.928477
$$117$$ 0 0
$$118$$ 8.00000 0.736460
$$119$$ −3.00000 −0.275010
$$120$$ 0 0
$$121$$ 14.0000 1.27273
$$122$$ 2.00000 0.181071
$$123$$ 0 0
$$124$$ 5.00000 0.449013
$$125$$ 0 0
$$126$$ 0 0
$$127$$ 12.0000 1.06483 0.532414 0.846484i $$-0.321285\pi$$
0.532414 + 0.846484i $$0.321285\pi$$
$$128$$ −1.00000 −0.0883883
$$129$$ 0 0
$$130$$ 0 0
$$131$$ 20.0000 1.74741 0.873704 0.486458i $$-0.161711\pi$$
0.873704 + 0.486458i $$0.161711\pi$$
$$132$$ 0 0
$$133$$ 3.00000 0.260133
$$134$$ 11.0000 0.950255
$$135$$ 0 0
$$136$$ 1.00000 0.0857493
$$137$$ −16.0000 −1.36697 −0.683486 0.729964i $$-0.739537\pi$$
−0.683486 + 0.729964i $$0.739537\pi$$
$$138$$ 0 0
$$139$$ 8.00000 0.678551 0.339276 0.940687i $$-0.389818\pi$$
0.339276 + 0.940687i $$0.389818\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 6.00000 0.503509
$$143$$ −10.0000 −0.836242
$$144$$ 0 0
$$145$$ 0 0
$$146$$ 12.0000 0.993127
$$147$$ 0 0
$$148$$ −3.00000 −0.246598
$$149$$ 6.00000 0.491539 0.245770 0.969328i $$-0.420959\pi$$
0.245770 + 0.969328i $$0.420959\pi$$
$$150$$ 0 0
$$151$$ 8.00000 0.651031 0.325515 0.945537i $$-0.394462\pi$$
0.325515 + 0.945537i $$0.394462\pi$$
$$152$$ −1.00000 −0.0811107
$$153$$ 0 0
$$154$$ −15.0000 −1.20873
$$155$$ 0 0
$$156$$ 0 0
$$157$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$158$$ −5.00000 −0.397779
$$159$$ 0 0
$$160$$ 0 0
$$161$$ −18.0000 −1.41860
$$162$$ 0 0
$$163$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$164$$ −6.00000 −0.468521
$$165$$ 0 0
$$166$$ 18.0000 1.39707
$$167$$ 18.0000 1.39288 0.696441 0.717614i $$-0.254766\pi$$
0.696441 + 0.717614i $$0.254766\pi$$
$$168$$ 0 0
$$169$$ −9.00000 −0.692308
$$170$$ 0 0
$$171$$ 0 0
$$172$$ −1.00000 −0.0762493
$$173$$ −20.0000 −1.52057 −0.760286 0.649589i $$-0.774941\pi$$
−0.760286 + 0.649589i $$0.774941\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 5.00000 0.376889
$$177$$ 0 0
$$178$$ 12.0000 0.899438
$$179$$ 12.0000 0.896922 0.448461 0.893802i $$-0.351972\pi$$
0.448461 + 0.893802i $$0.351972\pi$$
$$180$$ 0 0
$$181$$ −17.0000 −1.26360 −0.631800 0.775131i $$-0.717684\pi$$
−0.631800 + 0.775131i $$0.717684\pi$$
$$182$$ 6.00000 0.444750
$$183$$ 0 0
$$184$$ 6.00000 0.442326
$$185$$ 0 0
$$186$$ 0 0
$$187$$ −5.00000 −0.365636
$$188$$ −3.00000 −0.218797
$$189$$ 0 0
$$190$$ 0 0
$$191$$ −3.00000 −0.217072 −0.108536 0.994092i $$-0.534616\pi$$
−0.108536 + 0.994092i $$0.534616\pi$$
$$192$$ 0 0
$$193$$ −24.0000 −1.72756 −0.863779 0.503871i $$-0.831909\pi$$
−0.863779 + 0.503871i $$0.831909\pi$$
$$194$$ 14.0000 1.00514
$$195$$ 0 0
$$196$$ 2.00000 0.142857
$$197$$ −12.0000 −0.854965 −0.427482 0.904024i $$-0.640599\pi$$
−0.427482 + 0.904024i $$0.640599\pi$$
$$198$$ 0 0
$$199$$ 17.0000 1.20510 0.602549 0.798082i $$-0.294152\pi$$
0.602549 + 0.798082i $$0.294152\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ 11.0000 0.773957
$$203$$ −30.0000 −2.10559
$$204$$ 0 0
$$205$$ 0 0
$$206$$ −4.00000 −0.278693
$$207$$ 0 0
$$208$$ −2.00000 −0.138675
$$209$$ 5.00000 0.345857
$$210$$ 0 0
$$211$$ 18.0000 1.23917 0.619586 0.784929i $$-0.287301\pi$$
0.619586 + 0.784929i $$0.287301\pi$$
$$212$$ 1.00000 0.0686803
$$213$$ 0 0
$$214$$ −5.00000 −0.341793
$$215$$ 0 0
$$216$$ 0 0
$$217$$ 15.0000 1.01827
$$218$$ −5.00000 −0.338643
$$219$$ 0 0
$$220$$ 0 0
$$221$$ 2.00000 0.134535
$$222$$ 0 0
$$223$$ 18.0000 1.20537 0.602685 0.797980i $$-0.294098\pi$$
0.602685 + 0.797980i $$0.294098\pi$$
$$224$$ −3.00000 −0.200446
$$225$$ 0 0
$$226$$ 1.00000 0.0665190
$$227$$ 27.0000 1.79205 0.896026 0.444001i $$-0.146441\pi$$
0.896026 + 0.444001i $$0.146441\pi$$
$$228$$ 0 0
$$229$$ 24.0000 1.58596 0.792982 0.609245i $$-0.208527\pi$$
0.792982 + 0.609245i $$0.208527\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 10.0000 0.656532
$$233$$ 10.0000 0.655122 0.327561 0.944830i $$-0.393773\pi$$
0.327561 + 0.944830i $$0.393773\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ −8.00000 −0.520756
$$237$$ 0 0
$$238$$ 3.00000 0.194461
$$239$$ −13.0000 −0.840900 −0.420450 0.907316i $$-0.638128\pi$$
−0.420450 + 0.907316i $$0.638128\pi$$
$$240$$ 0 0
$$241$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$242$$ −14.0000 −0.899954
$$243$$ 0 0
$$244$$ −2.00000 −0.128037
$$245$$ 0 0
$$246$$ 0 0
$$247$$ −2.00000 −0.127257
$$248$$ −5.00000 −0.317500
$$249$$ 0 0
$$250$$ 0 0
$$251$$ 18.0000 1.13615 0.568075 0.822977i $$-0.307688\pi$$
0.568075 + 0.822977i $$0.307688\pi$$
$$252$$ 0 0
$$253$$ −30.0000 −1.88608
$$254$$ −12.0000 −0.752947
$$255$$ 0 0
$$256$$ 1.00000 0.0625000
$$257$$ −2.00000 −0.124757 −0.0623783 0.998053i $$-0.519869\pi$$
−0.0623783 + 0.998053i $$0.519869\pi$$
$$258$$ 0 0
$$259$$ −9.00000 −0.559233
$$260$$ 0 0
$$261$$ 0 0
$$262$$ −20.0000 −1.23560
$$263$$ −3.00000 −0.184988 −0.0924940 0.995713i $$-0.529484\pi$$
−0.0924940 + 0.995713i $$0.529484\pi$$
$$264$$ 0 0
$$265$$ 0 0
$$266$$ −3.00000 −0.183942
$$267$$ 0 0
$$268$$ −11.0000 −0.671932
$$269$$ 6.00000 0.365826 0.182913 0.983129i $$-0.441447\pi$$
0.182913 + 0.983129i $$0.441447\pi$$
$$270$$ 0 0
$$271$$ 14.0000 0.850439 0.425220 0.905090i $$-0.360197\pi$$
0.425220 + 0.905090i $$0.360197\pi$$
$$272$$ −1.00000 −0.0606339
$$273$$ 0 0
$$274$$ 16.0000 0.966595
$$275$$ 0 0
$$276$$ 0 0
$$277$$ −31.0000 −1.86261 −0.931305 0.364241i $$-0.881328\pi$$
−0.931305 + 0.364241i $$0.881328\pi$$
$$278$$ −8.00000 −0.479808
$$279$$ 0 0
$$280$$ 0 0
$$281$$ 30.0000 1.78965 0.894825 0.446417i $$-0.147300\pi$$
0.894825 + 0.446417i $$0.147300\pi$$
$$282$$ 0 0
$$283$$ −14.0000 −0.832214 −0.416107 0.909316i $$-0.636606\pi$$
−0.416107 + 0.909316i $$0.636606\pi$$
$$284$$ −6.00000 −0.356034
$$285$$ 0 0
$$286$$ 10.0000 0.591312
$$287$$ −18.0000 −1.06251
$$288$$ 0 0
$$289$$ 1.00000 0.0588235
$$290$$ 0 0
$$291$$ 0 0
$$292$$ −12.0000 −0.702247
$$293$$ 18.0000 1.05157 0.525786 0.850617i $$-0.323771\pi$$
0.525786 + 0.850617i $$0.323771\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ 3.00000 0.174371
$$297$$ 0 0
$$298$$ −6.00000 −0.347571
$$299$$ 12.0000 0.693978
$$300$$ 0 0
$$301$$ −3.00000 −0.172917
$$302$$ −8.00000 −0.460348
$$303$$ 0 0
$$304$$ 1.00000 0.0573539
$$305$$ 0 0
$$306$$ 0 0
$$307$$ 20.0000 1.14146 0.570730 0.821138i $$-0.306660\pi$$
0.570730 + 0.821138i $$0.306660\pi$$
$$308$$ 15.0000 0.854704
$$309$$ 0 0
$$310$$ 0 0
$$311$$ 2.00000 0.113410 0.0567048 0.998391i $$-0.481941\pi$$
0.0567048 + 0.998391i $$0.481941\pi$$
$$312$$ 0 0
$$313$$ −34.0000 −1.92179 −0.960897 0.276907i $$-0.910691\pi$$
−0.960897 + 0.276907i $$0.910691\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 5.00000 0.281272
$$317$$ 12.0000 0.673987 0.336994 0.941507i $$-0.390590\pi$$
0.336994 + 0.941507i $$0.390590\pi$$
$$318$$ 0 0
$$319$$ −50.0000 −2.79946
$$320$$ 0 0
$$321$$ 0 0
$$322$$ 18.0000 1.00310
$$323$$ −1.00000 −0.0556415
$$324$$ 0 0
$$325$$ 0 0
$$326$$ 0 0
$$327$$ 0 0
$$328$$ 6.00000 0.331295
$$329$$ −9.00000 −0.496186
$$330$$ 0 0
$$331$$ −25.0000 −1.37412 −0.687062 0.726599i $$-0.741100\pi$$
−0.687062 + 0.726599i $$0.741100\pi$$
$$332$$ −18.0000 −0.987878
$$333$$ 0 0
$$334$$ −18.0000 −0.984916
$$335$$ 0 0
$$336$$ 0 0
$$337$$ 12.0000 0.653682 0.326841 0.945079i $$-0.394016\pi$$
0.326841 + 0.945079i $$0.394016\pi$$
$$338$$ 9.00000 0.489535
$$339$$ 0 0
$$340$$ 0 0
$$341$$ 25.0000 1.35383
$$342$$ 0 0
$$343$$ −15.0000 −0.809924
$$344$$ 1.00000 0.0539164
$$345$$ 0 0
$$346$$ 20.0000 1.07521
$$347$$ 23.0000 1.23470 0.617352 0.786687i $$-0.288205\pi$$
0.617352 + 0.786687i $$0.288205\pi$$
$$348$$ 0 0
$$349$$ −14.0000 −0.749403 −0.374701 0.927146i $$-0.622255\pi$$
−0.374701 + 0.927146i $$0.622255\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ −5.00000 −0.266501
$$353$$ 2.00000 0.106449 0.0532246 0.998583i $$-0.483050\pi$$
0.0532246 + 0.998583i $$0.483050\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ −12.0000 −0.635999
$$357$$ 0 0
$$358$$ −12.0000 −0.634220
$$359$$ −15.0000 −0.791670 −0.395835 0.918322i $$-0.629545\pi$$
−0.395835 + 0.918322i $$0.629545\pi$$
$$360$$ 0 0
$$361$$ −18.0000 −0.947368
$$362$$ 17.0000 0.893500
$$363$$ 0 0
$$364$$ −6.00000 −0.314485
$$365$$ 0 0
$$366$$ 0 0
$$367$$ 5.00000 0.260998 0.130499 0.991448i $$-0.458342\pi$$
0.130499 + 0.991448i $$0.458342\pi$$
$$368$$ −6.00000 −0.312772
$$369$$ 0 0
$$370$$ 0 0
$$371$$ 3.00000 0.155752
$$372$$ 0 0
$$373$$ −18.0000 −0.932005 −0.466002 0.884783i $$-0.654306\pi$$
−0.466002 + 0.884783i $$0.654306\pi$$
$$374$$ 5.00000 0.258544
$$375$$ 0 0
$$376$$ 3.00000 0.154713
$$377$$ 20.0000 1.03005
$$378$$ 0 0
$$379$$ −8.00000 −0.410932 −0.205466 0.978664i $$-0.565871\pi$$
−0.205466 + 0.978664i $$0.565871\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 3.00000 0.153493
$$383$$ 8.00000 0.408781 0.204390 0.978889i $$-0.434479\pi$$
0.204390 + 0.978889i $$0.434479\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 24.0000 1.22157
$$387$$ 0 0
$$388$$ −14.0000 −0.710742
$$389$$ 5.00000 0.253510 0.126755 0.991934i $$-0.459544\pi$$
0.126755 + 0.991934i $$0.459544\pi$$
$$390$$ 0 0
$$391$$ 6.00000 0.303433
$$392$$ −2.00000 −0.101015
$$393$$ 0 0
$$394$$ 12.0000 0.604551
$$395$$ 0 0
$$396$$ 0 0
$$397$$ 21.0000 1.05396 0.526980 0.849878i $$-0.323324\pi$$
0.526980 + 0.849878i $$0.323324\pi$$
$$398$$ −17.0000 −0.852133
$$399$$ 0 0
$$400$$ 0 0
$$401$$ 18.0000 0.898877 0.449439 0.893311i $$-0.351624\pi$$
0.449439 + 0.893311i $$0.351624\pi$$
$$402$$ 0 0
$$403$$ −10.0000 −0.498135
$$404$$ −11.0000 −0.547270
$$405$$ 0 0
$$406$$ 30.0000 1.48888
$$407$$ −15.0000 −0.743522
$$408$$ 0 0
$$409$$ −2.00000 −0.0988936 −0.0494468 0.998777i $$-0.515746\pi$$
−0.0494468 + 0.998777i $$0.515746\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 4.00000 0.197066
$$413$$ −24.0000 −1.18096
$$414$$ 0 0
$$415$$ 0 0
$$416$$ 2.00000 0.0980581
$$417$$ 0 0
$$418$$ −5.00000 −0.244558
$$419$$ −24.0000 −1.17248 −0.586238 0.810139i $$-0.699392\pi$$
−0.586238 + 0.810139i $$0.699392\pi$$
$$420$$ 0 0
$$421$$ 18.0000 0.877266 0.438633 0.898666i $$-0.355463\pi$$
0.438633 + 0.898666i $$0.355463\pi$$
$$422$$ −18.0000 −0.876226
$$423$$ 0 0
$$424$$ −1.00000 −0.0485643
$$425$$ 0 0
$$426$$ 0 0
$$427$$ −6.00000 −0.290360
$$428$$ 5.00000 0.241684
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$432$$ 0 0
$$433$$ 21.0000 1.00920 0.504598 0.863355i $$-0.331641\pi$$
0.504598 + 0.863355i $$0.331641\pi$$
$$434$$ −15.0000 −0.720023
$$435$$ 0 0
$$436$$ 5.00000 0.239457
$$437$$ −6.00000 −0.287019
$$438$$ 0 0
$$439$$ 16.0000 0.763638 0.381819 0.924237i $$-0.375298\pi$$
0.381819 + 0.924237i $$0.375298\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ −2.00000 −0.0951303
$$443$$ 24.0000 1.14027 0.570137 0.821549i $$-0.306890\pi$$
0.570137 + 0.821549i $$0.306890\pi$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ −18.0000 −0.852325
$$447$$ 0 0
$$448$$ 3.00000 0.141737
$$449$$ −21.0000 −0.991051 −0.495526 0.868593i $$-0.665025\pi$$
−0.495526 + 0.868593i $$0.665025\pi$$
$$450$$ 0 0
$$451$$ −30.0000 −1.41264
$$452$$ −1.00000 −0.0470360
$$453$$ 0 0
$$454$$ −27.0000 −1.26717
$$455$$ 0 0
$$456$$ 0 0
$$457$$ −25.0000 −1.16945 −0.584725 0.811231i $$-0.698798\pi$$
−0.584725 + 0.811231i $$0.698798\pi$$
$$458$$ −24.0000 −1.12145
$$459$$ 0 0
$$460$$ 0 0
$$461$$ 15.0000 0.698620 0.349310 0.937007i $$-0.386416\pi$$
0.349310 + 0.937007i $$0.386416\pi$$
$$462$$ 0 0
$$463$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$464$$ −10.0000 −0.464238
$$465$$ 0 0
$$466$$ −10.0000 −0.463241
$$467$$ −18.0000 −0.832941 −0.416470 0.909149i $$-0.636733\pi$$
−0.416470 + 0.909149i $$0.636733\pi$$
$$468$$ 0 0
$$469$$ −33.0000 −1.52380
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 8.00000 0.368230
$$473$$ −5.00000 −0.229900
$$474$$ 0 0
$$475$$ 0 0
$$476$$ −3.00000 −0.137505
$$477$$ 0 0
$$478$$ 13.0000 0.594606
$$479$$ −26.0000 −1.18797 −0.593985 0.804476i $$-0.702446\pi$$
−0.593985 + 0.804476i $$0.702446\pi$$
$$480$$ 0 0
$$481$$ 6.00000 0.273576
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 14.0000 0.636364
$$485$$ 0 0
$$486$$ 0 0
$$487$$ −40.0000 −1.81257 −0.906287 0.422664i $$-0.861095\pi$$
−0.906287 + 0.422664i $$0.861095\pi$$
$$488$$ 2.00000 0.0905357
$$489$$ 0 0
$$490$$ 0 0
$$491$$ −4.00000 −0.180517 −0.0902587 0.995918i $$-0.528769\pi$$
−0.0902587 + 0.995918i $$0.528769\pi$$
$$492$$ 0 0
$$493$$ 10.0000 0.450377
$$494$$ 2.00000 0.0899843
$$495$$ 0 0
$$496$$ 5.00000 0.224507
$$497$$ −18.0000 −0.807410
$$498$$ 0 0
$$499$$ 22.0000 0.984855 0.492428 0.870353i $$-0.336110\pi$$
0.492428 + 0.870353i $$0.336110\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ −18.0000 −0.803379
$$503$$ −6.00000 −0.267527 −0.133763 0.991013i $$-0.542706\pi$$
−0.133763 + 0.991013i $$0.542706\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ 30.0000 1.33366
$$507$$ 0 0
$$508$$ 12.0000 0.532414
$$509$$ −9.00000 −0.398918 −0.199459 0.979906i $$-0.563918\pi$$
−0.199459 + 0.979906i $$0.563918\pi$$
$$510$$ 0 0
$$511$$ −36.0000 −1.59255
$$512$$ −1.00000 −0.0441942
$$513$$ 0 0
$$514$$ 2.00000 0.0882162
$$515$$ 0 0
$$516$$ 0 0
$$517$$ −15.0000 −0.659699
$$518$$ 9.00000 0.395437
$$519$$ 0 0
$$520$$ 0 0
$$521$$ 39.0000 1.70862 0.854311 0.519763i $$-0.173980\pi$$
0.854311 + 0.519763i $$0.173980\pi$$
$$522$$ 0 0
$$523$$ 20.0000 0.874539 0.437269 0.899331i $$-0.355946\pi$$
0.437269 + 0.899331i $$0.355946\pi$$
$$524$$ 20.0000 0.873704
$$525$$ 0 0
$$526$$ 3.00000 0.130806
$$527$$ −5.00000 −0.217803
$$528$$ 0 0
$$529$$ 13.0000 0.565217
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 3.00000 0.130066
$$533$$ 12.0000 0.519778
$$534$$ 0 0
$$535$$ 0 0
$$536$$ 11.0000 0.475128
$$537$$ 0 0
$$538$$ −6.00000 −0.258678
$$539$$ 10.0000 0.430730
$$540$$ 0 0
$$541$$ −41.0000 −1.76273 −0.881364 0.472438i $$-0.843374\pi$$
−0.881364 + 0.472438i $$0.843374\pi$$
$$542$$ −14.0000 −0.601351
$$543$$ 0 0
$$544$$ 1.00000 0.0428746
$$545$$ 0 0
$$546$$ 0 0
$$547$$ 22.0000 0.940652 0.470326 0.882493i $$-0.344136\pi$$
0.470326 + 0.882493i $$0.344136\pi$$
$$548$$ −16.0000 −0.683486
$$549$$ 0 0
$$550$$ 0 0
$$551$$ −10.0000 −0.426014
$$552$$ 0 0
$$553$$ 15.0000 0.637865
$$554$$ 31.0000 1.31706
$$555$$ 0 0
$$556$$ 8.00000 0.339276
$$557$$ −17.0000 −0.720313 −0.360157 0.932892i $$-0.617277\pi$$
−0.360157 + 0.932892i $$0.617277\pi$$
$$558$$ 0 0
$$559$$ 2.00000 0.0845910
$$560$$ 0 0
$$561$$ 0 0
$$562$$ −30.0000 −1.26547
$$563$$ 8.00000 0.337160 0.168580 0.985688i $$-0.446082\pi$$
0.168580 + 0.985688i $$0.446082\pi$$
$$564$$ 0 0
$$565$$ 0 0
$$566$$ 14.0000 0.588464
$$567$$ 0 0
$$568$$ 6.00000 0.251754
$$569$$ 36.0000 1.50920 0.754599 0.656186i $$-0.227831\pi$$
0.754599 + 0.656186i $$0.227831\pi$$
$$570$$ 0 0
$$571$$ −20.0000 −0.836974 −0.418487 0.908223i $$-0.637439\pi$$
−0.418487 + 0.908223i $$0.637439\pi$$
$$572$$ −10.0000 −0.418121
$$573$$ 0 0
$$574$$ 18.0000 0.751305
$$575$$ 0 0
$$576$$ 0 0
$$577$$ 33.0000 1.37381 0.686904 0.726748i $$-0.258969\pi$$
0.686904 + 0.726748i $$0.258969\pi$$
$$578$$ −1.00000 −0.0415945
$$579$$ 0 0
$$580$$ 0 0
$$581$$ −54.0000 −2.24030
$$582$$ 0 0
$$583$$ 5.00000 0.207079
$$584$$ 12.0000 0.496564
$$585$$ 0 0
$$586$$ −18.0000 −0.743573
$$587$$ 18.0000 0.742940 0.371470 0.928445i $$-0.378854\pi$$
0.371470 + 0.928445i $$0.378854\pi$$
$$588$$ 0 0
$$589$$ 5.00000 0.206021
$$590$$ 0 0
$$591$$ 0 0
$$592$$ −3.00000 −0.123299
$$593$$ −12.0000 −0.492781 −0.246390 0.969171i $$-0.579245\pi$$
−0.246390 + 0.969171i $$0.579245\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 6.00000 0.245770
$$597$$ 0 0
$$598$$ −12.0000 −0.490716
$$599$$ −35.0000 −1.43006 −0.715031 0.699093i $$-0.753587\pi$$
−0.715031 + 0.699093i $$0.753587\pi$$
$$600$$ 0 0
$$601$$ −22.0000 −0.897399 −0.448699 0.893683i $$-0.648113\pi$$
−0.448699 + 0.893683i $$0.648113\pi$$
$$602$$ 3.00000 0.122271
$$603$$ 0 0
$$604$$ 8.00000 0.325515
$$605$$ 0 0
$$606$$ 0 0
$$607$$ 20.0000 0.811775 0.405887 0.913923i $$-0.366962\pi$$
0.405887 + 0.913923i $$0.366962\pi$$
$$608$$ −1.00000 −0.0405554
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 6.00000 0.242734
$$612$$ 0 0
$$613$$ −26.0000 −1.05013 −0.525065 0.851062i $$-0.675959\pi$$
−0.525065 + 0.851062i $$0.675959\pi$$
$$614$$ −20.0000 −0.807134
$$615$$ 0 0
$$616$$ −15.0000 −0.604367
$$617$$ 13.0000 0.523360 0.261680 0.965155i $$-0.415723\pi$$
0.261680 + 0.965155i $$0.415723\pi$$
$$618$$ 0 0
$$619$$ −8.00000 −0.321547 −0.160774 0.986991i $$-0.551399\pi$$
−0.160774 + 0.986991i $$0.551399\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ −2.00000 −0.0801927
$$623$$ −36.0000 −1.44231
$$624$$ 0 0
$$625$$ 0 0
$$626$$ 34.0000 1.35891
$$627$$ 0 0
$$628$$ 0 0
$$629$$ 3.00000 0.119618
$$630$$ 0 0
$$631$$ −14.0000 −0.557331 −0.278666 0.960388i $$-0.589892\pi$$
−0.278666 + 0.960388i $$0.589892\pi$$
$$632$$ −5.00000 −0.198889
$$633$$ 0 0
$$634$$ −12.0000 −0.476581
$$635$$ 0 0
$$636$$ 0 0
$$637$$ −4.00000 −0.158486
$$638$$ 50.0000 1.97952
$$639$$ 0 0
$$640$$ 0 0
$$641$$ 30.0000 1.18493 0.592464 0.805597i $$-0.298155\pi$$
0.592464 + 0.805597i $$0.298155\pi$$
$$642$$ 0 0
$$643$$ 34.0000 1.34083 0.670415 0.741987i $$-0.266116\pi$$
0.670415 + 0.741987i $$0.266116\pi$$
$$644$$ −18.0000 −0.709299
$$645$$ 0 0
$$646$$ 1.00000 0.0393445
$$647$$ −24.0000 −0.943537 −0.471769 0.881722i $$-0.656384\pi$$
−0.471769 + 0.881722i $$0.656384\pi$$
$$648$$ 0 0
$$649$$ −40.0000 −1.57014
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ 16.0000 0.626128 0.313064 0.949732i $$-0.398644\pi$$
0.313064 + 0.949732i $$0.398644\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ −6.00000 −0.234261
$$657$$ 0 0
$$658$$ 9.00000 0.350857
$$659$$ −16.0000 −0.623272 −0.311636 0.950202i $$-0.600877\pi$$
−0.311636 + 0.950202i $$0.600877\pi$$
$$660$$ 0 0
$$661$$ 8.00000 0.311164 0.155582 0.987823i $$-0.450275\pi$$
0.155582 + 0.987823i $$0.450275\pi$$
$$662$$ 25.0000 0.971653
$$663$$ 0 0
$$664$$ 18.0000 0.698535
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 60.0000 2.32321
$$668$$ 18.0000 0.696441
$$669$$ 0 0
$$670$$ 0 0
$$671$$ −10.0000 −0.386046
$$672$$ 0 0
$$673$$ 14.0000 0.539660 0.269830 0.962908i $$-0.413032\pi$$
0.269830 + 0.962908i $$0.413032\pi$$
$$674$$ −12.0000 −0.462223
$$675$$ 0 0
$$676$$ −9.00000 −0.346154
$$677$$ −12.0000 −0.461197 −0.230599 0.973049i $$-0.574068\pi$$
−0.230599 + 0.973049i $$0.574068\pi$$
$$678$$ 0 0
$$679$$ −42.0000 −1.61181
$$680$$ 0 0
$$681$$ 0 0
$$682$$ −25.0000 −0.957299
$$683$$ 8.00000 0.306111 0.153056 0.988218i $$-0.451089\pi$$
0.153056 + 0.988218i $$0.451089\pi$$
$$684$$ 0 0
$$685$$ 0 0
$$686$$ 15.0000 0.572703
$$687$$ 0 0
$$688$$ −1.00000 −0.0381246
$$689$$ −2.00000 −0.0761939
$$690$$ 0 0
$$691$$ −48.0000 −1.82601 −0.913003 0.407953i $$-0.866243\pi$$
−0.913003 + 0.407953i $$0.866243\pi$$
$$692$$ −20.0000 −0.760286
$$693$$ 0 0
$$694$$ −23.0000 −0.873068
$$695$$ 0 0
$$696$$ 0 0
$$697$$ 6.00000 0.227266
$$698$$ 14.0000 0.529908
$$699$$ 0 0
$$700$$ 0 0
$$701$$ −18.0000 −0.679851 −0.339925 0.940452i $$-0.610402\pi$$
−0.339925 + 0.940452i $$0.610402\pi$$
$$702$$ 0 0
$$703$$ −3.00000 −0.113147
$$704$$ 5.00000 0.188445
$$705$$ 0 0
$$706$$ −2.00000 −0.0752710
$$707$$ −33.0000 −1.24109
$$708$$ 0 0
$$709$$ 25.0000 0.938895 0.469447 0.882960i $$-0.344453\pi$$
0.469447 + 0.882960i $$0.344453\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 12.0000 0.449719
$$713$$ −30.0000 −1.12351
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 12.0000 0.448461
$$717$$ 0 0
$$718$$ 15.0000 0.559795
$$719$$ −6.00000 −0.223762 −0.111881 0.993722i $$-0.535688\pi$$
−0.111881 + 0.993722i $$0.535688\pi$$
$$720$$ 0 0
$$721$$ 12.0000 0.446903
$$722$$ 18.0000 0.669891
$$723$$ 0 0
$$724$$ −17.0000 −0.631800
$$725$$ 0 0
$$726$$ 0 0
$$727$$ 2.00000 0.0741759 0.0370879 0.999312i $$-0.488192\pi$$
0.0370879 + 0.999312i $$0.488192\pi$$
$$728$$ 6.00000 0.222375
$$729$$ 0 0
$$730$$ 0 0
$$731$$ 1.00000 0.0369863
$$732$$ 0 0
$$733$$ −16.0000 −0.590973 −0.295487 0.955347i $$-0.595482\pi$$
−0.295487 + 0.955347i $$0.595482\pi$$
$$734$$ −5.00000 −0.184553
$$735$$ 0 0
$$736$$ 6.00000 0.221163
$$737$$ −55.0000 −2.02595
$$738$$ 0 0
$$739$$ −19.0000 −0.698926 −0.349463 0.936950i $$-0.613636\pi$$
−0.349463 + 0.936950i $$0.613636\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ −3.00000 −0.110133
$$743$$ −18.0000 −0.660356 −0.330178 0.943919i $$-0.607109\pi$$
−0.330178 + 0.943919i $$0.607109\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ 18.0000 0.659027
$$747$$ 0 0
$$748$$ −5.00000 −0.182818
$$749$$ 15.0000 0.548088
$$750$$ 0 0
$$751$$ −48.0000 −1.75154 −0.875772 0.482724i $$-0.839647\pi$$
−0.875772 + 0.482724i $$0.839647\pi$$
$$752$$ −3.00000 −0.109399
$$753$$ 0 0
$$754$$ −20.0000 −0.728357
$$755$$ 0 0
$$756$$ 0 0
$$757$$ 14.0000 0.508839 0.254419 0.967094i $$-0.418116\pi$$
0.254419 + 0.967094i $$0.418116\pi$$
$$758$$ 8.00000 0.290573
$$759$$ 0 0
$$760$$ 0 0
$$761$$ −36.0000 −1.30500 −0.652499 0.757789i $$-0.726280\pi$$
−0.652499 + 0.757789i $$0.726280\pi$$
$$762$$ 0 0
$$763$$ 15.0000 0.543036
$$764$$ −3.00000 −0.108536
$$765$$ 0 0
$$766$$ −8.00000 −0.289052
$$767$$ 16.0000 0.577727
$$768$$ 0 0
$$769$$ −37.0000 −1.33425 −0.667127 0.744944i $$-0.732476\pi$$
−0.667127 + 0.744944i $$0.732476\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ −24.0000 −0.863779
$$773$$ 34.0000 1.22290 0.611448 0.791285i $$-0.290588\pi$$
0.611448 + 0.791285i $$0.290588\pi$$
$$774$$ 0 0
$$775$$ 0 0
$$776$$ 14.0000 0.502571
$$777$$ 0 0
$$778$$ −5.00000 −0.179259
$$779$$ −6.00000 −0.214972
$$780$$ 0 0
$$781$$ −30.0000 −1.07348
$$782$$ −6.00000 −0.214560
$$783$$ 0 0
$$784$$ 2.00000 0.0714286
$$785$$ 0 0
$$786$$ 0 0
$$787$$ 18.0000 0.641631 0.320815 0.947142i $$-0.396043\pi$$
0.320815 + 0.947142i $$0.396043\pi$$
$$788$$ −12.0000 −0.427482
$$789$$ 0 0
$$790$$ 0 0
$$791$$ −3.00000 −0.106668
$$792$$ 0 0
$$793$$ 4.00000 0.142044
$$794$$ −21.0000 −0.745262
$$795$$ 0 0
$$796$$ 17.0000 0.602549
$$797$$ 11.0000 0.389640 0.194820 0.980839i $$-0.437588\pi$$
0.194820 + 0.980839i $$0.437588\pi$$
$$798$$ 0 0
$$799$$ 3.00000 0.106132
$$800$$ 0 0
$$801$$ 0 0
$$802$$ −18.0000 −0.635602
$$803$$ −60.0000 −2.11735
$$804$$ 0 0
$$805$$ 0 0
$$806$$ 10.0000 0.352235
$$807$$ 0 0
$$808$$ 11.0000 0.386979
$$809$$ 39.0000 1.37117 0.685583 0.727994i $$-0.259547\pi$$
0.685583 + 0.727994i $$0.259547\pi$$
$$810$$ 0 0
$$811$$ 56.0000 1.96643 0.983213 0.182462i $$-0.0584065\pi$$
0.983213 + 0.182462i $$0.0584065\pi$$
$$812$$ −30.0000 −1.05279
$$813$$ 0 0
$$814$$ 15.0000 0.525750
$$815$$ 0 0
$$816$$ 0 0
$$817$$ −1.00000 −0.0349856
$$818$$ 2.00000 0.0699284
$$819$$ 0 0
$$820$$ 0 0
$$821$$ −54.0000 −1.88461 −0.942306 0.334751i $$-0.891348\pi$$
−0.942306 + 0.334751i $$0.891348\pi$$
$$822$$ 0 0
$$823$$ 4.00000 0.139431 0.0697156 0.997567i $$-0.477791\pi$$
0.0697156 + 0.997567i $$0.477791\pi$$
$$824$$ −4.00000 −0.139347
$$825$$ 0 0
$$826$$ 24.0000 0.835067
$$827$$ 53.0000 1.84299 0.921495 0.388390i $$-0.126968\pi$$
0.921495 + 0.388390i $$0.126968\pi$$
$$828$$ 0 0
$$829$$ −30.0000 −1.04194 −0.520972 0.853574i $$-0.674430\pi$$
−0.520972 + 0.853574i $$0.674430\pi$$
$$830$$ 0 0
$$831$$ 0 0
$$832$$ −2.00000 −0.0693375
$$833$$ −2.00000 −0.0692959
$$834$$ 0 0
$$835$$ 0 0
$$836$$ 5.00000 0.172929
$$837$$ 0 0
$$838$$ 24.0000 0.829066
$$839$$ 8.00000 0.276191 0.138095 0.990419i $$-0.455902\pi$$
0.138095 + 0.990419i $$0.455902\pi$$
$$840$$ 0 0
$$841$$ 71.0000 2.44828
$$842$$ −18.0000 −0.620321
$$843$$ 0 0
$$844$$ 18.0000 0.619586
$$845$$ 0 0
$$846$$ 0 0
$$847$$ 42.0000 1.44314
$$848$$ 1.00000 0.0343401
$$849$$ 0 0
$$850$$ 0 0
$$851$$ 18.0000 0.617032
$$852$$ 0 0
$$853$$ −37.0000 −1.26686 −0.633428 0.773802i $$-0.718353\pi$$
−0.633428 + 0.773802i $$0.718353\pi$$
$$854$$ 6.00000 0.205316
$$855$$ 0 0
$$856$$ −5.00000 −0.170896
$$857$$ 21.0000 0.717346 0.358673 0.933463i $$-0.383229\pi$$
0.358673 + 0.933463i $$0.383229\pi$$
$$858$$ 0 0
$$859$$ −23.0000 −0.784750 −0.392375 0.919805i $$-0.628346\pi$$
−0.392375 + 0.919805i $$0.628346\pi$$
$$860$$ 0 0
$$861$$ 0 0
$$862$$ 0 0
$$863$$ 33.0000 1.12333 0.561667 0.827364i $$-0.310160\pi$$
0.561667 + 0.827364i $$0.310160\pi$$
$$864$$ 0 0
$$865$$ 0 0
$$866$$ −21.0000 −0.713609
$$867$$ 0 0
$$868$$ 15.0000 0.509133
$$869$$ 25.0000 0.848067
$$870$$ 0 0
$$871$$ 22.0000 0.745442
$$872$$ −5.00000 −0.169321
$$873$$ 0 0
$$874$$ 6.00000 0.202953
$$875$$ 0 0
$$876$$ 0 0
$$877$$ 14.0000 0.472746 0.236373 0.971662i $$-0.424041\pi$$
0.236373 + 0.971662i $$0.424041\pi$$
$$878$$ −16.0000 −0.539974
$$879$$ 0 0
$$880$$ 0 0
$$881$$ 9.00000 0.303218 0.151609 0.988441i $$-0.451555\pi$$
0.151609 + 0.988441i $$0.451555\pi$$
$$882$$ 0 0
$$883$$ −20.0000 −0.673054 −0.336527 0.941674i $$-0.609252\pi$$
−0.336527 + 0.941674i $$0.609252\pi$$
$$884$$ 2.00000 0.0672673
$$885$$ 0 0
$$886$$ −24.0000 −0.806296
$$887$$ −48.0000 −1.61168 −0.805841 0.592132i $$-0.798286\pi$$
−0.805841 + 0.592132i $$0.798286\pi$$
$$888$$ 0 0
$$889$$ 36.0000 1.20740
$$890$$ 0 0
$$891$$ 0 0
$$892$$ 18.0000 0.602685
$$893$$ −3.00000 −0.100391
$$894$$ 0 0
$$895$$ 0 0
$$896$$ −3.00000 −0.100223
$$897$$ 0 0
$$898$$ 21.0000 0.700779
$$899$$ −50.0000 −1.66759
$$900$$ 0 0
$$901$$ −1.00000 −0.0333148
$$902$$ 30.0000 0.998891
$$903$$ 0 0
$$904$$ 1.00000 0.0332595
$$905$$ 0 0
$$906$$ 0 0
$$907$$ −30.0000 −0.996134 −0.498067 0.867139i $$-0.665957\pi$$
−0.498067 + 0.867139i $$0.665957\pi$$
$$908$$ 27.0000 0.896026
$$909$$ 0 0
$$910$$ 0 0
$$911$$ −56.0000 −1.85536 −0.927681 0.373373i $$-0.878201\pi$$
−0.927681 + 0.373373i $$0.878201\pi$$
$$912$$ 0 0
$$913$$ −90.0000 −2.97857
$$914$$ 25.0000 0.826927
$$915$$ 0 0
$$916$$ 24.0000 0.792982
$$917$$ 60.0000 1.98137
$$918$$ 0 0
$$919$$ 44.0000 1.45143 0.725713 0.687998i $$-0.241510\pi$$
0.725713 + 0.687998i $$0.241510\pi$$
$$920$$ 0 0
$$921$$ 0 0
$$922$$ −15.0000 −0.493999
$$923$$ 12.0000 0.394985
$$924$$ 0 0
$$925$$ 0 0
$$926$$ 0 0
$$927$$ 0 0
$$928$$ 10.0000 0.328266
$$929$$ −27.0000 −0.885841 −0.442921 0.896561i $$-0.646058\pi$$
−0.442921 + 0.896561i $$0.646058\pi$$
$$930$$ 0 0
$$931$$ 2.00000 0.0655474
$$932$$ 10.0000 0.327561
$$933$$ 0 0
$$934$$ 18.0000 0.588978
$$935$$ 0 0
$$936$$ 0 0
$$937$$ 10.0000 0.326686 0.163343 0.986569i $$-0.447772\pi$$
0.163343 + 0.986569i $$0.447772\pi$$
$$938$$ 33.0000 1.07749
$$939$$ 0 0
$$940$$ 0 0
$$941$$ −22.0000 −0.717180 −0.358590 0.933495i $$-0.616742\pi$$
−0.358590 + 0.933495i $$0.616742\pi$$
$$942$$ 0 0
$$943$$ 36.0000 1.17232
$$944$$ −8.00000 −0.260378
$$945$$ 0 0
$$946$$ 5.00000 0.162564
$$947$$ −61.0000 −1.98223 −0.991117 0.132994i $$-0.957541\pi$$
−0.991117 + 0.132994i $$0.957541\pi$$
$$948$$ 0 0
$$949$$ 24.0000 0.779073
$$950$$ 0 0
$$951$$ 0 0
$$952$$ 3.00000 0.0972306
$$953$$ 14.0000 0.453504 0.226752 0.973952i $$-0.427189\pi$$
0.226752 + 0.973952i $$0.427189\pi$$
$$954$$ 0 0
$$955$$ 0 0
$$956$$ −13.0000 −0.420450
$$957$$ 0 0
$$958$$ 26.0000 0.840022
$$959$$ −48.0000 −1.55000
$$960$$ 0 0
$$961$$ −6.00000 −0.193548
$$962$$ −6.00000 −0.193448
$$963$$ 0 0
$$964$$ 0 0
$$965$$ 0 0
$$966$$ 0 0
$$967$$ −36.0000 −1.15768 −0.578841 0.815440i $$-0.696495\pi$$
−0.578841 + 0.815440i $$0.696495\pi$$
$$968$$ −14.0000 −0.449977
$$969$$ 0 0
$$970$$ 0 0
$$971$$ 38.0000 1.21948 0.609739 0.792602i $$-0.291274\pi$$
0.609739 + 0.792602i $$0.291274\pi$$
$$972$$ 0 0
$$973$$ 24.0000 0.769405
$$974$$ 40.0000 1.28168
$$975$$ 0 0
$$976$$ −2.00000 −0.0640184
$$977$$ 10.0000 0.319928 0.159964 0.987123i $$-0.448862\pi$$
0.159964 + 0.987123i $$0.448862\pi$$
$$978$$ 0 0
$$979$$ −60.0000 −1.91761
$$980$$ 0 0
$$981$$ 0 0
$$982$$ 4.00000 0.127645
$$983$$ 6.00000 0.191370 0.0956851 0.995412i $$-0.469496\pi$$
0.0956851 + 0.995412i $$0.469496\pi$$
$$984$$ 0 0
$$985$$ 0 0
$$986$$ −10.0000 −0.318465
$$987$$ 0 0
$$988$$ −2.00000 −0.0636285
$$989$$ 6.00000 0.190789
$$990$$ 0 0
$$991$$ 52.0000 1.65183 0.825917 0.563791i $$-0.190658\pi$$
0.825917 + 0.563791i $$0.190658\pi$$
$$992$$ −5.00000 −0.158750
$$993$$ 0 0
$$994$$ 18.0000 0.570925
$$995$$ 0 0
$$996$$ 0 0
$$997$$ −43.0000 −1.36182 −0.680912 0.732365i $$-0.738416\pi$$
−0.680912 + 0.732365i $$0.738416\pi$$
$$998$$ −22.0000 −0.696398
$$999$$ 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 7650.2.a.be.1.1 1
3.2 odd 2 2550.2.a.z.1.1 yes 1
5.4 even 2 7650.2.a.bl.1.1 1
15.2 even 4 2550.2.d.a.2449.2 2
15.8 even 4 2550.2.d.a.2449.1 2
15.14 odd 2 2550.2.a.h.1.1 1

By twisted newform
Twist Min Dim Char Parity Ord Type
2550.2.a.h.1.1 1 15.14 odd 2
2550.2.a.z.1.1 yes 1 3.2 odd 2
2550.2.d.a.2449.1 2 15.8 even 4
2550.2.d.a.2449.2 2 15.2 even 4
7650.2.a.be.1.1 1 1.1 even 1 trivial
7650.2.a.bl.1.1 1 5.4 even 2