# Properties

 Label 11.4.a.a.1.1 Level $11$ Weight $4$ Character 11.1 Self dual yes Analytic conductor $0.649$ Analytic rank $0$ Dimension $2$ CM no Inner twists $1$

# Learn more

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [11,4,Mod(1,11)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(11, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("11.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$11$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 11.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: $$0.649021010063$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(\zeta_{12})^+$$ comment: defining polynomial  gp: f.mod \\ as an extension of the character field Defining polynomial: $$x^{2} - 3$$ x^2 - 3 Coefficient ring: $$\Z[a_1, a_2]$$ Coefficient ring index: $$1$$ Twist minimal: yes Fricke sign: $$1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

 Embedding label 1.1 Root $$-1.73205$$ of defining polynomial Character $$\chi$$ $$=$$ 11.1

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q-0.732051 q^{2} +5.92820 q^{3} -7.46410 q^{4} -12.8564 q^{5} -4.33975 q^{6} +16.9282 q^{7} +11.3205 q^{8} +8.14359 q^{9} +O(q^{10})$$ $$q-0.732051 q^{2} +5.92820 q^{3} -7.46410 q^{4} -12.8564 q^{5} -4.33975 q^{6} +16.9282 q^{7} +11.3205 q^{8} +8.14359 q^{9} +9.41154 q^{10} -11.0000 q^{11} -44.2487 q^{12} +74.6410 q^{13} -12.3923 q^{14} -76.2154 q^{15} +51.4256 q^{16} -82.7846 q^{17} -5.96152 q^{18} -67.9230 q^{19} +95.9615 q^{20} +100.354 q^{21} +8.05256 q^{22} +13.3538 q^{23} +67.1103 q^{24} +40.2872 q^{25} -54.6410 q^{26} -111.785 q^{27} -126.354 q^{28} +168.995 q^{29} +55.7935 q^{30} -65.4974 q^{31} -128.210 q^{32} -65.2102 q^{33} +60.6025 q^{34} -217.636 q^{35} -60.7846 q^{36} +40.8564 q^{37} +49.7231 q^{38} +442.487 q^{39} -145.541 q^{40} +274.928 q^{41} -73.4641 q^{42} -2.28719 q^{43} +82.1051 q^{44} -104.697 q^{45} -9.77568 q^{46} +71.8461 q^{47} +304.862 q^{48} -56.4359 q^{49} -29.4923 q^{50} -490.764 q^{51} -557.128 q^{52} -149.005 q^{53} +81.8320 q^{54} +141.420 q^{55} +191.636 q^{56} -402.662 q^{57} -123.713 q^{58} +545.631 q^{59} +568.879 q^{60} +101.303 q^{61} +47.9474 q^{62} +137.856 q^{63} -317.549 q^{64} -959.615 q^{65} +47.7372 q^{66} +411.641 q^{67} +617.913 q^{68} +79.1642 q^{69} +159.321 q^{70} -470.636 q^{71} +92.1896 q^{72} +610.600 q^{73} -29.9090 q^{74} +238.831 q^{75} +506.985 q^{76} -186.210 q^{77} -323.923 q^{78} -978.225 q^{79} -661.149 q^{80} -882.559 q^{81} -201.261 q^{82} +26.1539 q^{83} -749.051 q^{84} +1064.31 q^{85} +1.67434 q^{86} +1001.84 q^{87} -124.526 q^{88} -352.887 q^{89} +76.6438 q^{90} +1263.54 q^{91} -99.6743 q^{92} -388.282 q^{93} -52.5950 q^{94} +873.246 q^{95} -760.056 q^{96} +847.585 q^{97} +41.3140 q^{98} -89.5795 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q + 2 q^{2} - 2 q^{3} - 8 q^{4} + 2 q^{5} - 26 q^{6} + 20 q^{7} - 12 q^{8} + 44 q^{9}+O(q^{10})$$ 2 * q + 2 * q^2 - 2 * q^3 - 8 * q^4 + 2 * q^5 - 26 * q^6 + 20 * q^7 - 12 * q^8 + 44 * q^9 $$2 q + 2 q^{2} - 2 q^{3} - 8 q^{4} + 2 q^{5} - 26 q^{6} + 20 q^{7} - 12 q^{8} + 44 q^{9} + 50 q^{10} - 22 q^{11} - 40 q^{12} + 80 q^{13} - 4 q^{14} - 194 q^{15} - 8 q^{16} - 124 q^{17} + 92 q^{18} + 72 q^{19} + 88 q^{20} + 76 q^{21} - 22 q^{22} - 98 q^{23} + 252 q^{24} + 136 q^{25} - 40 q^{26} - 182 q^{27} - 128 q^{28} + 144 q^{29} - 266 q^{30} - 34 q^{31} - 104 q^{32} + 22 q^{33} - 52 q^{34} - 172 q^{35} - 80 q^{36} + 54 q^{37} + 432 q^{38} + 400 q^{39} - 492 q^{40} + 536 q^{41} - 140 q^{42} - 60 q^{43} + 88 q^{44} + 428 q^{45} - 314 q^{46} - 272 q^{47} + 776 q^{48} - 390 q^{49} + 232 q^{50} - 164 q^{51} - 560 q^{52} - 492 q^{53} - 110 q^{54} - 22 q^{55} + 120 q^{56} - 1512 q^{57} - 192 q^{58} + 634 q^{59} + 632 q^{60} + 840 q^{61} + 134 q^{62} + 248 q^{63} + 224 q^{64} - 880 q^{65} + 286 q^{66} + 754 q^{67} + 640 q^{68} + 962 q^{69} + 284 q^{70} - 678 q^{71} - 744 q^{72} - 400 q^{73} + 6 q^{74} - 520 q^{75} + 432 q^{76} - 220 q^{77} - 440 q^{78} + 316 q^{79} - 1544 q^{80} - 1294 q^{81} + 512 q^{82} + 468 q^{83} - 736 q^{84} + 452 q^{85} - 156 q^{86} + 1200 q^{87} + 132 q^{88} - 1842 q^{89} + 1532 q^{90} + 1280 q^{91} - 40 q^{92} - 638 q^{93} - 992 q^{94} + 2952 q^{95} - 952 q^{96} + 2194 q^{97} - 870 q^{98} - 484 q^{99}+O(q^{100})$$ 2 * q + 2 * q^2 - 2 * q^3 - 8 * q^4 + 2 * q^5 - 26 * q^6 + 20 * q^7 - 12 * q^8 + 44 * q^9 + 50 * q^10 - 22 * q^11 - 40 * q^12 + 80 * q^13 - 4 * q^14 - 194 * q^15 - 8 * q^16 - 124 * q^17 + 92 * q^18 + 72 * q^19 + 88 * q^20 + 76 * q^21 - 22 * q^22 - 98 * q^23 + 252 * q^24 + 136 * q^25 - 40 * q^26 - 182 * q^27 - 128 * q^28 + 144 * q^29 - 266 * q^30 - 34 * q^31 - 104 * q^32 + 22 * q^33 - 52 * q^34 - 172 * q^35 - 80 * q^36 + 54 * q^37 + 432 * q^38 + 400 * q^39 - 492 * q^40 + 536 * q^41 - 140 * q^42 - 60 * q^43 + 88 * q^44 + 428 * q^45 - 314 * q^46 - 272 * q^47 + 776 * q^48 - 390 * q^49 + 232 * q^50 - 164 * q^51 - 560 * q^52 - 492 * q^53 - 110 * q^54 - 22 * q^55 + 120 * q^56 - 1512 * q^57 - 192 * q^58 + 634 * q^59 + 632 * q^60 + 840 * q^61 + 134 * q^62 + 248 * q^63 + 224 * q^64 - 880 * q^65 + 286 * q^66 + 754 * q^67 + 640 * q^68 + 962 * q^69 + 284 * q^70 - 678 * q^71 - 744 * q^72 - 400 * q^73 + 6 * q^74 - 520 * q^75 + 432 * q^76 - 220 * q^77 - 440 * q^78 + 316 * q^79 - 1544 * q^80 - 1294 * q^81 + 512 * q^82 + 468 * q^83 - 736 * q^84 + 452 * q^85 - 156 * q^86 + 1200 * q^87 + 132 * q^88 - 1842 * q^89 + 1532 * q^90 + 1280 * q^91 - 40 * q^92 - 638 * q^93 - 992 * q^94 + 2952 * q^95 - 952 * q^96 + 2194 * q^97 - 870 * q^98 - 484 * q^99

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −0.732051 −0.258819 −0.129410 0.991591i $$-0.541308\pi$$
−0.129410 + 0.991591i $$0.541308\pi$$
$$3$$ 5.92820 1.14088 0.570442 0.821338i $$-0.306772\pi$$
0.570442 + 0.821338i $$0.306772\pi$$
$$4$$ −7.46410 −0.933013
$$5$$ −12.8564 −1.14991 −0.574956 0.818184i $$-0.694981\pi$$
−0.574956 + 0.818184i $$0.694981\pi$$
$$6$$ −4.33975 −0.295282
$$7$$ 16.9282 0.914037 0.457019 0.889457i $$-0.348917\pi$$
0.457019 + 0.889457i $$0.348917\pi$$
$$8$$ 11.3205 0.500301
$$9$$ 8.14359 0.301615
$$10$$ 9.41154 0.297619
$$11$$ −11.0000 −0.301511
$$12$$ −44.2487 −1.06446
$$13$$ 74.6410 1.59244 0.796219 0.605009i $$-0.206830\pi$$
0.796219 + 0.605009i $$0.206830\pi$$
$$14$$ −12.3923 −0.236570
$$15$$ −76.2154 −1.31192
$$16$$ 51.4256 0.803525
$$17$$ −82.7846 −1.18107 −0.590536 0.807011i $$-0.701084\pi$$
−0.590536 + 0.807011i $$0.701084\pi$$
$$18$$ −5.96152 −0.0780636
$$19$$ −67.9230 −0.820138 −0.410069 0.912055i $$-0.634495\pi$$
−0.410069 + 0.912055i $$0.634495\pi$$
$$20$$ 95.9615 1.07288
$$21$$ 100.354 1.04281
$$22$$ 8.05256 0.0780369
$$23$$ 13.3538 0.121064 0.0605319 0.998166i $$-0.480720\pi$$
0.0605319 + 0.998166i $$0.480720\pi$$
$$24$$ 67.1103 0.570784
$$25$$ 40.2872 0.322297
$$26$$ −54.6410 −0.412153
$$27$$ −111.785 −0.796776
$$28$$ −126.354 −0.852808
$$29$$ 168.995 1.08212 0.541061 0.840983i $$-0.318023\pi$$
0.541061 + 0.840983i $$0.318023\pi$$
$$30$$ 55.7935 0.339549
$$31$$ −65.4974 −0.379474 −0.189737 0.981835i $$-0.560763\pi$$
−0.189737 + 0.981835i $$0.560763\pi$$
$$32$$ −128.210 −0.708268
$$33$$ −65.2102 −0.343989
$$34$$ 60.6025 0.305684
$$35$$ −217.636 −1.05106
$$36$$ −60.7846 −0.281410
$$37$$ 40.8564 0.181534 0.0907669 0.995872i $$-0.471068\pi$$
0.0907669 + 0.995872i $$0.471068\pi$$
$$38$$ 49.7231 0.212267
$$39$$ 442.487 1.81679
$$40$$ −145.541 −0.575302
$$41$$ 274.928 1.04723 0.523617 0.851954i $$-0.324582\pi$$
0.523617 + 0.851954i $$0.324582\pi$$
$$42$$ −73.4641 −0.269899
$$43$$ −2.28719 −0.00811146 −0.00405573 0.999992i $$-0.501291\pi$$
−0.00405573 + 0.999992i $$0.501291\pi$$
$$44$$ 82.1051 0.281314
$$45$$ −104.697 −0.346830
$$46$$ −9.77568 −0.0313336
$$47$$ 71.8461 0.222975 0.111488 0.993766i $$-0.464438\pi$$
0.111488 + 0.993766i $$0.464438\pi$$
$$48$$ 304.862 0.916729
$$49$$ −56.4359 −0.164536
$$50$$ −29.4923 −0.0834167
$$51$$ −490.764 −1.34746
$$52$$ −557.128 −1.48576
$$53$$ −149.005 −0.386178 −0.193089 0.981181i $$-0.561851\pi$$
−0.193089 + 0.981181i $$0.561851\pi$$
$$54$$ 81.8320 0.206221
$$55$$ 141.420 0.346711
$$56$$ 191.636 0.457293
$$57$$ −402.662 −0.935681
$$58$$ −123.713 −0.280074
$$59$$ 545.631 1.20398 0.601992 0.798502i $$-0.294374\pi$$
0.601992 + 0.798502i $$0.294374\pi$$
$$60$$ 568.879 1.22403
$$61$$ 101.303 0.212631 0.106315 0.994332i $$-0.466095\pi$$
0.106315 + 0.994332i $$0.466095\pi$$
$$62$$ 47.9474 0.0982150
$$63$$ 137.856 0.275687
$$64$$ −317.549 −0.620212
$$65$$ −959.615 −1.83116
$$66$$ 47.7372 0.0890310
$$67$$ 411.641 0.750596 0.375298 0.926904i $$-0.377540\pi$$
0.375298 + 0.926904i $$0.377540\pi$$
$$68$$ 617.913 1.10195
$$69$$ 79.1642 0.138120
$$70$$ 159.321 0.272035
$$71$$ −470.636 −0.786679 −0.393339 0.919393i $$-0.628680\pi$$
−0.393339 + 0.919393i $$0.628680\pi$$
$$72$$ 92.1896 0.150898
$$73$$ 610.600 0.978977 0.489488 0.872010i $$-0.337184\pi$$
0.489488 + 0.872010i $$0.337184\pi$$
$$74$$ −29.9090 −0.0469844
$$75$$ 238.831 0.367704
$$76$$ 506.985 0.765199
$$77$$ −186.210 −0.275593
$$78$$ −323.923 −0.470219
$$79$$ −978.225 −1.39315 −0.696576 0.717483i $$-0.745294\pi$$
−0.696576 + 0.717483i $$0.745294\pi$$
$$80$$ −661.149 −0.923983
$$81$$ −882.559 −1.21064
$$82$$ −201.261 −0.271044
$$83$$ 26.1539 0.0345875 0.0172938 0.999850i $$-0.494495\pi$$
0.0172938 + 0.999850i $$0.494495\pi$$
$$84$$ −749.051 −0.972955
$$85$$ 1064.31 1.35813
$$86$$ 1.67434 0.00209940
$$87$$ 1001.84 1.23458
$$88$$ −124.526 −0.150846
$$89$$ −352.887 −0.420292 −0.210146 0.977670i $$-0.567394\pi$$
−0.210146 + 0.977670i $$0.567394\pi$$
$$90$$ 76.6438 0.0897663
$$91$$ 1263.54 1.45555
$$92$$ −99.6743 −0.112954
$$93$$ −388.282 −0.432935
$$94$$ −52.5950 −0.0577102
$$95$$ 873.246 0.943086
$$96$$ −760.056 −0.808051
$$97$$ 847.585 0.887208 0.443604 0.896223i $$-0.353700\pi$$
0.443604 + 0.896223i $$0.353700\pi$$
$$98$$ 41.3140 0.0425851
$$99$$ −89.5795 −0.0909402
$$100$$ −300.708 −0.300708
$$101$$ 1293.46 1.27430 0.637150 0.770740i $$-0.280113\pi$$
0.637150 + 0.770740i $$0.280113\pi$$
$$102$$ 359.264 0.348750
$$103$$ −1725.24 −1.65042 −0.825209 0.564828i $$-0.808943\pi$$
−0.825209 + 0.564828i $$0.808943\pi$$
$$104$$ 844.974 0.796697
$$105$$ −1290.19 −1.19914
$$106$$ 109.079 0.0999502
$$107$$ −484.179 −0.437452 −0.218726 0.975786i $$-0.570190\pi$$
−0.218726 + 0.975786i $$0.570190\pi$$
$$108$$ 834.372 0.743402
$$109$$ −64.2563 −0.0564645 −0.0282323 0.999601i $$-0.508988\pi$$
−0.0282323 + 0.999601i $$0.508988\pi$$
$$110$$ −103.527 −0.0897355
$$111$$ 242.205 0.207109
$$112$$ 870.543 0.734452
$$113$$ −2005.08 −1.66922 −0.834612 0.550839i $$-0.814308\pi$$
−0.834612 + 0.550839i $$0.814308\pi$$
$$114$$ 294.769 0.242172
$$115$$ −171.682 −0.139213
$$116$$ −1261.39 −1.00963
$$117$$ 607.846 0.480302
$$118$$ −399.429 −0.311614
$$119$$ −1401.39 −1.07954
$$120$$ −862.797 −0.656352
$$121$$ 121.000 0.0909091
$$122$$ −74.1587 −0.0550329
$$123$$ 1629.83 1.19477
$$124$$ 488.879 0.354054
$$125$$ 1089.10 0.779298
$$126$$ −100.918 −0.0713530
$$127$$ 109.605 0.0765816 0.0382908 0.999267i $$-0.487809\pi$$
0.0382908 + 0.999267i $$0.487809\pi$$
$$128$$ 1258.14 0.868791
$$129$$ −13.5589 −0.00925423
$$130$$ 702.487 0.473940
$$131$$ 1156.71 0.771469 0.385734 0.922610i $$-0.373948\pi$$
0.385734 + 0.922610i $$0.373948\pi$$
$$132$$ 486.736 0.320946
$$133$$ −1149.82 −0.749636
$$134$$ −301.342 −0.194269
$$135$$ 1437.15 0.916223
$$136$$ −937.164 −0.590891
$$137$$ 198.323 0.123678 0.0618391 0.998086i $$-0.480303\pi$$
0.0618391 + 0.998086i $$0.480303\pi$$
$$138$$ −57.9522 −0.0357480
$$139$$ −2900.14 −1.76969 −0.884844 0.465888i $$-0.845735\pi$$
−0.884844 + 0.465888i $$0.845735\pi$$
$$140$$ 1624.46 0.980654
$$141$$ 425.918 0.254389
$$142$$ 344.529 0.203607
$$143$$ −821.051 −0.480138
$$144$$ 418.789 0.242355
$$145$$ −2172.67 −1.24435
$$146$$ −446.990 −0.253378
$$147$$ −334.564 −0.187717
$$148$$ −304.956 −0.169373
$$149$$ 3488.34 1.91796 0.958980 0.283472i $$-0.0914864\pi$$
0.958980 + 0.283472i $$0.0914864\pi$$
$$150$$ −174.836 −0.0951687
$$151$$ −1163.32 −0.626953 −0.313477 0.949596i $$-0.601494\pi$$
−0.313477 + 0.949596i $$0.601494\pi$$
$$152$$ −768.923 −0.410315
$$153$$ −674.164 −0.356228
$$154$$ 136.315 0.0713286
$$155$$ 842.061 0.436361
$$156$$ −3302.77 −1.69508
$$157$$ 342.057 0.173880 0.0869398 0.996214i $$-0.472291\pi$$
0.0869398 + 0.996214i $$0.472291\pi$$
$$158$$ 716.111 0.360574
$$159$$ −883.333 −0.440584
$$160$$ 1648.32 0.814446
$$161$$ 226.056 0.110657
$$162$$ 646.078 0.313338
$$163$$ −1394.89 −0.670285 −0.335142 0.942167i $$-0.608784\pi$$
−0.335142 + 0.942167i $$0.608784\pi$$
$$164$$ −2052.09 −0.977082
$$165$$ 838.369 0.395557
$$166$$ −19.1460 −0.00895191
$$167$$ 478.703 0.221815 0.110908 0.993831i $$-0.464624\pi$$
0.110908 + 0.993831i $$0.464624\pi$$
$$168$$ 1136.06 0.521718
$$169$$ 3374.28 1.53586
$$170$$ −779.131 −0.351509
$$171$$ −553.138 −0.247365
$$172$$ 17.0718 0.00756809
$$173$$ 1808.58 0.794822 0.397411 0.917641i $$-0.369909\pi$$
0.397411 + 0.917641i $$0.369909\pi$$
$$174$$ −733.395 −0.319532
$$175$$ 681.990 0.294592
$$176$$ −565.682 −0.242272
$$177$$ 3234.61 1.37361
$$178$$ 258.331 0.108780
$$179$$ −4429.85 −1.84973 −0.924867 0.380292i $$-0.875824\pi$$
−0.924867 + 0.380292i $$0.875824\pi$$
$$180$$ 781.472 0.323597
$$181$$ 3409.17 1.40001 0.700005 0.714138i $$-0.253181\pi$$
0.700005 + 0.714138i $$0.253181\pi$$
$$182$$ −924.974 −0.376723
$$183$$ 600.543 0.242587
$$184$$ 151.172 0.0605682
$$185$$ −525.267 −0.208748
$$186$$ 284.242 0.112052
$$187$$ 910.631 0.356106
$$188$$ −536.267 −0.208039
$$189$$ −1892.31 −0.728283
$$190$$ −639.261 −0.244089
$$191$$ 2923.75 1.10762 0.553810 0.832643i $$-0.313173\pi$$
0.553810 + 0.832643i $$0.313173\pi$$
$$192$$ −1882.49 −0.707590
$$193$$ −2484.18 −0.926505 −0.463253 0.886226i $$-0.653318\pi$$
−0.463253 + 0.886226i $$0.653318\pi$$
$$194$$ −620.475 −0.229626
$$195$$ −5688.79 −2.08914
$$196$$ 421.244 0.153514
$$197$$ −5125.67 −1.85375 −0.926876 0.375369i $$-0.877516\pi$$
−0.926876 + 0.375369i $$0.877516\pi$$
$$198$$ 65.5768 0.0235371
$$199$$ −7.69219 −0.00274013 −0.00137006 0.999999i $$-0.500436\pi$$
−0.00137006 + 0.999999i $$0.500436\pi$$
$$200$$ 456.071 0.161246
$$201$$ 2440.29 0.856343
$$202$$ −946.879 −0.329813
$$203$$ 2860.78 0.989100
$$204$$ 3663.11 1.25720
$$205$$ −3534.59 −1.20423
$$206$$ 1262.96 0.427160
$$207$$ 108.748 0.0365146
$$208$$ 3838.46 1.27956
$$209$$ 747.154 0.247281
$$210$$ 944.484 0.310360
$$211$$ 3107.34 1.01383 0.506915 0.861996i $$-0.330786\pi$$
0.506915 + 0.861996i $$0.330786\pi$$
$$212$$ 1112.19 0.360309
$$213$$ −2790.03 −0.897509
$$214$$ 354.444 0.113221
$$215$$ 29.4050 0.00932746
$$216$$ −1265.46 −0.398628
$$217$$ −1108.75 −0.346853
$$218$$ 47.0388 0.0146141
$$219$$ 3619.76 1.11690
$$220$$ −1055.58 −0.323486
$$221$$ −6179.13 −1.88078
$$222$$ −177.306 −0.0536037
$$223$$ −12.3185 −0.00369913 −0.00184957 0.999998i $$-0.500589\pi$$
−0.00184957 + 0.999998i $$0.500589\pi$$
$$224$$ −2170.37 −0.647383
$$225$$ 328.082 0.0972096
$$226$$ 1467.82 0.432027
$$227$$ 4615.90 1.34964 0.674820 0.737983i $$-0.264221\pi$$
0.674820 + 0.737983i $$0.264221\pi$$
$$228$$ 3005.51 0.873003
$$229$$ 5074.63 1.46437 0.732186 0.681105i $$-0.238500\pi$$
0.732186 + 0.681105i $$0.238500\pi$$
$$230$$ 125.680 0.0360309
$$231$$ −1103.89 −0.314419
$$232$$ 1913.11 0.541386
$$233$$ 211.683 0.0595184 0.0297592 0.999557i $$-0.490526\pi$$
0.0297592 + 0.999557i $$0.490526\pi$$
$$234$$ −444.974 −0.124311
$$235$$ −923.683 −0.256402
$$236$$ −4072.64 −1.12333
$$237$$ −5799.12 −1.58942
$$238$$ 1025.89 0.279406
$$239$$ 4312.49 1.16716 0.583581 0.812055i $$-0.301651\pi$$
0.583581 + 0.812055i $$0.301651\pi$$
$$240$$ −3919.42 −1.05416
$$241$$ −996.584 −0.266372 −0.133186 0.991091i $$-0.542521\pi$$
−0.133186 + 0.991091i $$0.542521\pi$$
$$242$$ −88.5781 −0.0235290
$$243$$ −2213.80 −0.584426
$$244$$ −756.133 −0.198387
$$245$$ 725.563 0.189202
$$246$$ −1193.12 −0.309230
$$247$$ −5069.85 −1.30602
$$248$$ −741.464 −0.189851
$$249$$ 155.046 0.0394603
$$250$$ −797.278 −0.201697
$$251$$ −276.892 −0.0696306 −0.0348153 0.999394i $$-0.511084\pi$$
−0.0348153 + 0.999394i $$0.511084\pi$$
$$252$$ −1028.97 −0.257219
$$253$$ −146.892 −0.0365021
$$254$$ −80.2364 −0.0198208
$$255$$ 6309.46 1.54947
$$256$$ 1619.36 0.395352
$$257$$ −3235.18 −0.785233 −0.392617 0.919702i $$-0.628430\pi$$
−0.392617 + 0.919702i $$0.628430\pi$$
$$258$$ 9.92581 0.00239517
$$259$$ 691.626 0.165929
$$260$$ 7162.67 1.70850
$$261$$ 1376.23 0.326384
$$262$$ −846.772 −0.199671
$$263$$ 207.944 0.0487544 0.0243772 0.999703i $$-0.492240\pi$$
0.0243772 + 0.999703i $$0.492240\pi$$
$$264$$ −738.213 −0.172098
$$265$$ 1915.67 0.444071
$$266$$ 841.723 0.194020
$$267$$ −2091.99 −0.479504
$$268$$ −3072.53 −0.700316
$$269$$ 5033.04 1.14078 0.570390 0.821374i $$-0.306792\pi$$
0.570390 + 0.821374i $$0.306792\pi$$
$$270$$ −1052.07 −0.237136
$$271$$ 1487.01 0.333319 0.166660 0.986015i $$-0.446702\pi$$
0.166660 + 0.986015i $$0.446702\pi$$
$$272$$ −4257.25 −0.949021
$$273$$ 7490.51 1.66061
$$274$$ −145.183 −0.0320102
$$275$$ −443.159 −0.0971764
$$276$$ −590.890 −0.128867
$$277$$ −235.836 −0.0511552 −0.0255776 0.999673i $$-0.508142\pi$$
−0.0255776 + 0.999673i $$0.508142\pi$$
$$278$$ 2123.05 0.458029
$$279$$ −533.384 −0.114455
$$280$$ −2463.75 −0.525847
$$281$$ −4915.01 −1.04343 −0.521717 0.853118i $$-0.674708\pi$$
−0.521717 + 0.853118i $$0.674708\pi$$
$$282$$ −311.794 −0.0658406
$$283$$ −5199.56 −1.09216 −0.546081 0.837733i $$-0.683881\pi$$
−0.546081 + 0.837733i $$0.683881\pi$$
$$284$$ 3512.87 0.733981
$$285$$ 5176.78 1.07595
$$286$$ 601.051 0.124269
$$287$$ 4654.04 0.957210
$$288$$ −1044.09 −0.213624
$$289$$ 1940.29 0.394930
$$290$$ 1590.50 0.322060
$$291$$ 5024.65 1.01220
$$292$$ −4557.58 −0.913398
$$293$$ −8880.92 −1.77075 −0.885373 0.464881i $$-0.846097\pi$$
−0.885373 + 0.464881i $$0.846097\pi$$
$$294$$ 244.918 0.0485846
$$295$$ −7014.85 −1.38448
$$296$$ 462.515 0.0908215
$$297$$ 1229.63 0.240237
$$298$$ −2553.64 −0.496405
$$299$$ 996.743 0.192786
$$300$$ −1782.66 −0.343072
$$301$$ −38.7180 −0.00741417
$$302$$ 851.612 0.162267
$$303$$ 7667.90 1.45383
$$304$$ −3492.99 −0.659001
$$305$$ −1302.39 −0.244507
$$306$$ 493.522 0.0921987
$$307$$ −1497.93 −0.278474 −0.139237 0.990259i $$-0.544465\pi$$
−0.139237 + 0.990259i $$0.544465\pi$$
$$308$$ 1389.89 0.257131
$$309$$ −10227.6 −1.88293
$$310$$ −616.432 −0.112939
$$311$$ −7484.71 −1.36469 −0.682345 0.731030i $$-0.739040\pi$$
−0.682345 + 0.731030i $$0.739040\pi$$
$$312$$ 5009.18 0.908939
$$313$$ −658.363 −0.118891 −0.0594455 0.998232i $$-0.518933\pi$$
−0.0594455 + 0.998232i $$0.518933\pi$$
$$314$$ −250.403 −0.0450034
$$315$$ −1772.34 −0.317016
$$316$$ 7301.57 1.29983
$$317$$ 233.708 0.0414080 0.0207040 0.999786i $$-0.493409\pi$$
0.0207040 + 0.999786i $$0.493409\pi$$
$$318$$ 646.645 0.114032
$$319$$ −1858.94 −0.326272
$$320$$ 4082.53 0.713189
$$321$$ −2870.31 −0.499082
$$322$$ −165.485 −0.0286401
$$323$$ 5622.98 0.968641
$$324$$ 6587.51 1.12955
$$325$$ 3007.08 0.513239
$$326$$ 1021.13 0.173482
$$327$$ −380.924 −0.0644194
$$328$$ 3112.33 0.523931
$$329$$ 1216.23 0.203808
$$330$$ −613.729 −0.102378
$$331$$ 8532.95 1.41696 0.708480 0.705731i $$-0.249381\pi$$
0.708480 + 0.705731i $$0.249381\pi$$
$$332$$ −195.215 −0.0322706
$$333$$ 332.718 0.0547533
$$334$$ −350.435 −0.0574100
$$335$$ −5292.22 −0.863120
$$336$$ 5160.76 0.837924
$$337$$ 11691.2 1.88979 0.944895 0.327373i $$-0.106163\pi$$
0.944895 + 0.327373i $$0.106163\pi$$
$$338$$ −2470.15 −0.397509
$$339$$ −11886.5 −1.90439
$$340$$ −7944.14 −1.26715
$$341$$ 720.472 0.114416
$$342$$ 404.925 0.0640229
$$343$$ −6761.73 −1.06443
$$344$$ −25.8921 −0.00405817
$$345$$ −1017.77 −0.158825
$$346$$ −1323.98 −0.205715
$$347$$ 4598.79 0.711459 0.355729 0.934589i $$-0.384232\pi$$
0.355729 + 0.934589i $$0.384232\pi$$
$$348$$ −7477.80 −1.15187
$$349$$ 6720.27 1.03074 0.515369 0.856968i $$-0.327655\pi$$
0.515369 + 0.856968i $$0.327655\pi$$
$$350$$ −499.251 −0.0762460
$$351$$ −8343.72 −1.26882
$$352$$ 1410.31 0.213551
$$353$$ 5738.70 0.865270 0.432635 0.901569i $$-0.357584\pi$$
0.432635 + 0.901569i $$0.357584\pi$$
$$354$$ −2367.90 −0.355515
$$355$$ 6050.69 0.904611
$$356$$ 2633.99 0.392138
$$357$$ −8307.75 −1.23163
$$358$$ 3242.87 0.478746
$$359$$ −4115.27 −0.605001 −0.302501 0.953149i $$-0.597821\pi$$
−0.302501 + 0.953149i $$0.597821\pi$$
$$360$$ −1185.23 −0.173519
$$361$$ −2245.46 −0.327374
$$362$$ −2495.69 −0.362349
$$363$$ 717.313 0.103717
$$364$$ −9431.18 −1.35804
$$365$$ −7850.12 −1.12574
$$366$$ −439.628 −0.0627861
$$367$$ 9662.99 1.37440 0.687199 0.726469i $$-0.258840\pi$$
0.687199 + 0.726469i $$0.258840\pi$$
$$368$$ 686.729 0.0972778
$$369$$ 2238.90 0.315861
$$370$$ 384.522 0.0540279
$$371$$ −2522.39 −0.352981
$$372$$ 2898.18 0.403934
$$373$$ −141.780 −0.0196812 −0.00984062 0.999952i $$-0.503132\pi$$
−0.00984062 + 0.999952i $$0.503132\pi$$
$$374$$ −666.628 −0.0921671
$$375$$ 6456.42 0.889088
$$376$$ 813.334 0.111555
$$377$$ 12613.9 1.72321
$$378$$ 1385.27 0.188494
$$379$$ −2819.73 −0.382163 −0.191082 0.981574i $$-0.561200\pi$$
−0.191082 + 0.981574i $$0.561200\pi$$
$$380$$ −6518.00 −0.879911
$$381$$ 649.760 0.0873707
$$382$$ −2140.34 −0.286673
$$383$$ −6337.84 −0.845557 −0.422778 0.906233i $$-0.638945\pi$$
−0.422778 + 0.906233i $$0.638945\pi$$
$$384$$ 7458.53 0.991189
$$385$$ 2393.99 0.316907
$$386$$ 1818.55 0.239797
$$387$$ −18.6259 −0.00244653
$$388$$ −6326.46 −0.827776
$$389$$ −8805.25 −1.14767 −0.573836 0.818970i $$-0.694545\pi$$
−0.573836 + 0.818970i $$0.694545\pi$$
$$390$$ 4164.49 0.540710
$$391$$ −1105.49 −0.142985
$$392$$ −638.883 −0.0823176
$$393$$ 6857.23 0.880156
$$394$$ 3752.25 0.479786
$$395$$ 12576.5 1.60200
$$396$$ 668.631 0.0848484
$$397$$ 4315.26 0.545534 0.272767 0.962080i $$-0.412061\pi$$
0.272767 + 0.962080i $$0.412061\pi$$
$$398$$ 5.63108 0.000709197 0
$$399$$ −6816.34 −0.855247
$$400$$ 2071.79 0.258974
$$401$$ 361.681 0.0450411 0.0225206 0.999746i $$-0.492831\pi$$
0.0225206 + 0.999746i $$0.492831\pi$$
$$402$$ −1786.42 −0.221638
$$403$$ −4888.79 −0.604288
$$404$$ −9654.53 −1.18894
$$405$$ 11346.5 1.39213
$$406$$ −2094.24 −0.255998
$$407$$ −449.420 −0.0547345
$$408$$ −5555.70 −0.674137
$$409$$ 9220.50 1.11473 0.557365 0.830268i $$-0.311812\pi$$
0.557365 + 0.830268i $$0.311812\pi$$
$$410$$ 2587.50 0.311677
$$411$$ 1175.70 0.141102
$$412$$ 12877.4 1.53986
$$413$$ 9236.55 1.10049
$$414$$ −79.6092 −0.00945067
$$415$$ −336.245 −0.0397726
$$416$$ −9569.74 −1.12787
$$417$$ −17192.6 −2.01901
$$418$$ −546.954 −0.0640010
$$419$$ −14912.9 −1.73876 −0.869380 0.494144i $$-0.835481\pi$$
−0.869380 + 0.494144i $$0.835481\pi$$
$$420$$ 9630.11 1.11881
$$421$$ −13486.0 −1.56121 −0.780603 0.625027i $$-0.785088\pi$$
−0.780603 + 0.625027i $$0.785088\pi$$
$$422$$ −2274.73 −0.262399
$$423$$ 585.085 0.0672525
$$424$$ −1686.81 −0.193205
$$425$$ −3335.16 −0.380656
$$426$$ 2042.44 0.232292
$$427$$ 1714.87 0.194352
$$428$$ 3613.96 0.408148
$$429$$ −4867.36 −0.547782
$$430$$ −21.5260 −0.00241413
$$431$$ 406.334 0.0454116 0.0227058 0.999742i $$-0.492772\pi$$
0.0227058 + 0.999742i $$0.492772\pi$$
$$432$$ −5748.59 −0.640230
$$433$$ −1766.69 −0.196078 −0.0980391 0.995183i $$-0.531257\pi$$
−0.0980391 + 0.995183i $$0.531257\pi$$
$$434$$ 811.664 0.0897722
$$435$$ −12880.0 −1.41965
$$436$$ 479.615 0.0526821
$$437$$ −907.033 −0.0992889
$$438$$ −2649.85 −0.289075
$$439$$ 7824.19 0.850634 0.425317 0.905044i $$-0.360163\pi$$
0.425317 + 0.905044i $$0.360163\pi$$
$$440$$ 1600.95 0.173460
$$441$$ −459.591 −0.0496265
$$442$$ 4523.44 0.486783
$$443$$ 11667.9 1.25137 0.625686 0.780075i $$-0.284819\pi$$
0.625686 + 0.780075i $$0.284819\pi$$
$$444$$ −1807.84 −0.193235
$$445$$ 4536.86 0.483299
$$446$$ 9.01776 0.000957406 0
$$447$$ 20679.6 2.18817
$$448$$ −5375.53 −0.566897
$$449$$ 16975.3 1.78421 0.892107 0.451825i $$-0.149227\pi$$
0.892107 + 0.451825i $$0.149227\pi$$
$$450$$ −240.173 −0.0251597
$$451$$ −3024.21 −0.315753
$$452$$ 14966.1 1.55741
$$453$$ −6896.42 −0.715280
$$454$$ −3379.07 −0.349312
$$455$$ −16244.6 −1.67375
$$456$$ −4558.33 −0.468122
$$457$$ −16192.9 −1.65748 −0.828741 0.559632i $$-0.810943\pi$$
−0.828741 + 0.559632i $$0.810943\pi$$
$$458$$ −3714.89 −0.379007
$$459$$ 9254.05 0.941050
$$460$$ 1281.45 0.129887
$$461$$ 8586.04 0.867444 0.433722 0.901047i $$-0.357200\pi$$
0.433722 + 0.901047i $$0.357200\pi$$
$$462$$ 808.105 0.0813776
$$463$$ −7917.20 −0.794694 −0.397347 0.917668i $$-0.630069\pi$$
−0.397347 + 0.917668i $$0.630069\pi$$
$$464$$ 8690.67 0.869513
$$465$$ 4991.91 0.497837
$$466$$ −154.962 −0.0154045
$$467$$ −15155.0 −1.50169 −0.750844 0.660480i $$-0.770353\pi$$
−0.750844 + 0.660480i $$0.770353\pi$$
$$468$$ −4537.03 −0.448128
$$469$$ 6968.34 0.686073
$$470$$ 676.183 0.0663617
$$471$$ 2027.78 0.198376
$$472$$ 6176.82 0.602354
$$473$$ 25.1591 0.00244570
$$474$$ 4245.25 0.411373
$$475$$ −2736.43 −0.264328
$$476$$ 10460.2 1.00723
$$477$$ −1213.44 −0.116477
$$478$$ −3156.96 −0.302084
$$479$$ 10001.1 0.953993 0.476996 0.878905i $$-0.341725\pi$$
0.476996 + 0.878905i $$0.341725\pi$$
$$480$$ 9771.59 0.929188
$$481$$ 3049.56 0.289081
$$482$$ 729.550 0.0689421
$$483$$ 1340.11 0.126246
$$484$$ −903.156 −0.0848193
$$485$$ −10896.9 −1.02021
$$486$$ 1620.62 0.151261
$$487$$ 7044.54 0.655480 0.327740 0.944768i $$-0.393713\pi$$
0.327740 + 0.944768i $$0.393713\pi$$
$$488$$ 1146.80 0.106379
$$489$$ −8269.21 −0.764717
$$490$$ −531.149 −0.0489691
$$491$$ −13326.4 −1.22487 −0.612437 0.790520i $$-0.709811\pi$$
−0.612437 + 0.790520i $$0.709811\pi$$
$$492$$ −12165.2 −1.11474
$$493$$ −13990.2 −1.27806
$$494$$ 3711.38 0.338022
$$495$$ 1151.67 0.104573
$$496$$ −3368.25 −0.304917
$$497$$ −7967.02 −0.719054
$$498$$ −113.501 −0.0102131
$$499$$ −20069.1 −1.80044 −0.900218 0.435440i $$-0.856593\pi$$
−0.900218 + 0.435440i $$0.856593\pi$$
$$500$$ −8129.17 −0.727095
$$501$$ 2837.85 0.253065
$$502$$ 202.699 0.0180217
$$503$$ 7782.35 0.689856 0.344928 0.938629i $$-0.387903\pi$$
0.344928 + 0.938629i $$0.387903\pi$$
$$504$$ 1560.60 0.137926
$$505$$ −16629.3 −1.46533
$$506$$ 107.532 0.00944744
$$507$$ 20003.4 1.75224
$$508$$ −818.102 −0.0714516
$$509$$ −1475.93 −0.128526 −0.0642628 0.997933i $$-0.520470\pi$$
−0.0642628 + 0.997933i $$0.520470\pi$$
$$510$$ −4618.85 −0.401031
$$511$$ 10336.4 0.894821
$$512$$ −11250.6 −0.971116
$$513$$ 7592.75 0.653466
$$514$$ 2368.32 0.203233
$$515$$ 22180.4 1.89784
$$516$$ 101.205 0.00863431
$$517$$ −790.307 −0.0672295
$$518$$ −506.305 −0.0429455
$$519$$ 10721.7 0.906799
$$520$$ −10863.3 −0.916132
$$521$$ 7609.43 0.639875 0.319938 0.947439i $$-0.396338\pi$$
0.319938 + 0.947439i $$0.396338\pi$$
$$522$$ −1007.47 −0.0844744
$$523$$ 12452.9 1.04116 0.520581 0.853812i $$-0.325715\pi$$
0.520581 + 0.853812i $$0.325715\pi$$
$$524$$ −8633.82 −0.719790
$$525$$ 4042.97 0.336095
$$526$$ −152.226 −0.0126186
$$527$$ 5422.18 0.448186
$$528$$ −3353.48 −0.276404
$$529$$ −11988.7 −0.985344
$$530$$ −1402.37 −0.114934
$$531$$ 4443.39 0.363139
$$532$$ 8582.34 0.699420
$$533$$ 20520.9 1.66765
$$534$$ 1531.44 0.124105
$$535$$ 6224.81 0.503031
$$536$$ 4659.99 0.375524
$$537$$ −26261.0 −2.11033
$$538$$ −3684.44 −0.295255
$$539$$ 620.795 0.0496095
$$540$$ −10727.0 −0.854847
$$541$$ 9312.17 0.740039 0.370020 0.929024i $$-0.379351\pi$$
0.370020 + 0.929024i $$0.379351\pi$$
$$542$$ −1088.57 −0.0862693
$$543$$ 20210.3 1.59725
$$544$$ 10613.8 0.836515
$$545$$ 826.105 0.0649292
$$546$$ −5483.44 −0.429797
$$547$$ −11018.6 −0.861278 −0.430639 0.902524i $$-0.641712\pi$$
−0.430639 + 0.902524i $$0.641712\pi$$
$$548$$ −1480.31 −0.115393
$$549$$ 824.968 0.0641325
$$550$$ 324.415 0.0251511
$$551$$ −11478.6 −0.887490
$$552$$ 896.179 0.0691013
$$553$$ −16559.6 −1.27339
$$554$$ 172.644 0.0132399
$$555$$ −3113.89 −0.238157
$$556$$ 21646.9 1.65114
$$557$$ −12018.4 −0.914250 −0.457125 0.889403i $$-0.651121\pi$$
−0.457125 + 0.889403i $$0.651121\pi$$
$$558$$ 390.464 0.0296231
$$559$$ −170.718 −0.0129170
$$560$$ −11192.1 −0.844555
$$561$$ 5398.40 0.406276
$$562$$ 3598.04 0.270061
$$563$$ −8763.89 −0.656046 −0.328023 0.944670i $$-0.606382\pi$$
−0.328023 + 0.944670i $$0.606382\pi$$
$$564$$ −3179.10 −0.237348
$$565$$ 25778.1 1.91946
$$566$$ 3806.34 0.282672
$$567$$ −14940.1 −1.10657
$$568$$ −5327.84 −0.393576
$$569$$ −10273.2 −0.756895 −0.378447 0.925623i $$-0.623542\pi$$
−0.378447 + 0.925623i $$0.623542\pi$$
$$570$$ −3789.67 −0.278477
$$571$$ 2602.62 0.190747 0.0953734 0.995442i $$-0.469596\pi$$
0.0953734 + 0.995442i $$0.469596\pi$$
$$572$$ 6128.41 0.447975
$$573$$ 17332.6 1.26366
$$574$$ −3406.99 −0.247744
$$575$$ 537.988 0.0390185
$$576$$ −2585.99 −0.187065
$$577$$ −19727.0 −1.42331 −0.711653 0.702532i $$-0.752053\pi$$
−0.711653 + 0.702532i $$0.752053\pi$$
$$578$$ −1420.39 −0.102215
$$579$$ −14726.7 −1.05703
$$580$$ 16217.0 1.16099
$$581$$ 442.739 0.0316143
$$582$$ −3678.30 −0.261977
$$583$$ 1639.06 0.116437
$$584$$ 6912.30 0.489783
$$585$$ −7814.72 −0.552306
$$586$$ 6501.28 0.458303
$$587$$ −10116.2 −0.711309 −0.355654 0.934618i $$-0.615742\pi$$
−0.355654 + 0.934618i $$0.615742\pi$$
$$588$$ 2497.22 0.175142
$$589$$ 4448.78 0.311221
$$590$$ 5135.23 0.358329
$$591$$ −30386.0 −2.11491
$$592$$ 2101.07 0.145867
$$593$$ 3130.32 0.216774 0.108387 0.994109i $$-0.465431\pi$$
0.108387 + 0.994109i $$0.465431\pi$$
$$594$$ −900.152 −0.0621779
$$595$$ 18016.9 1.24138
$$596$$ −26037.3 −1.78948
$$597$$ −45.6009 −0.00312616
$$598$$ −729.667 −0.0498968
$$599$$ 10080.1 0.687581 0.343790 0.939046i $$-0.388289\pi$$
0.343790 + 0.939046i $$0.388289\pi$$
$$600$$ 2703.68 0.183962
$$601$$ 4777.02 0.324224 0.162112 0.986772i $$-0.448169\pi$$
0.162112 + 0.986772i $$0.448169\pi$$
$$602$$ 28.3435 0.00191893
$$603$$ 3352.24 0.226391
$$604$$ 8683.16 0.584955
$$605$$ −1555.63 −0.104537
$$606$$ −5613.29 −0.376278
$$607$$ −2571.35 −0.171941 −0.0859703 0.996298i $$-0.527399\pi$$
−0.0859703 + 0.996298i $$0.527399\pi$$
$$608$$ 8708.43 0.580877
$$609$$ 16959.3 1.12845
$$610$$ 953.414 0.0632830
$$611$$ 5362.67 0.355074
$$612$$ 5032.03 0.332366
$$613$$ 12711.9 0.837564 0.418782 0.908087i $$-0.362457\pi$$
0.418782 + 0.908087i $$0.362457\pi$$
$$614$$ 1096.56 0.0720744
$$615$$ −20953.8 −1.37388
$$616$$ −2107.99 −0.137879
$$617$$ 16236.1 1.05939 0.529693 0.848189i $$-0.322307\pi$$
0.529693 + 0.848189i $$0.322307\pi$$
$$618$$ 7487.11 0.487339
$$619$$ 12657.3 0.821874 0.410937 0.911664i $$-0.365202\pi$$
0.410937 + 0.911664i $$0.365202\pi$$
$$620$$ −6285.23 −0.407131
$$621$$ −1492.75 −0.0964607
$$622$$ 5479.19 0.353208
$$623$$ −5973.75 −0.384162
$$624$$ 22755.2 1.45983
$$625$$ −19037.8 −1.21842
$$626$$ 481.955 0.0307713
$$627$$ 4429.28 0.282119
$$628$$ −2553.15 −0.162232
$$629$$ −3382.28 −0.214404
$$630$$ 1297.44 0.0820497
$$631$$ −3949.97 −0.249201 −0.124600 0.992207i $$-0.539765\pi$$
−0.124600 + 0.992207i $$0.539765\pi$$
$$632$$ −11074.0 −0.696994
$$633$$ 18421.0 1.15666
$$634$$ −171.086 −0.0107172
$$635$$ −1409.13 −0.0880621
$$636$$ 6593.29 0.411070
$$637$$ −4212.44 −0.262014
$$638$$ 1360.84 0.0844455
$$639$$ −3832.67 −0.237274
$$640$$ −16175.2 −0.999033
$$641$$ −7398.27 −0.455872 −0.227936 0.973676i $$-0.573198\pi$$
−0.227936 + 0.973676i $$0.573198\pi$$
$$642$$ 2101.22 0.129172
$$643$$ −12491.7 −0.766134 −0.383067 0.923721i $$-0.625132\pi$$
−0.383067 + 0.923721i $$0.625132\pi$$
$$644$$ −1687.31 −0.103244
$$645$$ 174.319 0.0106415
$$646$$ −4116.31 −0.250703
$$647$$ −10472.0 −0.636315 −0.318158 0.948038i $$-0.603064\pi$$
−0.318158 + 0.948038i $$0.603064\pi$$
$$648$$ −9991.02 −0.605685
$$649$$ −6001.94 −0.363015
$$650$$ −2201.33 −0.132836
$$651$$ −6572.92 −0.395719
$$652$$ 10411.6 0.625384
$$653$$ 6337.94 0.379820 0.189910 0.981801i $$-0.439180\pi$$
0.189910 + 0.981801i $$0.439180\pi$$
$$654$$ 278.856 0.0166730
$$655$$ −14871.2 −0.887121
$$656$$ 14138.4 0.841479
$$657$$ 4972.48 0.295274
$$658$$ −890.339 −0.0527493
$$659$$ 15196.7 0.898302 0.449151 0.893456i $$-0.351726\pi$$
0.449151 + 0.893456i $$0.351726\pi$$
$$660$$ −6257.67 −0.369060
$$661$$ 2298.17 0.135232 0.0676161 0.997711i $$-0.478461\pi$$
0.0676161 + 0.997711i $$0.478461\pi$$
$$662$$ −6246.55 −0.366736
$$663$$ −36631.1 −2.14575
$$664$$ 296.075 0.0173042
$$665$$ 14782.5 0.862016
$$666$$ −243.566 −0.0141712
$$667$$ 2256.73 0.131006
$$668$$ −3573.09 −0.206956
$$669$$ −73.0265 −0.00422028
$$670$$ 3874.18 0.223392
$$671$$ −1114.33 −0.0641106
$$672$$ −12866.4 −0.738589
$$673$$ 23199.6 1.32880 0.664398 0.747379i $$-0.268688\pi$$
0.664398 + 0.747379i $$0.268688\pi$$
$$674$$ −8558.54 −0.489114
$$675$$ −4503.49 −0.256799
$$676$$ −25186.0 −1.43298
$$677$$ −2145.38 −0.121793 −0.0608963 0.998144i $$-0.519396\pi$$
−0.0608963 + 0.998144i $$0.519396\pi$$
$$678$$ 8701.55 0.492892
$$679$$ 14348.1 0.810941
$$680$$ 12048.6 0.679472
$$681$$ 27364.0 1.53978
$$682$$ −527.422 −0.0296129
$$683$$ −29544.6 −1.65519 −0.827593 0.561329i $$-0.810290\pi$$
−0.827593 + 0.561329i $$0.810290\pi$$
$$684$$ 4128.68 0.230795
$$685$$ −2549.72 −0.142219
$$686$$ 4949.93 0.275495
$$687$$ 30083.4 1.67068
$$688$$ −117.620 −0.00651776
$$689$$ −11121.9 −0.614964
$$690$$ 745.057 0.0411070
$$691$$ 27803.1 1.53065 0.765325 0.643644i $$-0.222578\pi$$
0.765325 + 0.643644i $$0.222578\pi$$
$$692$$ −13499.5 −0.741579
$$693$$ −1516.42 −0.0831227
$$694$$ −3366.55 −0.184139
$$695$$ 37285.4 2.03498
$$696$$ 11341.3 0.617659
$$697$$ −22759.8 −1.23686
$$698$$ −4919.58 −0.266775
$$699$$ 1254.90 0.0679036
$$700$$ −5090.44 −0.274858
$$701$$ −19697.8 −1.06130 −0.530652 0.847590i $$-0.678053\pi$$
−0.530652 + 0.847590i $$0.678053\pi$$
$$702$$ 6108.02 0.328394
$$703$$ −2775.09 −0.148883
$$704$$ 3493.03 0.187001
$$705$$ −5475.78 −0.292524
$$706$$ −4201.02 −0.223948
$$707$$ 21896.0 1.16476
$$708$$ −24143.5 −1.28159
$$709$$ 19122.5 1.01292 0.506460 0.862263i $$-0.330954\pi$$
0.506460 + 0.862263i $$0.330954\pi$$
$$710$$ −4429.41 −0.234131
$$711$$ −7966.27 −0.420195
$$712$$ −3994.86 −0.210272
$$713$$ −874.641 −0.0459405
$$714$$ 6081.70 0.318770
$$715$$ 10555.8 0.552117
$$716$$ 33064.8 1.72582
$$717$$ 25565.3 1.33160
$$718$$ 3012.59 0.156586
$$719$$ 1837.44 0.0953060 0.0476530 0.998864i $$-0.484826\pi$$
0.0476530 + 0.998864i $$0.484826\pi$$
$$720$$ −5384.13 −0.278687
$$721$$ −29205.2 −1.50854
$$722$$ 1643.79 0.0847307
$$723$$ −5907.95 −0.303899
$$724$$ −25446.4 −1.30623
$$725$$ 6808.33 0.348765
$$726$$ −525.109 −0.0268438
$$727$$ −7555.46 −0.385442 −0.192721 0.981254i $$-0.561731\pi$$
−0.192721 + 0.981254i $$0.561731\pi$$
$$728$$ 14303.9 0.728211
$$729$$ 10705.2 0.543881
$$730$$ 5746.69 0.291362
$$731$$ 189.344 0.00958021
$$732$$ −4482.51 −0.226337
$$733$$ 11984.6 0.603905 0.301952 0.953323i $$-0.402362\pi$$
0.301952 + 0.953323i $$0.402362\pi$$
$$734$$ −7073.80 −0.355720
$$735$$ 4301.29 0.215858
$$736$$ −1712.10 −0.0857456
$$737$$ −4528.05 −0.226313
$$738$$ −1638.99 −0.0817508
$$739$$ −27142.5 −1.35109 −0.675543 0.737321i $$-0.736091\pi$$
−0.675543 + 0.737321i $$0.736091\pi$$
$$740$$ 3920.64 0.194764
$$741$$ −30055.1 −1.49001
$$742$$ 1846.52 0.0913582
$$743$$ −29222.6 −1.44290 −0.721450 0.692467i $$-0.756524\pi$$
−0.721450 + 0.692467i $$0.756524\pi$$
$$744$$ −4395.55 −0.216598
$$745$$ −44847.6 −2.20549
$$746$$ 103.790 0.00509388
$$747$$ 212.987 0.0104321
$$748$$ −6797.04 −0.332252
$$749$$ −8196.29 −0.399847
$$750$$ −4726.43 −0.230113
$$751$$ −8859.39 −0.430471 −0.215236 0.976562i $$-0.569052\pi$$
−0.215236 + 0.976562i $$0.569052\pi$$
$$752$$ 3694.73 0.179166
$$753$$ −1641.47 −0.0794404
$$754$$ −9234.05 −0.446000
$$755$$ 14956.2 0.720941
$$756$$ 14124.4 0.679497
$$757$$ 35734.4 1.71571 0.857853 0.513896i $$-0.171798\pi$$
0.857853 + 0.513896i $$0.171798\pi$$
$$758$$ 2064.19 0.0989112
$$759$$ −870.806 −0.0416446
$$760$$ 9885.59 0.471826
$$761$$ 34394.7 1.63838 0.819189 0.573524i $$-0.194424\pi$$
0.819189 + 0.573524i $$0.194424\pi$$
$$762$$ −475.658 −0.0226132
$$763$$ −1087.74 −0.0516107
$$764$$ −21823.2 −1.03342
$$765$$ 8667.33 0.409631
$$766$$ 4639.62 0.218846
$$767$$ 40726.4 1.91727
$$768$$ 9599.92 0.451051
$$769$$ −11602.7 −0.544091 −0.272045 0.962284i $$-0.587700\pi$$
−0.272045 + 0.962284i $$0.587700\pi$$
$$770$$ −1752.53 −0.0820216
$$771$$ −19178.8 −0.895859
$$772$$ 18542.2 0.864441
$$773$$ −12680.6 −0.590026 −0.295013 0.955493i $$-0.595324\pi$$
−0.295013 + 0.955493i $$0.595324\pi$$
$$774$$ 13.6351 0.000633210 0
$$775$$ −2638.71 −0.122303
$$776$$ 9595.09 0.443871
$$777$$ 4100.10 0.189305
$$778$$ 6445.89 0.297039
$$779$$ −18674.0 −0.858876
$$780$$ 42461.7 1.94920
$$781$$ 5176.99 0.237193
$$782$$ 809.276 0.0370072
$$783$$ −18891.0 −0.862210
$$784$$ −2902.25 −0.132209
$$785$$ −4397.62 −0.199946
$$786$$ −5019.84 −0.227801
$$787$$ −4417.61 −0.200090 −0.100045 0.994983i $$-0.531899\pi$$
−0.100045 + 0.994983i $$0.531899\pi$$
$$788$$ 38258.5 1.72957
$$789$$ 1232.74 0.0556231
$$790$$ −9206.61 −0.414628
$$791$$ −33942.4 −1.52573
$$792$$ −1014.09 −0.0454974
$$793$$ 7561.33 0.338601
$$794$$ −3158.99 −0.141194
$$795$$ 11356.5 0.506633
$$796$$ 57.4153 0.00255657
$$797$$ −27030.1 −1.20132 −0.600661 0.799504i $$-0.705096\pi$$
−0.600661 + 0.799504i $$0.705096\pi$$
$$798$$ 4989.91 0.221354
$$799$$ −5947.75 −0.263350
$$800$$ −5165.23 −0.228273
$$801$$ −2873.77 −0.126766
$$802$$ −264.769 −0.0116575
$$803$$ −6716.60 −0.295173
$$804$$ −18214.6 −0.798979
$$805$$ −2906.27 −0.127246
$$806$$ 3578.85 0.156401
$$807$$ 29836.9 1.30150
$$808$$ 14642.6 0.637533
$$809$$ 23647.0 1.02767 0.513835 0.857889i $$-0.328224\pi$$
0.513835 + 0.857889i $$0.328224\pi$$
$$810$$ −8306.24 −0.360311
$$811$$ 33486.1 1.44988 0.724941 0.688811i $$-0.241867\pi$$
0.724941 + 0.688811i $$0.241867\pi$$
$$812$$ −21353.1 −0.922843
$$813$$ 8815.30 0.380278
$$814$$ 328.999 0.0141663
$$815$$ 17933.3 0.770768
$$816$$ −25237.8 −1.08272
$$817$$ 155.353 0.00665251
$$818$$ −6749.88 −0.288513
$$819$$ 10289.7 0.439014
$$820$$ 26382.5 1.12356
$$821$$ 2605.69 0.110766 0.0553832 0.998465i $$-0.482362\pi$$
0.0553832 + 0.998465i $$0.482362\pi$$
$$822$$ −860.673 −0.0365200
$$823$$ 31976.2 1.35434 0.677169 0.735828i $$-0.263207\pi$$
0.677169 + 0.735828i $$0.263207\pi$$
$$824$$ −19530.6 −0.825705
$$825$$ −2627.14 −0.110867
$$826$$ −6761.62 −0.284827
$$827$$ −37759.0 −1.58768 −0.793839 0.608128i $$-0.791921\pi$$
−0.793839 + 0.608128i $$0.791921\pi$$
$$828$$ −811.707 −0.0340686
$$829$$ −1137.55 −0.0476584 −0.0238292 0.999716i $$-0.507586\pi$$
−0.0238292 + 0.999716i $$0.507586\pi$$
$$830$$ 246.149 0.0102939
$$831$$ −1398.08 −0.0583621
$$832$$ −23702.2 −0.987649
$$833$$ 4672.03 0.194329
$$834$$ 12585.9 0.522557
$$835$$ −6154.40 −0.255068
$$836$$ −5576.83 −0.230716
$$837$$ 7321.60 0.302356
$$838$$ 10917.0 0.450024
$$839$$ −37372.2 −1.53782 −0.768911 0.639356i $$-0.779201\pi$$
−0.768911 + 0.639356i $$0.779201\pi$$
$$840$$ −14605.6 −0.599930
$$841$$ 4170.26 0.170989
$$842$$ 9872.44 0.404070
$$843$$ −29137.2 −1.19044
$$844$$ −23193.5 −0.945917
$$845$$ −43381.1 −1.76610
$$846$$ −428.312 −0.0174062
$$847$$ 2048.31 0.0830943
$$848$$ −7662.68 −0.310304
$$849$$ −30824.0 −1.24603
$$850$$ 2441.51 0.0985211
$$851$$ 545.589 0.0219772
$$852$$ 20825.0 0.837387
$$853$$ −22490.8 −0.902780 −0.451390 0.892327i $$-0.649072\pi$$
−0.451390 + 0.892327i $$0.649072\pi$$
$$854$$ −1255.37 −0.0503021
$$855$$ 7111.36 0.284449
$$856$$ −5481.16 −0.218858
$$857$$ 43409.5 1.73027 0.865135 0.501539i $$-0.167233\pi$$
0.865135 + 0.501539i $$0.167233\pi$$
$$858$$ 3563.15 0.141776
$$859$$ 29533.2 1.17306 0.586532 0.809926i $$-0.300493\pi$$
0.586532 + 0.809926i $$0.300493\pi$$
$$860$$ −219.482 −0.00870264
$$861$$ 27590.1 1.09207
$$862$$ −297.457 −0.0117534
$$863$$ 14351.6 0.566090 0.283045 0.959107i $$-0.408655\pi$$
0.283045 + 0.959107i $$0.408655\pi$$
$$864$$ 14331.9 0.564331
$$865$$ −23251.9 −0.913975
$$866$$ 1293.31 0.0507488
$$867$$ 11502.4 0.450569
$$868$$ 8275.85 0.323618
$$869$$ 10760.5 0.420051
$$870$$ 9428.82 0.367433
$$871$$ 30725.3 1.19528
$$872$$ −727.413 −0.0282492
$$873$$ 6902.39 0.267595
$$874$$ 663.994 0.0256979
$$875$$ 18436.5 0.712307
$$876$$ −27018.3 −1.04208
$$877$$ −43248.7 −1.66523 −0.832614 0.553854i $$-0.813156\pi$$
−0.832614 + 0.553854i $$0.813156\pi$$
$$878$$ −5727.71 −0.220160
$$879$$ −52647.9 −2.02021
$$880$$ 7272.64 0.278591
$$881$$ 3816.13 0.145935 0.0729675 0.997334i $$-0.476753\pi$$
0.0729675 + 0.997334i $$0.476753\pi$$
$$882$$ 336.444 0.0128443
$$883$$ 48787.6 1.85938 0.929690 0.368343i $$-0.120075\pi$$
0.929690 + 0.368343i $$0.120075\pi$$
$$884$$ 46121.6 1.75479
$$885$$ −41585.5 −1.57953
$$886$$ −8541.49 −0.323879
$$887$$ 41495.1 1.57077 0.785384 0.619009i $$-0.212466\pi$$
0.785384 + 0.619009i $$0.212466\pi$$
$$888$$ 2741.88 0.103617
$$889$$ 1855.41 0.0699984
$$890$$ −3321.21 −0.125087
$$891$$ 9708.15 0.365023
$$892$$ 91.9464 0.00345134
$$893$$ −4880.01 −0.182870
$$894$$ −15138.5 −0.566340
$$895$$ 56951.9 2.12703
$$896$$ 21298.1 0.794107
$$897$$ 5908.90 0.219947
$$898$$ −12426.7 −0.461788
$$899$$ −11068.7 −0.410637
$$900$$ −2448.84 −0.0906978
$$901$$ 12335.3 0.456104
$$902$$ 2213.88 0.0817228
$$903$$ −229.528 −0.00845871
$$904$$ −22698.5 −0.835113
$$905$$ −43829.7 −1.60989
$$906$$ 5048.53 0.185128
$$907$$ 21615.3 0.791316 0.395658 0.918398i $$-0.370517\pi$$
0.395658 + 0.918398i $$0.370517\pi$$
$$908$$ −34453.6 −1.25923
$$909$$ 10533.4 0.384347
$$910$$ 11891.8 0.433199
$$911$$ 3646.35 0.132611 0.0663057 0.997799i $$-0.478879\pi$$
0.0663057 + 0.997799i $$0.478879\pi$$
$$912$$ −20707.1 −0.751844
$$913$$ −287.693 −0.0104285
$$914$$ 11854.0 0.428988
$$915$$ −7720.82 −0.278954
$$916$$ −37877.6 −1.36628
$$917$$ 19581.1 0.705151
$$918$$ −6774.43 −0.243562
$$919$$ 31280.0 1.12278 0.561388 0.827553i $$-0.310267\pi$$
0.561388 + 0.827553i $$0.310267\pi$$
$$920$$ −1943.53 −0.0696482
$$921$$ −8880.05 −0.317707
$$922$$ −6285.42 −0.224511
$$923$$ −35128.7 −1.25274
$$924$$ 8239.56 0.293357
$$925$$ 1645.99 0.0585079
$$926$$ 5795.79 0.205682
$$927$$ −14049.7 −0.497790
$$928$$ −21666.9 −0.766433
$$929$$ 6557.92 0.231602 0.115801 0.993272i $$-0.463056\pi$$
0.115801 + 0.993272i $$0.463056\pi$$
$$930$$ −3654.33 −0.128850
$$931$$ 3833.30 0.134942
$$932$$ −1580.02 −0.0555314
$$933$$ −44370.9 −1.55695
$$934$$ 11094.2 0.388665
$$935$$ −11707.4 −0.409491
$$936$$ 6881.13 0.240296
$$937$$ −24473.3 −0.853265 −0.426632 0.904425i $$-0.640300\pi$$
−0.426632 + 0.904425i $$0.640300\pi$$
$$938$$ −5101.18 −0.177569
$$939$$ −3902.91 −0.135641
$$940$$ 6894.46 0.239226
$$941$$ 15420.8 0.534224 0.267112 0.963665i $$-0.413931\pi$$
0.267112 + 0.963665i $$0.413931\pi$$
$$942$$ −1484.44 −0.0513436
$$943$$ 3671.34 0.126782
$$944$$ 28059.4 0.967432
$$945$$ 24328.3 0.837461
$$946$$ −18.4177 −0.000632993 0
$$947$$ −33141.2 −1.13722 −0.568608 0.822609i $$-0.692518\pi$$
−0.568608 + 0.822609i $$0.692518\pi$$
$$948$$ 43285.2 1.48295
$$949$$ 45575.8 1.55896
$$950$$ 2003.20 0.0684132
$$951$$ 1385.47 0.0472417
$$952$$ −15864.5 −0.540096
$$953$$ −20735.4 −0.704813 −0.352406 0.935847i $$-0.614637\pi$$
−0.352406 + 0.935847i $$0.614637\pi$$
$$954$$ 888.298 0.0301464
$$955$$ −37589.0 −1.27367
$$956$$ −32188.9 −1.08898
$$957$$ −11020.2 −0.372239
$$958$$ −7321.32 −0.246911
$$959$$ 3357.26 0.113046
$$960$$ 24202.1 0.813666
$$961$$ −25501.1 −0.856000
$$962$$ −2232.44 −0.0748198
$$963$$ −3942.96 −0.131942
$$964$$ 7438.60 0.248528
$$965$$ 31937.7 1.06540
$$966$$ −981.027 −0.0326750
$$967$$ −8178.87 −0.271990 −0.135995 0.990710i $$-0.543423\pi$$
−0.135995 + 0.990710i $$0.543423\pi$$
$$968$$ 1369.78 0.0454819
$$969$$ 33334.2 1.10511
$$970$$ 7977.08 0.264050
$$971$$ −20576.1 −0.680039 −0.340020 0.940418i $$-0.610434\pi$$
−0.340020 + 0.940418i $$0.610434\pi$$
$$972$$ 16524.1 0.545277
$$973$$ −49094.1 −1.61756
$$974$$ −5156.96 −0.169651
$$975$$ 17826.6 0.585546
$$976$$ 5209.55 0.170854
$$977$$ 14541.9 0.476188 0.238094 0.971242i $$-0.423477\pi$$
0.238094 + 0.971242i $$0.423477\pi$$
$$978$$ 6053.48 0.197923
$$979$$ 3881.76 0.126723
$$980$$ −5415.68 −0.176528
$$981$$ −523.277 −0.0170305
$$982$$ 9755.62 0.317021
$$983$$ −29285.7 −0.950223 −0.475111 0.879926i $$-0.657592\pi$$
−0.475111 + 0.879926i $$0.657592\pi$$
$$984$$ 18450.5 0.597745
$$985$$ 65897.7 2.13165
$$986$$ 10241.5 0.330787
$$987$$ 7210.03 0.232521
$$988$$ 37841.8 1.21853
$$989$$ −30.5427 −0.000982004 0
$$990$$ −843.082 −0.0270655
$$991$$ −38085.9 −1.22083 −0.610413 0.792083i $$-0.708997\pi$$
−0.610413 + 0.792083i $$0.708997\pi$$
$$992$$ 8397.44 0.268769
$$993$$ 50585.1 1.61658
$$994$$ 5832.26 0.186105
$$995$$ 98.8940 0.00315090
$$996$$ −1157.28 −0.0368170
$$997$$ −26803.6 −0.851434 −0.425717 0.904856i $$-0.639978\pi$$
−0.425717 + 0.904856i $$0.639978\pi$$
$$998$$ 14691.6 0.465987
$$999$$ −4567.12 −0.144642
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 11.4.a.a.1.1 2
3.2 odd 2 99.4.a.c.1.2 2
4.3 odd 2 176.4.a.i.1.1 2
5.2 odd 4 275.4.b.c.199.2 4
5.3 odd 4 275.4.b.c.199.3 4
5.4 even 2 275.4.a.b.1.2 2
7.6 odd 2 539.4.a.e.1.1 2
8.3 odd 2 704.4.a.n.1.2 2
8.5 even 2 704.4.a.p.1.1 2
11.2 odd 10 121.4.c.f.81.1 8
11.3 even 5 121.4.c.c.9.1 8
11.4 even 5 121.4.c.c.27.1 8
11.5 even 5 121.4.c.c.3.2 8
11.6 odd 10 121.4.c.f.3.1 8
11.7 odd 10 121.4.c.f.27.2 8
11.8 odd 10 121.4.c.f.9.2 8
11.9 even 5 121.4.c.c.81.2 8
11.10 odd 2 121.4.a.c.1.2 2
12.11 even 2 1584.4.a.bc.1.2 2
13.12 even 2 1859.4.a.a.1.2 2
15.14 odd 2 2475.4.a.q.1.1 2
33.32 even 2 1089.4.a.v.1.1 2
44.43 even 2 1936.4.a.w.1.1 2

By twisted newform
Twist Min Dim Char Parity Ord Type
11.4.a.a.1.1 2 1.1 even 1 trivial
99.4.a.c.1.2 2 3.2 odd 2
121.4.a.c.1.2 2 11.10 odd 2
121.4.c.c.3.2 8 11.5 even 5
121.4.c.c.9.1 8 11.3 even 5
121.4.c.c.27.1 8 11.4 even 5
121.4.c.c.81.2 8 11.9 even 5
121.4.c.f.3.1 8 11.6 odd 10
121.4.c.f.9.2 8 11.8 odd 10
121.4.c.f.27.2 8 11.7 odd 10
121.4.c.f.81.1 8 11.2 odd 10
176.4.a.i.1.1 2 4.3 odd 2
275.4.a.b.1.2 2 5.4 even 2
275.4.b.c.199.2 4 5.2 odd 4
275.4.b.c.199.3 4 5.3 odd 4
539.4.a.e.1.1 2 7.6 odd 2
704.4.a.n.1.2 2 8.3 odd 2
704.4.a.p.1.1 2 8.5 even 2
1089.4.a.v.1.1 2 33.32 even 2
1584.4.a.bc.1.2 2 12.11 even 2
1859.4.a.a.1.2 2 13.12 even 2
1936.4.a.w.1.1 2 44.43 even 2
2475.4.a.q.1.1 2 15.14 odd 2