# Properties

 Label 7605.2.a.bv.1.2 Level $7605$ Weight $2$ Character 7605.1 Self dual yes Analytic conductor $60.726$ Analytic rank $0$ 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: $$0$$ 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 1.2 Root $$-0.339877$$ 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)

 $$f(q)$$ $$=$$ $$q+0.339877 q^{2} -1.88448 q^{4} -1.00000 q^{5} +0.660123 q^{7} -1.32025 q^{8} +O(q^{10})$$ $$q+0.339877 q^{2} -1.88448 q^{4} -1.00000 q^{5} +0.660123 q^{7} -1.32025 q^{8} -0.339877 q^{10} -0.679754 q^{11} +0.224361 q^{14} +3.32025 q^{16} -7.42909 q^{17} +0.115516 q^{19} +1.88448 q^{20} -0.231033 q^{22} +7.76897 q^{23} +1.00000 q^{25} -1.24399 q^{28} -5.54461 q^{29} -9.97370 q^{31} +3.76897 q^{32} -2.52498 q^{34} -0.660123 q^{35} +9.76897 q^{37} +0.0392613 q^{38} +1.32025 q^{40} -4.22436 q^{41} -0.544607 q^{43} +1.28098 q^{44} +2.64049 q^{46} +5.01963 q^{47} -6.56424 q^{49} +0.339877 q^{50} -0.679754 q^{53} +0.679754 q^{55} -0.871525 q^{56} -1.88448 q^{58} -2.22436 q^{59} -4.20473 q^{61} -3.38983 q^{62} -5.35951 q^{64} -7.63382 q^{67} +14.0000 q^{68} -0.224361 q^{70} -7.31357 q^{71} +8.01963 q^{73} +3.32025 q^{74} -0.217689 q^{76} -0.448721 q^{77} +9.97370 q^{79} -3.32025 q^{80} -1.43576 q^{82} -1.76897 q^{83} +7.42909 q^{85} -0.185099 q^{86} +0.897442 q^{88} -13.5446 q^{89} -14.6405 q^{92} +1.70606 q^{94} -0.115516 q^{95} +9.90411 q^{97} -2.23103 q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$3 q + 6 q^{4} - 3 q^{5} + 3 q^{7} - 6 q^{8}+O(q^{10})$$ 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0.339877 0.240329 0.120165 0.992754i $$-0.461658\pi$$
0.120165 + 0.992754i $$0.461658\pi$$
$$3$$ 0 0
$$4$$ −1.88448 −0.942242
$$5$$ −1.00000 −0.447214
$$6$$ 0 0
$$7$$ 0.660123 0.249503 0.124752 0.992188i $$-0.460187\pi$$
0.124752 + 0.992188i $$0.460187\pi$$
$$8$$ −1.32025 −0.466778
$$9$$ 0 0
$$10$$ −0.339877 −0.107479
$$11$$ −0.679754 −0.204953 −0.102477 0.994735i $$-0.532677\pi$$
−0.102477 + 0.994735i $$0.532677\pi$$
$$12$$ 0 0
$$13$$ 0 0
$$14$$ 0.224361 0.0599629
$$15$$ 0 0
$$16$$ 3.32025 0.830062
$$17$$ −7.42909 −1.80182 −0.900910 0.434007i $$-0.857099\pi$$
−0.900910 + 0.434007i $$0.857099\pi$$
$$18$$ 0 0
$$19$$ 0.115516 0.0265013 0.0132506 0.999912i $$-0.495782\pi$$
0.0132506 + 0.999912i $$0.495782\pi$$
$$20$$ 1.88448 0.421383
$$21$$ 0 0
$$22$$ −0.231033 −0.0492563
$$23$$ 7.76897 1.61994 0.809971 0.586470i $$-0.199483\pi$$
0.809971 + 0.586470i $$0.199483\pi$$
$$24$$ 0 0
$$25$$ 1.00000 0.200000
$$26$$ 0 0
$$27$$ 0 0
$$28$$ −1.24399 −0.235092
$$29$$ −5.54461 −1.02961 −0.514804 0.857308i $$-0.672135\pi$$
−0.514804 + 0.857308i $$0.672135\pi$$
$$30$$ 0 0
$$31$$ −9.97370 −1.79133 −0.895664 0.444730i $$-0.853299\pi$$
−0.895664 + 0.444730i $$0.853299\pi$$
$$32$$ 3.76897 0.666266
$$33$$ 0 0
$$34$$ −2.52498 −0.433030
$$35$$ −0.660123 −0.111581
$$36$$ 0 0
$$37$$ 9.76897 1.60601 0.803004 0.595973i $$-0.203234\pi$$
0.803004 + 0.595973i $$0.203234\pi$$
$$38$$ 0.0392613 0.00636903
$$39$$ 0 0
$$40$$ 1.32025 0.208749
$$41$$ −4.22436 −0.659734 −0.329867 0.944027i $$-0.607004\pi$$
−0.329867 + 0.944027i $$0.607004\pi$$
$$42$$ 0 0
$$43$$ −0.544607 −0.0830518 −0.0415259 0.999137i $$-0.513222\pi$$
−0.0415259 + 0.999137i $$0.513222\pi$$
$$44$$ 1.28098 0.193116
$$45$$ 0 0
$$46$$ 2.64049 0.389319
$$47$$ 5.01963 0.732188 0.366094 0.930578i $$-0.380695\pi$$
0.366094 + 0.930578i $$0.380695\pi$$
$$48$$ 0 0
$$49$$ −6.56424 −0.937748
$$50$$ 0.339877 0.0480659
$$51$$ 0 0
$$52$$ 0 0
$$53$$ −0.679754 −0.0933714 −0.0466857 0.998910i $$-0.514866\pi$$
−0.0466857 + 0.998910i $$0.514866\pi$$
$$54$$ 0 0
$$55$$ 0.679754 0.0916580
$$56$$ −0.871525 −0.116462
$$57$$ 0 0
$$58$$ −1.88448 −0.247445
$$59$$ −2.22436 −0.289587 −0.144794 0.989462i $$-0.546252\pi$$
−0.144794 + 0.989462i $$0.546252\pi$$
$$60$$ 0 0
$$61$$ −4.20473 −0.538361 −0.269180 0.963090i $$-0.586753\pi$$
−0.269180 + 0.963090i $$0.586753\pi$$
$$62$$ −3.38983 −0.430509
$$63$$ 0 0
$$64$$ −5.35951 −0.669938
$$65$$ 0 0
$$66$$ 0 0
$$67$$ −7.63382 −0.932620 −0.466310 0.884621i $$-0.654417\pi$$
−0.466310 + 0.884621i $$0.654417\pi$$
$$68$$ 14.0000 1.69775
$$69$$ 0 0
$$70$$ −0.224361 −0.0268162
$$71$$ −7.31357 −0.867962 −0.433981 0.900922i $$-0.642891\pi$$
−0.433981 + 0.900922i $$0.642891\pi$$
$$72$$ 0 0
$$73$$ 8.01963 0.938627 0.469313 0.883032i $$-0.344501\pi$$
0.469313 + 0.883032i $$0.344501\pi$$
$$74$$ 3.32025 0.385971
$$75$$ 0 0
$$76$$ −0.217689 −0.0249706
$$77$$ −0.448721 −0.0511365
$$78$$ 0 0
$$79$$ 9.97370 1.12213 0.561064 0.827772i $$-0.310392\pi$$
0.561064 + 0.827772i $$0.310392\pi$$
$$80$$ −3.32025 −0.371215
$$81$$ 0 0
$$82$$ −1.43576 −0.158553
$$83$$ −1.76897 −0.194169 −0.0970847 0.995276i $$-0.530952\pi$$
−0.0970847 + 0.995276i $$0.530952\pi$$
$$84$$ 0 0
$$85$$ 7.42909 0.805798
$$86$$ −0.185099 −0.0199598
$$87$$ 0 0
$$88$$ 0.897442 0.0956677
$$89$$ −13.5446 −1.43573 −0.717863 0.696185i $$-0.754879\pi$$
−0.717863 + 0.696185i $$0.754879\pi$$
$$90$$ 0 0
$$91$$ 0 0
$$92$$ −14.6405 −1.52638
$$93$$ 0 0
$$94$$ 1.70606 0.175966
$$95$$ −0.115516 −0.0118517
$$96$$ 0 0
$$97$$ 9.90411 1.00561 0.502805 0.864400i $$-0.332301\pi$$
0.502805 + 0.864400i $$0.332301\pi$$
$$98$$ −2.23103 −0.225368
$$99$$ 0 0
$$100$$ −1.88448 −0.188448
$$101$$ 9.35951 0.931306 0.465653 0.884967i $$-0.345820\pi$$
0.465653 + 0.884967i $$0.345820\pi$$
$$102$$ 0 0
$$103$$ 4.50535 0.443925 0.221962 0.975055i $$-0.428754\pi$$
0.221962 + 0.975055i $$0.428754\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ −0.231033 −0.0224399
$$107$$ −0.570909 −0.0551919 −0.0275960 0.999619i $$-0.508785\pi$$
−0.0275960 + 0.999619i $$0.508785\pi$$
$$108$$ 0 0
$$109$$ 15.4095 1.47596 0.737979 0.674823i $$-0.235780\pi$$
0.737979 + 0.674823i $$0.235780\pi$$
$$110$$ 0.231033 0.0220281
$$111$$ 0 0
$$112$$ 2.19177 0.207103
$$113$$ 5.32025 0.500487 0.250243 0.968183i $$-0.419489\pi$$
0.250243 + 0.968183i $$0.419489\pi$$
$$114$$ 0 0
$$115$$ −7.76897 −0.724460
$$116$$ 10.4487 0.970139
$$117$$ 0 0
$$118$$ −0.756009 −0.0695962
$$119$$ −4.90411 −0.449559
$$120$$ 0 0
$$121$$ −10.5379 −0.957994
$$122$$ −1.42909 −0.129384
$$123$$ 0 0
$$124$$ 18.7953 1.68787
$$125$$ −1.00000 −0.0894427
$$126$$ 0 0
$$127$$ −12.0196 −1.06657 −0.533285 0.845936i $$-0.679043\pi$$
−0.533285 + 0.845936i $$0.679043\pi$$
$$128$$ −9.35951 −0.827271
$$129$$ 0 0
$$130$$ 0 0
$$131$$ −10.9041 −0.952697 −0.476348 0.879257i $$-0.658040\pi$$
−0.476348 + 0.879257i $$0.658040\pi$$
$$132$$ 0 0
$$133$$ 0.0762550 0.00661215
$$134$$ −2.59456 −0.224136
$$135$$ 0 0
$$136$$ 9.80823 0.841049
$$137$$ −3.38983 −0.289613 −0.144806 0.989460i $$-0.546256\pi$$
−0.144806 + 0.989460i $$0.546256\pi$$
$$138$$ 0 0
$$139$$ 14.8082 1.25602 0.628009 0.778206i $$-0.283870\pi$$
0.628009 + 0.778206i $$0.283870\pi$$
$$140$$ 1.24399 0.105136
$$141$$ 0 0
$$142$$ −2.48571 −0.208597
$$143$$ 0 0
$$144$$ 0 0
$$145$$ 5.54461 0.460455
$$146$$ 2.72569 0.225579
$$147$$ 0 0
$$148$$ −18.4095 −1.51325
$$149$$ 17.0892 1.40000 0.700001 0.714141i $$-0.253183\pi$$
0.700001 + 0.714141i $$0.253183\pi$$
$$150$$ 0 0
$$151$$ 13.0130 1.05898 0.529490 0.848316i $$-0.322383\pi$$
0.529490 + 0.848316i $$0.322383\pi$$
$$152$$ −0.152510 −0.0123702
$$153$$ 0 0
$$154$$ −0.152510 −0.0122896
$$155$$ 9.97370 0.801107
$$156$$ 0 0
$$157$$ −0.775639 −0.0619028 −0.0309514 0.999521i $$-0.509854\pi$$
−0.0309514 + 0.999521i $$0.509854\pi$$
$$158$$ 3.38983 0.269680
$$159$$ 0 0
$$160$$ −3.76897 −0.297963
$$161$$ 5.12847 0.404180
$$162$$ 0 0
$$163$$ 12.1981 0.955426 0.477713 0.878516i $$-0.341466\pi$$
0.477713 + 0.878516i $$0.341466\pi$$
$$164$$ 7.96074 0.621629
$$165$$ 0 0
$$166$$ −0.601231 −0.0466646
$$167$$ 1.59054 0.123080 0.0615398 0.998105i $$-0.480399\pi$$
0.0615398 + 0.998105i $$0.480399\pi$$
$$168$$ 0 0
$$169$$ 0 0
$$170$$ 2.52498 0.193657
$$171$$ 0 0
$$172$$ 1.02630 0.0782548
$$173$$ −12.7493 −0.969314 −0.484657 0.874704i $$-0.661056\pi$$
−0.484657 + 0.874704i $$0.661056\pi$$
$$174$$ 0 0
$$175$$ 0.660123 0.0499006
$$176$$ −2.25695 −0.170124
$$177$$ 0 0
$$178$$ −4.60350 −0.345047
$$179$$ −17.7623 −1.32762 −0.663808 0.747903i $$-0.731061\pi$$
−0.663808 + 0.747903i $$0.731061\pi$$
$$180$$ 0 0
$$181$$ 7.02630 0.522261 0.261130 0.965304i $$-0.415905\pi$$
0.261130 + 0.965304i $$0.415905\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ −10.2569 −0.756152
$$185$$ −9.76897 −0.718229
$$186$$ 0 0
$$187$$ 5.04995 0.369289
$$188$$ −9.45941 −0.689899
$$189$$ 0 0
$$190$$ −0.0392613 −0.00284832
$$191$$ 13.9541 1.00968 0.504840 0.863213i $$-0.331551\pi$$
0.504840 + 0.863213i $$0.331551\pi$$
$$192$$ 0 0
$$193$$ 23.7493 1.70951 0.854757 0.519028i $$-0.173706\pi$$
0.854757 + 0.519028i $$0.173706\pi$$
$$194$$ 3.36618 0.241678
$$195$$ 0 0
$$196$$ 12.3702 0.883586
$$197$$ −15.8082 −1.12629 −0.563145 0.826358i $$-0.690409\pi$$
−0.563145 + 0.826358i $$0.690409\pi$$
$$198$$ 0 0
$$199$$ 8.76897 0.621616 0.310808 0.950473i $$-0.399400\pi$$
0.310808 + 0.950473i $$0.399400\pi$$
$$200$$ −1.32025 −0.0933555
$$201$$ 0 0
$$202$$ 3.18108 0.223820
$$203$$ −3.66012 −0.256890
$$204$$ 0 0
$$205$$ 4.22436 0.295042
$$206$$ 1.53126 0.106688
$$207$$ 0 0
$$208$$ 0 0
$$209$$ −0.0785226 −0.00543152
$$210$$ 0 0
$$211$$ 8.80823 0.606383 0.303192 0.952930i $$-0.401948\pi$$
0.303192 + 0.952930i $$0.401948\pi$$
$$212$$ 1.28098 0.0879784
$$213$$ 0 0
$$214$$ −0.194039 −0.0132642
$$215$$ 0.544607 0.0371419
$$216$$ 0 0
$$217$$ −6.58387 −0.446942
$$218$$ 5.23732 0.354716
$$219$$ 0 0
$$220$$ −1.28098 −0.0863640
$$221$$ 0 0
$$222$$ 0 0
$$223$$ 10.0393 0.672279 0.336139 0.941812i $$-0.390879\pi$$
0.336139 + 0.941812i $$0.390879\pi$$
$$224$$ 2.48798 0.166235
$$225$$ 0 0
$$226$$ 1.80823 0.120282
$$227$$ −1.21140 −0.0804036 −0.0402018 0.999192i $$-0.512800\pi$$
−0.0402018 + 0.999192i $$0.512800\pi$$
$$228$$ 0 0
$$229$$ 19.2440 1.27168 0.635839 0.771821i $$-0.280654\pi$$
0.635839 + 0.771821i $$0.280654\pi$$
$$230$$ −2.64049 −0.174109
$$231$$ 0 0
$$232$$ 7.32025 0.480598
$$233$$ 23.9081 1.56627 0.783137 0.621849i $$-0.213618\pi$$
0.783137 + 0.621849i $$0.213618\pi$$
$$234$$ 0 0
$$235$$ −5.01963 −0.327445
$$236$$ 4.19177 0.272861
$$237$$ 0 0
$$238$$ −1.66680 −0.108042
$$239$$ −18.6798 −1.20829 −0.604146 0.796873i $$-0.706486\pi$$
−0.604146 + 0.796873i $$0.706486\pi$$
$$240$$ 0 0
$$241$$ 6.11552 0.393935 0.196968 0.980410i $$-0.436891\pi$$
0.196968 + 0.980410i $$0.436891\pi$$
$$242$$ −3.58160 −0.230234
$$243$$ 0 0
$$244$$ 7.92375 0.507266
$$245$$ 6.56424 0.419374
$$246$$ 0 0
$$247$$ 0 0
$$248$$ 13.1677 0.836152
$$249$$ 0 0
$$250$$ −0.339877 −0.0214957
$$251$$ −3.35951 −0.212050 −0.106025 0.994363i $$-0.533812\pi$$
−0.106025 + 0.994363i $$0.533812\pi$$
$$252$$ 0 0
$$253$$ −5.28098 −0.332013
$$254$$ −4.08519 −0.256328
$$255$$ 0 0
$$256$$ 7.53793 0.471121
$$257$$ 10.1088 0.630572 0.315286 0.948997i $$-0.397899\pi$$
0.315286 + 0.948997i $$0.397899\pi$$
$$258$$ 0 0
$$259$$ 6.44872 0.400704
$$260$$ 0 0
$$261$$ 0 0
$$262$$ −3.70606 −0.228961
$$263$$ 22.5183 1.38854 0.694269 0.719716i $$-0.255728\pi$$
0.694269 + 0.719716i $$0.255728\pi$$
$$264$$ 0 0
$$265$$ 0.679754 0.0417569
$$266$$ 0.0259173 0.00158909
$$267$$ 0 0
$$268$$ 14.3858 0.878753
$$269$$ −8.49465 −0.517928 −0.258964 0.965887i $$-0.583381\pi$$
−0.258964 + 0.965887i $$0.583381\pi$$
$$270$$ 0 0
$$271$$ 9.37020 0.569199 0.284600 0.958647i $$-0.408139\pi$$
0.284600 + 0.958647i $$0.408139\pi$$
$$272$$ −24.6664 −1.49562
$$273$$ 0 0
$$274$$ −1.15212 −0.0696024
$$275$$ −0.679754 −0.0409907
$$276$$ 0 0
$$277$$ 0.719015 0.0432014 0.0216007 0.999767i $$-0.493124\pi$$
0.0216007 + 0.999767i $$0.493124\pi$$
$$278$$ 5.03297 0.301858
$$279$$ 0 0
$$280$$ 0.871525 0.0520836
$$281$$ −1.54461 −0.0921435 −0.0460718 0.998938i $$-0.514670\pi$$
−0.0460718 + 0.998938i $$0.514670\pi$$
$$282$$ 0 0
$$283$$ −18.1195 −1.07709 −0.538547 0.842595i $$-0.681027\pi$$
−0.538547 + 0.842595i $$0.681027\pi$$
$$284$$ 13.7823 0.817830
$$285$$ 0 0
$$286$$ 0 0
$$287$$ −2.78860 −0.164606
$$288$$ 0 0
$$289$$ 38.1914 2.24655
$$290$$ 1.88448 0.110661
$$291$$ 0 0
$$292$$ −15.1129 −0.884413
$$293$$ 30.5050 1.78212 0.891059 0.453887i $$-0.149963\pi$$
0.891059 + 0.453887i $$0.149963\pi$$
$$294$$ 0 0
$$295$$ 2.22436 0.129507
$$296$$ −12.8974 −0.749649
$$297$$ 0 0
$$298$$ 5.80823 0.336462
$$299$$ 0 0
$$300$$ 0 0
$$301$$ −0.359508 −0.0207217
$$302$$ 4.42280 0.254504
$$303$$ 0 0
$$304$$ 0.383543 0.0219977
$$305$$ 4.20473 0.240762
$$306$$ 0 0
$$307$$ −4.77564 −0.272560 −0.136280 0.990670i $$-0.543515\pi$$
−0.136280 + 0.990670i $$0.543515\pi$$
$$308$$ 0.845608 0.0481830
$$309$$ 0 0
$$310$$ 3.38983 0.192529
$$311$$ −30.5812 −1.73410 −0.867051 0.498220i $$-0.833987\pi$$
−0.867051 + 0.498220i $$0.833987\pi$$
$$312$$ 0 0
$$313$$ −26.7230 −1.51048 −0.755238 0.655451i $$-0.772479\pi$$
−0.755238 + 0.655451i $$0.772479\pi$$
$$314$$ −0.263622 −0.0148770
$$315$$ 0 0
$$316$$ −18.7953 −1.05732
$$317$$ 20.6271 1.15854 0.579268 0.815137i $$-0.303338\pi$$
0.579268 + 0.815137i $$0.303338\pi$$
$$318$$ 0 0
$$319$$ 3.76897 0.211022
$$320$$ 5.35951 0.299606
$$321$$ 0 0
$$322$$ 1.74305 0.0971364
$$323$$ −0.858181 −0.0477505
$$324$$ 0 0
$$325$$ 0 0
$$326$$ 4.14584 0.229617
$$327$$ 0 0
$$328$$ 5.57720 0.307949
$$329$$ 3.31357 0.182683
$$330$$ 0 0
$$331$$ 5.37020 0.295173 0.147586 0.989049i $$-0.452850\pi$$
0.147586 + 0.989049i $$0.452850\pi$$
$$332$$ 3.33359 0.182955
$$333$$ 0 0
$$334$$ 0.540588 0.0295797
$$335$$ 7.63382 0.417080
$$336$$ 0 0
$$337$$ 28.7623 1.56678 0.783391 0.621529i $$-0.213488\pi$$
0.783391 + 0.621529i $$0.213488\pi$$
$$338$$ 0 0
$$339$$ 0 0
$$340$$ −14.0000 −0.759257
$$341$$ 6.77966 0.367139
$$342$$ 0 0
$$343$$ −8.95407 −0.483474
$$344$$ 0.719015 0.0387667
$$345$$ 0 0
$$346$$ −4.33320 −0.232955
$$347$$ −22.3961 −1.20229 −0.601143 0.799141i $$-0.705288\pi$$
−0.601143 + 0.799141i $$0.705288\pi$$
$$348$$ 0 0
$$349$$ −11.9737 −0.640937 −0.320469 0.947259i $$-0.603840\pi$$
−0.320469 + 0.947259i $$0.603840\pi$$
$$350$$ 0.224361 0.0119926
$$351$$ 0 0
$$352$$ −2.56197 −0.136553
$$353$$ 17.0366 0.906767 0.453384 0.891316i $$-0.350217\pi$$
0.453384 + 0.891316i $$0.350217\pi$$
$$354$$ 0 0
$$355$$ 7.31357 0.388164
$$356$$ 25.5246 1.35280
$$357$$ 0 0
$$358$$ −6.03699 −0.319065
$$359$$ 35.0825 1.85159 0.925793 0.378031i $$-0.123399\pi$$
0.925793 + 0.378031i $$0.123399\pi$$
$$360$$ 0 0
$$361$$ −18.9867 −0.999298
$$362$$ 2.38808 0.125515
$$363$$ 0 0
$$364$$ 0 0
$$365$$ −8.01963 −0.419767
$$366$$ 0 0
$$367$$ 20.0825 1.04830 0.524150 0.851626i $$-0.324383\pi$$
0.524150 + 0.851626i $$0.324383\pi$$
$$368$$ 25.7949 1.34465
$$369$$ 0 0
$$370$$ −3.32025 −0.172611
$$371$$ −0.448721 −0.0232964
$$372$$ 0 0
$$373$$ −23.4790 −1.21570 −0.607849 0.794052i $$-0.707968\pi$$
−0.607849 + 0.794052i $$0.707968\pi$$
$$374$$ 1.71636 0.0887510
$$375$$ 0 0
$$376$$ −6.62715 −0.341769
$$377$$ 0 0
$$378$$ 0 0
$$379$$ 21.1414 1.08596 0.542981 0.839745i $$-0.317295\pi$$
0.542981 + 0.839745i $$0.317295\pi$$
$$380$$ 0.217689 0.0111672
$$381$$ 0 0
$$382$$ 4.74266 0.242656
$$383$$ −1.73865 −0.0888406 −0.0444203 0.999013i $$-0.514144\pi$$
−0.0444203 + 0.999013i $$0.514144\pi$$
$$384$$ 0 0
$$385$$ 0.448721 0.0228689
$$386$$ 8.07185 0.410846
$$387$$ 0 0
$$388$$ −18.6641 −0.947528
$$389$$ 26.6664 1.35204 0.676020 0.736883i $$-0.263703\pi$$
0.676020 + 0.736883i $$0.263703\pi$$
$$390$$ 0 0
$$391$$ −57.7164 −2.91884
$$392$$ 8.66641 0.437720
$$393$$ 0 0
$$394$$ −5.37285 −0.270680
$$395$$ −9.97370 −0.501831
$$396$$ 0 0
$$397$$ 14.5446 0.729973 0.364986 0.931013i $$-0.381074\pi$$
0.364986 + 0.931013i $$0.381074\pi$$
$$398$$ 2.98037 0.149392
$$399$$ 0 0
$$400$$ 3.32025 0.166012
$$401$$ 8.37020 0.417988 0.208994 0.977917i $$-0.432981\pi$$
0.208994 + 0.977917i $$0.432981\pi$$
$$402$$ 0 0
$$403$$ 0 0
$$404$$ −17.6378 −0.877515
$$405$$ 0 0
$$406$$ −1.24399 −0.0617382
$$407$$ −6.64049 −0.329157
$$408$$ 0 0
$$409$$ 17.2547 0.853189 0.426595 0.904443i $$-0.359713\pi$$
0.426595 + 0.904443i $$0.359713\pi$$
$$410$$ 1.43576 0.0709073
$$411$$ 0 0
$$412$$ −8.49025 −0.418285
$$413$$ −1.46835 −0.0722529
$$414$$ 0 0
$$415$$ 1.76897 0.0868352
$$416$$ 0 0
$$417$$ 0 0
$$418$$ −0.0266880 −0.00130535
$$419$$ −12.8649 −0.628489 −0.314245 0.949342i $$-0.601751\pi$$
−0.314245 + 0.949342i $$0.601751\pi$$
$$420$$ 0 0
$$421$$ 24.5616 1.19706 0.598529 0.801101i $$-0.295752\pi$$
0.598529 + 0.801101i $$0.295752\pi$$
$$422$$ 2.99371 0.145732
$$423$$ 0 0
$$424$$ 0.897442 0.0435837
$$425$$ −7.42909 −0.360364
$$426$$ 0 0
$$427$$ −2.77564 −0.134323
$$428$$ 1.07587 0.0520041
$$429$$ 0 0
$$430$$ 0.185099 0.00892628
$$431$$ −24.7797 −1.19359 −0.596797 0.802392i $$-0.703560\pi$$
−0.596797 + 0.802392i $$0.703560\pi$$
$$432$$ 0 0
$$433$$ −14.0589 −0.675627 −0.337814 0.941213i $$-0.609687\pi$$
−0.337814 + 0.941213i $$0.609687\pi$$
$$434$$ −2.23770 −0.107413
$$435$$ 0 0
$$436$$ −29.0389 −1.39071
$$437$$ 0.897442 0.0429305
$$438$$ 0 0
$$439$$ 20.8452 0.994888 0.497444 0.867496i $$-0.334272\pi$$
0.497444 + 0.867496i $$0.334272\pi$$
$$440$$ −0.897442 −0.0427839
$$441$$ 0 0
$$442$$ 0 0
$$443$$ 11.4291 0.543012 0.271506 0.962437i $$-0.412478\pi$$
0.271506 + 0.962437i $$0.412478\pi$$
$$444$$ 0 0
$$445$$ 13.5446 0.642076
$$446$$ 3.41211 0.161568
$$447$$ 0 0
$$448$$ −3.53793 −0.167152
$$449$$ −25.9081 −1.22268 −0.611340 0.791368i $$-0.709369\pi$$
−0.611340 + 0.791368i $$0.709369\pi$$
$$450$$ 0 0
$$451$$ 2.87153 0.135215
$$452$$ −10.0259 −0.471579
$$453$$ 0 0
$$454$$ −0.411728 −0.0193233
$$455$$ 0 0
$$456$$ 0 0
$$457$$ 5.90411 0.276183 0.138091 0.990419i $$-0.455903\pi$$
0.138091 + 0.990419i $$0.455903\pi$$
$$458$$ 6.54059 0.305622
$$459$$ 0 0
$$460$$ 14.6405 0.682616
$$461$$ 15.4920 0.721534 0.360767 0.932656i $$-0.382515\pi$$
0.360767 + 0.932656i $$0.382515\pi$$
$$462$$ 0 0
$$463$$ 17.4420 0.810601 0.405300 0.914184i $$-0.367167\pi$$
0.405300 + 0.914184i $$0.367167\pi$$
$$464$$ −18.4095 −0.854638
$$465$$ 0 0
$$466$$ 8.12582 0.376421
$$467$$ 20.4790 0.947657 0.473829 0.880617i $$-0.342872\pi$$
0.473829 + 0.880617i $$0.342872\pi$$
$$468$$ 0 0
$$469$$ −5.03926 −0.232691
$$470$$ −1.70606 −0.0786945
$$471$$ 0 0
$$472$$ 2.93670 0.135173
$$473$$ 0.370199 0.0170217
$$474$$ 0 0
$$475$$ 0.115516 0.00530025
$$476$$ 9.24172 0.423594
$$477$$ 0 0
$$478$$ −6.34882 −0.290388
$$479$$ 40.9907 1.87291 0.936456 0.350785i $$-0.114085\pi$$
0.936456 + 0.350785i $$0.114085\pi$$
$$480$$ 0 0
$$481$$ 0 0
$$482$$ 2.07852 0.0946741
$$483$$ 0 0
$$484$$ 19.8586 0.902662
$$485$$ −9.90411 −0.449723
$$486$$ 0 0
$$487$$ 24.0629 1.09039 0.545197 0.838308i $$-0.316455\pi$$
0.545197 + 0.838308i $$0.316455\pi$$
$$488$$ 5.55128 0.251295
$$489$$ 0 0
$$490$$ 2.23103 0.100788
$$491$$ −36.7730 −1.65954 −0.829771 0.558104i $$-0.811529\pi$$
−0.829771 + 0.558104i $$0.811529\pi$$
$$492$$ 0 0
$$493$$ 41.1914 1.85517
$$494$$ 0 0
$$495$$ 0 0
$$496$$ −33.1151 −1.48691
$$497$$ −4.82786 −0.216559
$$498$$ 0 0
$$499$$ 34.8212 1.55881 0.779405 0.626520i $$-0.215521\pi$$
0.779405 + 0.626520i $$0.215521\pi$$
$$500$$ 1.88448 0.0842767
$$501$$ 0 0
$$502$$ −1.14182 −0.0509619
$$503$$ 32.0259 1.42797 0.713983 0.700164i $$-0.246890\pi$$
0.713983 + 0.700164i $$0.246890\pi$$
$$504$$ 0 0
$$505$$ −9.35951 −0.416493
$$506$$ −1.79488 −0.0797924
$$507$$ 0 0
$$508$$ 22.6508 1.00497
$$509$$ 41.3462 1.83264 0.916318 0.400451i $$-0.131146\pi$$
0.916318 + 0.400451i $$0.131146\pi$$
$$510$$ 0 0
$$511$$ 5.29394 0.234190
$$512$$ 21.2810 0.940496
$$513$$ 0 0
$$514$$ 3.43576 0.151545
$$515$$ −4.50535 −0.198529
$$516$$ 0 0
$$517$$ −3.41211 −0.150065
$$518$$ 2.19177 0.0963009
$$519$$ 0 0
$$520$$ 0 0
$$521$$ −4.40279 −0.192890 −0.0964448 0.995338i $$-0.530747\pi$$
−0.0964448 + 0.995338i $$0.530747\pi$$
$$522$$ 0 0
$$523$$ −32.4487 −1.41888 −0.709442 0.704764i $$-0.751053\pi$$
−0.709442 + 0.704764i $$0.751053\pi$$
$$524$$ 20.5486 0.897671
$$525$$ 0 0
$$526$$ 7.65345 0.333706
$$527$$ 74.0955 3.22765
$$528$$ 0 0
$$529$$ 37.3569 1.62421
$$530$$ 0.231033 0.0100354
$$531$$ 0 0
$$532$$ −0.143701 −0.00623024
$$533$$ 0 0
$$534$$ 0 0
$$535$$ 0.570909 0.0246826
$$536$$ 10.0785 0.435326
$$537$$ 0 0
$$538$$ −2.88714 −0.124473
$$539$$ 4.46207 0.192195
$$540$$ 0 0
$$541$$ −8.57720 −0.368762 −0.184381 0.982855i $$-0.559028\pi$$
−0.184381 + 0.982855i $$0.559028\pi$$
$$542$$ 3.18471 0.136795
$$543$$ 0 0
$$544$$ −28.0000 −1.20049
$$545$$ −15.4095 −0.660069
$$546$$ 0 0
$$547$$ −32.4920 −1.38926 −0.694629 0.719368i $$-0.744431\pi$$
−0.694629 + 0.719368i $$0.744431\pi$$
$$548$$ 6.38808 0.272885
$$549$$ 0 0
$$550$$ −0.231033 −0.00985126
$$551$$ −0.640492 −0.0272859
$$552$$ 0 0
$$553$$ 6.58387 0.279975
$$554$$ 0.244377 0.0103826
$$555$$ 0 0
$$556$$ −27.9059 −1.18347
$$557$$ 41.2150 1.74634 0.873169 0.487418i $$-0.162061\pi$$
0.873169 + 0.487418i $$0.162061\pi$$
$$558$$ 0 0
$$559$$ 0 0
$$560$$ −2.19177 −0.0926192
$$561$$ 0 0
$$562$$ −0.524976 −0.0221448
$$563$$ 12.1784 0.513260 0.256630 0.966510i $$-0.417388\pi$$
0.256630 + 0.966510i $$0.417388\pi$$
$$564$$ 0 0
$$565$$ −5.32025 −0.223824
$$566$$ −6.15841 −0.258857
$$567$$ 0 0
$$568$$ 9.65572 0.405145
$$569$$ −6.94338 −0.291081 −0.145541 0.989352i $$-0.546492\pi$$
−0.145541 + 0.989352i $$0.546492\pi$$
$$570$$ 0 0
$$571$$ 3.51429 0.147068 0.0735341 0.997293i $$-0.476572\pi$$
0.0735341 + 0.997293i $$0.476572\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ −0.947780 −0.0395596
$$575$$ 7.76897 0.323988
$$576$$ 0 0
$$577$$ 3.14182 0.130796 0.0653978 0.997859i $$-0.479168\pi$$
0.0653978 + 0.997859i $$0.479168\pi$$
$$578$$ 12.9804 0.539912
$$579$$ 0 0
$$580$$ −10.4487 −0.433860
$$581$$ −1.16774 −0.0484459
$$582$$ 0 0
$$583$$ 0.462065 0.0191368
$$584$$ −10.5879 −0.438130
$$585$$ 0 0
$$586$$ 10.3679 0.428295
$$587$$ −37.9777 −1.56751 −0.783754 0.621071i $$-0.786698\pi$$
−0.783754 + 0.621071i $$0.786698\pi$$
$$588$$ 0 0
$$589$$ −1.15212 −0.0474725
$$590$$ 0.756009 0.0311244
$$591$$ 0 0
$$592$$ 32.4354 1.33309
$$593$$ −10.4487 −0.429078 −0.214539 0.976715i $$-0.568825\pi$$
−0.214539 + 0.976715i $$0.568825\pi$$
$$594$$ 0 0
$$595$$ 4.90411 0.201049
$$596$$ −32.2043 −1.31914
$$597$$ 0 0
$$598$$ 0 0
$$599$$ 45.5705 1.86196 0.930981 0.365069i $$-0.118955\pi$$
0.930981 + 0.365069i $$0.118955\pi$$
$$600$$ 0 0
$$601$$ −14.7819 −0.602967 −0.301484 0.953471i $$-0.597482\pi$$
−0.301484 + 0.953471i $$0.597482\pi$$
$$602$$ −0.122188 −0.00498002
$$603$$ 0 0
$$604$$ −24.5227 −0.997815
$$605$$ 10.5379 0.428428
$$606$$ 0 0
$$607$$ −18.9344 −0.768525 −0.384263 0.923224i $$-0.625544\pi$$
−0.384263 + 0.923224i $$0.625544\pi$$
$$608$$ 0.435377 0.0176569
$$609$$ 0 0
$$610$$ 1.42909 0.0578622
$$611$$ 0 0
$$612$$ 0 0
$$613$$ −2.58387 −0.104361 −0.0521807 0.998638i $$-0.516617\pi$$
−0.0521807 + 0.998638i $$0.516617\pi$$
$$614$$ −1.62313 −0.0655042
$$615$$ 0 0
$$616$$ 0.592422 0.0238694
$$617$$ −14.0393 −0.565199 −0.282600 0.959238i $$-0.591197\pi$$
−0.282600 + 0.959238i $$0.591197\pi$$
$$618$$ 0 0
$$619$$ −17.8582 −0.717781 −0.358890 0.933380i $$-0.616845\pi$$
−0.358890 + 0.933380i $$0.616845\pi$$
$$620$$ −18.7953 −0.754836
$$621$$ 0 0
$$622$$ −10.3938 −0.416755
$$623$$ −8.94111 −0.358218
$$624$$ 0 0
$$625$$ 1.00000 0.0400000
$$626$$ −9.08254 −0.363011
$$627$$ 0 0
$$628$$ 1.46168 0.0583274
$$629$$ −72.5745 −2.89374
$$630$$ 0 0
$$631$$ −24.9630 −0.993762 −0.496881 0.867819i $$-0.665521\pi$$
−0.496881 + 0.867819i $$0.665521\pi$$
$$632$$ −13.1677 −0.523784
$$633$$ 0 0
$$634$$ 7.01069 0.278430
$$635$$ 12.0196 0.476984
$$636$$ 0 0
$$637$$ 0 0
$$638$$ 1.28098 0.0507147
$$639$$ 0 0
$$640$$ 9.35951 0.369967
$$641$$ −23.3069 −0.920567 −0.460284 0.887772i $$-0.652252\pi$$
−0.460284 + 0.887772i $$0.652252\pi$$
$$642$$ 0 0
$$643$$ 45.4790 1.79352 0.896759 0.442519i $$-0.145915\pi$$
0.896759 + 0.442519i $$0.145915\pi$$
$$644$$ −9.66453 −0.380836
$$645$$ 0 0
$$646$$ −0.291676 −0.0114758
$$647$$ −6.40946 −0.251982 −0.125991 0.992031i $$-0.540211\pi$$
−0.125991 + 0.992031i $$0.540211\pi$$
$$648$$ 0 0
$$649$$ 1.51202 0.0593519
$$650$$ 0 0
$$651$$ 0 0
$$652$$ −22.9870 −0.900242
$$653$$ −1.48170 −0.0579832 −0.0289916 0.999580i $$-0.509230\pi$$
−0.0289916 + 0.999580i $$0.509230\pi$$
$$654$$ 0 0
$$655$$ 10.9041 0.426059
$$656$$ −14.0259 −0.547620
$$657$$ 0 0
$$658$$ 1.12621 0.0439041
$$659$$ 7.08921 0.276157 0.138078 0.990421i $$-0.455907\pi$$
0.138078 + 0.990421i $$0.455907\pi$$
$$660$$ 0 0
$$661$$ 1.17843 0.0458355 0.0229178 0.999737i $$-0.492704\pi$$
0.0229178 + 0.999737i $$0.492704\pi$$
$$662$$ 1.82521 0.0709387
$$663$$ 0 0
$$664$$ 2.33547 0.0906339
$$665$$ −0.0762550 −0.00295704
$$666$$ 0 0
$$667$$ −43.0759 −1.66790
$$668$$ −2.99735 −0.115971
$$669$$ 0 0
$$670$$ 2.59456 0.100237
$$671$$ 2.85818 0.110339
$$672$$ 0 0
$$673$$ 13.5576 0.522606 0.261303 0.965257i $$-0.415848\pi$$
0.261303 + 0.965257i $$0.415848\pi$$
$$674$$ 9.77564 0.376544
$$675$$ 0 0
$$676$$ 0 0
$$677$$ −9.53793 −0.366573 −0.183286 0.983060i $$-0.558674\pi$$
−0.183286 + 0.983060i $$0.558674\pi$$
$$678$$ 0 0
$$679$$ 6.53793 0.250903
$$680$$ −9.80823 −0.376128
$$681$$ 0 0
$$682$$ 2.30425 0.0882343
$$683$$ 44.5183 1.70345 0.851723 0.523993i $$-0.175558\pi$$
0.851723 + 0.523993i $$0.175558\pi$$
$$684$$ 0 0
$$685$$ 3.38983 0.129519
$$686$$ −3.04328 −0.116193
$$687$$ 0 0
$$688$$ −1.80823 −0.0689381
$$689$$ 0 0
$$690$$ 0 0
$$691$$ −5.28060 −0.200883 −0.100442 0.994943i $$-0.532026\pi$$
−0.100442 + 0.994943i $$0.532026\pi$$
$$692$$ 24.0259 0.913328
$$693$$ 0 0
$$694$$ −7.61192 −0.288945
$$695$$ −14.8082 −0.561708
$$696$$ 0 0
$$697$$ 31.3832 1.18872
$$698$$ −4.06958 −0.154036
$$699$$ 0 0
$$700$$ −1.24399 −0.0470184
$$701$$ −20.1392 −0.760646 −0.380323 0.924854i $$-0.624187\pi$$
−0.380323 + 0.924854i $$0.624187\pi$$
$$702$$ 0 0
$$703$$ 1.12847 0.0425612
$$704$$ 3.64315 0.137306
$$705$$ 0 0
$$706$$ 5.79035 0.217923
$$707$$ 6.17843 0.232364
$$708$$ 0 0
$$709$$ 1.54059 0.0578580 0.0289290 0.999581i $$-0.490790\pi$$
0.0289290 + 0.999581i $$0.490790\pi$$
$$710$$ 2.48571 0.0932872
$$711$$ 0 0
$$712$$ 17.8822 0.670164
$$713$$ −77.4853 −2.90185
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 33.4728 1.25094
$$717$$ 0 0
$$718$$ 11.9237 0.444990
$$719$$ −37.0040 −1.38002 −0.690009 0.723801i $$-0.742393\pi$$
−0.690009 + 0.723801i $$0.742393\pi$$
$$720$$ 0 0
$$721$$ 2.97408 0.110761
$$722$$ −6.45313 −0.240160
$$723$$ 0 0
$$724$$ −13.2410 −0.492096
$$725$$ −5.54461 −0.205922
$$726$$ 0 0
$$727$$ −44.9015 −1.66530 −0.832652 0.553797i $$-0.813178\pi$$
−0.832652 + 0.553797i $$0.813178\pi$$
$$728$$ 0 0
$$729$$ 0 0
$$730$$ −2.72569 −0.100882
$$731$$ 4.04593 0.149644
$$732$$ 0 0
$$733$$ −4.94072 −0.182490 −0.0912449 0.995828i $$-0.529085\pi$$
−0.0912449 + 0.995828i $$0.529085\pi$$
$$734$$ 6.82559 0.251937
$$735$$ 0 0
$$736$$ 29.2810 1.07931
$$737$$ 5.18912 0.191144
$$738$$ 0 0
$$739$$ 6.03926 0.222158 0.111079 0.993812i $$-0.464569\pi$$
0.111079 + 0.993812i $$0.464569\pi$$
$$740$$ 18.4095 0.676745
$$741$$ 0 0
$$742$$ −0.152510 −0.00559882
$$743$$ 13.0589 0.479084 0.239542 0.970886i $$-0.423003\pi$$
0.239542 + 0.970886i $$0.423003\pi$$
$$744$$ 0 0
$$745$$ −17.0892 −0.626100
$$746$$ −7.97998 −0.292168
$$747$$ 0 0
$$748$$ −9.51655 −0.347960
$$749$$ −0.376871 −0.0137706
$$750$$ 0 0
$$751$$ 48.0236 1.75241 0.876204 0.481941i $$-0.160068\pi$$
0.876204 + 0.481941i $$0.160068\pi$$
$$752$$ 16.6664 0.607761
$$753$$ 0 0
$$754$$ 0 0
$$755$$ −13.0130 −0.473590
$$756$$ 0 0
$$757$$ −4.56424 −0.165890 −0.0829450 0.996554i $$-0.526433\pi$$
−0.0829450 + 0.996554i $$0.526433\pi$$
$$758$$ 7.18548 0.260989
$$759$$ 0 0
$$760$$ 0.152510 0.00553212
$$761$$ −21.0892 −0.764483 −0.382242 0.924062i $$-0.624848\pi$$
−0.382242 + 0.924062i $$0.624848\pi$$
$$762$$ 0 0
$$763$$ 10.1721 0.368256
$$764$$ −26.2962 −0.951364
$$765$$ 0 0
$$766$$ −0.590926 −0.0213510
$$767$$ 0 0
$$768$$ 0 0
$$769$$ 42.3332 1.52657 0.763287 0.646059i $$-0.223584\pi$$
0.763287 + 0.646059i $$0.223584\pi$$
$$770$$ 0.152510 0.00549608
$$771$$ 0 0
$$772$$ −44.7552 −1.61078
$$773$$ −50.2436 −1.80714 −0.903568 0.428444i $$-0.859062\pi$$
−0.903568 + 0.428444i $$0.859062\pi$$
$$774$$ 0 0
$$775$$ −9.97370 −0.358266
$$776$$ −13.0759 −0.469396
$$777$$ 0 0
$$778$$ 9.06330 0.324935
$$779$$ −0.487982 −0.0174838
$$780$$ 0 0
$$781$$ 4.97143 0.177892
$$782$$ −19.6165 −0.701483
$$783$$ 0 0
$$784$$ −21.7949 −0.778389
$$785$$ 0.775639 0.0276838
$$786$$ 0 0
$$787$$ −10.5816 −0.377193 −0.188597 0.982055i $$-0.560394\pi$$
−0.188597 + 0.982055i $$0.560394\pi$$
$$788$$ 29.7903 1.06124
$$789$$ 0 0
$$790$$ −3.38983 −0.120605
$$791$$ 3.51202 0.124873
$$792$$ 0 0
$$793$$ 0 0
$$794$$ 4.94338 0.175434
$$795$$ 0 0
$$796$$ −16.5250 −0.585712
$$797$$ 20.1481 0.713683 0.356841 0.934165i $$-0.383854\pi$$
0.356841 + 0.934165i $$0.383854\pi$$
$$798$$ 0 0
$$799$$ −37.2913 −1.31927
$$800$$ 3.76897 0.133253
$$801$$ 0 0
$$802$$ 2.84484 0.100455
$$803$$ −5.45137 −0.192375
$$804$$ 0 0
$$805$$ −5.12847 −0.180755
$$806$$ 0 0
$$807$$ 0 0
$$808$$ −12.3569 −0.434713
$$809$$ −12.9108 −0.453919 −0.226960 0.973904i $$-0.572879\pi$$
−0.226960 + 0.973904i $$0.572879\pi$$
$$810$$ 0 0
$$811$$ −15.8974 −0.558235 −0.279117 0.960257i $$-0.590042\pi$$
−0.279117 + 0.960257i $$0.590042\pi$$
$$812$$ 6.89744 0.242053
$$813$$ 0 0
$$814$$ −2.25695 −0.0791061
$$815$$ −12.1981 −0.427279
$$816$$ 0 0
$$817$$ −0.0629110 −0.00220098
$$818$$ 5.86447 0.205046
$$819$$ 0 0
$$820$$ −7.96074 −0.278001
$$821$$ 37.2284 1.29928 0.649640 0.760242i $$-0.274920\pi$$
0.649640 + 0.760242i $$0.274920\pi$$
$$822$$ 0 0
$$823$$ −4.89744 −0.170714 −0.0853571 0.996350i $$-0.527203\pi$$
−0.0853571 + 0.996350i $$0.527203\pi$$
$$824$$ −5.94817 −0.207214
$$825$$ 0 0
$$826$$ −0.499059 −0.0173645
$$827$$ −37.6334 −1.30864 −0.654321 0.756217i $$-0.727046\pi$$
−0.654321 + 0.756217i $$0.727046\pi$$
$$828$$ 0 0
$$829$$ −48.9104 −1.69873 −0.849364 0.527807i $$-0.823014\pi$$
−0.849364 + 0.527807i $$0.823014\pi$$
$$830$$ 0.601231 0.0208690
$$831$$ 0 0
$$832$$ 0 0
$$833$$ 48.7663 1.68965
$$834$$ 0 0
$$835$$ −1.59054 −0.0550429
$$836$$ 0.147975 0.00511781
$$837$$ 0 0
$$838$$ −4.37247 −0.151044
$$839$$ −48.2783 −1.66675 −0.833377 0.552706i $$-0.813595\pi$$
−0.833377 + 0.552706i $$0.813595\pi$$
$$840$$ 0 0
$$841$$ 1.74266 0.0600919
$$842$$ 8.34791 0.287688
$$843$$ 0 0
$$844$$ −16.5990 −0.571360
$$845$$ 0 0
$$846$$ 0 0
$$847$$ −6.95633 −0.239022
$$848$$ −2.25695 −0.0775040
$$849$$ 0 0
$$850$$ −2.52498 −0.0866060
$$851$$ 75.8948 2.60164
$$852$$ 0 0
$$853$$ −14.4291 −0.494043 −0.247021 0.969010i $$-0.579452\pi$$
−0.247021 + 0.969010i $$0.579452\pi$$
$$854$$ −0.943376 −0.0322817
$$855$$ 0 0
$$856$$ 0.753741 0.0257623
$$857$$ −3.64678 −0.124572 −0.0622858 0.998058i $$-0.519839\pi$$
−0.0622858 + 0.998058i $$0.519839\pi$$
$$858$$ 0 0
$$859$$ 21.7427 0.741850 0.370925 0.928663i $$-0.379041\pi$$
0.370925 + 0.928663i $$0.379041\pi$$
$$860$$ −1.02630 −0.0349966
$$861$$ 0 0
$$862$$ −8.42203 −0.286856
$$863$$ 17.0892 0.581724 0.290862 0.956765i $$-0.406058\pi$$
0.290862 + 0.956765i $$0.406058\pi$$
$$864$$ 0 0
$$865$$ 12.7493 0.433490
$$866$$ −4.77829 −0.162373
$$867$$ 0 0
$$868$$ 12.4072 0.421128
$$869$$ −6.77966 −0.229984
$$870$$ 0 0
$$871$$ 0 0
$$872$$ −20.3443 −0.688944
$$873$$ 0 0
$$874$$ 0.305020 0.0103175
$$875$$ −0.660123 −0.0223162
$$876$$ 0 0
$$877$$ −4.85818 −0.164049 −0.0820246 0.996630i $$-0.526139\pi$$
−0.0820246 + 0.996630i $$0.526139\pi$$
$$878$$ 7.08481 0.239101
$$879$$ 0 0
$$880$$ 2.25695 0.0760818
$$881$$ 23.3202 0.785679 0.392840 0.919607i $$-0.371493\pi$$
0.392840 + 0.919607i $$0.371493\pi$$
$$882$$ 0 0
$$883$$ −12.8934 −0.433898 −0.216949 0.976183i $$-0.569611\pi$$
−0.216949 + 0.976183i $$0.569611\pi$$
$$884$$ 0 0
$$885$$ 0 0
$$886$$ 3.88448 0.130502
$$887$$ −30.9278 −1.03845 −0.519226 0.854637i $$-0.673780\pi$$
−0.519226 + 0.854637i $$0.673780\pi$$
$$888$$ 0 0
$$889$$ −7.93444 −0.266112
$$890$$ 4.60350 0.154310
$$891$$ 0 0
$$892$$ −18.9188 −0.633449
$$893$$ 0.579849 0.0194039
$$894$$ 0 0
$$895$$ 17.7623 0.593728
$$896$$ −6.17843 −0.206407
$$897$$ 0 0
$$898$$ −8.80558 −0.293846
$$899$$ 55.3002 1.84437
$$900$$ 0 0
$$901$$ 5.04995 0.168238
$$902$$ 0.975965 0.0324961
$$903$$ 0 0
$$904$$ −7.02404 −0.233616
$$905$$ −7.02630 −0.233562
$$906$$ 0 0
$$907$$ −16.9604 −0.563159 −0.281580 0.959538i $$-0.590858\pi$$
−0.281580 + 0.959538i $$0.590858\pi$$
$$908$$ 2.28287 0.0757596
$$909$$ 0 0
$$910$$ 0 0
$$911$$ −37.7297 −1.25004 −0.625020 0.780608i $$-0.714909\pi$$
−0.625020 + 0.780608i $$0.714909\pi$$
$$912$$ 0 0
$$913$$ 1.20246 0.0397957
$$914$$ 2.00667 0.0663748
$$915$$ 0 0
$$916$$ −36.2650 −1.19823
$$917$$ −7.19806 −0.237701
$$918$$ 0 0
$$919$$ 40.1628 1.32485 0.662425 0.749129i $$-0.269528\pi$$
0.662425 + 0.749129i $$0.269528\pi$$
$$920$$ 10.2569 0.338162
$$921$$ 0 0
$$922$$ 5.26537 0.173406
$$923$$ 0 0
$$924$$ 0 0
$$925$$ 9.76897 0.321202
$$926$$ 5.92815 0.194811
$$927$$ 0 0
$$928$$ −20.8974 −0.685992
$$929$$ −23.7690 −0.779835 −0.389917 0.920850i $$-0.627496\pi$$
−0.389917 + 0.920850i $$0.627496\pi$$
$$930$$ 0 0
$$931$$ −0.758276 −0.0248515
$$932$$ −45.0545 −1.47581
$$933$$ 0 0
$$934$$ 6.96035 0.227750
$$935$$ −5.04995 −0.165151
$$936$$ 0 0
$$937$$ −7.43803 −0.242990 −0.121495 0.992592i $$-0.538769\pi$$
−0.121495 + 0.992592i $$0.538769\pi$$
$$938$$ −1.71273 −0.0559226
$$939$$ 0 0
$$940$$ 9.45941 0.308532
$$941$$ 19.3528 0.630884 0.315442 0.948945i $$-0.397847\pi$$
0.315442 + 0.948945i $$0.397847\pi$$
$$942$$ 0 0
$$943$$ −32.8189 −1.06873
$$944$$ −7.38542 −0.240375
$$945$$ 0 0
$$946$$ 0.125822 0.00409082
$$947$$ −13.9171 −0.452244 −0.226122 0.974099i $$-0.572605\pi$$
−0.226122 + 0.974099i $$0.572605\pi$$
$$948$$ 0 0
$$949$$ 0 0
$$950$$ 0.0392613 0.00127381
$$951$$ 0 0
$$952$$ 6.47464 0.209844
$$953$$ 10.6271 0.344247 0.172124 0.985075i $$-0.444937\pi$$
0.172124 + 0.985075i $$0.444937\pi$$
$$954$$ 0 0
$$955$$ −13.9541 −0.451543
$$956$$ 35.2017 1.13850
$$957$$ 0 0
$$958$$ 13.9318 0.450115
$$959$$ −2.23770 −0.0722593
$$960$$ 0 0
$$961$$ 68.4746 2.20886
$$962$$ 0 0
$$963$$ 0 0
$$964$$ −11.5246 −0.371182
$$965$$ −23.7493 −0.764518
$$966$$ 0 0
$$967$$ 51.6771 1.66182 0.830912 0.556404i $$-0.187819\pi$$
0.830912 + 0.556404i $$0.187819\pi$$
$$968$$ 13.9127 0.447170
$$969$$ 0 0
$$970$$ −3.36618 −0.108082
$$971$$ 42.8974 1.37664 0.688322 0.725405i $$-0.258348\pi$$
0.688322 + 0.725405i $$0.258348\pi$$
$$972$$ 0 0
$$973$$ 9.77525 0.313380
$$974$$ 8.17843 0.262054
$$975$$ 0 0
$$976$$ −13.9607 −0.446872
$$977$$ −18.1651 −0.581153 −0.290576 0.956852i $$-0.593847\pi$$
−0.290576 + 0.956852i $$0.593847\pi$$
$$978$$ 0 0
$$979$$ 9.20700 0.294257
$$980$$ −12.3702 −0.395151
$$981$$ 0 0
$$982$$ −12.4983 −0.398836
$$983$$ 10.8582 0.346322 0.173161 0.984894i $$-0.444602\pi$$
0.173161 + 0.984894i $$0.444602\pi$$
$$984$$ 0 0
$$985$$ 15.8082 0.503692
$$986$$ 14.0000 0.445851
$$987$$ 0 0
$$988$$ 0 0
$$989$$ −4.23103 −0.134539
$$990$$ 0 0
$$991$$ −22.3725 −0.710685 −0.355342 0.934736i $$-0.615636\pi$$
−0.355342 + 0.934736i $$0.615636\pi$$
$$992$$ −37.5905 −1.19350
$$993$$ 0 0
$$994$$ −1.64088 −0.0520455
$$995$$ −8.76897 −0.277995
$$996$$ 0 0
$$997$$ −24.2373 −0.767604 −0.383802 0.923415i $$-0.625385\pi$$
−0.383802 + 0.923415i $$0.625385\pi$$
$$998$$ 11.8349 0.374628
$$999$$ 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.bv.1.2 3
3.2 odd 2 2535.2.a.bb.1.2 3
13.3 even 3 585.2.j.f.451.2 6
13.9 even 3 585.2.j.f.406.2 6
13.12 even 2 7605.2.a.bw.1.2 3
39.29 odd 6 195.2.i.d.61.2 yes 6
39.35 odd 6 195.2.i.d.16.2 6
39.38 odd 2 2535.2.a.ba.1.2 3
195.29 odd 6 975.2.i.l.451.2 6
195.68 even 12 975.2.bb.k.724.3 12
195.74 odd 6 975.2.i.l.601.2 6
195.107 even 12 975.2.bb.k.724.4 12
195.113 even 12 975.2.bb.k.874.4 12
195.152 even 12 975.2.bb.k.874.3 12

By twisted newform
Twist Min Dim Char Parity Ord Type
195.2.i.d.16.2 6 39.35 odd 6
195.2.i.d.61.2 yes 6 39.29 odd 6
585.2.j.f.406.2 6 13.9 even 3
585.2.j.f.451.2 6 13.3 even 3
975.2.i.l.451.2 6 195.29 odd 6
975.2.i.l.601.2 6 195.74 odd 6
975.2.bb.k.724.3 12 195.68 even 12
975.2.bb.k.724.4 12 195.107 even 12
975.2.bb.k.874.3 12 195.152 even 12
975.2.bb.k.874.4 12 195.113 even 12
2535.2.a.ba.1.2 3 39.38 odd 2
2535.2.a.bb.1.2 3 3.2 odd 2
7605.2.a.bv.1.2 3 1.1 even 1 trivial
7605.2.a.bw.1.2 3 13.12 even 2