# Properties

 Label 7605.2.a.bw.1.1 Level $7605$ Weight $2$ Character 7605.1 Self dual yes Analytic conductor $60.726$ Analytic rank $1$ Dimension $3$ CM no Inner twists $1$

# Related objects

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [7605,2,Mod(1,7605)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7605, 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("7605.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$7605 = 3^{2} \cdot 5 \cdot 13^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 7605.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: $$60.7262307372$$ Analytic rank: $$1$$ Dimension: $$3$$ Coefficient field: 3.3.756.1 comment: defining polynomial  gp: f.mod \\ as an extension of the character field Defining polynomial: $$x^{3} - 6x - 2$$ x^3 - 6*x - 2 Coefficient ring: $$\Z[a_1, a_2]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 195) Fricke sign: $$1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

 Embedding label 1.1 Root $$-2.26180$$ of defining polynomial Character $$\chi$$ $$=$$ 7605.1

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q-2.26180 q^{2} +3.11575 q^{4} +1.00000 q^{5} +1.26180 q^{7} -2.52360 q^{8} +O(q^{10})$$ $$q-2.26180 q^{2} +3.11575 q^{4} +1.00000 q^{5} +1.26180 q^{7} -2.52360 q^{8} -2.26180 q^{10} +4.52360 q^{11} -2.85395 q^{14} -0.523604 q^{16} +4.49330 q^{17} -5.11575 q^{19} +3.11575 q^{20} -10.2315 q^{22} -2.23150 q^{23} +1.00000 q^{25} +3.93146 q^{28} +1.37755 q^{29} -8.87085 q^{31} +6.23150 q^{32} -10.1630 q^{34} +1.26180 q^{35} +0.231499 q^{37} +11.5708 q^{38} -2.52360 q^{40} +1.14605 q^{41} +6.37755 q^{43} +14.0944 q^{44} +5.04721 q^{46} -10.7854 q^{47} -5.40786 q^{49} -2.26180 q^{50} -4.52360 q^{53} +4.52360 q^{55} -3.18429 q^{56} -3.11575 q^{58} -0.853947 q^{59} +4.63935 q^{61} +20.0641 q^{62} -13.0472 q^{64} -13.1327 q^{67} +14.0000 q^{68} -2.85395 q^{70} -9.60905 q^{71} -13.7854 q^{73} -0.523604 q^{74} -15.9394 q^{76} +5.70789 q^{77} -8.87085 q^{79} -0.523604 q^{80} -2.59214 q^{82} -8.23150 q^{83} +4.49330 q^{85} -14.4248 q^{86} -11.4158 q^{88} +6.62245 q^{89} -6.95279 q^{92} +24.3945 q^{94} -5.11575 q^{95} -10.6697 q^{97} +12.2315 q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$3 q + 6 q^{4} + 3 q^{5} - 3 q^{7} + 6 q^{8}+O(q^{10})$$ 3 * q + 6 * q^4 + 3 * q^5 - 3 * q^7 + 6 * q^8 $$3 q + 6 q^{4} + 3 q^{5} - 3 q^{7} + 6 q^{8} - 12 q^{14} + 12 q^{16} - 12 q^{19} + 6 q^{20} - 24 q^{22} + 3 q^{25} - 12 q^{28} - 6 q^{29} - 3 q^{31} + 12 q^{32} - 3 q^{35} - 6 q^{37} - 6 q^{38} + 6 q^{40} + 9 q^{43} - 12 q^{44} - 12 q^{46} - 12 q^{47} - 6 q^{49} - 30 q^{56} - 6 q^{58} - 6 q^{59} - 3 q^{61} + 6 q^{62} - 12 q^{64} - 9 q^{67} + 42 q^{68} - 12 q^{70} - 12 q^{71} - 21 q^{73} + 12 q^{74} - 48 q^{76} + 24 q^{77} - 3 q^{79} + 12 q^{80} - 18 q^{82} - 18 q^{83} - 6 q^{86} - 48 q^{88} + 30 q^{89} - 48 q^{92} + 36 q^{94} - 12 q^{95} - 15 q^{97} + 30 q^{98}+O(q^{100})$$ 3 * q + 6 * q^4 + 3 * q^5 - 3 * q^7 + 6 * q^8 - 12 * q^14 + 12 * q^16 - 12 * q^19 + 6 * q^20 - 24 * q^22 + 3 * q^25 - 12 * q^28 - 6 * q^29 - 3 * q^31 + 12 * q^32 - 3 * q^35 - 6 * q^37 - 6 * q^38 + 6 * q^40 + 9 * q^43 - 12 * q^44 - 12 * q^46 - 12 * q^47 - 6 * q^49 - 30 * q^56 - 6 * q^58 - 6 * q^59 - 3 * q^61 + 6 * q^62 - 12 * q^64 - 9 * q^67 + 42 * q^68 - 12 * q^70 - 12 * q^71 - 21 * q^73 + 12 * q^74 - 48 * q^76 + 24 * q^77 - 3 * q^79 + 12 * q^80 - 18 * q^82 - 18 * q^83 - 6 * q^86 - 48 * q^88 + 30 * q^89 - 48 * q^92 + 36 * q^94 - 12 * q^95 - 15 * q^97 + 30 * q^98

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −2.26180 −1.59934 −0.799668 0.600443i $$-0.794991\pi$$
−0.799668 + 0.600443i $$0.794991\pi$$
$$3$$ 0 0
$$4$$ 3.11575 1.55787
$$5$$ 1.00000 0.447214
$$6$$ 0 0
$$7$$ 1.26180 0.476916 0.238458 0.971153i $$-0.423358\pi$$
0.238458 + 0.971153i $$0.423358\pi$$
$$8$$ −2.52360 −0.892229
$$9$$ 0 0
$$10$$ −2.26180 −0.715245
$$11$$ 4.52360 1.36392 0.681959 0.731390i $$-0.261128\pi$$
0.681959 + 0.731390i $$0.261128\pi$$
$$12$$ 0 0
$$13$$ 0 0
$$14$$ −2.85395 −0.762749
$$15$$ 0 0
$$16$$ −0.523604 −0.130901
$$17$$ 4.49330 1.08979 0.544893 0.838506i $$-0.316570\pi$$
0.544893 + 0.838506i $$0.316570\pi$$
$$18$$ 0 0
$$19$$ −5.11575 −1.17363 −0.586817 0.809720i $$-0.699619\pi$$
−0.586817 + 0.809720i $$0.699619\pi$$
$$20$$ 3.11575 0.696703
$$21$$ 0 0
$$22$$ −10.2315 −2.18136
$$23$$ −2.23150 −0.465300 −0.232650 0.972561i $$-0.574740\pi$$
−0.232650 + 0.972561i $$0.574740\pi$$
$$24$$ 0 0
$$25$$ 1.00000 0.200000
$$26$$ 0 0
$$27$$ 0 0
$$28$$ 3.93146 0.742976
$$29$$ 1.37755 0.255805 0.127902 0.991787i $$-0.459176\pi$$
0.127902 + 0.991787i $$0.459176\pi$$
$$30$$ 0 0
$$31$$ −8.87085 −1.59325 −0.796626 0.604472i $$-0.793384\pi$$
−0.796626 + 0.604472i $$0.793384\pi$$
$$32$$ 6.23150 1.10158
$$33$$ 0 0
$$34$$ −10.1630 −1.74293
$$35$$ 1.26180 0.213284
$$36$$ 0 0
$$37$$ 0.231499 0.0380582 0.0190291 0.999819i $$-0.493942\pi$$
0.0190291 + 0.999819i $$0.493942\pi$$
$$38$$ 11.5708 1.87703
$$39$$ 0 0
$$40$$ −2.52360 −0.399017
$$41$$ 1.14605 0.178983 0.0894917 0.995988i $$-0.471476\pi$$
0.0894917 + 0.995988i $$0.471476\pi$$
$$42$$ 0 0
$$43$$ 6.37755 0.972568 0.486284 0.873801i $$-0.338352\pi$$
0.486284 + 0.873801i $$0.338352\pi$$
$$44$$ 14.0944 2.12481
$$45$$ 0 0
$$46$$ 5.04721 0.744170
$$47$$ −10.7854 −1.57321 −0.786607 0.617454i $$-0.788164\pi$$
−0.786607 + 0.617454i $$0.788164\pi$$
$$48$$ 0 0
$$49$$ −5.40786 −0.772551
$$50$$ −2.26180 −0.319867
$$51$$ 0 0
$$52$$ 0 0
$$53$$ −4.52360 −0.621365 −0.310682 0.950514i $$-0.600558\pi$$
−0.310682 + 0.950514i $$0.600558\pi$$
$$54$$ 0 0
$$55$$ 4.52360 0.609963
$$56$$ −3.18429 −0.425519
$$57$$ 0 0
$$58$$ −3.11575 −0.409118
$$59$$ −0.853947 −0.111174 −0.0555872 0.998454i $$-0.517703\pi$$
−0.0555872 + 0.998454i $$0.517703\pi$$
$$60$$ 0 0
$$61$$ 4.63935 0.594008 0.297004 0.954876i $$-0.404012\pi$$
0.297004 + 0.954876i $$0.404012\pi$$
$$62$$ 20.0641 2.54815
$$63$$ 0 0
$$64$$ −13.0472 −1.63090
$$65$$ 0 0
$$66$$ 0 0
$$67$$ −13.1327 −1.60441 −0.802205 0.597049i $$-0.796340\pi$$
−0.802205 + 0.597049i $$0.796340\pi$$
$$68$$ 14.0000 1.69775
$$69$$ 0 0
$$70$$ −2.85395 −0.341112
$$71$$ −9.60905 −1.14038 −0.570192 0.821511i $$-0.693131\pi$$
−0.570192 + 0.821511i $$0.693131\pi$$
$$72$$ 0 0
$$73$$ −13.7854 −1.61346 −0.806730 0.590920i $$-0.798765\pi$$
−0.806730 + 0.590920i $$0.798765\pi$$
$$74$$ −0.523604 −0.0608678
$$75$$ 0 0
$$76$$ −15.9394 −1.82837
$$77$$ 5.70789 0.650475
$$78$$ 0 0
$$79$$ −8.87085 −0.998049 −0.499024 0.866588i $$-0.666308\pi$$
−0.499024 + 0.866588i $$0.666308\pi$$
$$80$$ −0.523604 −0.0585408
$$81$$ 0 0
$$82$$ −2.59214 −0.286255
$$83$$ −8.23150 −0.903524 −0.451762 0.892138i $$-0.649204\pi$$
−0.451762 + 0.892138i $$0.649204\pi$$
$$84$$ 0 0
$$85$$ 4.49330 0.487367
$$86$$ −14.4248 −1.55546
$$87$$ 0 0
$$88$$ −11.4158 −1.21693
$$89$$ 6.62245 0.701978 0.350989 0.936380i $$-0.385845\pi$$
0.350989 + 0.936380i $$0.385845\pi$$
$$90$$ 0 0
$$91$$ 0 0
$$92$$ −6.95279 −0.724879
$$93$$ 0 0
$$94$$ 24.3945 2.51610
$$95$$ −5.11575 −0.524865
$$96$$ 0 0
$$97$$ −10.6697 −1.08334 −0.541670 0.840591i $$-0.682208\pi$$
−0.541670 + 0.840591i $$0.682208\pi$$
$$98$$ 12.2315 1.23557
$$99$$ 0 0
$$100$$ 3.11575 0.311575
$$101$$ 17.0472 1.69626 0.848130 0.529788i $$-0.177728\pi$$
0.848130 + 0.529788i $$0.177728\pi$$
$$102$$ 0 0
$$103$$ −13.9484 −1.37437 −0.687187 0.726481i $$-0.741155\pi$$
−0.687187 + 0.726481i $$0.741155\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 10.2315 0.993771
$$107$$ −12.4933 −1.20777 −0.603886 0.797070i $$-0.706382\pi$$
−0.603886 + 0.797070i $$0.706382\pi$$
$$108$$ 0 0
$$109$$ 2.27871 0.218261 0.109130 0.994027i $$-0.465193\pi$$
0.109130 + 0.994027i $$0.465193\pi$$
$$110$$ −10.2315 −0.975535
$$111$$ 0 0
$$112$$ −0.660685 −0.0624289
$$113$$ 1.47640 0.138888 0.0694438 0.997586i $$-0.477878\pi$$
0.0694438 + 0.997586i $$0.477878\pi$$
$$114$$ 0 0
$$115$$ −2.23150 −0.208088
$$116$$ 4.29211 0.398512
$$117$$ 0 0
$$118$$ 1.93146 0.177805
$$119$$ 5.66966 0.519737
$$120$$ 0 0
$$121$$ 9.46300 0.860273
$$122$$ −10.4933 −0.950019
$$123$$ 0 0
$$124$$ −27.6394 −2.48209
$$125$$ 1.00000 0.0894427
$$126$$ 0 0
$$127$$ −17.7854 −1.57820 −0.789100 0.614265i $$-0.789453\pi$$
−0.789100 + 0.614265i $$0.789453\pi$$
$$128$$ 17.0472 1.50677
$$129$$ 0 0
$$130$$ 0 0
$$131$$ −11.6697 −1.01958 −0.509791 0.860298i $$-0.670277\pi$$
−0.509791 + 0.860298i $$0.670277\pi$$
$$132$$ 0 0
$$133$$ −6.45506 −0.559725
$$134$$ 29.7035 2.56599
$$135$$ 0 0
$$136$$ −11.3393 −0.972338
$$137$$ −20.0641 −1.71419 −0.857096 0.515156i $$-0.827734\pi$$
−0.857096 + 0.515156i $$0.827734\pi$$
$$138$$ 0 0
$$139$$ 16.3393 1.38588 0.692941 0.720994i $$-0.256314\pi$$
0.692941 + 0.720994i $$0.256314\pi$$
$$140$$ 3.93146 0.332269
$$141$$ 0 0
$$142$$ 21.7338 1.82386
$$143$$ 0 0
$$144$$ 0 0
$$145$$ 1.37755 0.114399
$$146$$ 31.1799 2.58046
$$147$$ 0 0
$$148$$ 0.721292 0.0592899
$$149$$ −3.24490 −0.265832 −0.132916 0.991127i $$-0.542434\pi$$
−0.132916 + 0.991127i $$0.542434\pi$$
$$150$$ 0 0
$$151$$ −5.69996 −0.463856 −0.231928 0.972733i $$-0.574503\pi$$
−0.231928 + 0.972733i $$0.574503\pi$$
$$152$$ 12.9101 1.04715
$$153$$ 0 0
$$154$$ −12.9101 −1.04033
$$155$$ −8.87085 −0.712524
$$156$$ 0 0
$$157$$ −3.85395 −0.307578 −0.153789 0.988104i $$-0.549148\pi$$
−0.153789 + 0.988104i $$0.549148\pi$$
$$158$$ 20.0641 1.59622
$$159$$ 0 0
$$160$$ 6.23150 0.492643
$$161$$ −2.81571 −0.221909
$$162$$ 0 0
$$163$$ 9.72480 0.761705 0.380853 0.924636i $$-0.375631\pi$$
0.380853 + 0.924636i $$0.375631\pi$$
$$164$$ 3.57081 0.278834
$$165$$ 0 0
$$166$$ 18.6180 1.44504
$$167$$ −19.2787 −1.49183 −0.745916 0.666040i $$-0.767988\pi$$
−0.745916 + 0.666040i $$0.767988\pi$$
$$168$$ 0 0
$$169$$ 0 0
$$170$$ −10.1630 −0.779463
$$171$$ 0 0
$$172$$ 19.8709 1.51514
$$173$$ 3.01691 0.229371 0.114686 0.993402i $$-0.463414\pi$$
0.114686 + 0.993402i $$0.463414\pi$$
$$174$$ 0 0
$$175$$ 1.26180 0.0953833
$$176$$ −2.36858 −0.178538
$$177$$ 0 0
$$178$$ −14.9787 −1.12270
$$179$$ 5.31694 0.397407 0.198704 0.980060i $$-0.436327\pi$$
0.198704 + 0.980060i $$0.436327\pi$$
$$180$$ 0 0
$$181$$ 25.8709 1.92297 0.961483 0.274866i $$-0.0886333\pi$$
0.961483 + 0.274866i $$0.0886333\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 5.63142 0.415154
$$185$$ 0.231499 0.0170201
$$186$$ 0 0
$$187$$ 20.3259 1.48638
$$188$$ −33.6046 −2.45087
$$189$$ 0 0
$$190$$ 11.5708 0.839435
$$191$$ −10.6563 −0.771060 −0.385530 0.922695i $$-0.625981\pi$$
−0.385530 + 0.922695i $$0.625981\pi$$
$$192$$ 0 0
$$193$$ −7.98309 −0.574636 −0.287318 0.957835i $$-0.592764\pi$$
−0.287318 + 0.957835i $$0.592764\pi$$
$$194$$ 24.1327 1.73262
$$195$$ 0 0
$$196$$ −16.8495 −1.20354
$$197$$ 17.3393 1.23538 0.617688 0.786424i $$-0.288070\pi$$
0.617688 + 0.786424i $$0.288070\pi$$
$$198$$ 0 0
$$199$$ −1.23150 −0.0872986 −0.0436493 0.999047i $$-0.513898\pi$$
−0.0436493 + 0.999047i $$0.513898\pi$$
$$200$$ −2.52360 −0.178446
$$201$$ 0 0
$$202$$ −38.5574 −2.71289
$$203$$ 1.73820 0.121998
$$204$$ 0 0
$$205$$ 1.14605 0.0800438
$$206$$ 31.5484 2.19808
$$207$$ 0 0
$$208$$ 0 0
$$209$$ −23.1416 −1.60074
$$210$$ 0 0
$$211$$ 10.3393 0.711788 0.355894 0.934526i $$-0.384176\pi$$
0.355894 + 0.934526i $$0.384176\pi$$
$$212$$ −14.0944 −0.968009
$$213$$ 0 0
$$214$$ 28.2574 1.93163
$$215$$ 6.37755 0.434945
$$216$$ 0 0
$$217$$ −11.1933 −0.759848
$$218$$ −5.15399 −0.349072
$$219$$ 0 0
$$220$$ 14.0944 0.950245
$$221$$ 0 0
$$222$$ 0 0
$$223$$ −21.5708 −1.44449 −0.722244 0.691638i $$-0.756889\pi$$
−0.722244 + 0.691638i $$0.756889\pi$$
$$224$$ 7.86292 0.525363
$$225$$ 0 0
$$226$$ −3.33931 −0.222128
$$227$$ 5.44609 0.361470 0.180735 0.983532i $$-0.442152\pi$$
0.180735 + 0.983532i $$0.442152\pi$$
$$228$$ 0 0
$$229$$ −21.9315 −1.44927 −0.724636 0.689132i $$-0.757992\pi$$
−0.724636 + 0.689132i $$0.757992\pi$$
$$230$$ 5.04721 0.332803
$$231$$ 0 0
$$232$$ −3.47640 −0.228237
$$233$$ −25.3125 −1.65828 −0.829139 0.559042i $$-0.811169\pi$$
−0.829139 + 0.559042i $$0.811169\pi$$
$$234$$ 0 0
$$235$$ −10.7854 −0.703562
$$236$$ −2.66069 −0.173196
$$237$$ 0 0
$$238$$ −12.8236 −0.831233
$$239$$ 22.5236 1.45693 0.728465 0.685083i $$-0.240234\pi$$
0.728465 + 0.685083i $$0.240234\pi$$
$$240$$ 0 0
$$241$$ −11.1157 −0.716028 −0.358014 0.933716i $$-0.616546\pi$$
−0.358014 + 0.933716i $$0.616546\pi$$
$$242$$ −21.4034 −1.37586
$$243$$ 0 0
$$244$$ 14.4551 0.925391
$$245$$ −5.40786 −0.345495
$$246$$ 0 0
$$247$$ 0 0
$$248$$ 22.3865 1.42155
$$249$$ 0 0
$$250$$ −2.26180 −0.143049
$$251$$ −11.0472 −0.697294 −0.348647 0.937254i $$-0.613359\pi$$
−0.348647 + 0.937254i $$0.613359\pi$$
$$252$$ 0 0
$$253$$ −10.0944 −0.634631
$$254$$ 40.2271 2.52407
$$255$$ 0 0
$$256$$ −12.4630 −0.778937
$$257$$ 2.03030 0.126647 0.0633234 0.997993i $$-0.479830\pi$$
0.0633234 + 0.997993i $$0.479830\pi$$
$$258$$ 0 0
$$259$$ 0.292106 0.0181506
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 26.3945 1.63066
$$263$$ −3.24840 −0.200305 −0.100153 0.994972i $$-0.531933\pi$$
−0.100153 + 0.994972i $$0.531933\pi$$
$$264$$ 0 0
$$265$$ −4.52360 −0.277883
$$266$$ 14.6001 0.895188
$$267$$ 0 0
$$268$$ −40.9181 −2.49947
$$269$$ −26.9484 −1.64307 −0.821535 0.570157i $$-0.806882\pi$$
−0.821535 + 0.570157i $$0.806882\pi$$
$$270$$ 0 0
$$271$$ 19.8495 1.20577 0.602886 0.797827i $$-0.294017\pi$$
0.602886 + 0.797827i $$0.294017\pi$$
$$272$$ −2.35271 −0.142654
$$273$$ 0 0
$$274$$ 45.3811 2.74157
$$275$$ 4.52360 0.272784
$$276$$ 0 0
$$277$$ 16.0944 0.967020 0.483510 0.875339i $$-0.339362\pi$$
0.483510 + 0.875339i $$0.339362\pi$$
$$278$$ −36.9563 −2.21649
$$279$$ 0 0
$$280$$ −3.18429 −0.190298
$$281$$ −5.37755 −0.320798 −0.160399 0.987052i $$-0.551278\pi$$
−0.160399 + 0.987052i $$0.551278\pi$$
$$282$$ 0 0
$$283$$ 26.8664 1.59704 0.798522 0.601966i $$-0.205616\pi$$
0.798522 + 0.601966i $$0.205616\pi$$
$$284$$ −29.9394 −1.77658
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 1.44609 0.0853601
$$288$$ 0 0
$$289$$ 3.18975 0.187633
$$290$$ −3.11575 −0.182963
$$291$$ 0 0
$$292$$ −42.9519 −2.51357
$$293$$ 21.4193 1.25133 0.625664 0.780092i $$-0.284828\pi$$
0.625664 + 0.780092i $$0.284828\pi$$
$$294$$ 0 0
$$295$$ −0.853947 −0.0497187
$$296$$ −0.584211 −0.0339566
$$297$$ 0 0
$$298$$ 7.33931 0.425155
$$299$$ 0 0
$$300$$ 0 0
$$301$$ 8.04721 0.463833
$$302$$ 12.8922 0.741862
$$303$$ 0 0
$$304$$ 2.67863 0.153630
$$305$$ 4.63935 0.265649
$$306$$ 0 0
$$307$$ 7.85395 0.448248 0.224124 0.974561i $$-0.428048\pi$$
0.224124 + 0.974561i $$0.428048\pi$$
$$308$$ 17.7844 1.01336
$$309$$ 0 0
$$310$$ 20.0641 1.13957
$$311$$ 27.8744 1.58061 0.790305 0.612714i $$-0.209922\pi$$
0.790305 + 0.612714i $$0.209922\pi$$
$$312$$ 0 0
$$313$$ 7.88776 0.445842 0.222921 0.974836i $$-0.428441\pi$$
0.222921 + 0.974836i $$0.428441\pi$$
$$314$$ 8.71687 0.491921
$$315$$ 0 0
$$316$$ −27.6394 −1.55484
$$317$$ 13.2181 0.742403 0.371201 0.928552i $$-0.378946\pi$$
0.371201 + 0.928552i $$0.378946\pi$$
$$318$$ 0 0
$$319$$ 6.23150 0.348897
$$320$$ −13.0472 −0.729361
$$321$$ 0 0
$$322$$ 6.36858 0.354907
$$323$$ −22.9866 −1.27901
$$324$$ 0 0
$$325$$ 0 0
$$326$$ −21.9956 −1.21822
$$327$$ 0 0
$$328$$ −2.89218 −0.159694
$$329$$ −13.6091 −0.750291
$$330$$ 0 0
$$331$$ 23.8495 1.31089 0.655444 0.755244i $$-0.272481\pi$$
0.655444 + 0.755244i $$0.272481\pi$$
$$332$$ −25.6473 −1.40758
$$333$$ 0 0
$$334$$ 43.6046 2.38594
$$335$$ −13.1327 −0.717514
$$336$$ 0 0
$$337$$ 5.68306 0.309576 0.154788 0.987948i $$-0.450531\pi$$
0.154788 + 0.987948i $$0.450531\pi$$
$$338$$ 0 0
$$339$$ 0 0
$$340$$ 14.0000 0.759257
$$341$$ −40.1282 −2.17307
$$342$$ 0 0
$$343$$ −15.6563 −0.845359
$$344$$ −16.0944 −0.867753
$$345$$ 0 0
$$346$$ −6.82364 −0.366841
$$347$$ 21.4496 1.15147 0.575737 0.817635i $$-0.304715\pi$$
0.575737 + 0.817635i $$0.304715\pi$$
$$348$$ 0 0
$$349$$ −6.87085 −0.367788 −0.183894 0.982946i $$-0.558870\pi$$
−0.183894 + 0.982946i $$0.558870\pi$$
$$350$$ −2.85395 −0.152550
$$351$$ 0 0
$$352$$ 28.1888 1.50247
$$353$$ 34.4968 1.83608 0.918040 0.396488i $$-0.129771\pi$$
0.918040 + 0.396488i $$0.129771\pi$$
$$354$$ 0 0
$$355$$ −9.60905 −0.509995
$$356$$ 20.6339 1.09359
$$357$$ 0 0
$$358$$ −12.0259 −0.635587
$$359$$ −8.15945 −0.430639 −0.215320 0.976544i $$-0.569079\pi$$
−0.215320 + 0.976544i $$0.569079\pi$$
$$360$$ 0 0
$$361$$ 7.17089 0.377415
$$362$$ −58.5148 −3.07547
$$363$$ 0 0
$$364$$ 0 0
$$365$$ −13.7854 −0.721561
$$366$$ 0 0
$$367$$ −6.84055 −0.357074 −0.178537 0.983933i $$-0.557136\pi$$
−0.178537 + 0.983933i $$0.557136\pi$$
$$368$$ 1.16842 0.0609082
$$369$$ 0 0
$$370$$ −0.523604 −0.0272209
$$371$$ −5.70789 −0.296339
$$372$$ 0 0
$$373$$ 13.8192 0.715532 0.357766 0.933811i $$-0.383539\pi$$
0.357766 + 0.933811i $$0.383539\pi$$
$$374$$ −45.9732 −2.37722
$$375$$ 0 0
$$376$$ 27.2181 1.40367
$$377$$ 0 0
$$378$$ 0 0
$$379$$ −11.5157 −0.591520 −0.295760 0.955262i $$-0.595573\pi$$
−0.295760 + 0.955262i $$0.595573\pi$$
$$380$$ −15.9394 −0.817674
$$381$$ 0 0
$$382$$ 24.1024 1.23318
$$383$$ 22.8798 1.16910 0.584552 0.811356i $$-0.301270\pi$$
0.584552 + 0.811356i $$0.301270\pi$$
$$384$$ 0 0
$$385$$ 5.70789 0.290901
$$386$$ 18.0562 0.919035
$$387$$ 0 0
$$388$$ −33.2440 −1.68771
$$389$$ 4.35271 0.220691 0.110346 0.993893i $$-0.464804\pi$$
0.110346 + 0.993893i $$0.464804\pi$$
$$390$$ 0 0
$$391$$ −10.0268 −0.507077
$$392$$ 13.6473 0.689292
$$393$$ 0 0
$$394$$ −39.2181 −1.97578
$$395$$ −8.87085 −0.446341
$$396$$ 0 0
$$397$$ −7.62245 −0.382560 −0.191280 0.981536i $$-0.561264\pi$$
−0.191280 + 0.981536i $$0.561264\pi$$
$$398$$ 2.78541 0.139620
$$399$$ 0 0
$$400$$ −0.523604 −0.0261802
$$401$$ 20.8495 1.04118 0.520588 0.853808i $$-0.325713\pi$$
0.520588 + 0.853808i $$0.325713\pi$$
$$402$$ 0 0
$$403$$ 0 0
$$404$$ 53.1148 2.64256
$$405$$ 0 0
$$406$$ −3.93146 −0.195115
$$407$$ 1.04721 0.0519082
$$408$$ 0 0
$$409$$ 16.9653 0.838879 0.419439 0.907783i $$-0.362227\pi$$
0.419439 + 0.907783i $$0.362227\pi$$
$$410$$ −2.59214 −0.128017
$$411$$ 0 0
$$412$$ −43.4596 −2.14110
$$413$$ −1.07751 −0.0530209
$$414$$ 0 0
$$415$$ −8.23150 −0.404068
$$416$$ 0 0
$$417$$ 0 0
$$418$$ 52.3418 2.56012
$$419$$ −2.09884 −0.102535 −0.0512676 0.998685i $$-0.516326\pi$$
−0.0512676 + 0.998685i $$0.516326\pi$$
$$420$$ 0 0
$$421$$ 39.6598 1.93290 0.966449 0.256857i $$-0.0826870\pi$$
0.966449 + 0.256857i $$0.0826870\pi$$
$$422$$ −23.3855 −1.13839
$$423$$ 0 0
$$424$$ 11.4158 0.554400
$$425$$ 4.49330 0.217957
$$426$$ 0 0
$$427$$ 5.85395 0.283292
$$428$$ −38.9260 −1.88156
$$429$$ 0 0
$$430$$ −14.4248 −0.695624
$$431$$ −22.1282 −1.06588 −0.532940 0.846153i $$-0.678913\pi$$
−0.532940 + 0.846153i $$0.678913\pi$$
$$432$$ 0 0
$$433$$ −31.3562 −1.50688 −0.753442 0.657515i $$-0.771608\pi$$
−0.753442 + 0.657515i $$0.771608\pi$$
$$434$$ 25.3169 1.21525
$$435$$ 0 0
$$436$$ 7.09988 0.340023
$$437$$ 11.4158 0.546091
$$438$$ 0 0
$$439$$ 4.31344 0.205869 0.102935 0.994688i $$-0.467177\pi$$
0.102935 + 0.994688i $$0.467177\pi$$
$$440$$ −11.4158 −0.544226
$$441$$ 0 0
$$442$$ 0 0
$$443$$ −0.493301 −0.0234374 −0.0117187 0.999931i $$-0.503730\pi$$
−0.0117187 + 0.999931i $$0.503730\pi$$
$$444$$ 0 0
$$445$$ 6.62245 0.313934
$$446$$ 48.7889 2.31022
$$447$$ 0 0
$$448$$ −16.4630 −0.777804
$$449$$ −23.3125 −1.10019 −0.550093 0.835103i $$-0.685408\pi$$
−0.550093 + 0.835103i $$0.685408\pi$$
$$450$$ 0 0
$$451$$ 5.18429 0.244119
$$452$$ 4.60008 0.216369
$$453$$ 0 0
$$454$$ −12.3180 −0.578112
$$455$$ 0 0
$$456$$ 0 0
$$457$$ −6.66966 −0.311993 −0.155997 0.987758i $$-0.549859\pi$$
−0.155997 + 0.987758i $$0.549859\pi$$
$$458$$ 49.6046 2.31787
$$459$$ 0 0
$$460$$ −6.95279 −0.324176
$$461$$ 29.1193 1.35622 0.678110 0.734961i $$-0.262800\pi$$
0.678110 + 0.734961i $$0.262800\pi$$
$$462$$ 0 0
$$463$$ 1.79334 0.0833436 0.0416718 0.999131i $$-0.486732\pi$$
0.0416718 + 0.999131i $$0.486732\pi$$
$$464$$ −0.721292 −0.0334852
$$465$$ 0 0
$$466$$ 57.2519 2.65214
$$467$$ −16.8192 −0.778301 −0.389150 0.921174i $$-0.627231\pi$$
−0.389150 + 0.921174i $$0.627231\pi$$
$$468$$ 0 0
$$469$$ −16.5708 −0.765169
$$470$$ 24.3945 1.12523
$$471$$ 0 0
$$472$$ 2.15502 0.0991931
$$473$$ 28.8495 1.32650
$$474$$ 0 0
$$475$$ −5.11575 −0.234727
$$476$$ 17.6652 0.809685
$$477$$ 0 0
$$478$$ −50.9439 −2.33012
$$479$$ 35.1531 1.60618 0.803092 0.595855i $$-0.203187\pi$$
0.803092 + 0.595855i $$0.203187\pi$$
$$480$$ 0 0
$$481$$ 0 0
$$482$$ 25.1416 1.14517
$$483$$ 0 0
$$484$$ 29.4843 1.34020
$$485$$ −10.6697 −0.484484
$$486$$ 0 0
$$487$$ 8.62596 0.390879 0.195440 0.980716i $$-0.437387\pi$$
0.195440 + 0.980716i $$0.437387\pi$$
$$488$$ −11.7079 −0.529991
$$489$$ 0 0
$$490$$ 12.2315 0.552563
$$491$$ 23.2137 1.04762 0.523809 0.851836i $$-0.324510\pi$$
0.523809 + 0.851836i $$0.324510\pi$$
$$492$$ 0 0
$$493$$ 6.18975 0.278773
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 4.64482 0.208558
$$497$$ −12.1247 −0.543868
$$498$$ 0 0
$$499$$ −29.0393 −1.29998 −0.649988 0.759944i $$-0.725226\pi$$
−0.649988 + 0.759944i $$0.725226\pi$$
$$500$$ 3.11575 0.139341
$$501$$ 0 0
$$502$$ 24.9866 1.11521
$$503$$ 17.3999 0.775824 0.387912 0.921696i $$-0.373196\pi$$
0.387912 + 0.921696i $$0.373196\pi$$
$$504$$ 0 0
$$505$$ 17.0472 0.758591
$$506$$ 22.8316 1.01499
$$507$$ 0 0
$$508$$ −55.4149 −2.45864
$$509$$ −22.8763 −1.01397 −0.506987 0.861953i $$-0.669241\pi$$
−0.506987 + 0.861953i $$0.669241\pi$$
$$510$$ 0 0
$$511$$ −17.3945 −0.769485
$$512$$ −5.90558 −0.260992
$$513$$ 0 0
$$514$$ −4.59214 −0.202551
$$515$$ −13.9484 −0.614638
$$516$$ 0 0
$$517$$ −48.7889 −2.14573
$$518$$ −0.660685 −0.0290288
$$519$$ 0 0
$$520$$ 0 0
$$521$$ 26.3642 1.15503 0.577517 0.816378i $$-0.304022\pi$$
0.577517 + 0.816378i $$0.304022\pi$$
$$522$$ 0 0
$$523$$ −26.2921 −1.14967 −0.574837 0.818268i $$-0.694934\pi$$
−0.574837 + 0.818268i $$0.694934\pi$$
$$524$$ −36.3597 −1.58838
$$525$$ 0 0
$$526$$ 7.34725 0.320355
$$527$$ −39.8594 −1.73630
$$528$$ 0 0
$$529$$ −18.0204 −0.783496
$$530$$ 10.2315 0.444428
$$531$$ 0 0
$$532$$ −20.1124 −0.871981
$$533$$ 0 0
$$534$$ 0 0
$$535$$ −12.4933 −0.540133
$$536$$ 33.1416 1.43150
$$537$$ 0 0
$$538$$ 60.9519 2.62782
$$539$$ −24.4630 −1.05370
$$540$$ 0 0
$$541$$ 0.107816 0.00463537 0.00231768 0.999997i $$-0.499262\pi$$
0.00231768 + 0.999997i $$0.499262\pi$$
$$542$$ −44.8957 −1.92844
$$543$$ 0 0
$$544$$ 28.0000 1.20049
$$545$$ 2.27871 0.0976091
$$546$$ 0 0
$$547$$ 12.1193 0.518182 0.259091 0.965853i $$-0.416577\pi$$
0.259091 + 0.965853i $$0.416577\pi$$
$$548$$ −62.5148 −2.67050
$$549$$ 0 0
$$550$$ −10.2315 −0.436273
$$551$$ −7.04721 −0.300221
$$552$$ 0 0
$$553$$ −11.1933 −0.475986
$$554$$ −36.4024 −1.54659
$$555$$ 0 0
$$556$$ 50.9092 2.15903
$$557$$ 38.0070 1.61041 0.805204 0.592997i $$-0.202056\pi$$
0.805204 + 0.592997i $$0.202056\pi$$
$$558$$ 0 0
$$559$$ 0 0
$$560$$ −0.660685 −0.0279191
$$561$$ 0 0
$$562$$ 12.1630 0.513063
$$563$$ −15.5102 −0.653677 −0.326839 0.945080i $$-0.605983\pi$$
−0.326839 + 0.945080i $$0.605983\pi$$
$$564$$ 0 0
$$565$$ 1.47640 0.0621124
$$566$$ −60.7665 −2.55421
$$567$$ 0 0
$$568$$ 24.2494 1.01748
$$569$$ −19.2405 −0.806602 −0.403301 0.915067i $$-0.632137\pi$$
−0.403301 + 0.915067i $$0.632137\pi$$
$$570$$ 0 0
$$571$$ 27.7338 1.16062 0.580311 0.814395i $$-0.302931\pi$$
0.580311 + 0.814395i $$0.302931\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ −3.27077 −0.136519
$$575$$ −2.23150 −0.0930599
$$576$$ 0 0
$$577$$ −26.9866 −1.12347 −0.561733 0.827318i $$-0.689865\pi$$
−0.561733 + 0.827318i $$0.689865\pi$$
$$578$$ −7.21459 −0.300088
$$579$$ 0 0
$$580$$ 4.29211 0.178220
$$581$$ −10.3865 −0.430906
$$582$$ 0 0
$$583$$ −20.4630 −0.847491
$$584$$ 34.7889 1.43958
$$585$$ 0 0
$$586$$ −48.4462 −2.00129
$$587$$ −30.8530 −1.27344 −0.636720 0.771095i $$-0.719709\pi$$
−0.636720 + 0.771095i $$0.719709\pi$$
$$588$$ 0 0
$$589$$ 45.3811 1.86989
$$590$$ 1.93146 0.0795169
$$591$$ 0 0
$$592$$ −0.121214 −0.00498186
$$593$$ 4.29211 0.176256 0.0881278 0.996109i $$-0.471912\pi$$
0.0881278 + 0.996109i $$0.471912\pi$$
$$594$$ 0 0
$$595$$ 5.66966 0.232433
$$596$$ −10.1103 −0.414133
$$597$$ 0 0
$$598$$ 0 0
$$599$$ 24.0224 0.981527 0.490764 0.871293i $$-0.336718\pi$$
0.490764 + 0.871293i $$0.336718\pi$$
$$600$$ 0 0
$$601$$ 2.53154 0.103264 0.0516318 0.998666i $$-0.483558\pi$$
0.0516318 + 0.998666i $$0.483558\pi$$
$$602$$ −18.2012 −0.741825
$$603$$ 0 0
$$604$$ −17.7596 −0.722630
$$605$$ 9.46300 0.384726
$$606$$ 0 0
$$607$$ 11.4417 0.464403 0.232201 0.972668i $$-0.425407\pi$$
0.232201 + 0.972668i $$0.425407\pi$$
$$608$$ −31.8788 −1.29286
$$609$$ 0 0
$$610$$ −10.4933 −0.424861
$$611$$ 0 0
$$612$$ 0 0
$$613$$ 7.19326 0.290533 0.145267 0.989393i $$-0.453596\pi$$
0.145267 + 0.989393i $$0.453596\pi$$
$$614$$ −17.7641 −0.716900
$$615$$ 0 0
$$616$$ −14.4045 −0.580373
$$617$$ 25.5708 1.02944 0.514721 0.857358i $$-0.327895\pi$$
0.514721 + 0.857358i $$0.327895\pi$$
$$618$$ 0 0
$$619$$ −5.98660 −0.240622 −0.120311 0.992736i $$-0.538389\pi$$
−0.120311 + 0.992736i $$0.538389\pi$$
$$620$$ −27.6394 −1.11002
$$621$$ 0 0
$$622$$ −63.0463 −2.52793
$$623$$ 8.35622 0.334785
$$624$$ 0 0
$$625$$ 1.00000 0.0400000
$$626$$ −17.8405 −0.713052
$$627$$ 0 0
$$628$$ −12.0079 −0.479169
$$629$$ 1.04019 0.0414752
$$630$$ 0 0
$$631$$ 43.0259 1.71283 0.856417 0.516285i $$-0.172686\pi$$
0.856417 + 0.516285i $$0.172686\pi$$
$$632$$ 22.3865 0.890488
$$633$$ 0 0
$$634$$ −29.8967 −1.18735
$$635$$ −17.7854 −0.705792
$$636$$ 0 0
$$637$$ 0 0
$$638$$ −14.0944 −0.558003
$$639$$ 0 0
$$640$$ 17.0472 0.673850
$$641$$ 6.69450 0.264417 0.132208 0.991222i $$-0.457793\pi$$
0.132208 + 0.991222i $$0.457793\pi$$
$$642$$ 0 0
$$643$$ −8.18078 −0.322619 −0.161309 0.986904i $$-0.551572\pi$$
−0.161309 + 0.986904i $$0.551572\pi$$
$$644$$ −8.77305 −0.345706
$$645$$ 0 0
$$646$$ 51.9911 2.04556
$$647$$ 11.2787 0.443412 0.221706 0.975114i $$-0.428838\pi$$
0.221706 + 0.975114i $$0.428838\pi$$
$$648$$ 0 0
$$649$$ −3.86292 −0.151633
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 30.3000 1.18664
$$653$$ −27.2484 −1.06631 −0.533156 0.846017i $$-0.678994\pi$$
−0.533156 + 0.846017i $$0.678994\pi$$
$$654$$ 0 0
$$655$$ −11.6697 −0.455971
$$656$$ −0.600078 −0.0234291
$$657$$ 0 0
$$658$$ 30.7810 1.19997
$$659$$ −6.75510 −0.263141 −0.131571 0.991307i $$-0.542002\pi$$
−0.131571 + 0.991307i $$0.542002\pi$$
$$660$$ 0 0
$$661$$ 26.5102 1.03113 0.515564 0.856851i $$-0.327583\pi$$
0.515564 + 0.856851i $$0.327583\pi$$
$$662$$ −53.9429 −2.09655
$$663$$ 0 0
$$664$$ 20.7730 0.806151
$$665$$ −6.45506 −0.250317
$$666$$ 0 0
$$667$$ −3.07400 −0.119026
$$668$$ −60.0676 −2.32409
$$669$$ 0 0
$$670$$ 29.7035 1.14755
$$671$$ 20.9866 0.810179
$$672$$ 0 0
$$673$$ −0.677591 −0.0261192 −0.0130596 0.999915i $$-0.504157\pi$$
−0.0130596 + 0.999915i $$0.504157\pi$$
$$674$$ −12.8539 −0.495116
$$675$$ 0 0
$$676$$ 0 0
$$677$$ 10.4630 0.402126 0.201063 0.979578i $$-0.435560\pi$$
0.201063 + 0.979578i $$0.435560\pi$$
$$678$$ 0 0
$$679$$ −13.4630 −0.516662
$$680$$ −11.3393 −0.434843
$$681$$ 0 0
$$682$$ 90.7621 3.47546
$$683$$ −18.7516 −0.717510 −0.358755 0.933432i $$-0.616799\pi$$
−0.358755 + 0.933432i $$0.616799\pi$$
$$684$$ 0 0
$$685$$ −20.0641 −0.766610
$$686$$ 35.4114 1.35201
$$687$$ 0 0
$$688$$ −3.33931 −0.127310
$$689$$ 0 0
$$690$$ 0 0
$$691$$ −43.5653 −1.65730 −0.828652 0.559764i $$-0.810892\pi$$
−0.828652 + 0.559764i $$0.810892\pi$$
$$692$$ 9.39992 0.357331
$$693$$ 0 0
$$694$$ −48.5148 −1.84159
$$695$$ 16.3393 0.619786
$$696$$ 0 0
$$697$$ 5.14956 0.195054
$$698$$ 15.5405 0.588217
$$699$$ 0 0
$$700$$ 3.93146 0.148595
$$701$$ 19.0810 0.720680 0.360340 0.932821i $$-0.382661\pi$$
0.360340 + 0.932821i $$0.382661\pi$$
$$702$$ 0 0
$$703$$ −1.18429 −0.0446663
$$704$$ −59.0204 −2.22442
$$705$$ 0 0
$$706$$ −78.0250 −2.93651
$$707$$ 21.5102 0.808975
$$708$$ 0 0
$$709$$ −44.6046 −1.67516 −0.837581 0.546313i $$-0.816031\pi$$
−0.837581 + 0.546313i $$0.816031\pi$$
$$710$$ 21.7338 0.815654
$$711$$ 0 0
$$712$$ −16.7124 −0.626325
$$713$$ 19.7953 0.741340
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 16.5663 0.619110
$$717$$ 0 0
$$718$$ 18.4551 0.688737
$$719$$ 12.9822 0.484153 0.242077 0.970257i $$-0.422171\pi$$
0.242077 + 0.970257i $$0.422171\pi$$
$$720$$ 0 0
$$721$$ −17.6001 −0.655461
$$722$$ −16.2191 −0.603614
$$723$$ 0 0
$$724$$ 80.6071 2.99574
$$725$$ 1.37755 0.0511610
$$726$$ 0 0
$$727$$ 17.3980 0.645255 0.322627 0.946526i $$-0.395434\pi$$
0.322627 + 0.946526i $$0.395434\pi$$
$$728$$ 0 0
$$729$$ 0 0
$$730$$ 31.1799 1.15402
$$731$$ 28.6563 1.05989
$$732$$ 0 0
$$733$$ −45.8272 −1.69266 −0.846332 0.532655i $$-0.821194\pi$$
−0.846332 + 0.532655i $$0.821194\pi$$
$$734$$ 15.4720 0.571081
$$735$$ 0 0
$$736$$ −13.9056 −0.512567
$$737$$ −59.4069 −2.18828
$$738$$ 0 0
$$739$$ −17.5708 −0.646353 −0.323176 0.946339i $$-0.604751\pi$$
−0.323176 + 0.946339i $$0.604751\pi$$
$$740$$ 0.721292 0.0265152
$$741$$ 0 0
$$742$$ 12.9101 0.473946
$$743$$ −30.3562 −1.11366 −0.556831 0.830626i $$-0.687983\pi$$
−0.556831 + 0.830626i $$0.687983\pi$$
$$744$$ 0 0
$$745$$ −3.24490 −0.118884
$$746$$ −31.2563 −1.14438
$$747$$ 0 0
$$748$$ 63.3305 2.31559
$$749$$ −15.7641 −0.576007
$$750$$ 0 0
$$751$$ 3.80323 0.138782 0.0693909 0.997590i $$-0.477894\pi$$
0.0693909 + 0.997590i $$0.477894\pi$$
$$752$$ 5.64729 0.205935
$$753$$ 0 0
$$754$$ 0 0
$$755$$ −5.69996 −0.207443
$$756$$ 0 0
$$757$$ −3.40786 −0.123861 −0.0619303 0.998080i $$-0.519726\pi$$
−0.0619303 + 0.998080i $$0.519726\pi$$
$$758$$ 26.0462 0.946040
$$759$$ 0 0
$$760$$ 12.9101 0.468300
$$761$$ 7.24490 0.262627 0.131314 0.991341i $$-0.458081\pi$$
0.131314 + 0.991341i $$0.458081\pi$$
$$762$$ 0 0
$$763$$ 2.87528 0.104092
$$764$$ −33.2022 −1.20121
$$765$$ 0 0
$$766$$ −51.7496 −1.86979
$$767$$ 0 0
$$768$$ 0 0
$$769$$ −31.1764 −1.12425 −0.562124 0.827053i $$-0.690016\pi$$
−0.562124 + 0.827053i $$0.690016\pi$$
$$770$$ −12.9101 −0.465249
$$771$$ 0 0
$$772$$ −24.8733 −0.895210
$$773$$ 19.4605 0.699947 0.349973 0.936760i $$-0.386191\pi$$
0.349973 + 0.936760i $$0.386191\pi$$
$$774$$ 0 0
$$775$$ −8.87085 −0.318650
$$776$$ 26.9260 0.966587
$$777$$ 0 0
$$778$$ −9.84498 −0.352959
$$779$$ −5.86292 −0.210061
$$780$$ 0 0
$$781$$ −43.4675 −1.55539
$$782$$ 22.6786 0.810986
$$783$$ 0 0
$$784$$ 2.83158 0.101128
$$785$$ −3.85395 −0.137553
$$786$$ 0 0
$$787$$ −14.4034 −0.513427 −0.256713 0.966488i $$-0.582640\pi$$
−0.256713 + 0.966488i $$0.582640\pi$$
$$788$$ 54.0250 1.92456
$$789$$ 0 0
$$790$$ 20.0641 0.713849
$$791$$ 1.86292 0.0662378
$$792$$ 0 0
$$793$$ 0 0
$$794$$ 17.2405 0.611841
$$795$$ 0 0
$$796$$ −3.83704 −0.136000
$$797$$ 23.6011 0.835994 0.417997 0.908448i $$-0.362732\pi$$
0.417997 + 0.908448i $$0.362732\pi$$
$$798$$ 0 0
$$799$$ −48.4621 −1.71447
$$800$$ 6.23150 0.220317
$$801$$ 0 0
$$802$$ −47.1575 −1.66519
$$803$$ −62.3597 −2.20063
$$804$$ 0 0
$$805$$ −2.81571 −0.0992407
$$806$$ 0 0
$$807$$ 0 0
$$808$$ −43.0204 −1.51345
$$809$$ −26.7551 −0.940659 −0.470330 0.882491i $$-0.655865\pi$$
−0.470330 + 0.882491i $$0.655865\pi$$
$$810$$ 0 0
$$811$$ 3.58421 0.125859 0.0629293 0.998018i $$-0.479956\pi$$
0.0629293 + 0.998018i $$0.479956\pi$$
$$812$$ 5.41579 0.190057
$$813$$ 0 0
$$814$$ −2.36858 −0.0830187
$$815$$ 9.72480 0.340645
$$816$$ 0 0
$$817$$ −32.6260 −1.14144
$$818$$ −38.3721 −1.34165
$$819$$ 0 0
$$820$$ 3.57081 0.124698
$$821$$ 15.8361 0.552685 0.276342 0.961059i $$-0.410878\pi$$
0.276342 + 0.961059i $$0.410878\pi$$
$$822$$ 0 0
$$823$$ 7.41579 0.258498 0.129249 0.991612i $$-0.458743\pi$$
0.129249 + 0.991612i $$0.458743\pi$$
$$824$$ 35.2002 1.22626
$$825$$ 0 0
$$826$$ 2.43712 0.0847983
$$827$$ −16.6036 −0.577363 −0.288682 0.957425i $$-0.593217\pi$$
−0.288682 + 0.957425i $$0.593217\pi$$
$$828$$ 0 0
$$829$$ −29.2842 −1.01708 −0.508541 0.861038i $$-0.669815\pi$$
−0.508541 + 0.861038i $$0.669815\pi$$
$$830$$ 18.6180 0.646241
$$831$$ 0 0
$$832$$ 0 0
$$833$$ −24.2991 −0.841915
$$834$$ 0 0
$$835$$ −19.2787 −0.667167
$$836$$ −72.1035 −2.49375
$$837$$ 0 0
$$838$$ 4.74717 0.163988
$$839$$ −30.1620 −1.04131 −0.520655 0.853767i $$-0.674312\pi$$
−0.520655 + 0.853767i $$0.674312\pi$$
$$840$$ 0 0
$$841$$ −27.1024 −0.934564
$$842$$ −89.7026 −3.09135
$$843$$ 0 0
$$844$$ 32.2147 1.10888
$$845$$ 0 0
$$846$$ 0 0
$$847$$ 11.9404 0.410278
$$848$$ 2.36858 0.0813374
$$849$$ 0 0
$$850$$ −10.1630 −0.348587
$$851$$ −0.516589 −0.0177085
$$852$$ 0 0
$$853$$ 2.50670 0.0858277 0.0429139 0.999079i $$-0.486336\pi$$
0.0429139 + 0.999079i $$0.486336\pi$$
$$854$$ −13.2405 −0.453080
$$855$$ 0 0
$$856$$ 31.5282 1.07761
$$857$$ 24.4327 0.834605 0.417302 0.908768i $$-0.362976\pi$$
0.417302 + 0.908768i $$0.362976\pi$$
$$858$$ 0 0
$$859$$ −7.10235 −0.242329 −0.121165 0.992632i $$-0.538663\pi$$
−0.121165 + 0.992632i $$0.538663\pi$$
$$860$$ 19.8709 0.677590
$$861$$ 0 0
$$862$$ 50.0497 1.70470
$$863$$ −3.24490 −0.110458 −0.0552288 0.998474i $$-0.517589\pi$$
−0.0552288 + 0.998474i $$0.517589\pi$$
$$864$$ 0 0
$$865$$ 3.01691 0.102578
$$866$$ 70.9216 2.41001
$$867$$ 0 0
$$868$$ −34.8754 −1.18375
$$869$$ −40.1282 −1.36126
$$870$$ 0 0
$$871$$ 0 0
$$872$$ −5.75056 −0.194738
$$873$$ 0 0
$$874$$ −25.8203 −0.873383
$$875$$ 1.26180 0.0426567
$$876$$ 0 0
$$877$$ −18.9866 −0.641132 −0.320566 0.947226i $$-0.603873\pi$$
−0.320566 + 0.947226i $$0.603873\pi$$
$$878$$ −9.75614 −0.329254
$$879$$ 0 0
$$880$$ −2.36858 −0.0798448
$$881$$ 19.4764 0.656176 0.328088 0.944647i $$-0.393596\pi$$
0.328088 + 0.944647i $$0.393596\pi$$
$$882$$ 0 0
$$883$$ −50.5664 −1.70169 −0.850847 0.525413i $$-0.823911\pi$$
−0.850847 + 0.525413i $$0.823911\pi$$
$$884$$ 0 0
$$885$$ 0 0
$$886$$ 1.11575 0.0374843
$$887$$ 12.5271 0.420619 0.210310 0.977635i $$-0.432553\pi$$
0.210310 + 0.977635i $$0.432553\pi$$
$$888$$ 0 0
$$889$$ −22.4417 −0.752669
$$890$$ −14.9787 −0.502086
$$891$$ 0 0
$$892$$ −67.2092 −2.25033
$$893$$ 55.1754 1.84638
$$894$$ 0 0
$$895$$ 5.31694 0.177726
$$896$$ 21.5102 0.718606
$$897$$ 0 0
$$898$$ 52.7283 1.75957
$$899$$ −12.2201 −0.407562
$$900$$ 0 0
$$901$$ −20.3259 −0.677154
$$902$$ −11.7258 −0.390428
$$903$$ 0 0
$$904$$ −3.72584 −0.123920
$$905$$ 25.8709 0.859976
$$906$$ 0 0
$$907$$ 28.0417 0.931111 0.465555 0.885019i $$-0.345855\pi$$
0.465555 + 0.885019i $$0.345855\pi$$
$$908$$ 16.9687 0.563125
$$909$$ 0 0
$$910$$ 0 0
$$911$$ −16.1977 −0.536653 −0.268327 0.963328i $$-0.586471\pi$$
−0.268327 + 0.963328i $$0.586471\pi$$
$$912$$ 0 0
$$913$$ −37.2360 −1.23233
$$914$$ 15.0854 0.498982
$$915$$ 0 0
$$916$$ −68.3329 −2.25778
$$917$$ −14.7248 −0.486256
$$918$$ 0 0
$$919$$ −43.2778 −1.42760 −0.713801 0.700348i $$-0.753028\pi$$
−0.713801 + 0.700348i $$0.753028\pi$$
$$920$$ 5.63142 0.185662
$$921$$ 0 0
$$922$$ −65.8620 −2.16905
$$923$$ 0 0
$$924$$ 0 0
$$925$$ 0.231499 0.00761163
$$926$$ −4.05618 −0.133294
$$927$$ 0 0
$$928$$ 8.58421 0.281791
$$929$$ 13.7685 0.451730 0.225865 0.974159i $$-0.427479\pi$$
0.225865 + 0.974159i $$0.427479\pi$$
$$930$$ 0 0
$$931$$ 27.6652 0.906691
$$932$$ −78.8675 −2.58339
$$933$$ 0 0
$$934$$ 38.0417 1.24476
$$935$$ 20.3259 0.664729
$$936$$ 0 0
$$937$$ −38.1888 −1.24757 −0.623787 0.781594i $$-0.714407\pi$$
−0.623787 + 0.781594i $$0.714407\pi$$
$$938$$ 37.4799 1.22376
$$939$$ 0 0
$$940$$ −33.6046 −1.09606
$$941$$ −13.9618 −0.455140 −0.227570 0.973762i $$-0.573078\pi$$
−0.227570 + 0.973762i $$0.573078\pi$$
$$942$$ 0 0
$$943$$ −2.55742 −0.0832809
$$944$$ 0.447131 0.0145529
$$945$$ 0 0
$$946$$ −65.2519 −2.12152
$$947$$ 7.36962 0.239480 0.119740 0.992805i $$-0.461794\pi$$
0.119740 + 0.992805i $$0.461794\pi$$
$$948$$ 0 0
$$949$$ 0 0
$$950$$ 11.5708 0.375407
$$951$$ 0 0
$$952$$ −14.3080 −0.463724
$$953$$ −23.2181 −0.752108 −0.376054 0.926598i $$-0.622719\pi$$
−0.376054 + 0.926598i $$0.622719\pi$$
$$954$$ 0 0
$$955$$ −10.6563 −0.344828
$$956$$ 70.1779 2.26972
$$957$$ 0 0
$$958$$ −79.5093 −2.56883
$$959$$ −25.3169 −0.817527
$$960$$ 0 0
$$961$$ 47.6920 1.53845
$$962$$ 0 0
$$963$$ 0 0
$$964$$ −34.6339 −1.11548
$$965$$ −7.98309 −0.256985
$$966$$ 0 0
$$967$$ 7.54402 0.242599 0.121300 0.992616i $$-0.461294\pi$$
0.121300 + 0.992616i $$0.461294\pi$$
$$968$$ −23.8809 −0.767560
$$969$$ 0 0
$$970$$ 24.1327 0.774853
$$971$$ 30.5842 0.981494 0.490747 0.871302i $$-0.336724\pi$$
0.490747 + 0.871302i $$0.336724\pi$$
$$972$$ 0 0
$$973$$ 20.6170 0.660950
$$974$$ −19.5102 −0.625147
$$975$$ 0 0
$$976$$ −2.42919 −0.0777564
$$977$$ −35.6811 −1.14154 −0.570770 0.821110i $$-0.693355\pi$$
−0.570770 + 0.821110i $$0.693355\pi$$
$$978$$ 0 0
$$979$$ 29.9573 0.957441
$$980$$ −16.8495 −0.538238
$$981$$ 0 0
$$982$$ −52.5047 −1.67549
$$983$$ 12.9866 0.414208 0.207104 0.978319i $$-0.433596\pi$$
0.207104 + 0.978319i $$0.433596\pi$$
$$984$$ 0 0
$$985$$ 17.3393 0.552477
$$986$$ −14.0000 −0.445851
$$987$$ 0 0
$$988$$ 0 0
$$989$$ −14.2315 −0.452535
$$990$$ 0 0
$$991$$ −22.7472 −0.722588 −0.361294 0.932452i $$-0.617665\pi$$
−0.361294 + 0.932452i $$0.617665\pi$$
$$992$$ −55.2787 −1.75510
$$993$$ 0 0
$$994$$ 27.4237 0.869828
$$995$$ −1.23150 −0.0390411
$$996$$ 0 0
$$997$$ −13.8460 −0.438508 −0.219254 0.975668i $$-0.570362\pi$$
−0.219254 + 0.975668i $$0.570362\pi$$
$$998$$ 65.6811 2.07910
$$999$$ 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 7605.2.a.bw.1.1 3
3.2 odd 2 2535.2.a.ba.1.3 3
13.4 even 6 585.2.j.f.406.1 6
13.10 even 6 585.2.j.f.451.1 6
13.12 even 2 7605.2.a.bv.1.3 3
39.17 odd 6 195.2.i.d.16.3 6
39.23 odd 6 195.2.i.d.61.3 yes 6
39.38 odd 2 2535.2.a.bb.1.1 3
195.17 even 12 975.2.bb.k.874.2 12
195.23 even 12 975.2.bb.k.724.2 12
195.62 even 12 975.2.bb.k.724.5 12
195.134 odd 6 975.2.i.l.601.1 6
195.173 even 12 975.2.bb.k.874.5 12
195.179 odd 6 975.2.i.l.451.1 6

By twisted newform
Twist Min Dim Char Parity Ord Type
195.2.i.d.16.3 6 39.17 odd 6
195.2.i.d.61.3 yes 6 39.23 odd 6
585.2.j.f.406.1 6 13.4 even 6
585.2.j.f.451.1 6 13.10 even 6
975.2.i.l.451.1 6 195.179 odd 6
975.2.i.l.601.1 6 195.134 odd 6
975.2.bb.k.724.2 12 195.23 even 12
975.2.bb.k.724.5 12 195.62 even 12
975.2.bb.k.874.2 12 195.17 even 12
975.2.bb.k.874.5 12 195.173 even 12
2535.2.a.ba.1.3 3 3.2 odd 2
2535.2.a.bb.1.1 3 39.38 odd 2
7605.2.a.bv.1.3 3 13.12 even 2
7605.2.a.bw.1.1 3 1.1 even 1 trivial