# Properties

 Label 13.4.a.b.1.2 Level $13$ Weight $4$ Character 13.1 Self dual yes Analytic conductor $0.767$ Analytic rank $0$ Dimension $2$ CM no Inner twists $1$

# Related objects

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [13,4,Mod(1,13)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(13, 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("13.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$13$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 13.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: $$0.767024830075$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(\sqrt{17})$$ comment: defining polynomial  gp: f.mod \\ as an extension of the character field Defining polynomial: $$x^{2} - x - 4$$ x^2 - x - 4 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 1.2 Root $$2.56155$$ of defining polynomial Character $$\chi$$ $$=$$ 13.1

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+2.56155 q^{2} -3.68466 q^{3} -1.43845 q^{4} +0.561553 q^{5} -9.43845 q^{6} +18.1771 q^{7} -24.1771 q^{8} -13.4233 q^{9} +O(q^{10})$$ $$q+2.56155 q^{2} -3.68466 q^{3} -1.43845 q^{4} +0.561553 q^{5} -9.43845 q^{6} +18.1771 q^{7} -24.1771 q^{8} -13.4233 q^{9} +1.43845 q^{10} +64.7386 q^{11} +5.30019 q^{12} -13.0000 q^{13} +46.5616 q^{14} -2.06913 q^{15} -50.4233 q^{16} -25.5464 q^{17} -34.3845 q^{18} -107.970 q^{19} -0.807764 q^{20} -66.9763 q^{21} +165.831 q^{22} +73.2614 q^{23} +89.0843 q^{24} -124.685 q^{25} -33.3002 q^{26} +148.946 q^{27} -26.1468 q^{28} +175.909 q^{29} -5.30019 q^{30} -113.093 q^{31} +64.2547 q^{32} -238.540 q^{33} -65.4384 q^{34} +10.2074 q^{35} +19.3087 q^{36} +114.808 q^{37} -276.570 q^{38} +47.9006 q^{39} -13.5767 q^{40} -69.6458 q^{41} -171.563 q^{42} +438.302 q^{43} -93.1231 q^{44} -7.53789 q^{45} +187.663 q^{46} -31.9479 q^{47} +185.793 q^{48} -12.5937 q^{49} -319.386 q^{50} +94.1298 q^{51} +18.6998 q^{52} +2.84658 q^{53} +381.533 q^{54} +36.3542 q^{55} -439.469 q^{56} +397.831 q^{57} +450.600 q^{58} +71.6325 q^{59} +2.97633 q^{60} -920.695 q^{61} -289.693 q^{62} -243.996 q^{63} +567.978 q^{64} -7.30019 q^{65} -611.032 q^{66} -444.280 q^{67} +36.7471 q^{68} -269.943 q^{69} +26.1468 q^{70} -541.719 q^{71} +324.536 q^{72} +764.004 q^{73} +294.086 q^{74} +459.420 q^{75} +155.309 q^{76} +1176.76 q^{77} +122.700 q^{78} -421.538 q^{79} -28.3153 q^{80} -186.386 q^{81} -178.401 q^{82} +603.797 q^{83} +96.3419 q^{84} -14.3457 q^{85} +1122.73 q^{86} -648.165 q^{87} -1565.19 q^{88} -1159.88 q^{89} -19.3087 q^{90} -236.302 q^{91} -105.383 q^{92} +416.708 q^{93} -81.8362 q^{94} -60.6307 q^{95} -236.757 q^{96} +583.269 q^{97} -32.2595 q^{98} -869.006 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q + q^{2} + 5 q^{3} - 7 q^{4} - 3 q^{5} - 23 q^{6} - 9 q^{7} - 3 q^{8} + 35 q^{9}+O(q^{10})$$ 2 * q + q^2 + 5 * q^3 - 7 * q^4 - 3 * q^5 - 23 * q^6 - 9 * q^7 - 3 * q^8 + 35 * q^9 $$2 q + q^{2} + 5 q^{3} - 7 q^{4} - 3 q^{5} - 23 q^{6} - 9 q^{7} - 3 q^{8} + 35 q^{9} + 7 q^{10} + 80 q^{11} - 43 q^{12} - 26 q^{13} + 89 q^{14} - 33 q^{15} - 39 q^{16} + 19 q^{17} - 110 q^{18} - 84 q^{19} + 19 q^{20} - 303 q^{21} + 142 q^{22} + 196 q^{23} + 273 q^{24} - 237 q^{25} - 13 q^{26} + 335 q^{27} + 125 q^{28} - 44 q^{29} + 43 q^{30} - 86 q^{31} - 123 q^{32} - 106 q^{33} - 135 q^{34} + 107 q^{35} - 250 q^{36} + 209 q^{37} - 314 q^{38} - 65 q^{39} - 89 q^{40} - 230 q^{41} + 197 q^{42} + 287 q^{43} - 178 q^{44} - 180 q^{45} - 4 q^{46} + 435 q^{47} + 285 q^{48} + 383 q^{49} - 144 q^{50} + 481 q^{51} + 91 q^{52} - 118 q^{53} + 91 q^{54} - 18 q^{55} - 1015 q^{56} + 606 q^{57} + 794 q^{58} - 368 q^{59} + 175 q^{60} - 1058 q^{61} - 332 q^{62} - 1560 q^{63} + 769 q^{64} + 39 q^{65} - 818 q^{66} + 68 q^{67} - 211 q^{68} + 796 q^{69} - 125 q^{70} - 131 q^{71} + 1350 q^{72} + 456 q^{73} + 147 q^{74} - 516 q^{75} + 22 q^{76} + 762 q^{77} + 299 q^{78} - 1008 q^{79} - 69 q^{80} + 122 q^{81} + 72 q^{82} + 1958 q^{83} + 1409 q^{84} - 173 q^{85} + 1359 q^{86} - 2558 q^{87} - 1242 q^{88} - 720 q^{89} + 250 q^{90} + 117 q^{91} - 788 q^{92} + 652 q^{93} - 811 q^{94} - 146 q^{95} - 1863 q^{96} - 928 q^{97} - 650 q^{98} - 130 q^{99}+O(q^{100})$$ 2 * q + q^2 + 5 * q^3 - 7 * q^4 - 3 * q^5 - 23 * q^6 - 9 * q^7 - 3 * q^8 + 35 * q^9 + 7 * q^10 + 80 * q^11 - 43 * q^12 - 26 * q^13 + 89 * q^14 - 33 * q^15 - 39 * q^16 + 19 * q^17 - 110 * q^18 - 84 * q^19 + 19 * q^20 - 303 * q^21 + 142 * q^22 + 196 * q^23 + 273 * q^24 - 237 * q^25 - 13 * q^26 + 335 * q^27 + 125 * q^28 - 44 * q^29 + 43 * q^30 - 86 * q^31 - 123 * q^32 - 106 * q^33 - 135 * q^34 + 107 * q^35 - 250 * q^36 + 209 * q^37 - 314 * q^38 - 65 * q^39 - 89 * q^40 - 230 * q^41 + 197 * q^42 + 287 * q^43 - 178 * q^44 - 180 * q^45 - 4 * q^46 + 435 * q^47 + 285 * q^48 + 383 * q^49 - 144 * q^50 + 481 * q^51 + 91 * q^52 - 118 * q^53 + 91 * q^54 - 18 * q^55 - 1015 * q^56 + 606 * q^57 + 794 * q^58 - 368 * q^59 + 175 * q^60 - 1058 * q^61 - 332 * q^62 - 1560 * q^63 + 769 * q^64 + 39 * q^65 - 818 * q^66 + 68 * q^67 - 211 * q^68 + 796 * q^69 - 125 * q^70 - 131 * q^71 + 1350 * q^72 + 456 * q^73 + 147 * q^74 - 516 * q^75 + 22 * q^76 + 762 * q^77 + 299 * q^78 - 1008 * q^79 - 69 * q^80 + 122 * q^81 + 72 * q^82 + 1958 * q^83 + 1409 * q^84 - 173 * q^85 + 1359 * q^86 - 2558 * q^87 - 1242 * q^88 - 720 * q^89 + 250 * q^90 + 117 * q^91 - 788 * q^92 + 652 * q^93 - 811 * q^94 - 146 * q^95 - 1863 * q^96 - 928 * q^97 - 650 * q^98 - 130 * 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 2.56155 0.905646 0.452823 0.891601i $$-0.350417\pi$$
0.452823 + 0.891601i $$0.350417\pi$$
$$3$$ −3.68466 −0.709113 −0.354556 0.935035i $$-0.615368\pi$$
−0.354556 + 0.935035i $$0.615368\pi$$
$$4$$ −1.43845 −0.179806
$$5$$ 0.561553 0.0502268 0.0251134 0.999685i $$-0.492005\pi$$
0.0251134 + 0.999685i $$0.492005\pi$$
$$6$$ −9.43845 −0.642205
$$7$$ 18.1771 0.981470 0.490735 0.871309i $$-0.336728\pi$$
0.490735 + 0.871309i $$0.336728\pi$$
$$8$$ −24.1771 −1.06849
$$9$$ −13.4233 −0.497159
$$10$$ 1.43845 0.0454877
$$11$$ 64.7386 1.77449 0.887247 0.461295i $$-0.152615\pi$$
0.887247 + 0.461295i $$0.152615\pi$$
$$12$$ 5.30019 0.127503
$$13$$ −13.0000 −0.277350
$$14$$ 46.5616 0.888864
$$15$$ −2.06913 −0.0356165
$$16$$ −50.4233 −0.787864
$$17$$ −25.5464 −0.364465 −0.182233 0.983255i $$-0.558332\pi$$
−0.182233 + 0.983255i $$0.558332\pi$$
$$18$$ −34.3845 −0.450250
$$19$$ −107.970 −1.30368 −0.651841 0.758356i $$-0.726003\pi$$
−0.651841 + 0.758356i $$0.726003\pi$$
$$20$$ −0.807764 −0.00903108
$$21$$ −66.9763 −0.695973
$$22$$ 165.831 1.60706
$$23$$ 73.2614 0.664176 0.332088 0.943248i $$-0.392247\pi$$
0.332088 + 0.943248i $$0.392247\pi$$
$$24$$ 89.0843 0.757677
$$25$$ −124.685 −0.997477
$$26$$ −33.3002 −0.251181
$$27$$ 148.946 1.06165
$$28$$ −26.1468 −0.176474
$$29$$ 175.909 1.12640 0.563198 0.826322i $$-0.309571\pi$$
0.563198 + 0.826322i $$0.309571\pi$$
$$30$$ −5.30019 −0.0322559
$$31$$ −113.093 −0.655228 −0.327614 0.944812i $$-0.606245\pi$$
−0.327614 + 0.944812i $$0.606245\pi$$
$$32$$ 64.2547 0.354961
$$33$$ −238.540 −1.25832
$$34$$ −65.4384 −0.330077
$$35$$ 10.2074 0.0492961
$$36$$ 19.3087 0.0893921
$$37$$ 114.808 0.510116 0.255058 0.966926i $$-0.417905\pi$$
0.255058 + 0.966926i $$0.417905\pi$$
$$38$$ −276.570 −1.18067
$$39$$ 47.9006 0.196673
$$40$$ −13.5767 −0.0536666
$$41$$ −69.6458 −0.265289 −0.132645 0.991164i $$-0.542347\pi$$
−0.132645 + 0.991164i $$0.542347\pi$$
$$42$$ −171.563 −0.630305
$$43$$ 438.302 1.55443 0.777214 0.629236i $$-0.216632\pi$$
0.777214 + 0.629236i $$0.216632\pi$$
$$44$$ −93.1231 −0.319064
$$45$$ −7.53789 −0.0249707
$$46$$ 187.663 0.601508
$$47$$ −31.9479 −0.0991506 −0.0495753 0.998770i $$-0.515787\pi$$
−0.0495753 + 0.998770i $$0.515787\pi$$
$$48$$ 185.793 0.558684
$$49$$ −12.5937 −0.0367164
$$50$$ −319.386 −0.903361
$$51$$ 94.1298 0.258447
$$52$$ 18.6998 0.0498692
$$53$$ 2.84658 0.00737752 0.00368876 0.999993i $$-0.498826\pi$$
0.00368876 + 0.999993i $$0.498826\pi$$
$$54$$ 381.533 0.961483
$$55$$ 36.3542 0.0891272
$$56$$ −439.469 −1.04869
$$57$$ 397.831 0.924457
$$58$$ 450.600 1.02012
$$59$$ 71.6325 0.158064 0.0790319 0.996872i $$-0.474817\pi$$
0.0790319 + 0.996872i $$0.474817\pi$$
$$60$$ 2.97633 0.00640405
$$61$$ −920.695 −1.93251 −0.966253 0.257593i $$-0.917071\pi$$
−0.966253 + 0.257593i $$0.917071\pi$$
$$62$$ −289.693 −0.593404
$$63$$ −243.996 −0.487947
$$64$$ 567.978 1.10933
$$65$$ −7.30019 −0.0139304
$$66$$ −611.032 −1.13959
$$67$$ −444.280 −0.810112 −0.405056 0.914292i $$-0.632748\pi$$
−0.405056 + 0.914292i $$0.632748\pi$$
$$68$$ 36.7471 0.0655330
$$69$$ −269.943 −0.470976
$$70$$ 26.1468 0.0446448
$$71$$ −541.719 −0.905496 −0.452748 0.891639i $$-0.649556\pi$$
−0.452748 + 0.891639i $$0.649556\pi$$
$$72$$ 324.536 0.531207
$$73$$ 764.004 1.22493 0.612465 0.790498i $$-0.290178\pi$$
0.612465 + 0.790498i $$0.290178\pi$$
$$74$$ 294.086 0.461984
$$75$$ 459.420 0.707324
$$76$$ 155.309 0.234410
$$77$$ 1176.76 1.74161
$$78$$ 122.700 0.178116
$$79$$ −421.538 −0.600338 −0.300169 0.953886i $$-0.597043\pi$$
−0.300169 + 0.953886i $$0.597043\pi$$
$$80$$ −28.3153 −0.0395719
$$81$$ −186.386 −0.255674
$$82$$ −178.401 −0.240258
$$83$$ 603.797 0.798498 0.399249 0.916842i $$-0.369271\pi$$
0.399249 + 0.916842i $$0.369271\pi$$
$$84$$ 96.3419 0.125140
$$85$$ −14.3457 −0.0183059
$$86$$ 1122.73 1.40776
$$87$$ −648.165 −0.798742
$$88$$ −1565.19 −1.89602
$$89$$ −1159.88 −1.38143 −0.690715 0.723127i $$-0.742704\pi$$
−0.690715 + 0.723127i $$0.742704\pi$$
$$90$$ −19.3087 −0.0226146
$$91$$ −236.302 −0.272211
$$92$$ −105.383 −0.119423
$$93$$ 416.708 0.464631
$$94$$ −81.8362 −0.0897953
$$95$$ −60.6307 −0.0654798
$$96$$ −236.757 −0.251707
$$97$$ 583.269 0.610536 0.305268 0.952267i $$-0.401254\pi$$
0.305268 + 0.952267i $$0.401254\pi$$
$$98$$ −32.2595 −0.0332521
$$99$$ −869.006 −0.882206
$$100$$ 179.352 0.179352
$$101$$ 921.740 0.908085 0.454043 0.890980i $$-0.349981\pi$$
0.454043 + 0.890980i $$0.349981\pi$$
$$102$$ 241.118 0.234061
$$103$$ −930.712 −0.890347 −0.445174 0.895444i $$-0.646858\pi$$
−0.445174 + 0.895444i $$0.646858\pi$$
$$104$$ 314.302 0.296345
$$105$$ −37.6107 −0.0349565
$$106$$ 7.29168 0.00668142
$$107$$ 857.383 0.774638 0.387319 0.921946i $$-0.373401\pi$$
0.387319 + 0.921946i $$0.373401\pi$$
$$108$$ −214.251 −0.190892
$$109$$ 671.853 0.590384 0.295192 0.955438i $$-0.404616\pi$$
0.295192 + 0.955438i $$0.404616\pi$$
$$110$$ 93.1231 0.0807176
$$111$$ −423.027 −0.361730
$$112$$ −916.548 −0.773265
$$113$$ 641.474 0.534024 0.267012 0.963693i $$-0.413964\pi$$
0.267012 + 0.963693i $$0.413964\pi$$
$$114$$ 1019.07 0.837231
$$115$$ 41.1401 0.0333594
$$116$$ −253.036 −0.202533
$$117$$ 174.503 0.137887
$$118$$ 183.491 0.143150
$$119$$ −464.359 −0.357712
$$120$$ 50.0255 0.0380557
$$121$$ 2860.09 2.14883
$$122$$ −2358.41 −1.75017
$$123$$ 256.621 0.188120
$$124$$ 162.678 0.117814
$$125$$ −140.211 −0.100327
$$126$$ −625.009 −0.441907
$$127$$ −553.174 −0.386506 −0.193253 0.981149i $$-0.561904\pi$$
−0.193253 + 0.981149i $$0.561904\pi$$
$$128$$ 940.868 0.649702
$$129$$ −1614.99 −1.10227
$$130$$ −18.6998 −0.0126160
$$131$$ 2056.40 1.37152 0.685758 0.727830i $$-0.259471\pi$$
0.685758 + 0.727830i $$0.259471\pi$$
$$132$$ 343.127 0.226253
$$133$$ −1962.57 −1.27952
$$134$$ −1138.05 −0.733674
$$135$$ 83.6411 0.0533235
$$136$$ 617.637 0.389426
$$137$$ −1808.57 −1.12786 −0.563928 0.825824i $$-0.690710\pi$$
−0.563928 + 0.825824i $$0.690710\pi$$
$$138$$ −691.474 −0.426537
$$139$$ 1493.64 0.911428 0.455714 0.890126i $$-0.349384\pi$$
0.455714 + 0.890126i $$0.349384\pi$$
$$140$$ −14.6828 −0.00886373
$$141$$ 117.717 0.0703090
$$142$$ −1387.64 −0.820058
$$143$$ −841.602 −0.492156
$$144$$ 676.847 0.391694
$$145$$ 98.7822 0.0565753
$$146$$ 1957.04 1.10935
$$147$$ 46.4036 0.0260361
$$148$$ −165.145 −0.0917218
$$149$$ −2759.02 −1.51696 −0.758482 0.651694i $$-0.774059\pi$$
−0.758482 + 0.651694i $$0.774059\pi$$
$$150$$ 1176.83 0.640585
$$151$$ −976.355 −0.526190 −0.263095 0.964770i $$-0.584743\pi$$
−0.263095 + 0.964770i $$0.584743\pi$$
$$152$$ 2610.39 1.39297
$$153$$ 342.917 0.181197
$$154$$ 3014.33 1.57728
$$155$$ −63.5076 −0.0329100
$$156$$ −68.9024 −0.0353629
$$157$$ −564.875 −0.287146 −0.143573 0.989640i $$-0.545859\pi$$
−0.143573 + 0.989640i $$0.545859\pi$$
$$158$$ −1079.79 −0.543694
$$159$$ −10.4887 −0.00523149
$$160$$ 36.0824 0.0178285
$$161$$ 1331.68 0.651869
$$162$$ −477.438 −0.231550
$$163$$ 1508.53 0.724892 0.362446 0.932005i $$-0.381942\pi$$
0.362446 + 0.932005i $$0.381942\pi$$
$$164$$ 100.182 0.0477005
$$165$$ −133.953 −0.0632012
$$166$$ 1546.66 0.723157
$$167$$ 592.521 0.274555 0.137277 0.990533i $$-0.456165\pi$$
0.137277 + 0.990533i $$0.456165\pi$$
$$168$$ 1619.29 0.743638
$$169$$ 169.000 0.0769231
$$170$$ −36.7471 −0.0165787
$$171$$ 1449.31 0.648137
$$172$$ −630.474 −0.279495
$$173$$ −4495.57 −1.97568 −0.987838 0.155488i $$-0.950305\pi$$
−0.987838 + 0.155488i $$0.950305\pi$$
$$174$$ −1660.31 −0.723377
$$175$$ −2266.40 −0.978994
$$176$$ −3264.34 −1.39806
$$177$$ −263.941 −0.112085
$$178$$ −2971.10 −1.25109
$$179$$ −154.285 −0.0644235 −0.0322117 0.999481i $$-0.510255\pi$$
−0.0322117 + 0.999481i $$0.510255\pi$$
$$180$$ 10.8429 0.00448988
$$181$$ 1071.35 0.439959 0.219979 0.975505i $$-0.429401\pi$$
0.219979 + 0.975505i $$0.429401\pi$$
$$182$$ −605.300 −0.246527
$$183$$ 3392.45 1.37037
$$184$$ −1771.25 −0.709663
$$185$$ 64.4706 0.0256215
$$186$$ 1067.42 0.420791
$$187$$ −1653.84 −0.646742
$$188$$ 45.9554 0.0178279
$$189$$ 2707.40 1.04198
$$190$$ −155.309 −0.0593015
$$191$$ 677.203 0.256548 0.128274 0.991739i $$-0.459056\pi$$
0.128274 + 0.991739i $$0.459056\pi$$
$$192$$ −2092.81 −0.786642
$$193$$ 1321.68 0.492936 0.246468 0.969151i $$-0.420730\pi$$
0.246468 + 0.969151i $$0.420730\pi$$
$$194$$ 1494.07 0.552929
$$195$$ 26.8987 0.00987823
$$196$$ 18.1154 0.00660183
$$197$$ 1267.37 0.458356 0.229178 0.973385i $$-0.426396\pi$$
0.229178 + 0.973385i $$0.426396\pi$$
$$198$$ −2226.00 −0.798966
$$199$$ 2396.24 0.853593 0.426796 0.904348i $$-0.359642\pi$$
0.426796 + 0.904348i $$0.359642\pi$$
$$200$$ 3014.51 1.06579
$$201$$ 1637.02 0.574460
$$202$$ 2361.09 0.822403
$$203$$ 3197.51 1.10552
$$204$$ −135.401 −0.0464703
$$205$$ −39.1098 −0.0133246
$$206$$ −2384.07 −0.806339
$$207$$ −983.409 −0.330201
$$208$$ 655.503 0.218514
$$209$$ −6989.81 −2.31337
$$210$$ −96.3419 −0.0316582
$$211$$ −91.5539 −0.0298712 −0.0149356 0.999888i $$-0.504754\pi$$
−0.0149356 + 0.999888i $$0.504754\pi$$
$$212$$ −4.09466 −0.00132652
$$213$$ 1996.05 0.642099
$$214$$ 2196.23 0.701548
$$215$$ 246.130 0.0780740
$$216$$ −3601.08 −1.13436
$$217$$ −2055.70 −0.643087
$$218$$ 1720.99 0.534679
$$219$$ −2815.09 −0.868613
$$220$$ −52.2935 −0.0160256
$$221$$ 332.103 0.101085
$$222$$ −1083.61 −0.327599
$$223$$ 1235.42 0.370985 0.185493 0.982646i $$-0.440612\pi$$
0.185493 + 0.982646i $$0.440612\pi$$
$$224$$ 1167.96 0.348383
$$225$$ 1673.68 0.495905
$$226$$ 1643.17 0.483637
$$227$$ 3301.66 0.965370 0.482685 0.875794i $$-0.339662\pi$$
0.482685 + 0.875794i $$0.339662\pi$$
$$228$$ −572.260 −0.166223
$$229$$ 211.283 0.0609694 0.0304847 0.999535i $$-0.490295\pi$$
0.0304847 + 0.999535i $$0.490295\pi$$
$$230$$ 105.383 0.0302118
$$231$$ −4335.96 −1.23500
$$232$$ −4252.97 −1.20354
$$233$$ −256.724 −0.0721827 −0.0360913 0.999348i $$-0.511491\pi$$
−0.0360913 + 0.999348i $$0.511491\pi$$
$$234$$ 446.998 0.124877
$$235$$ −17.9404 −0.00498002
$$236$$ −103.040 −0.0284208
$$237$$ 1553.22 0.425708
$$238$$ −1189.48 −0.323960
$$239$$ −3549.62 −0.960694 −0.480347 0.877078i $$-0.659489\pi$$
−0.480347 + 0.877078i $$0.659489\pi$$
$$240$$ 104.332 0.0280609
$$241$$ −5030.10 −1.34447 −0.672235 0.740338i $$-0.734665\pi$$
−0.672235 + 0.740338i $$0.734665\pi$$
$$242$$ 7326.27 1.94608
$$243$$ −3334.77 −0.880353
$$244$$ 1324.37 0.347476
$$245$$ −7.07204 −0.00184415
$$246$$ 657.349 0.170370
$$247$$ 1403.61 0.361576
$$248$$ 2734.25 0.700102
$$249$$ −2224.79 −0.566226
$$250$$ −359.158 −0.0908606
$$251$$ −718.784 −0.180754 −0.0903770 0.995908i $$-0.528807\pi$$
−0.0903770 + 0.995908i $$0.528807\pi$$
$$252$$ 350.976 0.0877357
$$253$$ 4742.84 1.17858
$$254$$ −1416.98 −0.350038
$$255$$ 52.8588 0.0129810
$$256$$ −2133.74 −0.520933
$$257$$ 1280.79 0.310871 0.155435 0.987846i $$-0.450322\pi$$
0.155435 + 0.987846i $$0.450322\pi$$
$$258$$ −4136.89 −0.998262
$$259$$ 2086.87 0.500663
$$260$$ 10.5009 0.00250477
$$261$$ −2361.28 −0.559998
$$262$$ 5267.58 1.24211
$$263$$ 5225.55 1.22517 0.612587 0.790403i $$-0.290129\pi$$
0.612587 + 0.790403i $$0.290129\pi$$
$$264$$ 5767.19 1.34449
$$265$$ 1.59851 0.000370549 0
$$266$$ −5027.24 −1.15880
$$267$$ 4273.77 0.979590
$$268$$ 639.074 0.145663
$$269$$ 6443.80 1.46054 0.730270 0.683158i $$-0.239394\pi$$
0.730270 + 0.683158i $$0.239394\pi$$
$$270$$ 214.251 0.0482922
$$271$$ −3929.93 −0.880909 −0.440455 0.897775i $$-0.645183\pi$$
−0.440455 + 0.897775i $$0.645183\pi$$
$$272$$ 1288.13 0.287149
$$273$$ 870.692 0.193028
$$274$$ −4632.74 −1.02144
$$275$$ −8071.91 −1.77002
$$276$$ 388.299 0.0846842
$$277$$ −5884.40 −1.27639 −0.638194 0.769876i $$-0.720318\pi$$
−0.638194 + 0.769876i $$0.720318\pi$$
$$278$$ 3826.03 0.825431
$$279$$ 1518.08 0.325752
$$280$$ −246.785 −0.0526722
$$281$$ 3529.79 0.749358 0.374679 0.927155i $$-0.377753\pi$$
0.374679 + 0.927155i $$0.377753\pi$$
$$282$$ 301.538 0.0636750
$$283$$ −2611.00 −0.548438 −0.274219 0.961667i $$-0.588419\pi$$
−0.274219 + 0.961667i $$0.588419\pi$$
$$284$$ 779.234 0.162813
$$285$$ 223.403 0.0464325
$$286$$ −2155.81 −0.445719
$$287$$ −1265.96 −0.260373
$$288$$ −862.510 −0.176472
$$289$$ −4260.38 −0.867165
$$290$$ 253.036 0.0512372
$$291$$ −2149.15 −0.432939
$$292$$ −1098.98 −0.220250
$$293$$ −5491.03 −1.09484 −0.547422 0.836857i $$-0.684391\pi$$
−0.547422 + 0.836857i $$0.684391\pi$$
$$294$$ 118.865 0.0235795
$$295$$ 40.2255 0.00793904
$$296$$ −2775.72 −0.545052
$$297$$ 9642.56 1.88390
$$298$$ −7067.37 −1.37383
$$299$$ −952.398 −0.184209
$$300$$ −660.852 −0.127181
$$301$$ 7967.05 1.52563
$$302$$ −2500.99 −0.476542
$$303$$ −3396.30 −0.643935
$$304$$ 5444.19 1.02712
$$305$$ −517.019 −0.0970637
$$306$$ 878.399 0.164100
$$307$$ −7307.59 −1.35852 −0.679261 0.733897i $$-0.737700\pi$$
−0.679261 + 0.733897i $$0.737700\pi$$
$$308$$ −1692.71 −0.313152
$$309$$ 3429.36 0.631357
$$310$$ −162.678 −0.0298048
$$311$$ 7904.92 1.44131 0.720654 0.693295i $$-0.243842\pi$$
0.720654 + 0.693295i $$0.243842\pi$$
$$312$$ −1158.10 −0.210142
$$313$$ 10002.4 1.80629 0.903145 0.429336i $$-0.141252\pi$$
0.903145 + 0.429336i $$0.141252\pi$$
$$314$$ −1446.96 −0.260053
$$315$$ −137.017 −0.0245080
$$316$$ 606.360 0.107944
$$317$$ −6230.81 −1.10397 −0.551983 0.833856i $$-0.686129\pi$$
−0.551983 + 0.833856i $$0.686129\pi$$
$$318$$ −26.8673 −0.00473788
$$319$$ 11388.1 1.99878
$$320$$ 318.950 0.0557182
$$321$$ −3159.16 −0.549306
$$322$$ 3411.16 0.590362
$$323$$ 2758.24 0.475147
$$324$$ 268.107 0.0459717
$$325$$ 1620.90 0.276650
$$326$$ 3864.19 0.656495
$$327$$ −2475.55 −0.418649
$$328$$ 1683.83 0.283458
$$329$$ −580.719 −0.0973134
$$330$$ −343.127 −0.0572379
$$331$$ −4634.51 −0.769594 −0.384797 0.923001i $$-0.625729\pi$$
−0.384797 + 0.923001i $$0.625729\pi$$
$$332$$ −868.531 −0.143575
$$333$$ −1541.10 −0.253609
$$334$$ 1517.77 0.248649
$$335$$ −249.487 −0.0406893
$$336$$ 3377.17 0.548332
$$337$$ 3029.82 0.489747 0.244874 0.969555i $$-0.421254\pi$$
0.244874 + 0.969555i $$0.421254\pi$$
$$338$$ 432.902 0.0696651
$$339$$ −2363.61 −0.378684
$$340$$ 20.6355 0.00329151
$$341$$ −7321.47 −1.16270
$$342$$ 3712.48 0.586982
$$343$$ −6463.66 −1.01751
$$344$$ −10596.9 −1.66089
$$345$$ −151.587 −0.0236556
$$346$$ −11515.6 −1.78926
$$347$$ 2841.60 0.439611 0.219805 0.975544i $$-0.429458\pi$$
0.219805 + 0.975544i $$0.429458\pi$$
$$348$$ 932.351 0.143619
$$349$$ 7565.68 1.16040 0.580202 0.814472i $$-0.302973\pi$$
0.580202 + 0.814472i $$0.302973\pi$$
$$350$$ −5805.51 −0.886622
$$351$$ −1936.30 −0.294450
$$352$$ 4159.76 0.629875
$$353$$ −2339.44 −0.352736 −0.176368 0.984324i $$-0.556435\pi$$
−0.176368 + 0.984324i $$0.556435\pi$$
$$354$$ −676.100 −0.101509
$$355$$ −304.204 −0.0454802
$$356$$ 1668.43 0.248389
$$357$$ 1711.00 0.253658
$$358$$ −395.209 −0.0583449
$$359$$ −2531.68 −0.372192 −0.186096 0.982532i $$-0.559583\pi$$
−0.186096 + 0.982532i $$0.559583\pi$$
$$360$$ 182.244 0.0266809
$$361$$ 4798.45 0.699585
$$362$$ 2744.31 0.398447
$$363$$ −10538.5 −1.52376
$$364$$ 339.908 0.0489451
$$365$$ 429.028 0.0615243
$$366$$ 8689.93 1.24107
$$367$$ 6577.81 0.935583 0.467792 0.883839i $$-0.345050\pi$$
0.467792 + 0.883839i $$0.345050\pi$$
$$368$$ −3694.08 −0.523280
$$369$$ 934.876 0.131891
$$370$$ 165.145 0.0232040
$$371$$ 51.7426 0.00724081
$$372$$ −599.413 −0.0835433
$$373$$ 2902.72 0.402942 0.201471 0.979495i $$-0.435428\pi$$
0.201471 + 0.979495i $$0.435428\pi$$
$$374$$ −4236.40 −0.585719
$$375$$ 516.630 0.0711431
$$376$$ 772.407 0.105941
$$377$$ −2286.82 −0.312406
$$378$$ 6935.16 0.943667
$$379$$ −1865.73 −0.252866 −0.126433 0.991975i $$-0.540353\pi$$
−0.126433 + 0.991975i $$0.540353\pi$$
$$380$$ 87.2140 0.0117736
$$381$$ 2038.26 0.274076
$$382$$ 1734.69 0.232342
$$383$$ 10836.0 1.44567 0.722837 0.691019i $$-0.242838\pi$$
0.722837 + 0.691019i $$0.242838\pi$$
$$384$$ −3466.78 −0.460712
$$385$$ 660.813 0.0874757
$$386$$ 3385.55 0.446425
$$387$$ −5883.46 −0.772798
$$388$$ −839.001 −0.109778
$$389$$ −9520.34 −1.24088 −0.620438 0.784256i $$-0.713045\pi$$
−0.620438 + 0.784256i $$0.713045\pi$$
$$390$$ 68.9024 0.00894618
$$391$$ −1871.56 −0.242069
$$392$$ 304.480 0.0392310
$$393$$ −7577.13 −0.972559
$$394$$ 3246.43 0.415108
$$395$$ −236.716 −0.0301531
$$396$$ 1250.02 0.158626
$$397$$ −10108.8 −1.27796 −0.638978 0.769225i $$-0.720642\pi$$
−0.638978 + 0.769225i $$0.720642\pi$$
$$398$$ 6138.10 0.773053
$$399$$ 7231.41 0.907327
$$400$$ 6287.01 0.785876
$$401$$ 2084.38 0.259573 0.129787 0.991542i $$-0.458571\pi$$
0.129787 + 0.991542i $$0.458571\pi$$
$$402$$ 4193.32 0.520258
$$403$$ 1470.21 0.181728
$$404$$ −1325.88 −0.163279
$$405$$ −104.666 −0.0128417
$$406$$ 8190.60 1.00121
$$407$$ 7432.50 0.905197
$$408$$ −2275.78 −0.276147
$$409$$ −9716.53 −1.17470 −0.587349 0.809334i $$-0.699828\pi$$
−0.587349 + 0.809334i $$0.699828\pi$$
$$410$$ −100.182 −0.0120674
$$411$$ 6663.95 0.799777
$$412$$ 1338.78 0.160090
$$413$$ 1302.07 0.155135
$$414$$ −2519.05 −0.299045
$$415$$ 339.064 0.0401060
$$416$$ −835.311 −0.0984483
$$417$$ −5503.54 −0.646305
$$418$$ −17904.8 −2.09510
$$419$$ 13381.9 1.56026 0.780129 0.625619i $$-0.215153\pi$$
0.780129 + 0.625619i $$0.215153\pi$$
$$420$$ 54.1011 0.00628539
$$421$$ −9463.37 −1.09553 −0.547763 0.836633i $$-0.684521\pi$$
−0.547763 + 0.836633i $$0.684521\pi$$
$$422$$ −234.520 −0.0270527
$$423$$ 428.846 0.0492936
$$424$$ −68.8221 −0.00788278
$$425$$ 3185.24 0.363546
$$426$$ 5112.98 0.581514
$$427$$ −16735.5 −1.89670
$$428$$ −1233.30 −0.139285
$$429$$ 3101.02 0.348994
$$430$$ 630.474 0.0707074
$$431$$ 4852.28 0.542288 0.271144 0.962539i $$-0.412598\pi$$
0.271144 + 0.962539i $$0.412598\pi$$
$$432$$ −7510.35 −0.836439
$$433$$ −8208.00 −0.910973 −0.455486 0.890243i $$-0.650535\pi$$
−0.455486 + 0.890243i $$0.650535\pi$$
$$434$$ −5265.78 −0.582409
$$435$$ −363.979 −0.0401183
$$436$$ −966.425 −0.106155
$$437$$ −7910.01 −0.865874
$$438$$ −7211.01 −0.786656
$$439$$ −2993.80 −0.325481 −0.162741 0.986669i $$-0.552033\pi$$
−0.162741 + 0.986669i $$0.552033\pi$$
$$440$$ −878.938 −0.0952311
$$441$$ 169.049 0.0182539
$$442$$ 850.700 0.0915468
$$443$$ 9743.67 1.04500 0.522501 0.852639i $$-0.324999\pi$$
0.522501 + 0.852639i $$0.324999\pi$$
$$444$$ 608.503 0.0650411
$$445$$ −651.335 −0.0693848
$$446$$ 3164.59 0.335981
$$447$$ 10166.0 1.07570
$$448$$ 10324.2 1.08878
$$449$$ −561.459 −0.0590131 −0.0295065 0.999565i $$-0.509394\pi$$
−0.0295065 + 0.999565i $$0.509394\pi$$
$$450$$ 4287.22 0.449114
$$451$$ −4508.78 −0.470754
$$452$$ −922.726 −0.0960207
$$453$$ 3597.54 0.373128
$$454$$ 8457.38 0.874283
$$455$$ −132.696 −0.0136723
$$456$$ −9618.40 −0.987770
$$457$$ 13758.4 1.40830 0.704148 0.710054i $$-0.251329\pi$$
0.704148 + 0.710054i $$0.251329\pi$$
$$458$$ 541.213 0.0552166
$$459$$ −3805.03 −0.386936
$$460$$ −59.1779 −0.00599823
$$461$$ 12009.2 1.21329 0.606644 0.794974i $$-0.292515\pi$$
0.606644 + 0.794974i $$0.292515\pi$$
$$462$$ −11106.8 −1.11847
$$463$$ 13635.7 1.36870 0.684348 0.729156i $$-0.260087\pi$$
0.684348 + 0.729156i $$0.260087\pi$$
$$464$$ −8869.91 −0.887447
$$465$$ 234.004 0.0233369
$$466$$ −657.613 −0.0653719
$$467$$ 8821.95 0.874157 0.437079 0.899423i $$-0.356013\pi$$
0.437079 + 0.899423i $$0.356013\pi$$
$$468$$ −251.013 −0.0247929
$$469$$ −8075.72 −0.795100
$$470$$ −45.9554 −0.00451013
$$471$$ 2081.37 0.203619
$$472$$ −1731.87 −0.168889
$$473$$ 28375.1 2.75832
$$474$$ 3978.66 0.385540
$$475$$ 13462.2 1.30039
$$476$$ 667.956 0.0643187
$$477$$ −38.2105 −0.00366780
$$478$$ −9092.54 −0.870049
$$479$$ −14620.0 −1.39459 −0.697293 0.716786i $$-0.745612\pi$$
−0.697293 + 0.716786i $$0.745612\pi$$
$$480$$ −132.951 −0.0126424
$$481$$ −1492.50 −0.141481
$$482$$ −12884.9 −1.21761
$$483$$ −4906.78 −0.462249
$$484$$ −4114.09 −0.386372
$$485$$ 327.536 0.0306653
$$486$$ −8542.20 −0.797288
$$487$$ −9798.86 −0.911763 −0.455882 0.890040i $$-0.650676\pi$$
−0.455882 + 0.890040i $$0.650676\pi$$
$$488$$ 22259.7 2.06486
$$489$$ −5558.43 −0.514030
$$490$$ −18.1154 −0.00167014
$$491$$ −10836.1 −0.995977 −0.497989 0.867184i $$-0.665928\pi$$
−0.497989 + 0.867184i $$0.665928\pi$$
$$492$$ −369.136 −0.0338251
$$493$$ −4493.84 −0.410532
$$494$$ 3595.41 0.327460
$$495$$ −487.993 −0.0443104
$$496$$ 5702.51 0.516230
$$497$$ −9846.86 −0.888717
$$498$$ −5698.91 −0.512800
$$499$$ 2589.96 0.232349 0.116175 0.993229i $$-0.462937\pi$$
0.116175 + 0.993229i $$0.462937\pi$$
$$500$$ 201.686 0.0180394
$$501$$ −2183.24 −0.194690
$$502$$ −1841.20 −0.163699
$$503$$ −17067.5 −1.51292 −0.756462 0.654038i $$-0.773074\pi$$
−0.756462 + 0.654038i $$0.773074\pi$$
$$504$$ 5899.12 0.521364
$$505$$ 517.606 0.0456102
$$506$$ 12149.0 1.06737
$$507$$ −622.707 −0.0545471
$$508$$ 795.712 0.0694961
$$509$$ −1012.89 −0.0882038 −0.0441019 0.999027i $$-0.514043\pi$$
−0.0441019 + 0.999027i $$0.514043\pi$$
$$510$$ 135.401 0.0117562
$$511$$ 13887.4 1.20223
$$512$$ −12992.6 −1.12148
$$513$$ −16081.7 −1.38406
$$514$$ 3280.82 0.281539
$$515$$ −522.644 −0.0447193
$$516$$ 2323.08 0.198194
$$517$$ −2068.26 −0.175942
$$518$$ 5345.63 0.453424
$$519$$ 16564.6 1.40098
$$520$$ 176.497 0.0148845
$$521$$ −14367.7 −1.20818 −0.604089 0.796917i $$-0.706463\pi$$
−0.604089 + 0.796917i $$0.706463\pi$$
$$522$$ −6048.54 −0.507160
$$523$$ −16219.9 −1.35611 −0.678057 0.735010i $$-0.737178\pi$$
−0.678057 + 0.735010i $$0.737178\pi$$
$$524$$ −2958.02 −0.246607
$$525$$ 8350.92 0.694217
$$526$$ 13385.5 1.10957
$$527$$ 2889.11 0.238808
$$528$$ 12028.0 0.991382
$$529$$ −6799.77 −0.558870
$$530$$ 4.09466 0.000335586 0
$$531$$ −961.545 −0.0785828
$$532$$ 2823.06 0.230066
$$533$$ 905.396 0.0735780
$$534$$ 10947.5 0.887161
$$535$$ 481.466 0.0389076
$$536$$ 10741.4 0.865593
$$537$$ 568.488 0.0456835
$$538$$ 16506.1 1.32273
$$539$$ −815.301 −0.0651530
$$540$$ −120.313 −0.00958788
$$541$$ 17592.2 1.39806 0.699029 0.715094i $$-0.253616\pi$$
0.699029 + 0.715094i $$0.253616\pi$$
$$542$$ −10066.7 −0.797792
$$543$$ −3947.55 −0.311980
$$544$$ −1641.48 −0.129371
$$545$$ 377.281 0.0296531
$$546$$ 2230.32 0.174815
$$547$$ 10504.6 0.821103 0.410552 0.911837i $$-0.365336\pi$$
0.410552 + 0.911837i $$0.365336\pi$$
$$548$$ 2601.53 0.202795
$$549$$ 12358.8 0.960763
$$550$$ −20676.6 −1.60301
$$551$$ −18992.8 −1.46846
$$552$$ 6526.44 0.503231
$$553$$ −7662.33 −0.589214
$$554$$ −15073.2 −1.15596
$$555$$ −237.552 −0.0181685
$$556$$ −2148.52 −0.163880
$$557$$ −507.558 −0.0386102 −0.0193051 0.999814i $$-0.506145\pi$$
−0.0193051 + 0.999814i $$0.506145\pi$$
$$558$$ 3888.64 0.295016
$$559$$ −5697.93 −0.431121
$$560$$ −514.690 −0.0388386
$$561$$ 6093.83 0.458613
$$562$$ 9041.75 0.678653
$$563$$ −3443.14 −0.257746 −0.128873 0.991661i $$-0.541136\pi$$
−0.128873 + 0.991661i $$0.541136\pi$$
$$564$$ −169.330 −0.0126420
$$565$$ 360.221 0.0268223
$$566$$ −6688.21 −0.496690
$$567$$ −3387.96 −0.250936
$$568$$ 13097.2 0.967509
$$569$$ 23972.2 1.76620 0.883098 0.469189i $$-0.155454\pi$$
0.883098 + 0.469189i $$0.155454\pi$$
$$570$$ 572.260 0.0420514
$$571$$ −7458.32 −0.546622 −0.273311 0.961926i $$-0.588119\pi$$
−0.273311 + 0.961926i $$0.588119\pi$$
$$572$$ 1210.60 0.0884926
$$573$$ −2495.26 −0.181922
$$574$$ −3242.82 −0.235806
$$575$$ −9134.57 −0.662501
$$576$$ −7624.14 −0.551515
$$577$$ 5669.57 0.409059 0.204530 0.978860i $$-0.434434\pi$$
0.204530 + 0.978860i $$0.434434\pi$$
$$578$$ −10913.2 −0.785344
$$579$$ −4869.94 −0.349547
$$580$$ −142.093 −0.0101726
$$581$$ 10975.3 0.783702
$$582$$ −5505.15 −0.392089
$$583$$ 184.284 0.0130914
$$584$$ −18471.4 −1.30882
$$585$$ 97.9925 0.00692563
$$586$$ −14065.6 −0.991541
$$587$$ 1017.39 0.0715371 0.0357685 0.999360i $$-0.488612\pi$$
0.0357685 + 0.999360i $$0.488612\pi$$
$$588$$ −66.7491 −0.00468144
$$589$$ 12210.6 0.854208
$$590$$ 103.040 0.00718996
$$591$$ −4669.81 −0.325026
$$592$$ −5788.99 −0.401902
$$593$$ −10198.2 −0.706221 −0.353111 0.935582i $$-0.614876\pi$$
−0.353111 + 0.935582i $$0.614876\pi$$
$$594$$ 24699.9 1.70615
$$595$$ −260.762 −0.0179667
$$596$$ 3968.70 0.272759
$$597$$ −8829.33 −0.605294
$$598$$ −2439.62 −0.166828
$$599$$ 12516.3 0.853763 0.426881 0.904308i $$-0.359612\pi$$
0.426881 + 0.904308i $$0.359612\pi$$
$$600$$ −11107.4 −0.755766
$$601$$ 9627.46 0.653431 0.326716 0.945123i $$-0.394058\pi$$
0.326716 + 0.945123i $$0.394058\pi$$
$$602$$ 20408.0 1.38168
$$603$$ 5963.70 0.402754
$$604$$ 1404.44 0.0946120
$$605$$ 1606.09 0.107929
$$606$$ −8699.80 −0.583177
$$607$$ 6667.20 0.445821 0.222910 0.974839i $$-0.428444\pi$$
0.222910 + 0.974839i $$0.428444\pi$$
$$608$$ −6937.56 −0.462755
$$609$$ −11781.7 −0.783942
$$610$$ −1324.37 −0.0879053
$$611$$ 415.323 0.0274994
$$612$$ −493.268 −0.0325803
$$613$$ −23085.4 −1.52106 −0.760530 0.649302i $$-0.775061\pi$$
−0.760530 + 0.649302i $$0.775061\pi$$
$$614$$ −18718.8 −1.23034
$$615$$ 144.106 0.00944866
$$616$$ −28450.6 −1.86089
$$617$$ 3049.24 0.198959 0.0994796 0.995040i $$-0.468282\pi$$
0.0994796 + 0.995040i $$0.468282\pi$$
$$618$$ 8784.48 0.571786
$$619$$ 7296.58 0.473787 0.236894 0.971536i $$-0.423871\pi$$
0.236894 + 0.971536i $$0.423871\pi$$
$$620$$ 91.3523 0.00591741
$$621$$ 10912.0 0.705126
$$622$$ 20248.9 1.30531
$$623$$ −21083.3 −1.35583
$$624$$ −2415.30 −0.154951
$$625$$ 15506.8 0.992438
$$626$$ 25621.7 1.63586
$$627$$ 25755.1 1.64044
$$628$$ 812.543 0.0516305
$$629$$ −2932.92 −0.185920
$$630$$ −350.976 −0.0221956
$$631$$ −23829.5 −1.50339 −0.751694 0.659512i $$-0.770763\pi$$
−0.751694 + 0.659512i $$0.770763\pi$$
$$632$$ 10191.6 0.641453
$$633$$ 337.345 0.0211821
$$634$$ −15960.5 −0.999801
$$635$$ −310.637 −0.0194130
$$636$$ 15.0874 0.000940653 0
$$637$$ 163.718 0.0101833
$$638$$ 29171.3 1.81019
$$639$$ 7271.65 0.450175
$$640$$ 528.347 0.0326324
$$641$$ 13405.3 0.826016 0.413008 0.910727i $$-0.364478\pi$$
0.413008 + 0.910727i $$0.364478\pi$$
$$642$$ −8092.36 −0.497477
$$643$$ 5251.51 0.322083 0.161042 0.986948i $$-0.448515\pi$$
0.161042 + 0.986948i $$0.448515\pi$$
$$644$$ −1915.55 −0.117210
$$645$$ −906.904 −0.0553633
$$646$$ 7065.37 0.430315
$$647$$ 21611.4 1.31319 0.656595 0.754244i $$-0.271996\pi$$
0.656595 + 0.754244i $$0.271996\pi$$
$$648$$ 4506.28 0.273184
$$649$$ 4637.39 0.280483
$$650$$ 4152.02 0.250547
$$651$$ 7574.54 0.456021
$$652$$ −2169.94 −0.130340
$$653$$ −21595.8 −1.29420 −0.647099 0.762406i $$-0.724018\pi$$
−0.647099 + 0.762406i $$0.724018\pi$$
$$654$$ −6341.25 −0.379148
$$655$$ 1154.78 0.0688869
$$656$$ 3511.77 0.209012
$$657$$ −10255.4 −0.608985
$$658$$ −1487.54 −0.0881314
$$659$$ −16642.6 −0.983768 −0.491884 0.870661i $$-0.663692\pi$$
−0.491884 + 0.870661i $$0.663692\pi$$
$$660$$ 192.684 0.0113640
$$661$$ 26981.1 1.58766 0.793831 0.608139i $$-0.208084\pi$$
0.793831 + 0.608139i $$0.208084\pi$$
$$662$$ −11871.5 −0.696980
$$663$$ −1223.69 −0.0716803
$$664$$ −14598.1 −0.853185
$$665$$ −1102.09 −0.0642664
$$666$$ −3947.60 −0.229680
$$667$$ 12887.3 0.748126
$$668$$ −852.310 −0.0493665
$$669$$ −4552.09 −0.263070
$$670$$ −639.074 −0.0368501
$$671$$ −59604.5 −3.42922
$$672$$ −4303.55 −0.247043
$$673$$ 11149.2 0.638591 0.319296 0.947655i $$-0.396554\pi$$
0.319296 + 0.947655i $$0.396554\pi$$
$$674$$ 7761.04 0.443537
$$675$$ −18571.3 −1.05898
$$676$$ −243.098 −0.0138312
$$677$$ 3314.33 0.188154 0.0940769 0.995565i $$-0.470010\pi$$
0.0940769 + 0.995565i $$0.470010\pi$$
$$678$$ −6054.51 −0.342953
$$679$$ 10602.1 0.599223
$$680$$ 346.836 0.0195596
$$681$$ −12165.5 −0.684556
$$682$$ −18754.3 −1.05299
$$683$$ 24505.2 1.37287 0.686433 0.727193i $$-0.259176\pi$$
0.686433 + 0.727193i $$0.259176\pi$$
$$684$$ −2084.75 −0.116539
$$685$$ −1015.61 −0.0566486
$$686$$ −16557.0 −0.921500
$$687$$ −778.506 −0.0432342
$$688$$ −22100.6 −1.22468
$$689$$ −37.0056 −0.00204616
$$690$$ −388.299 −0.0214236
$$691$$ −21752.8 −1.19756 −0.598782 0.800912i $$-0.704348\pi$$
−0.598782 + 0.800912i $$0.704348\pi$$
$$692$$ 6466.64 0.355238
$$693$$ −15796.0 −0.865858
$$694$$ 7278.90 0.398132
$$695$$ 838.755 0.0457781
$$696$$ 15670.7 0.853445
$$697$$ 1779.20 0.0966887
$$698$$ 19379.9 1.05092
$$699$$ 945.941 0.0511857
$$700$$ 3260.10 0.176029
$$701$$ 34250.9 1.84542 0.922709 0.385496i $$-0.125970\pi$$
0.922709 + 0.385496i $$0.125970\pi$$
$$702$$ −4959.93 −0.266667
$$703$$ −12395.8 −0.665028
$$704$$ 36770.1 1.96850
$$705$$ 66.1043 0.00353140
$$706$$ −5992.59 −0.319454
$$707$$ 16754.6 0.891259
$$708$$ 379.666 0.0201536
$$709$$ −5527.11 −0.292771 −0.146386 0.989228i $$-0.546764\pi$$
−0.146386 + 0.989228i $$0.546764\pi$$
$$710$$ −779.234 −0.0411889
$$711$$ 5658.43 0.298464
$$712$$ 28042.6 1.47604
$$713$$ −8285.33 −0.435187
$$714$$ 4382.83 0.229724
$$715$$ −472.604 −0.0247194
$$716$$ 221.931 0.0115837
$$717$$ 13079.1 0.681241
$$718$$ −6485.02 −0.337074
$$719$$ −3777.78 −0.195949 −0.0979745 0.995189i $$-0.531236\pi$$
−0.0979745 + 0.995189i $$0.531236\pi$$
$$720$$ 380.085 0.0196735
$$721$$ −16917.6 −0.873849
$$722$$ 12291.5 0.633576
$$723$$ 18534.2 0.953380
$$724$$ −1541.08 −0.0791072
$$725$$ −21933.2 −1.12355
$$726$$ −26994.8 −1.37999
$$727$$ 19076.8 0.973204 0.486602 0.873624i $$-0.338236\pi$$
0.486602 + 0.873624i $$0.338236\pi$$
$$728$$ 5713.09 0.290853
$$729$$ 17319.9 0.879944
$$730$$ 1098.98 0.0557192
$$731$$ −11197.0 −0.566535
$$732$$ −4879.86 −0.246400
$$733$$ 7997.30 0.402984 0.201492 0.979490i $$-0.435421\pi$$
0.201492 + 0.979490i $$0.435421\pi$$
$$734$$ 16849.4 0.847307
$$735$$ 26.0581 0.00130771
$$736$$ 4707.39 0.235756
$$737$$ −28762.1 −1.43754
$$738$$ 2394.74 0.119446
$$739$$ 28983.6 1.44273 0.721367 0.692553i $$-0.243514\pi$$
0.721367 + 0.692553i $$0.243514\pi$$
$$740$$ −92.7376 −0.00460689
$$741$$ −5171.81 −0.256398
$$742$$ 132.541 0.00655761
$$743$$ −19145.4 −0.945324 −0.472662 0.881244i $$-0.656707\pi$$
−0.472662 + 0.881244i $$0.656707\pi$$
$$744$$ −10074.8 −0.496451
$$745$$ −1549.33 −0.0761923
$$746$$ 7435.47 0.364922
$$747$$ −8104.95 −0.396981
$$748$$ 2378.96 0.116288
$$749$$ 15584.7 0.760284
$$750$$ 1323.38 0.0644304
$$751$$ −25516.9 −1.23985 −0.619923 0.784663i $$-0.712836\pi$$
−0.619923 + 0.784663i $$0.712836\pi$$
$$752$$ 1610.92 0.0781172
$$753$$ 2648.47 0.128175
$$754$$ −5857.80 −0.282929
$$755$$ −548.275 −0.0264288
$$756$$ −3894.46 −0.187355
$$757$$ −17230.6 −0.827289 −0.413645 0.910438i $$-0.635744\pi$$
−0.413645 + 0.910438i $$0.635744\pi$$
$$758$$ −4779.17 −0.229007
$$759$$ −17475.7 −0.835744
$$760$$ 1465.87 0.0699642
$$761$$ −2343.06 −0.111611 −0.0558053 0.998442i $$-0.517773\pi$$
−0.0558053 + 0.998442i $$0.517773\pi$$
$$762$$ 5221.11 0.248216
$$763$$ 12212.3 0.579444
$$764$$ −974.121 −0.0461289
$$765$$ 192.566 0.00910096
$$766$$ 27756.9 1.30927
$$767$$ −931.223 −0.0438390
$$768$$ 7862.11 0.369400
$$769$$ −7100.18 −0.332950 −0.166475 0.986046i $$-0.553239\pi$$
−0.166475 + 0.986046i $$0.553239\pi$$
$$770$$ 1692.71 0.0792219
$$771$$ −4719.29 −0.220442
$$772$$ −1901.17 −0.0886328
$$773$$ 12270.4 0.570940 0.285470 0.958388i $$-0.407850\pi$$
0.285470 + 0.958388i $$0.407850\pi$$
$$774$$ −15070.8 −0.699881
$$775$$ 14100.9 0.653575
$$776$$ −14101.7 −0.652349
$$777$$ −7689.40 −0.355027
$$778$$ −24386.9 −1.12379
$$779$$ 7519.64 0.345852
$$780$$ −38.6924 −0.00177616
$$781$$ −35070.1 −1.60680
$$782$$ −4794.11 −0.219229
$$783$$ 26201.0 1.19584
$$784$$ 635.017 0.0289275
$$785$$ −317.207 −0.0144224
$$786$$ −19409.2 −0.880794
$$787$$ 3425.04 0.155133 0.0775663 0.996987i $$-0.475285\pi$$
0.0775663 + 0.996987i $$0.475285\pi$$
$$788$$ −1823.04 −0.0824151
$$789$$ −19254.3 −0.868787
$$790$$ −606.360 −0.0273080
$$791$$ 11660.1 0.524129
$$792$$ 21010.0 0.942624
$$793$$ 11969.0 0.535981
$$794$$ −25894.3 −1.15737
$$795$$ −5.88995 −0.000262761 0
$$796$$ −3446.87 −0.153481
$$797$$ −11781.1 −0.523600 −0.261800 0.965122i $$-0.584316\pi$$
−0.261800 + 0.965122i $$0.584316\pi$$
$$798$$ 18523.6 0.821717
$$799$$ 816.154 0.0361370
$$800$$ −8011.58 −0.354065
$$801$$ 15569.4 0.686790
$$802$$ 5339.24 0.235081
$$803$$ 49460.6 2.17363
$$804$$ −2354.77 −0.103291
$$805$$ 747.807 0.0327413
$$806$$ 3766.01 0.164581
$$807$$ −23743.2 −1.03569
$$808$$ −22285.0 −0.970276
$$809$$ 18910.1 0.821810 0.410905 0.911678i $$-0.365213\pi$$
0.410905 + 0.911678i $$0.365213\pi$$
$$810$$ −268.107 −0.0116300
$$811$$ 12803.3 0.554359 0.277180 0.960818i $$-0.410600\pi$$
0.277180 + 0.960818i $$0.410600\pi$$
$$812$$ −4599.45 −0.198780
$$813$$ 14480.5 0.624664
$$814$$ 19038.7 0.819788
$$815$$ 847.121 0.0364090
$$816$$ −4746.33 −0.203621
$$817$$ −47323.3 −2.02648
$$818$$ −24889.4 −1.06386
$$819$$ 3171.95 0.135332
$$820$$ 56.2574 0.00239585
$$821$$ 19335.1 0.821923 0.410962 0.911653i $$-0.365193\pi$$
0.410962 + 0.911653i $$0.365193\pi$$
$$822$$ 17070.1 0.724315
$$823$$ −2125.90 −0.0900417 −0.0450209 0.998986i $$-0.514335\pi$$
−0.0450209 + 0.998986i $$0.514335\pi$$
$$824$$ 22501.9 0.951324
$$825$$ 29742.2 1.25514
$$826$$ 3335.32 0.140497
$$827$$ −6989.24 −0.293881 −0.146941 0.989145i $$-0.546943\pi$$
−0.146941 + 0.989145i $$0.546943\pi$$
$$828$$ 1414.58 0.0593721
$$829$$ −32649.7 −1.36788 −0.683938 0.729540i $$-0.739734\pi$$
−0.683938 + 0.729540i $$0.739734\pi$$
$$830$$ 868.531 0.0363219
$$831$$ 21682.0 0.905103
$$832$$ −7383.72 −0.307673
$$833$$ 321.724 0.0133819
$$834$$ −14097.6 −0.585324
$$835$$ 332.732 0.0137900
$$836$$ 10054.5 0.415958
$$837$$ −16844.7 −0.695626
$$838$$ 34278.4 1.41304
$$839$$ −4038.23 −0.166168 −0.0830841 0.996543i $$-0.526477\pi$$
−0.0830841 + 0.996543i $$0.526477\pi$$
$$840$$ 909.318 0.0373505
$$841$$ 6555.00 0.268769
$$842$$ −24240.9 −0.992159
$$843$$ −13006.1 −0.531380
$$844$$ 131.695 0.00537102
$$845$$ 94.9024 0.00386360
$$846$$ 1098.51 0.0446426
$$847$$ 51988.1 2.10901
$$848$$ −143.534 −0.00581248
$$849$$ 9620.64 0.388904
$$850$$ 8159.17 0.329244
$$851$$ 8410.97 0.338807
$$852$$ −2871.21 −0.115453
$$853$$ 8114.12 0.325700 0.162850 0.986651i $$-0.447931\pi$$
0.162850 + 0.986651i $$0.447931\pi$$
$$854$$ −42869.0 −1.71774
$$855$$ 813.863 0.0325538
$$856$$ −20729.0 −0.827690
$$857$$ −22298.1 −0.888786 −0.444393 0.895832i $$-0.646581\pi$$
−0.444393 + 0.895832i $$0.646581\pi$$
$$858$$ 7943.42 0.316065
$$859$$ 33550.5 1.33263 0.666315 0.745670i $$-0.267870\pi$$
0.666315 + 0.745670i $$0.267870\pi$$
$$860$$ −354.045 −0.0140382
$$861$$ 4664.62 0.184634
$$862$$ 12429.4 0.491121
$$863$$ −14120.5 −0.556972 −0.278486 0.960440i $$-0.589833\pi$$
−0.278486 + 0.960440i $$0.589833\pi$$
$$864$$ 9570.49 0.376846
$$865$$ −2524.50 −0.0992319
$$866$$ −21025.2 −0.825018
$$867$$ 15698.1 0.614918
$$868$$ 2957.01 0.115631
$$869$$ −27289.8 −1.06530
$$870$$ −932.351 −0.0363329
$$871$$ 5775.64 0.224685
$$872$$ −16243.4 −0.630817
$$873$$ −7829.39 −0.303533
$$874$$ −20261.9 −0.784175
$$875$$ −2548.63 −0.0984679
$$876$$ 4049.36 0.156182
$$877$$ −1941.69 −0.0747619 −0.0373809 0.999301i $$-0.511901\pi$$
−0.0373809 + 0.999301i $$0.511901\pi$$
$$878$$ −7668.78 −0.294771
$$879$$ 20232.6 0.776368
$$880$$ −1833.10 −0.0702201
$$881$$ −790.231 −0.0302197 −0.0151099 0.999886i $$-0.504810\pi$$
−0.0151099 + 0.999886i $$0.504810\pi$$
$$882$$ 433.029 0.0165316
$$883$$ −36638.6 −1.39636 −0.698180 0.715922i $$-0.746007\pi$$
−0.698180 + 0.715922i $$0.746007\pi$$
$$884$$ −477.713 −0.0181756
$$885$$ −148.217 −0.00562968
$$886$$ 24958.9 0.946401
$$887$$ −40686.3 −1.54015 −0.770075 0.637954i $$-0.779781\pi$$
−0.770075 + 0.637954i $$0.779781\pi$$
$$888$$ 10227.6 0.386503
$$889$$ −10055.1 −0.379344
$$890$$ −1668.43 −0.0628381
$$891$$ −12066.4 −0.453692
$$892$$ −1777.08 −0.0667053
$$893$$ 3449.40 0.129261
$$894$$ 26040.9 0.974202
$$895$$ −86.6392 −0.00323579
$$896$$ 17102.2 0.637663
$$897$$ 3509.26 0.130625
$$898$$ −1438.21 −0.0534449
$$899$$ −19894.0 −0.738046
$$900$$ −2407.50 −0.0891666
$$901$$ −72.7200 −0.00268885
$$902$$ −11549.5 −0.426336
$$903$$ −29355.9 −1.08184
$$904$$ −15509.0 −0.570598
$$905$$ 601.618 0.0220977
$$906$$ 9215.28 0.337922
$$907$$ −10464.4 −0.383093 −0.191547 0.981484i $$-0.561350\pi$$
−0.191547 + 0.981484i $$0.561350\pi$$
$$908$$ −4749.26 −0.173579
$$909$$ −12372.8 −0.451463
$$910$$ −339.908 −0.0123822
$$911$$ −35611.5 −1.29513 −0.647563 0.762011i $$-0.724212\pi$$
−0.647563 + 0.762011i $$0.724212\pi$$
$$912$$ −20060.0 −0.728346
$$913$$ 39089.0 1.41693
$$914$$ 35242.9 1.27542
$$915$$ 1905.04 0.0688291
$$916$$ −303.920 −0.0109627
$$917$$ 37379.4 1.34610
$$918$$ −9746.80 −0.350427
$$919$$ 1077.25 0.0386674 0.0193337 0.999813i $$-0.493846\pi$$
0.0193337 + 0.999813i $$0.493846\pi$$
$$920$$ −994.648 −0.0356441
$$921$$ 26926.0 0.963346
$$922$$ 30762.3 1.09881
$$923$$ 7042.34 0.251139
$$924$$ 6237.04 0.222060
$$925$$ −14314.8 −0.508829
$$926$$ 34928.6 1.23955
$$927$$ 12493.2 0.442644
$$928$$ 11303.0 0.399826
$$929$$ 55733.8 1.96832 0.984159 0.177290i $$-0.0567330\pi$$
0.984159 + 0.177290i $$0.0567330\pi$$
$$930$$ 599.413 0.0211350
$$931$$ 1359.74 0.0478665
$$932$$ 369.284 0.0129789
$$933$$ −29126.9 −1.02205
$$934$$ 22597.9 0.791677
$$935$$ −928.718 −0.0324838
$$936$$ −4218.97 −0.147330
$$937$$ −3198.60 −0.111519 −0.0557596 0.998444i $$-0.517758\pi$$
−0.0557596 + 0.998444i $$0.517758\pi$$
$$938$$ −20686.4 −0.720079
$$939$$ −36855.4 −1.28086
$$940$$ 25.8064 0.000895437 0
$$941$$ 8823.35 0.305667 0.152834 0.988252i $$-0.451160\pi$$
0.152834 + 0.988252i $$0.451160\pi$$
$$942$$ 5331.54 0.184407
$$943$$ −5102.35 −0.176199
$$944$$ −3611.95 −0.124533
$$945$$ 1520.35 0.0523354
$$946$$ 72684.3 2.49806
$$947$$ 28290.4 0.970766 0.485383 0.874301i $$-0.338680\pi$$
0.485383 + 0.874301i $$0.338680\pi$$
$$948$$ −2234.23 −0.0765447
$$949$$ −9932.05 −0.339734
$$950$$ 34484.0 1.17769
$$951$$ 22958.4 0.782836
$$952$$ 11226.8 0.382210
$$953$$ −12399.0 −0.421452 −0.210726 0.977545i $$-0.567583\pi$$
−0.210726 + 0.977545i $$0.567583\pi$$
$$954$$ −97.8783 −0.00332173
$$955$$ 380.285 0.0128856
$$956$$ 5105.94 0.172739
$$957$$ −41961.3 −1.41736
$$958$$ −37450.0 −1.26300
$$959$$ −32874.5 −1.10696
$$960$$ −1175.22 −0.0395105
$$961$$ −17001.0 −0.570676
$$962$$ −3823.12 −0.128131
$$963$$ −11508.9 −0.385118
$$964$$ 7235.53 0.241744
$$965$$ 742.193 0.0247586
$$966$$ −12569.0 −0.418634
$$967$$ −26667.1 −0.886820 −0.443410 0.896319i $$-0.646231\pi$$
−0.443410 + 0.896319i $$0.646231\pi$$
$$968$$ −69148.6 −2.29599
$$969$$ −10163.2 −0.336933
$$970$$ 839.001 0.0277719
$$971$$ 49420.7 1.63335 0.816676 0.577096i $$-0.195814\pi$$
0.816676 + 0.577096i $$0.195814\pi$$
$$972$$ 4796.89 0.158293
$$973$$ 27149.9 0.894539
$$974$$ −25100.3 −0.825735
$$975$$ −5972.46 −0.196176
$$976$$ 46424.5 1.52255
$$977$$ 778.759 0.0255012 0.0127506 0.999919i $$-0.495941\pi$$
0.0127506 + 0.999919i $$0.495941\pi$$
$$978$$ −14238.2 −0.465529
$$979$$ −75089.2 −2.45134
$$980$$ 10.1728 0.000331589 0
$$981$$ −9018.48 −0.293515
$$982$$ −27757.2 −0.902003
$$983$$ 5997.90 0.194612 0.0973059 0.995255i $$-0.468977\pi$$
0.0973059 + 0.995255i $$0.468977\pi$$
$$984$$ −6204.35 −0.201004
$$985$$ 711.693 0.0230218
$$986$$ −11511.2 −0.371797
$$987$$ 2139.75 0.0690062
$$988$$ −2019.01 −0.0650135
$$989$$ 32110.6 1.03241
$$990$$ −1250.02 −0.0401295
$$991$$ 8974.94 0.287688 0.143844 0.989600i $$-0.454054\pi$$
0.143844 + 0.989600i $$0.454054\pi$$
$$992$$ −7266.75 −0.232580
$$993$$ 17076.6 0.545729
$$994$$ −25223.3 −0.804863
$$995$$ 1345.62 0.0428732
$$996$$ 3200.24 0.101811
$$997$$ 28530.2 0.906280 0.453140 0.891439i $$-0.350304\pi$$
0.453140 + 0.891439i $$0.350304\pi$$
$$998$$ 6634.31 0.210426
$$999$$ 17100.2 0.541567
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 13.4.a.b.1.2 2
3.2 odd 2 117.4.a.d.1.1 2
4.3 odd 2 208.4.a.h.1.2 2
5.2 odd 4 325.4.b.e.274.4 4
5.3 odd 4 325.4.b.e.274.1 4
5.4 even 2 325.4.a.f.1.1 2
7.6 odd 2 637.4.a.b.1.2 2
8.3 odd 2 832.4.a.z.1.1 2
8.5 even 2 832.4.a.s.1.2 2
11.10 odd 2 1573.4.a.b.1.1 2
12.11 even 2 1872.4.a.bb.1.1 2
13.2 odd 12 169.4.e.f.147.4 8
13.3 even 3 169.4.c.g.22.1 4
13.4 even 6 169.4.c.j.146.2 4
13.5 odd 4 169.4.b.f.168.1 4
13.6 odd 12 169.4.e.f.23.1 8
13.7 odd 12 169.4.e.f.23.4 8
13.8 odd 4 169.4.b.f.168.4 4
13.9 even 3 169.4.c.g.146.1 4
13.10 even 6 169.4.c.j.22.2 4
13.11 odd 12 169.4.e.f.147.1 8
13.12 even 2 169.4.a.g.1.1 2
39.38 odd 2 1521.4.a.r.1.2 2

By twisted newform
Twist Min Dim Char Parity Ord Type
13.4.a.b.1.2 2 1.1 even 1 trivial
117.4.a.d.1.1 2 3.2 odd 2
169.4.a.g.1.1 2 13.12 even 2
169.4.b.f.168.1 4 13.5 odd 4
169.4.b.f.168.4 4 13.8 odd 4
169.4.c.g.22.1 4 13.3 even 3
169.4.c.g.146.1 4 13.9 even 3
169.4.c.j.22.2 4 13.10 even 6
169.4.c.j.146.2 4 13.4 even 6
169.4.e.f.23.1 8 13.6 odd 12
169.4.e.f.23.4 8 13.7 odd 12
169.4.e.f.147.1 8 13.11 odd 12
169.4.e.f.147.4 8 13.2 odd 12
208.4.a.h.1.2 2 4.3 odd 2
325.4.a.f.1.1 2 5.4 even 2
325.4.b.e.274.1 4 5.3 odd 4
325.4.b.e.274.4 4 5.2 odd 4
637.4.a.b.1.2 2 7.6 odd 2
832.4.a.s.1.2 2 8.5 even 2
832.4.a.z.1.1 2 8.3 odd 2
1521.4.a.r.1.2 2 39.38 odd 2
1573.4.a.b.1.1 2 11.10 odd 2
1872.4.a.bb.1.1 2 12.11 even 2