# Properties

 Label 35.6.a.b.1.1 Level $35$ Weight $6$ Character 35.1 Self dual yes Analytic conductor $5.613$ Analytic rank $1$ Dimension $2$ CM no Inner twists $1$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$35 = 5 \cdot 7$$ Weight: $$k$$ $$=$$ $$6$$ Character orbit: $$[\chi]$$ $$=$$ 35.a (trivial)

## Newform invariants

 Self dual: yes Analytic conductor: $$5.61343369345$$ Analytic rank: $$1$$ Dimension: $$2$$ Coefficient field: $$\Q(\sqrt{65})$$ Defining polynomial: $$x^{2} - x - 16$$ x^2 - x - 16 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 $$-3.53113$$ of defining polynomial Character $$\chi$$ $$=$$ 35.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q-3.53113 q^{2} +13.5934 q^{3} -19.5311 q^{4} -25.0000 q^{5} -48.0000 q^{6} -49.0000 q^{7} +181.963 q^{8} -58.2198 q^{9} +O(q^{10})$$ $$q-3.53113 q^{2} +13.5934 q^{3} -19.5311 q^{4} -25.0000 q^{5} -48.0000 q^{6} -49.0000 q^{7} +181.963 q^{8} -58.2198 q^{9} +88.2782 q^{10} -691.520 q^{11} -265.494 q^{12} -502.150 q^{13} +173.025 q^{14} -339.835 q^{15} -17.5389 q^{16} -991.313 q^{17} +205.582 q^{18} +661.677 q^{19} +488.278 q^{20} -666.076 q^{21} +2441.84 q^{22} +3415.08 q^{23} +2473.49 q^{24} +625.000 q^{25} +1773.16 q^{26} -4094.60 q^{27} +957.025 q^{28} +6751.92 q^{29} +1200.00 q^{30} -3922.76 q^{31} -5760.89 q^{32} -9400.09 q^{33} +3500.46 q^{34} +1225.00 q^{35} +1137.10 q^{36} +627.222 q^{37} -2336.47 q^{38} -6825.92 q^{39} -4549.08 q^{40} +16277.9 q^{41} +2352.00 q^{42} -17277.7 q^{43} +13506.2 q^{44} +1455.50 q^{45} -12059.1 q^{46} -4295.47 q^{47} -238.413 q^{48} +2401.00 q^{49} -2206.96 q^{50} -13475.3 q^{51} +9807.55 q^{52} -25960.9 q^{53} +14458.6 q^{54} +17288.0 q^{55} -8916.19 q^{56} +8994.43 q^{57} -23841.9 q^{58} +8902.63 q^{59} +6637.35 q^{60} -48924.6 q^{61} +13851.8 q^{62} +2852.77 q^{63} +20903.7 q^{64} +12553.7 q^{65} +33192.9 q^{66} -4257.80 q^{67} +19361.5 q^{68} +46422.5 q^{69} -4325.63 q^{70} +18990.9 q^{71} -10593.9 q^{72} +10132.5 q^{73} -2214.80 q^{74} +8495.87 q^{75} -12923.3 q^{76} +33884.5 q^{77} +24103.2 q^{78} -96986.5 q^{79} +438.472 q^{80} -41512.0 q^{81} -57479.2 q^{82} +70732.1 q^{83} +13009.2 q^{84} +24782.8 q^{85} +61009.8 q^{86} +91781.4 q^{87} -125831. q^{88} +4241.12 q^{89} -5139.54 q^{90} +24605.3 q^{91} -66700.3 q^{92} -53323.6 q^{93} +15167.9 q^{94} -16541.9 q^{95} -78309.9 q^{96} -104376. q^{97} -8478.24 q^{98} +40260.2 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q + q^{2} + 3 q^{3} - 31 q^{4} - 50 q^{5} - 96 q^{6} - 98 q^{7} - 15 q^{8} - 189 q^{9}+O(q^{10})$$ 2 * q + q^2 + 3 * q^3 - 31 * q^4 - 50 * q^5 - 96 * q^6 - 98 * q^7 - 15 * q^8 - 189 * q^9 $$2 q + q^{2} + 3 q^{3} - 31 q^{4} - 50 q^{5} - 96 q^{6} - 98 q^{7} - 15 q^{8} - 189 q^{9} - 25 q^{10} - 601 q^{11} - 144 q^{12} - 577 q^{13} - 49 q^{14} - 75 q^{15} - 543 q^{16} + 41 q^{17} - 387 q^{18} + 630 q^{19} + 775 q^{20} - 147 q^{21} + 2852 q^{22} - 442 q^{23} + 4560 q^{24} + 1250 q^{25} + 1434 q^{26} - 135 q^{27} + 1519 q^{28} + 5885 q^{29} + 2400 q^{30} - 396 q^{31} - 1839 q^{32} - 10359 q^{33} + 8178 q^{34} + 2450 q^{35} + 2637 q^{36} - 8904 q^{37} - 2480 q^{38} - 6033 q^{39} + 375 q^{40} + 1774 q^{41} + 4704 q^{42} - 27122 q^{43} + 12468 q^{44} + 4725 q^{45} - 29536 q^{46} - 21289 q^{47} + 5328 q^{48} + 4802 q^{49} + 625 q^{50} - 24411 q^{51} + 10666 q^{52} - 55582 q^{53} + 32400 q^{54} + 15025 q^{55} + 735 q^{56} + 9330 q^{57} - 27770 q^{58} + 59600 q^{59} + 3600 q^{60} - 51846 q^{61} + 29832 q^{62} + 9261 q^{63} + 55489 q^{64} + 14425 q^{65} + 28848 q^{66} - 45344 q^{67} + 7522 q^{68} + 87282 q^{69} + 1225 q^{70} + 80744 q^{71} + 15165 q^{72} - 13532 q^{73} - 45402 q^{74} + 1875 q^{75} - 12560 q^{76} + 29449 q^{77} + 27696 q^{78} - 51795 q^{79} + 13575 q^{80} - 51678 q^{81} - 123198 q^{82} + 109828 q^{83} + 7056 q^{84} - 1025 q^{85} + 16404 q^{86} + 100965 q^{87} - 143660 q^{88} - 37650 q^{89} + 9675 q^{90} + 28273 q^{91} - 22464 q^{92} - 90684 q^{93} - 61832 q^{94} - 15750 q^{95} - 119856 q^{96} - 96339 q^{97} + 2401 q^{98} + 28422 q^{99}+O(q^{100})$$ 2 * q + q^2 + 3 * q^3 - 31 * q^4 - 50 * q^5 - 96 * q^6 - 98 * q^7 - 15 * q^8 - 189 * q^9 - 25 * q^10 - 601 * q^11 - 144 * q^12 - 577 * q^13 - 49 * q^14 - 75 * q^15 - 543 * q^16 + 41 * q^17 - 387 * q^18 + 630 * q^19 + 775 * q^20 - 147 * q^21 + 2852 * q^22 - 442 * q^23 + 4560 * q^24 + 1250 * q^25 + 1434 * q^26 - 135 * q^27 + 1519 * q^28 + 5885 * q^29 + 2400 * q^30 - 396 * q^31 - 1839 * q^32 - 10359 * q^33 + 8178 * q^34 + 2450 * q^35 + 2637 * q^36 - 8904 * q^37 - 2480 * q^38 - 6033 * q^39 + 375 * q^40 + 1774 * q^41 + 4704 * q^42 - 27122 * q^43 + 12468 * q^44 + 4725 * q^45 - 29536 * q^46 - 21289 * q^47 + 5328 * q^48 + 4802 * q^49 + 625 * q^50 - 24411 * q^51 + 10666 * q^52 - 55582 * q^53 + 32400 * q^54 + 15025 * q^55 + 735 * q^56 + 9330 * q^57 - 27770 * q^58 + 59600 * q^59 + 3600 * q^60 - 51846 * q^61 + 29832 * q^62 + 9261 * q^63 + 55489 * q^64 + 14425 * q^65 + 28848 * q^66 - 45344 * q^67 + 7522 * q^68 + 87282 * q^69 + 1225 * q^70 + 80744 * q^71 + 15165 * q^72 - 13532 * q^73 - 45402 * q^74 + 1875 * q^75 - 12560 * q^76 + 29449 * q^77 + 27696 * q^78 - 51795 * q^79 + 13575 * q^80 - 51678 * q^81 - 123198 * q^82 + 109828 * q^83 + 7056 * q^84 - 1025 * q^85 + 16404 * q^86 + 100965 * q^87 - 143660 * q^88 - 37650 * q^89 + 9675 * q^90 + 28273 * q^91 - 22464 * q^92 - 90684 * q^93 - 61832 * q^94 - 15750 * q^95 - 119856 * q^96 - 96339 * q^97 + 2401 * q^98 + 28422 * 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −3.53113 −0.624221 −0.312111 0.950046i $$-0.601036\pi$$
−0.312111 + 0.950046i $$0.601036\pi$$
$$3$$ 13.5934 0.872016 0.436008 0.899943i $$-0.356392\pi$$
0.436008 + 0.899943i $$0.356392\pi$$
$$4$$ −19.5311 −0.610348
$$5$$ −25.0000 −0.447214
$$6$$ −48.0000 −0.544331
$$7$$ −49.0000 −0.377964
$$8$$ 181.963 1.00521
$$9$$ −58.2198 −0.239588
$$10$$ 88.2782 0.279160
$$11$$ −691.520 −1.72315 −0.861574 0.507632i $$-0.830521\pi$$
−0.861574 + 0.507632i $$0.830521\pi$$
$$12$$ −265.494 −0.532233
$$13$$ −502.150 −0.824091 −0.412045 0.911163i $$-0.635185\pi$$
−0.412045 + 0.911163i $$0.635185\pi$$
$$14$$ 173.025 0.235933
$$15$$ −339.835 −0.389977
$$16$$ −17.5389 −0.0171278
$$17$$ −991.313 −0.831934 −0.415967 0.909380i $$-0.636557\pi$$
−0.415967 + 0.909380i $$0.636557\pi$$
$$18$$ 205.582 0.149556
$$19$$ 661.677 0.420496 0.210248 0.977648i $$-0.432573\pi$$
0.210248 + 0.977648i $$0.432573\pi$$
$$20$$ 488.278 0.272956
$$21$$ −666.076 −0.329591
$$22$$ 2441.84 1.07563
$$23$$ 3415.08 1.34611 0.673056 0.739592i $$-0.264981\pi$$
0.673056 + 0.739592i $$0.264981\pi$$
$$24$$ 2473.49 0.876562
$$25$$ 625.000 0.200000
$$26$$ 1773.16 0.514415
$$27$$ −4094.60 −1.08094
$$28$$ 957.025 0.230690
$$29$$ 6751.92 1.49084 0.745422 0.666593i $$-0.232248\pi$$
0.745422 + 0.666593i $$0.232248\pi$$
$$30$$ 1200.00 0.243432
$$31$$ −3922.76 −0.733142 −0.366571 0.930390i $$-0.619468\pi$$
−0.366571 + 0.930390i $$0.619468\pi$$
$$32$$ −5760.89 −0.994522
$$33$$ −9400.09 −1.50261
$$34$$ 3500.46 0.519311
$$35$$ 1225.00 0.169031
$$36$$ 1137.10 0.146232
$$37$$ 627.222 0.0753212 0.0376606 0.999291i $$-0.488009\pi$$
0.0376606 + 0.999291i $$0.488009\pi$$
$$38$$ −2336.47 −0.262483
$$39$$ −6825.92 −0.718620
$$40$$ −4549.08 −0.449545
$$41$$ 16277.9 1.51230 0.756149 0.654399i $$-0.227078\pi$$
0.756149 + 0.654399i $$0.227078\pi$$
$$42$$ 2352.00 0.205738
$$43$$ −17277.7 −1.42500 −0.712500 0.701672i $$-0.752437\pi$$
−0.712500 + 0.701672i $$0.752437\pi$$
$$44$$ 13506.2 1.05172
$$45$$ 1455.50 0.107147
$$46$$ −12059.1 −0.840272
$$47$$ −4295.47 −0.283639 −0.141820 0.989893i $$-0.545295\pi$$
−0.141820 + 0.989893i $$0.545295\pi$$
$$48$$ −238.413 −0.0149357
$$49$$ 2401.00 0.142857
$$50$$ −2206.96 −0.124844
$$51$$ −13475.3 −0.725460
$$52$$ 9807.55 0.502982
$$53$$ −25960.9 −1.26949 −0.634745 0.772721i $$-0.718895\pi$$
−0.634745 + 0.772721i $$0.718895\pi$$
$$54$$ 14458.6 0.674746
$$55$$ 17288.0 0.770615
$$56$$ −8916.19 −0.379935
$$57$$ 8994.43 0.366679
$$58$$ −23841.9 −0.930616
$$59$$ 8902.63 0.332957 0.166479 0.986045i $$-0.446760\pi$$
0.166479 + 0.986045i $$0.446760\pi$$
$$60$$ 6637.35 0.238022
$$61$$ −48924.6 −1.68346 −0.841730 0.539898i $$-0.818463\pi$$
−0.841730 + 0.539898i $$0.818463\pi$$
$$62$$ 13851.8 0.457643
$$63$$ 2852.77 0.0905557
$$64$$ 20903.7 0.637930
$$65$$ 12553.7 0.368545
$$66$$ 33192.9 0.937963
$$67$$ −4257.80 −0.115877 −0.0579387 0.998320i $$-0.518453\pi$$
−0.0579387 + 0.998320i $$0.518453\pi$$
$$68$$ 19361.5 0.507769
$$69$$ 46422.5 1.17383
$$70$$ −4325.63 −0.105513
$$71$$ 18990.9 0.447095 0.223547 0.974693i $$-0.428236\pi$$
0.223547 + 0.974693i $$0.428236\pi$$
$$72$$ −10593.9 −0.240837
$$73$$ 10132.5 0.222541 0.111270 0.993790i $$-0.464508\pi$$
0.111270 + 0.993790i $$0.464508\pi$$
$$74$$ −2214.80 −0.0470171
$$75$$ 8495.87 0.174403
$$76$$ −12923.3 −0.256649
$$77$$ 33884.5 0.651289
$$78$$ 24103.2 0.448578
$$79$$ −96986.5 −1.74841 −0.874205 0.485557i $$-0.838617\pi$$
−0.874205 + 0.485557i $$0.838617\pi$$
$$80$$ 438.472 0.00765979
$$81$$ −41512.0 −0.703010
$$82$$ −57479.2 −0.944009
$$83$$ 70732.1 1.12699 0.563497 0.826118i $$-0.309456\pi$$
0.563497 + 0.826118i $$0.309456\pi$$
$$84$$ 13009.2 0.201165
$$85$$ 24782.8 0.372052
$$86$$ 61009.8 0.889515
$$87$$ 91781.4 1.30004
$$88$$ −125831. −1.73213
$$89$$ 4241.12 0.0567552 0.0283776 0.999597i $$-0.490966\pi$$
0.0283776 + 0.999597i $$0.490966\pi$$
$$90$$ −5139.54 −0.0668834
$$91$$ 24605.3 0.311477
$$92$$ −66700.3 −0.821596
$$93$$ −53323.6 −0.639311
$$94$$ 15167.9 0.177054
$$95$$ −16541.9 −0.188052
$$96$$ −78309.9 −0.867239
$$97$$ −104376. −1.12634 −0.563170 0.826341i $$-0.690418\pi$$
−0.563170 + 0.826341i $$0.690418\pi$$
$$98$$ −8478.24 −0.0891745
$$99$$ 40260.2 0.412845
$$100$$ −12207.0 −0.122070
$$101$$ −45715.1 −0.445919 −0.222959 0.974828i $$-0.571572\pi$$
−0.222959 + 0.974828i $$0.571572\pi$$
$$102$$ 47583.0 0.452847
$$103$$ 89278.1 0.829186 0.414593 0.910007i $$-0.363924\pi$$
0.414593 + 0.910007i $$0.363924\pi$$
$$104$$ −91372.7 −0.828387
$$105$$ 16651.9 0.147398
$$106$$ 91671.2 0.792443
$$107$$ −106330. −0.897834 −0.448917 0.893573i $$-0.648190\pi$$
−0.448917 + 0.893573i $$0.648190\pi$$
$$108$$ 79972.1 0.659750
$$109$$ −49816.5 −0.401613 −0.200806 0.979631i $$-0.564356\pi$$
−0.200806 + 0.979631i $$0.564356\pi$$
$$110$$ −61046.1 −0.481035
$$111$$ 8526.08 0.0656813
$$112$$ 859.405 0.00647370
$$113$$ −37160.7 −0.273771 −0.136886 0.990587i $$-0.543709\pi$$
−0.136886 + 0.990587i $$0.543709\pi$$
$$114$$ −31760.5 −0.228889
$$115$$ −85377.0 −0.601999
$$116$$ −131873. −0.909933
$$117$$ 29235.1 0.197442
$$118$$ −31436.3 −0.207839
$$119$$ 48574.4 0.314441
$$120$$ −61837.4 −0.392011
$$121$$ 317148. 1.96924
$$122$$ 172759. 1.05085
$$123$$ 221271. 1.31875
$$124$$ 76616.0 0.447471
$$125$$ −15625.0 −0.0894427
$$126$$ −10073.5 −0.0565268
$$127$$ −46510.2 −0.255882 −0.127941 0.991782i $$-0.540837\pi$$
−0.127941 + 0.991782i $$0.540837\pi$$
$$128$$ 110535. 0.596313
$$129$$ −234862. −1.24262
$$130$$ −44328.9 −0.230053
$$131$$ 381771. 1.94368 0.971839 0.235646i $$-0.0757206\pi$$
0.971839 + 0.235646i $$0.0757206\pi$$
$$132$$ 183594. 0.917117
$$133$$ −32422.2 −0.158933
$$134$$ 15034.9 0.0723331
$$135$$ 102365. 0.483411
$$136$$ −180382. −0.836271
$$137$$ −1894.54 −0.00862389 −0.00431194 0.999991i $$-0.501373\pi$$
−0.00431194 + 0.999991i $$0.501373\pi$$
$$138$$ −163924. −0.732730
$$139$$ 201798. 0.885889 0.442944 0.896549i $$-0.353934\pi$$
0.442944 + 0.896549i $$0.353934\pi$$
$$140$$ −23925.6 −0.103168
$$141$$ −58390.0 −0.247338
$$142$$ −67059.3 −0.279086
$$143$$ 347246. 1.42003
$$144$$ 1021.11 0.00410362
$$145$$ −168798. −0.666726
$$146$$ −35779.1 −0.138915
$$147$$ 32637.7 0.124574
$$148$$ −12250.4 −0.0459721
$$149$$ −466237. −1.72045 −0.860224 0.509917i $$-0.829676\pi$$
−0.860224 + 0.509917i $$0.829676\pi$$
$$150$$ −30000.0 −0.108866
$$151$$ −122212. −0.436185 −0.218093 0.975928i $$-0.569983\pi$$
−0.218093 + 0.975928i $$0.569983\pi$$
$$152$$ 120401. 0.422688
$$153$$ 57714.1 0.199321
$$154$$ −119650. −0.406548
$$155$$ 98069.1 0.327871
$$156$$ 133318. 0.438608
$$157$$ −410638. −1.32957 −0.664784 0.747036i $$-0.731476\pi$$
−0.664784 + 0.747036i $$0.731476\pi$$
$$158$$ 342472. 1.09139
$$159$$ −352896. −1.10702
$$160$$ 144022. 0.444764
$$161$$ −167339. −0.508782
$$162$$ 146584. 0.438834
$$163$$ 78525.4 0.231495 0.115747 0.993279i $$-0.463074\pi$$
0.115747 + 0.993279i $$0.463074\pi$$
$$164$$ −317925. −0.923028
$$165$$ 235002. 0.671989
$$166$$ −249764. −0.703494
$$167$$ −597714. −1.65845 −0.829224 0.558916i $$-0.811217\pi$$
−0.829224 + 0.558916i $$0.811217\pi$$
$$168$$ −121201. −0.331309
$$169$$ −119139. −0.320875
$$170$$ −87511.4 −0.232243
$$171$$ −38522.7 −0.100746
$$172$$ 337453. 0.869745
$$173$$ −59874.0 −0.152098 −0.0760490 0.997104i $$-0.524231\pi$$
−0.0760490 + 0.997104i $$0.524231\pi$$
$$174$$ −324092. −0.811512
$$175$$ −30625.0 −0.0755929
$$176$$ 12128.5 0.0295138
$$177$$ 121017. 0.290344
$$178$$ −14975.9 −0.0354278
$$179$$ 616812. 1.43887 0.719433 0.694562i $$-0.244402\pi$$
0.719433 + 0.694562i $$0.244402\pi$$
$$180$$ −28427.5 −0.0653969
$$181$$ −37287.0 −0.0845981 −0.0422990 0.999105i $$-0.513468\pi$$
−0.0422990 + 0.999105i $$0.513468\pi$$
$$182$$ −86884.6 −0.194431
$$183$$ −665051. −1.46800
$$184$$ 621418. 1.35313
$$185$$ −15680.6 −0.0336847
$$186$$ 188293. 0.399072
$$187$$ 685513. 1.43355
$$188$$ 83895.4 0.173119
$$189$$ 200635. 0.408557
$$190$$ 58411.7 0.117386
$$191$$ 326760. 0.648106 0.324053 0.946039i $$-0.394954\pi$$
0.324053 + 0.946039i $$0.394954\pi$$
$$192$$ 284152. 0.556285
$$193$$ −265735. −0.513518 −0.256759 0.966475i $$-0.582655\pi$$
−0.256759 + 0.966475i $$0.582655\pi$$
$$194$$ 368563. 0.703085
$$195$$ 170648. 0.321377
$$196$$ −46894.2 −0.0871925
$$197$$ −517865. −0.950716 −0.475358 0.879792i $$-0.657682\pi$$
−0.475358 + 0.879792i $$0.657682\pi$$
$$198$$ −142164. −0.257707
$$199$$ −148687. −0.266158 −0.133079 0.991105i $$-0.542486\pi$$
−0.133079 + 0.991105i $$0.542486\pi$$
$$200$$ 113727. 0.201043
$$201$$ −57878.0 −0.101047
$$202$$ 161426. 0.278352
$$203$$ −330844. −0.563486
$$204$$ 263188. 0.442783
$$205$$ −406946. −0.676320
$$206$$ −315252. −0.517595
$$207$$ −198825. −0.322512
$$208$$ 8807.15 0.0141149
$$209$$ −457563. −0.724577
$$210$$ −58800.0 −0.0920087
$$211$$ 7443.09 0.0115093 0.00575463 0.999983i $$-0.498168\pi$$
0.00575463 + 0.999983i $$0.498168\pi$$
$$212$$ 507045. 0.774831
$$213$$ 258151. 0.389874
$$214$$ 375465. 0.560447
$$215$$ 431943. 0.637279
$$216$$ −745066. −1.08658
$$217$$ 192215. 0.277101
$$218$$ 175909. 0.250695
$$219$$ 137735. 0.194059
$$220$$ −337654. −0.470343
$$221$$ 497788. 0.685589
$$222$$ −30106.7 −0.0409997
$$223$$ 119157. 0.160456 0.0802280 0.996777i $$-0.474435\pi$$
0.0802280 + 0.996777i $$0.474435\pi$$
$$224$$ 282283. 0.375894
$$225$$ −36387.4 −0.0479176
$$226$$ 131219. 0.170894
$$227$$ −388843. −0.500852 −0.250426 0.968136i $$-0.580571\pi$$
−0.250426 + 0.968136i $$0.580571\pi$$
$$228$$ −175671. −0.223802
$$229$$ 732622. 0.923191 0.461595 0.887091i $$-0.347277\pi$$
0.461595 + 0.887091i $$0.347277\pi$$
$$230$$ 301477. 0.375781
$$231$$ 460605. 0.567934
$$232$$ 1.22860e6 1.49862
$$233$$ −1.12639e6 −1.35925 −0.679626 0.733559i $$-0.737858\pi$$
−0.679626 + 0.733559i $$0.737858\pi$$
$$234$$ −103233. −0.123248
$$235$$ 107387. 0.126847
$$236$$ −173878. −0.203220
$$237$$ −1.31837e6 −1.52464
$$238$$ −171522. −0.196281
$$239$$ 772317. 0.874583 0.437292 0.899320i $$-0.355938\pi$$
0.437292 + 0.899320i $$0.355938\pi$$
$$240$$ 5960.32 0.00667946
$$241$$ 1.40297e6 1.55598 0.777991 0.628275i $$-0.216239\pi$$
0.777991 + 0.628275i $$0.216239\pi$$
$$242$$ −1.11989e6 −1.22924
$$243$$ 430698. 0.467905
$$244$$ 955553. 1.02750
$$245$$ −60025.0 −0.0638877
$$246$$ −781337. −0.823191
$$247$$ −332261. −0.346527
$$248$$ −713798. −0.736964
$$249$$ 961489. 0.982757
$$250$$ 55173.9 0.0558320
$$251$$ −1.63922e6 −1.64230 −0.821151 0.570712i $$-0.806667\pi$$
−0.821151 + 0.570712i $$0.806667\pi$$
$$252$$ −55717.9 −0.0552705
$$253$$ −2.36159e6 −2.31955
$$254$$ 164234. 0.159727
$$255$$ 336883. 0.324435
$$256$$ −1.05923e6 −1.01016
$$257$$ −223664. −0.211234 −0.105617 0.994407i $$-0.533682\pi$$
−0.105617 + 0.994407i $$0.533682\pi$$
$$258$$ 829330. 0.775672
$$259$$ −30733.9 −0.0284687
$$260$$ −245189. −0.224940
$$261$$ −393096. −0.357188
$$262$$ −1.34808e6 −1.21329
$$263$$ 299519. 0.267014 0.133507 0.991048i $$-0.457376\pi$$
0.133507 + 0.991048i $$0.457376\pi$$
$$264$$ −1.71047e6 −1.51045
$$265$$ 649022. 0.567734
$$266$$ 114487. 0.0992091
$$267$$ 57651.2 0.0494914
$$268$$ 83159.7 0.0707255
$$269$$ 134341. 0.113195 0.0565974 0.998397i $$-0.481975\pi$$
0.0565974 + 0.998397i $$0.481975\pi$$
$$270$$ −361464. −0.301756
$$271$$ 1.93414e6 1.59980 0.799898 0.600136i $$-0.204887\pi$$
0.799898 + 0.600136i $$0.204887\pi$$
$$272$$ 17386.5 0.0142492
$$273$$ 334470. 0.271613
$$274$$ 6689.88 0.00538321
$$275$$ −432200. −0.344630
$$276$$ −906683. −0.716445
$$277$$ 177599. 0.139072 0.0695362 0.997579i $$-0.477848\pi$$
0.0695362 + 0.997579i $$0.477848\pi$$
$$278$$ −712574. −0.552991
$$279$$ 228383. 0.175652
$$280$$ 222905. 0.169912
$$281$$ 1.85131e6 1.39867 0.699333 0.714796i $$-0.253481\pi$$
0.699333 + 0.714796i $$0.253481\pi$$
$$282$$ 206183. 0.154394
$$283$$ 2.39851e6 1.78023 0.890114 0.455737i $$-0.150624\pi$$
0.890114 + 0.455737i $$0.150624\pi$$
$$284$$ −370914. −0.272883
$$285$$ −224861. −0.163984
$$286$$ −1.22617e6 −0.886413
$$287$$ −797615. −0.571595
$$288$$ 335398. 0.238275
$$289$$ −437155. −0.307887
$$290$$ 596047. 0.416184
$$291$$ −1.41882e6 −0.982186
$$292$$ −197899. −0.135827
$$293$$ 2.49922e6 1.70073 0.850364 0.526196i $$-0.176382\pi$$
0.850364 + 0.526196i $$0.176382\pi$$
$$294$$ −115248. −0.0777616
$$295$$ −222566. −0.148903
$$296$$ 114131. 0.0757139
$$297$$ 2.83149e6 1.86262
$$298$$ 1.64634e6 1.07394
$$299$$ −1.71488e6 −1.10932
$$300$$ −165934. −0.106447
$$301$$ 846607. 0.538599
$$302$$ 431546. 0.272276
$$303$$ −621422. −0.388848
$$304$$ −11605.1 −0.00720218
$$305$$ 1.22312e6 0.752866
$$306$$ −203796. −0.124421
$$307$$ 3.07195e6 1.86024 0.930119 0.367258i $$-0.119703\pi$$
0.930119 + 0.367258i $$0.119703\pi$$
$$308$$ −661802. −0.397513
$$309$$ 1.21359e6 0.723063
$$310$$ −346295. −0.204664
$$311$$ 661233. 0.387662 0.193831 0.981035i $$-0.437909\pi$$
0.193831 + 0.981035i $$0.437909\pi$$
$$312$$ −1.24206e6 −0.722367
$$313$$ −3.29393e6 −1.90043 −0.950217 0.311588i $$-0.899139\pi$$
−0.950217 + 0.311588i $$0.899139\pi$$
$$314$$ 1.45002e6 0.829944
$$315$$ −71319.3 −0.0404977
$$316$$ 1.89426e6 1.06714
$$317$$ 639724. 0.357556 0.178778 0.983889i $$-0.442786\pi$$
0.178778 + 0.983889i $$0.442786\pi$$
$$318$$ 1.24612e6 0.691023
$$319$$ −4.66908e6 −2.56894
$$320$$ −522592. −0.285291
$$321$$ −1.44538e6 −0.782926
$$322$$ 590895. 0.317593
$$323$$ −655929. −0.349825
$$324$$ 810777. 0.429081
$$325$$ −313844. −0.164818
$$326$$ −277283. −0.144504
$$327$$ −677175. −0.350213
$$328$$ 2.96197e6 1.52018
$$329$$ 210478. 0.107206
$$330$$ −829823. −0.419470
$$331$$ −1.13876e6 −0.571298 −0.285649 0.958334i $$-0.592209\pi$$
−0.285649 + 0.958334i $$0.592209\pi$$
$$332$$ −1.38148e6 −0.687858
$$333$$ −36516.8 −0.0180460
$$334$$ 2.11060e6 1.03524
$$335$$ 106445. 0.0518219
$$336$$ 11682.2 0.00564518
$$337$$ 685493. 0.328797 0.164399 0.986394i $$-0.447432\pi$$
0.164399 + 0.986394i $$0.447432\pi$$
$$338$$ 420694. 0.200297
$$339$$ −505140. −0.238733
$$340$$ −484037. −0.227081
$$341$$ 2.71267e6 1.26331
$$342$$ 136029. 0.0628877
$$343$$ −117649. −0.0539949
$$344$$ −3.14390e6 −1.43243
$$345$$ −1.16056e6 −0.524953
$$346$$ 211423. 0.0949428
$$347$$ −1.25151e6 −0.557970 −0.278985 0.960295i $$-0.589998\pi$$
−0.278985 + 0.960295i $$0.589998\pi$$
$$348$$ −1.79259e6 −0.793476
$$349$$ −3.16606e6 −1.39141 −0.695706 0.718327i $$-0.744908\pi$$
−0.695706 + 0.718327i $$0.744908\pi$$
$$350$$ 108141. 0.0471867
$$351$$ 2.05610e6 0.890793
$$352$$ 3.98376e6 1.71371
$$353$$ −2.43368e6 −1.03951 −0.519754 0.854316i $$-0.673976\pi$$
−0.519754 + 0.854316i $$0.673976\pi$$
$$354$$ −427326. −0.181239
$$355$$ −474772. −0.199947
$$356$$ −82833.8 −0.0346404
$$357$$ 660290. 0.274198
$$358$$ −2.17804e6 −0.898171
$$359$$ −2.13021e6 −0.872341 −0.436170 0.899864i $$-0.643665\pi$$
−0.436170 + 0.899864i $$0.643665\pi$$
$$360$$ 264847. 0.107706
$$361$$ −2.03828e6 −0.823183
$$362$$ 131665. 0.0528079
$$363$$ 4.31112e6 1.71721
$$364$$ −480570. −0.190109
$$365$$ −253312. −0.0995232
$$366$$ 2.34838e6 0.916360
$$367$$ −3.10976e6 −1.20521 −0.602604 0.798041i $$-0.705870\pi$$
−0.602604 + 0.798041i $$0.705870\pi$$
$$368$$ −59896.7 −0.0230559
$$369$$ −947694. −0.362328
$$370$$ 55370.1 0.0210267
$$371$$ 1.27208e6 0.479822
$$372$$ 1.04147e6 0.390202
$$373$$ −3.15189e6 −1.17300 −0.586502 0.809948i $$-0.699495\pi$$
−0.586502 + 0.809948i $$0.699495\pi$$
$$374$$ −2.42063e6 −0.894849
$$375$$ −212397. −0.0779955
$$376$$ −781617. −0.285118
$$377$$ −3.39047e6 −1.22859
$$378$$ −708469. −0.255030
$$379$$ 342350. 0.122426 0.0612129 0.998125i $$-0.480503\pi$$
0.0612129 + 0.998125i $$0.480503\pi$$
$$380$$ 323083. 0.114777
$$381$$ −632231. −0.223133
$$382$$ −1.15383e6 −0.404562
$$383$$ 3.69387e6 1.28672 0.643361 0.765563i $$-0.277539\pi$$
0.643361 + 0.765563i $$0.277539\pi$$
$$384$$ 1.50254e6 0.519994
$$385$$ −847111. −0.291265
$$386$$ 938345. 0.320549
$$387$$ 1.00590e6 0.341413
$$388$$ 2.03857e6 0.687459
$$389$$ 2.05313e6 0.687928 0.343964 0.938983i $$-0.388230\pi$$
0.343964 + 0.938983i $$0.388230\pi$$
$$390$$ −602580. −0.200610
$$391$$ −3.38541e6 −1.11988
$$392$$ 436893. 0.143602
$$393$$ 5.18956e6 1.69492
$$394$$ 1.82865e6 0.593457
$$395$$ 2.42466e6 0.781913
$$396$$ −786326. −0.251979
$$397$$ −2.28107e6 −0.726377 −0.363189 0.931716i $$-0.618312\pi$$
−0.363189 + 0.931716i $$0.618312\pi$$
$$398$$ 525031. 0.166141
$$399$$ −440727. −0.138592
$$400$$ −10961.8 −0.00342556
$$401$$ 3.32082e6 1.03130 0.515649 0.856800i $$-0.327551\pi$$
0.515649 + 0.856800i $$0.327551\pi$$
$$402$$ 204375. 0.0630756
$$403$$ 1.96981e6 0.604175
$$404$$ 892867. 0.272166
$$405$$ 1.03780e6 0.314396
$$406$$ 1.16825e6 0.351740
$$407$$ −433737. −0.129790
$$408$$ −2.45201e6 −0.729242
$$409$$ 5.15938e6 1.52507 0.762534 0.646948i $$-0.223955\pi$$
0.762534 + 0.646948i $$0.223955\pi$$
$$410$$ 1.43698e6 0.422174
$$411$$ −25753.3 −0.00752017
$$412$$ −1.74370e6 −0.506092
$$413$$ −436229. −0.125846
$$414$$ 702078. 0.201319
$$415$$ −1.76830e6 −0.504007
$$416$$ 2.89283e6 0.819576
$$417$$ 2.74311e6 0.772509
$$418$$ 1.61571e6 0.452297
$$419$$ −4.85187e6 −1.35012 −0.675062 0.737761i $$-0.735883\pi$$
−0.675062 + 0.737761i $$0.735883\pi$$
$$420$$ −325230. −0.0899638
$$421$$ −6.14767e6 −1.69046 −0.845231 0.534401i $$-0.820537\pi$$
−0.845231 + 0.534401i $$0.820537\pi$$
$$422$$ −26282.5 −0.00718432
$$423$$ 250082. 0.0679565
$$424$$ −4.72392e6 −1.27611
$$425$$ −619571. −0.166387
$$426$$ −911563. −0.243368
$$427$$ 2.39731e6 0.636288
$$428$$ 2.07674e6 0.547991
$$429$$ 4.72025e6 1.23829
$$430$$ −1.52524e6 −0.397803
$$431$$ 3.55411e6 0.921590 0.460795 0.887507i $$-0.347564\pi$$
0.460795 + 0.887507i $$0.347564\pi$$
$$432$$ 71814.7 0.0185141
$$433$$ 2.82650e6 0.724485 0.362243 0.932084i $$-0.382011\pi$$
0.362243 + 0.932084i $$0.382011\pi$$
$$434$$ −678737. −0.172973
$$435$$ −2.29454e6 −0.581395
$$436$$ 972973. 0.245123
$$437$$ 2.25968e6 0.566035
$$438$$ −486360. −0.121136
$$439$$ 4.64410e6 1.15011 0.575056 0.818114i $$-0.304980\pi$$
0.575056 + 0.818114i $$0.304980\pi$$
$$440$$ 3.14578e6 0.774633
$$441$$ −139786. −0.0342268
$$442$$ −1.75775e6 −0.427959
$$443$$ −6.15534e6 −1.49019 −0.745097 0.666957i $$-0.767597\pi$$
−0.745097 + 0.666957i $$0.767597\pi$$
$$444$$ −166524. −0.0400884
$$445$$ −106028. −0.0253817
$$446$$ −420757. −0.100160
$$447$$ −6.33774e6 −1.50026
$$448$$ −1.02428e6 −0.241115
$$449$$ 3.67035e6 0.859196 0.429598 0.903020i $$-0.358655\pi$$
0.429598 + 0.903020i $$0.358655\pi$$
$$450$$ 128489. 0.0299112
$$451$$ −1.12565e7 −2.60591
$$452$$ 725791. 0.167096
$$453$$ −1.66127e6 −0.380360
$$454$$ 1.37305e6 0.312642
$$455$$ −615134. −0.139297
$$456$$ 1.63665e6 0.368591
$$457$$ −866327. −0.194040 −0.0970201 0.995282i $$-0.530931\pi$$
−0.0970201 + 0.995282i $$0.530931\pi$$
$$458$$ −2.58698e6 −0.576275
$$459$$ 4.05903e6 0.899271
$$460$$ 1.66751e6 0.367429
$$461$$ −1.88572e6 −0.413261 −0.206631 0.978419i $$-0.566250\pi$$
−0.206631 + 0.978419i $$0.566250\pi$$
$$462$$ −1.62645e6 −0.354517
$$463$$ −8.49017e6 −1.84062 −0.920309 0.391192i $$-0.872063\pi$$
−0.920309 + 0.391192i $$0.872063\pi$$
$$464$$ −118421. −0.0255349
$$465$$ 1.33309e6 0.285909
$$466$$ 3.97744e6 0.848474
$$467$$ 1.82738e6 0.387737 0.193868 0.981028i $$-0.437896\pi$$
0.193868 + 0.981028i $$0.437896\pi$$
$$468$$ −570994. −0.120508
$$469$$ 208632. 0.0437975
$$470$$ −379197. −0.0791808
$$471$$ −5.58197e6 −1.15940
$$472$$ 1.61995e6 0.334693
$$473$$ 1.19479e7 2.45549
$$474$$ 4.65535e6 0.951714
$$475$$ 413548. 0.0840992
$$476$$ −948712. −0.191919
$$477$$ 1.51144e6 0.304155
$$478$$ −2.72715e6 −0.545933
$$479$$ 4.68744e6 0.933463 0.466731 0.884399i $$-0.345432\pi$$
0.466731 + 0.884399i $$0.345432\pi$$
$$480$$ 1.95775e6 0.387841
$$481$$ −314960. −0.0620715
$$482$$ −4.95405e6 −0.971277
$$483$$ −2.27470e6 −0.443666
$$484$$ −6.19426e6 −1.20192
$$485$$ 2.60939e6 0.503714
$$486$$ −1.52085e6 −0.292076
$$487$$ 4.59651e6 0.878225 0.439112 0.898432i $$-0.355293\pi$$
0.439112 + 0.898432i $$0.355293\pi$$
$$488$$ −8.90247e6 −1.69224
$$489$$ 1.06743e6 0.201867
$$490$$ 211956. 0.0398800
$$491$$ 6.62099e6 1.23942 0.619711 0.784830i $$-0.287250\pi$$
0.619711 + 0.784830i $$0.287250\pi$$
$$492$$ −4.32167e6 −0.804895
$$493$$ −6.69327e6 −1.24028
$$494$$ 1.17326e6 0.216310
$$495$$ −1.00650e6 −0.184630
$$496$$ 68800.9 0.0125571
$$497$$ −930554. −0.168986
$$498$$ −3.39514e6 −0.613458
$$499$$ −4.52632e6 −0.813756 −0.406878 0.913482i $$-0.633383\pi$$
−0.406878 + 0.913482i $$0.633383\pi$$
$$500$$ 305174. 0.0545912
$$501$$ −8.12495e6 −1.44619
$$502$$ 5.78829e6 1.02516
$$503$$ 3.83316e6 0.675518 0.337759 0.941233i $$-0.390331\pi$$
0.337759 + 0.941233i $$0.390331\pi$$
$$504$$ 519099. 0.0910278
$$505$$ 1.14288e6 0.199421
$$506$$ 8.33909e6 1.44791
$$507$$ −1.61950e6 −0.279808
$$508$$ 908397. 0.156177
$$509$$ −3.25460e6 −0.556806 −0.278403 0.960464i $$-0.589805\pi$$
−0.278403 + 0.960464i $$0.589805\pi$$
$$510$$ −1.18958e6 −0.202519
$$511$$ −496492. −0.0841124
$$512$$ 203165. 0.0342511
$$513$$ −2.70930e6 −0.454531
$$514$$ 789788. 0.131857
$$515$$ −2.23195e6 −0.370823
$$516$$ 4.58713e6 0.758432
$$517$$ 2.97040e6 0.488752
$$518$$ 108525. 0.0177708
$$519$$ −813891. −0.132632
$$520$$ 2.28432e6 0.370466
$$521$$ −1.07842e6 −0.174057 −0.0870287 0.996206i $$-0.527737\pi$$
−0.0870287 + 0.996206i $$0.527737\pi$$
$$522$$ 1.38807e6 0.222964
$$523$$ 408626. 0.0653238 0.0326619 0.999466i $$-0.489602\pi$$
0.0326619 + 0.999466i $$0.489602\pi$$
$$524$$ −7.45641e6 −1.18632
$$525$$ −416297. −0.0659182
$$526$$ −1.05764e6 −0.166676
$$527$$ 3.88869e6 0.609925
$$528$$ 164867. 0.0257365
$$529$$ 5.22642e6 0.812016
$$530$$ −2.29178e6 −0.354391
$$531$$ −518310. −0.0797724
$$532$$ 633242. 0.0970042
$$533$$ −8.17392e6 −1.24627
$$534$$ −203574. −0.0308936
$$535$$ 2.65825e6 0.401524
$$536$$ −774763. −0.116481
$$537$$ 8.38456e6 1.25471
$$538$$ −474374. −0.0706586
$$539$$ −1.66034e6 −0.246164
$$540$$ −1.99930e6 −0.295049
$$541$$ 1.13918e7 1.67340 0.836701 0.547659i $$-0.184481\pi$$
0.836701 + 0.547659i $$0.184481\pi$$
$$542$$ −6.82970e6 −0.998627
$$543$$ −506856. −0.0737709
$$544$$ 5.71084e6 0.827376
$$545$$ 1.24541e6 0.179607
$$546$$ −1.18106e6 −0.169547
$$547$$ −3.44866e6 −0.492813 −0.246406 0.969167i $$-0.579250\pi$$
−0.246406 + 0.969167i $$0.579250\pi$$
$$548$$ 37002.6 0.00526357
$$549$$ 2.84838e6 0.403337
$$550$$ 1.52615e6 0.215125
$$551$$ 4.46759e6 0.626894
$$552$$ 8.44718e6 1.17995
$$553$$ 4.75234e6 0.660837
$$554$$ −627124. −0.0868119
$$555$$ −213152. −0.0293736
$$556$$ −3.94134e6 −0.540700
$$557$$ −4.69772e6 −0.641577 −0.320789 0.947151i $$-0.603948\pi$$
−0.320789 + 0.947151i $$0.603948\pi$$
$$558$$ −806449. −0.109646
$$559$$ 8.67599e6 1.17433
$$560$$ −21485.1 −0.00289513
$$561$$ 9.31844e6 1.25007
$$562$$ −6.53722e6 −0.873077
$$563$$ −561642. −0.0746772 −0.0373386 0.999303i $$-0.511888\pi$$
−0.0373386 + 0.999303i $$0.511888\pi$$
$$564$$ 1.14042e6 0.150962
$$565$$ 929018. 0.122434
$$566$$ −8.46945e6 −1.11126
$$567$$ 2.03409e6 0.265713
$$568$$ 3.45564e6 0.449426
$$569$$ 5.19019e6 0.672051 0.336026 0.941853i $$-0.390917\pi$$
0.336026 + 0.941853i $$0.390917\pi$$
$$570$$ 794012. 0.102362
$$571$$ −5.20274e6 −0.667793 −0.333897 0.942610i $$-0.608364\pi$$
−0.333897 + 0.942610i $$0.608364\pi$$
$$572$$ −6.78211e6 −0.866712
$$573$$ 4.44178e6 0.565159
$$574$$ 2.81648e6 0.356802
$$575$$ 2.13442e6 0.269222
$$576$$ −1.21701e6 −0.152840
$$577$$ 8.70662e6 1.08870 0.544352 0.838857i $$-0.316775\pi$$
0.544352 + 0.838857i $$0.316775\pi$$
$$578$$ 1.54365e6 0.192189
$$579$$ −3.61224e6 −0.447796
$$580$$ 3.29681e6 0.406934
$$581$$ −3.46588e6 −0.425964
$$582$$ 5.01003e6 0.613102
$$583$$ 1.79524e7 2.18752
$$584$$ 1.84374e6 0.223701
$$585$$ −730877. −0.0882988
$$586$$ −8.82505e6 −1.06163
$$587$$ −4.35717e6 −0.521926 −0.260963 0.965349i $$-0.584040\pi$$
−0.260963 + 0.965349i $$0.584040\pi$$
$$588$$ −637452. −0.0760333
$$589$$ −2.59560e6 −0.308283
$$590$$ 785908. 0.0929484
$$591$$ −7.03954e6 −0.829040
$$592$$ −11000.8 −0.00129009
$$593$$ −3.22991e6 −0.377184 −0.188592 0.982055i $$-0.560392\pi$$
−0.188592 + 0.982055i $$0.560392\pi$$
$$594$$ −9.99837e6 −1.16269
$$595$$ −1.21436e6 −0.140622
$$596$$ 9.10614e6 1.05007
$$597$$ −2.02115e6 −0.232094
$$598$$ 6.05547e6 0.692460
$$599$$ −7.23988e6 −0.824450 −0.412225 0.911082i $$-0.635248\pi$$
−0.412225 + 0.911082i $$0.635248\pi$$
$$600$$ 1.54593e6 0.175312
$$601$$ −1.06837e7 −1.20652 −0.603262 0.797543i $$-0.706133\pi$$
−0.603262 + 0.797543i $$0.706133\pi$$
$$602$$ −2.98948e6 −0.336205
$$603$$ 247889. 0.0277628
$$604$$ 2.38693e6 0.266225
$$605$$ −7.92871e6 −0.880671
$$606$$ 2.19432e6 0.242727
$$607$$ 2.51528e6 0.277086 0.138543 0.990356i $$-0.455758\pi$$
0.138543 + 0.990356i $$0.455758\pi$$
$$608$$ −3.81185e6 −0.418193
$$609$$ −4.49729e6 −0.491369
$$610$$ −4.31898e6 −0.469955
$$611$$ 2.15697e6 0.233744
$$612$$ −1.12722e6 −0.121655
$$613$$ 213999. 0.0230017 0.0115009 0.999934i $$-0.496339\pi$$
0.0115009 + 0.999934i $$0.496339\pi$$
$$614$$ −1.08475e7 −1.16120
$$615$$ −5.53178e6 −0.589762
$$616$$ 6.16572e6 0.654684
$$617$$ −127951. −0.0135310 −0.00676552 0.999977i $$-0.502154\pi$$
−0.00676552 + 0.999977i $$0.502154\pi$$
$$618$$ −4.28535e6 −0.451352
$$619$$ −1.23980e7 −1.30054 −0.650272 0.759701i $$-0.725345\pi$$
−0.650272 + 0.759701i $$0.725345\pi$$
$$620$$ −1.91540e6 −0.200115
$$621$$ −1.39834e7 −1.45507
$$622$$ −2.33490e6 −0.241987
$$623$$ −207815. −0.0214514
$$624$$ 119719. 0.0123084
$$625$$ 390625. 0.0400000
$$626$$ 1.16313e7 1.18629
$$627$$ −6.21983e6 −0.631843
$$628$$ 8.02023e6 0.811499
$$629$$ −621774. −0.0626622
$$630$$ 251838. 0.0252795
$$631$$ −5.87683e6 −0.587584 −0.293792 0.955869i $$-0.594917\pi$$
−0.293792 + 0.955869i $$0.594917\pi$$
$$632$$ −1.76480e7 −1.75753
$$633$$ 101177. 0.0100363
$$634$$ −2.25895e6 −0.223194
$$635$$ 1.16275e6 0.114434
$$636$$ 6.89246e6 0.675665
$$637$$ −1.20566e6 −0.117727
$$638$$ 1.64871e7 1.60359
$$639$$ −1.10565e6 −0.107118
$$640$$ −2.76337e6 −0.266679
$$641$$ −2.60122e6 −0.250053 −0.125026 0.992153i $$-0.539902\pi$$
−0.125026 + 0.992153i $$0.539902\pi$$
$$642$$ 5.10384e6 0.488719
$$643$$ 1.31345e7 1.25282 0.626408 0.779495i $$-0.284524\pi$$
0.626408 + 0.779495i $$0.284524\pi$$
$$644$$ 3.26832e6 0.310534
$$645$$ 5.87156e6 0.555718
$$646$$ 2.31617e6 0.218368
$$647$$ 5.54662e6 0.520916 0.260458 0.965485i $$-0.416126\pi$$
0.260458 + 0.965485i $$0.416126\pi$$
$$648$$ −7.55366e6 −0.706675
$$649$$ −6.15634e6 −0.573734
$$650$$ 1.10822e6 0.102883
$$651$$ 2.61286e6 0.241637
$$652$$ −1.53369e6 −0.141292
$$653$$ −1.54993e7 −1.42242 −0.711212 0.702978i $$-0.751853\pi$$
−0.711212 + 0.702978i $$0.751853\pi$$
$$654$$ 2.39119e6 0.218610
$$655$$ −9.54427e6 −0.869239
$$656$$ −285495. −0.0259024
$$657$$ −589912. −0.0533180
$$658$$ −743225. −0.0669200
$$659$$ −4.30145e6 −0.385835 −0.192917 0.981215i $$-0.561795\pi$$
−0.192917 + 0.981215i $$0.561795\pi$$
$$660$$ −4.58986e6 −0.410147
$$661$$ 861980. 0.0767350 0.0383675 0.999264i $$-0.487784\pi$$
0.0383675 + 0.999264i $$0.487784\pi$$
$$662$$ 4.02111e6 0.356616
$$663$$ 6.76662e6 0.597844
$$664$$ 1.28706e7 1.13287
$$665$$ 810554. 0.0710768
$$666$$ 128945. 0.0112647
$$667$$ 2.30583e7 2.00684
$$668$$ 1.16740e7 1.01223
$$669$$ 1.61974e6 0.139920
$$670$$ −375871. −0.0323484
$$671$$ 3.38323e7 2.90085
$$672$$ 3.83719e6 0.327786
$$673$$ −953818. −0.0811760 −0.0405880 0.999176i $$-0.512923\pi$$
−0.0405880 + 0.999176i $$0.512923\pi$$
$$674$$ −2.42056e6 −0.205242
$$675$$ −2.55912e6 −0.216188
$$676$$ 2.32691e6 0.195845
$$677$$ −1.48606e7 −1.24613 −0.623065 0.782170i $$-0.714113\pi$$
−0.623065 + 0.782170i $$0.714113\pi$$
$$678$$ 1.78371e6 0.149022
$$679$$ 5.11440e6 0.425716
$$680$$ 4.50956e6 0.373992
$$681$$ −5.28569e6 −0.436751
$$682$$ −9.57878e6 −0.788586
$$683$$ −1.57605e7 −1.29276 −0.646381 0.763015i $$-0.723718\pi$$
−0.646381 + 0.763015i $$0.723718\pi$$
$$684$$ 752392. 0.0614900
$$685$$ 47363.6 0.00385672
$$686$$ 415434. 0.0337048
$$687$$ 9.95882e6 0.805037
$$688$$ 303032. 0.0244071
$$689$$ 1.30362e7 1.04618
$$690$$ 4.09809e6 0.327687
$$691$$ 1.59740e7 1.27267 0.636337 0.771411i $$-0.280449\pi$$
0.636337 + 0.771411i $$0.280449\pi$$
$$692$$ 1.16941e6 0.0928326
$$693$$ −1.97275e6 −0.156041
$$694$$ 4.41925e6 0.348297
$$695$$ −5.04494e6 −0.396182
$$696$$ 1.67008e7 1.30682
$$697$$ −1.61365e7 −1.25813
$$698$$ 1.11798e7 0.868549
$$699$$ −1.53115e7 −1.18529
$$700$$ 598141. 0.0461380
$$701$$ −1.85736e7 −1.42758 −0.713790 0.700360i $$-0.753023\pi$$
−0.713790 + 0.700360i $$0.753023\pi$$
$$702$$ −7.26036e6 −0.556052
$$703$$ 415019. 0.0316723
$$704$$ −1.44553e7 −1.09925
$$705$$ 1.45975e6 0.110613
$$706$$ 8.59365e6 0.648883
$$707$$ 2.24004e6 0.168541
$$708$$ −2.36360e6 −0.177211
$$709$$ −1.71029e7 −1.27778 −0.638888 0.769300i $$-0.720605\pi$$
−0.638888 + 0.769300i $$0.720605\pi$$
$$710$$ 1.67648e6 0.124811
$$711$$ 5.64654e6 0.418898
$$712$$ 771727. 0.0570511
$$713$$ −1.33965e7 −0.986890
$$714$$ −2.33157e6 −0.171160
$$715$$ −8.68116e6 −0.635057
$$716$$ −1.20470e7 −0.878208
$$717$$ 1.04984e7 0.762651
$$718$$ 7.52204e6 0.544534
$$719$$ −1.40945e7 −1.01678 −0.508390 0.861127i $$-0.669759\pi$$
−0.508390 + 0.861127i $$0.669759\pi$$
$$720$$ −25527.8 −0.00183519
$$721$$ −4.37463e6 −0.313403
$$722$$ 7.19744e6 0.513848
$$723$$ 1.90711e7 1.35684
$$724$$ 728256. 0.0516343
$$725$$ 4.21995e6 0.298169
$$726$$ −1.52231e7 −1.07192
$$727$$ 2.24196e7 1.57323 0.786616 0.617443i $$-0.211831\pi$$
0.786616 + 0.617443i $$0.211831\pi$$
$$728$$ 4.47726e6 0.313101
$$729$$ 1.59421e7 1.11103
$$730$$ 894478. 0.0621245
$$731$$ 1.71276e7 1.18551
$$732$$ 1.29892e7 0.895993
$$733$$ −8.02464e6 −0.551653 −0.275826 0.961208i $$-0.588951\pi$$
−0.275826 + 0.961208i $$0.588951\pi$$
$$734$$ 1.09810e7 0.752316
$$735$$ −815943. −0.0557111
$$736$$ −1.96739e7 −1.33874
$$737$$ 2.94435e6 0.199674
$$738$$ 3.34643e6 0.226173
$$739$$ 1.15678e7 0.779181 0.389591 0.920988i $$-0.372616\pi$$
0.389591 + 0.920988i $$0.372616\pi$$
$$740$$ 306259. 0.0205594
$$741$$ −4.51655e6 −0.302177
$$742$$ −4.49189e6 −0.299515
$$743$$ 3.79387e6 0.252122 0.126061 0.992023i $$-0.459767\pi$$
0.126061 + 0.992023i $$0.459767\pi$$
$$744$$ −9.70293e6 −0.642644
$$745$$ 1.16559e7 0.769407
$$746$$ 1.11297e7 0.732214
$$747$$ −4.11801e6 −0.270014
$$748$$ −1.33888e7 −0.874961
$$749$$ 5.21017e6 0.339349
$$750$$ 750000. 0.0486864
$$751$$ −9.07884e6 −0.587395 −0.293698 0.955898i $$-0.594886\pi$$
−0.293698 + 0.955898i $$0.594886\pi$$
$$752$$ 75337.8 0.00485812
$$753$$ −2.22825e7 −1.43211
$$754$$ 1.19722e7 0.766912
$$755$$ 3.05530e6 0.195068
$$756$$ −3.91863e6 −0.249362
$$757$$ −2.33210e7 −1.47913 −0.739565 0.673085i $$-0.764969\pi$$
−0.739565 + 0.673085i $$0.764969\pi$$
$$758$$ −1.20888e6 −0.0764208
$$759$$ −3.21020e7 −2.02269
$$760$$ −3.01002e6 −0.189032
$$761$$ 1.44859e7 0.906745 0.453373 0.891321i $$-0.350221\pi$$
0.453373 + 0.891321i $$0.350221\pi$$
$$762$$ 2.23249e6 0.139284
$$763$$ 2.44101e6 0.151795
$$764$$ −6.38200e6 −0.395570
$$765$$ −1.44285e6 −0.0891391
$$766$$ −1.30435e7 −0.803200
$$767$$ −4.47045e6 −0.274387
$$768$$ −1.43985e7 −0.880876
$$769$$ 1.59424e7 0.972162 0.486081 0.873914i $$-0.338426\pi$$
0.486081 + 0.873914i $$0.338426\pi$$
$$770$$ 2.99126e6 0.181814
$$771$$ −3.04036e6 −0.184200
$$772$$ 5.19011e6 0.313425
$$773$$ −3.36066e6 −0.202290 −0.101145 0.994872i $$-0.532251\pi$$
−0.101145 + 0.994872i $$0.532251\pi$$
$$774$$ −3.55198e6 −0.213117
$$775$$ −2.45173e6 −0.146628
$$776$$ −1.89925e7 −1.13221
$$777$$ −417778. −0.0248252
$$778$$ −7.24988e6 −0.429419
$$779$$ 1.07707e7 0.635916
$$780$$ −3.33295e6 −0.196152
$$781$$ −1.31326e7 −0.770411
$$782$$ 1.19543e7 0.699050
$$783$$ −2.76464e7 −1.61151
$$784$$ −42110.9 −0.00244683
$$785$$ 1.02660e7 0.594601
$$786$$ −1.83250e7 −1.05800
$$787$$ −3.28918e6 −0.189300 −0.0946500 0.995511i $$-0.530173\pi$$
−0.0946500 + 0.995511i $$0.530173\pi$$
$$788$$ 1.01145e7 0.580268
$$789$$ 4.07147e6 0.232841
$$790$$ −8.56179e6 −0.488087
$$791$$ 1.82088e6 0.103476
$$792$$ 7.32586e6 0.414998
$$793$$ 2.45675e7 1.38732
$$794$$ 8.05475e6 0.453420
$$795$$ 8.82240e6 0.495073
$$796$$ 2.90402e6 0.162449
$$797$$ −2.51939e6 −0.140492 −0.0702458 0.997530i $$-0.522378\pi$$
−0.0702458 + 0.997530i $$0.522378\pi$$
$$798$$ 1.55626e6 0.0865120
$$799$$ 4.25816e6 0.235969
$$800$$ −3.60055e6 −0.198904
$$801$$ −246917. −0.0135978
$$802$$ −1.17262e7 −0.643758
$$803$$ −7.00682e6 −0.383470
$$804$$ 1.13042e6 0.0616738
$$805$$ 4.18347e6 0.227534
$$806$$ −6.95567e6 −0.377139
$$807$$ 1.82614e6 0.0987077
$$808$$ −8.31845e6 −0.448244
$$809$$ 8.93808e6 0.480146 0.240073 0.970755i $$-0.422829\pi$$
0.240073 + 0.970755i $$0.422829\pi$$
$$810$$ −3.66461e6 −0.196252
$$811$$ 3.01341e7 1.60881 0.804406 0.594080i $$-0.202484\pi$$
0.804406 + 0.594080i $$0.202484\pi$$
$$812$$ 6.46176e6 0.343922
$$813$$ 2.62915e7 1.39505
$$814$$ 1.53158e6 0.0810174
$$815$$ −1.96313e6 −0.103528
$$816$$ 236342. 0.0124255
$$817$$ −1.14323e7 −0.599207
$$818$$ −1.82184e7 −0.951980
$$819$$ −1.43252e6 −0.0746261
$$820$$ 7.94812e6 0.412791
$$821$$ −3.25440e7 −1.68505 −0.842524 0.538658i $$-0.818931\pi$$
−0.842524 + 0.538658i $$0.818931\pi$$
$$822$$ 90938.1 0.00469425
$$823$$ −499640. −0.0257133 −0.0128566 0.999917i $$-0.504093\pi$$
−0.0128566 + 0.999917i $$0.504093\pi$$
$$824$$ 1.62453e7 0.833509
$$825$$ −5.87506e6 −0.300523
$$826$$ 1.54038e6 0.0785557
$$827$$ −4.64084e6 −0.235957 −0.117978 0.993016i $$-0.537641\pi$$
−0.117978 + 0.993016i $$0.537641\pi$$
$$828$$ 3.88328e6 0.196844
$$829$$ −3.08794e7 −1.56057 −0.780283 0.625427i $$-0.784925\pi$$
−0.780283 + 0.625427i $$0.784925\pi$$
$$830$$ 6.24411e6 0.314612
$$831$$ 2.41417e6 0.121273
$$832$$ −1.04968e7 −0.525712
$$833$$ −2.38014e6 −0.118848
$$834$$ −9.68629e6 −0.482217
$$835$$ 1.49428e7 0.741681
$$836$$ 8.93671e6 0.442244
$$837$$ 1.60621e7 0.792482
$$838$$ 1.71326e7 0.842777
$$839$$ 1.93485e7 0.948948 0.474474 0.880269i $$-0.342638\pi$$
0.474474 + 0.880269i $$0.342638\pi$$
$$840$$ 3.03003e6 0.148166
$$841$$ 2.50772e7 1.22261
$$842$$ 2.17082e7 1.05522
$$843$$ 2.51656e7 1.21966
$$844$$ −145372. −0.00702465
$$845$$ 2.97846e6 0.143500
$$846$$ −883071. −0.0424199
$$847$$ −1.55403e7 −0.744303
$$848$$ 455325. 0.0217436
$$849$$ 3.26039e7 1.55239
$$850$$ 2.18778e6 0.103862
$$851$$ 2.14201e6 0.101391
$$852$$ −5.04197e6 −0.237959
$$853$$ −3.05998e7 −1.43994 −0.719972 0.694003i $$-0.755845\pi$$
−0.719972 + 0.694003i $$0.755845\pi$$
$$854$$ −8.46520e6 −0.397185
$$855$$ 963068. 0.0450549
$$856$$ −1.93481e7 −0.902515
$$857$$ −1.33039e7 −0.618766 −0.309383 0.950937i $$-0.600123\pi$$
−0.309383 + 0.950937i $$0.600123\pi$$
$$858$$ −1.66678e7 −0.772967
$$859$$ −1.27708e7 −0.590520 −0.295260 0.955417i $$-0.595406\pi$$
−0.295260 + 0.955417i $$0.595406\pi$$
$$860$$ −8.43633e6 −0.388962
$$861$$ −1.08423e7 −0.498440
$$862$$ −1.25500e7 −0.575276
$$863$$ 1.37987e7 0.630684 0.315342 0.948978i $$-0.397881\pi$$
0.315342 + 0.948978i $$0.397881\pi$$
$$864$$ 2.35885e7 1.07502
$$865$$ 1.49685e6 0.0680203
$$866$$ −9.98074e6 −0.452239
$$867$$ −5.94241e6 −0.268482
$$868$$ −3.75418e6 −0.169128
$$869$$ 6.70680e7 3.01277
$$870$$ 8.10230e6 0.362919
$$871$$ 2.13806e6 0.0954934
$$872$$ −9.06477e6 −0.403706
$$873$$ 6.07673e6 0.269857
$$874$$ −7.97922e6 −0.353331
$$875$$ 765625. 0.0338062
$$876$$ −2.69012e6 −0.118443
$$877$$ 6.68992e6 0.293712 0.146856 0.989158i $$-0.453085\pi$$
0.146856 + 0.989158i $$0.453085\pi$$
$$878$$ −1.63989e7 −0.717924
$$879$$ 3.39728e7 1.48306
$$880$$ −303212. −0.0131990
$$881$$ −7.25051e6 −0.314723 −0.157362 0.987541i $$-0.550299\pi$$
−0.157362 + 0.987541i $$0.550299\pi$$
$$882$$ 493602. 0.0213651
$$883$$ −2.55944e7 −1.10470 −0.552348 0.833613i $$-0.686268\pi$$
−0.552348 + 0.833613i $$0.686268\pi$$
$$884$$ −9.72236e6 −0.418447
$$885$$ −3.02542e6 −0.129846
$$886$$ 2.17353e7 0.930210
$$887$$ −2.33204e7 −0.995240 −0.497620 0.867395i $$-0.665793\pi$$
−0.497620 + 0.867395i $$0.665793\pi$$
$$888$$ 1.55143e6 0.0660237
$$889$$ 2.27900e6 0.0967141
$$890$$ 374398. 0.0158438
$$891$$ 2.87064e7 1.21139
$$892$$ −2.32726e6 −0.0979340
$$893$$ −2.84222e6 −0.119269
$$894$$ 2.23794e7 0.936493
$$895$$ −1.54203e7 −0.643480
$$896$$ −5.41620e6 −0.225385
$$897$$ −2.33110e7 −0.967343
$$898$$ −1.29605e7 −0.536328
$$899$$ −2.64862e7 −1.09300
$$900$$ 710687. 0.0292464
$$901$$ 2.57354e7 1.05613
$$902$$ 3.97480e7 1.62667
$$903$$ 1.15083e7 0.469667
$$904$$ −6.76188e6 −0.275199
$$905$$ 932174. 0.0378334
$$906$$ 5.86617e6 0.237429
$$907$$ 3.71721e7 1.50037 0.750187 0.661226i $$-0.229964\pi$$
0.750187 + 0.661226i $$0.229964\pi$$
$$908$$ 7.59453e6 0.305694
$$909$$ 2.66152e6 0.106837
$$910$$ 2.17212e6 0.0869520
$$911$$ −2.89923e7 −1.15741 −0.578704 0.815537i $$-0.696441\pi$$
−0.578704 + 0.815537i $$0.696441\pi$$
$$912$$ −157752. −0.00628042
$$913$$ −4.89127e7 −1.94198
$$914$$ 3.05911e6 0.121124
$$915$$ 1.66263e7 0.656512
$$916$$ −1.43089e7 −0.563468
$$917$$ −1.87068e7 −0.734641
$$918$$ −1.43330e7 −0.561344
$$919$$ −1.25020e6 −0.0488306 −0.0244153 0.999702i $$-0.507772\pi$$
−0.0244153 + 0.999702i $$0.507772\pi$$
$$920$$ −1.55355e7 −0.605138
$$921$$ 4.17582e7 1.62216
$$922$$ 6.65872e6 0.257966
$$923$$ −9.53627e6 −0.368447
$$924$$ −8.99613e6 −0.346638
$$925$$ 392014. 0.0150642
$$926$$ 2.99799e7 1.14895
$$927$$ −5.19776e6 −0.198663
$$928$$ −3.88970e7 −1.48268
$$929$$ 6.87875e6 0.261499 0.130749 0.991415i $$-0.458262\pi$$
0.130749 + 0.991415i $$0.458262\pi$$
$$930$$ −4.70732e6 −0.178470
$$931$$ 1.58869e6 0.0600709
$$932$$ 2.19997e7 0.829616
$$933$$ 8.98840e6 0.338048
$$934$$ −6.45272e6 −0.242034
$$935$$ −1.71378e7 −0.641101
$$936$$ 5.31971e6 0.198471
$$937$$ 2.18600e7 0.813396 0.406698 0.913563i $$-0.366680\pi$$
0.406698 + 0.913563i $$0.366680\pi$$
$$938$$ −736708. −0.0273393
$$939$$ −4.47756e7 −1.65721
$$940$$ −2.09739e6 −0.0774210
$$941$$ 2.26450e6 0.0833679 0.0416840 0.999131i $$-0.486728\pi$$
0.0416840 + 0.999131i $$0.486728\pi$$
$$942$$ 1.97106e7 0.723725
$$943$$ 5.55901e7 2.03572
$$944$$ −156142. −0.00570283
$$945$$ −5.01588e6 −0.182712
$$946$$ −4.21895e7 −1.53277
$$947$$ −2.45846e7 −0.890815 −0.445408 0.895328i $$-0.646941\pi$$
−0.445408 + 0.895328i $$0.646941\pi$$
$$948$$ 2.57493e7 0.930562
$$949$$ −5.08803e6 −0.183394
$$950$$ −1.46029e6 −0.0524965
$$951$$ 8.69601e6 0.311795
$$952$$ 8.83874e6 0.316081
$$953$$ 4.59681e7 1.63955 0.819774 0.572687i $$-0.194099\pi$$
0.819774 + 0.572687i $$0.194099\pi$$
$$954$$ −5.33708e6 −0.189860
$$955$$ −8.16901e6 −0.289842
$$956$$ −1.50842e7 −0.533800
$$957$$ −6.34686e7 −2.24016
$$958$$ −1.65520e7 −0.582687
$$959$$ 92832.6 0.00325952
$$960$$ −7.10379e6 −0.248778
$$961$$ −1.32411e7 −0.462503
$$962$$ 1.11216e6 0.0387463
$$963$$ 6.19051e6 0.215110
$$964$$ −2.74015e7 −0.949690
$$965$$ 6.64338e6 0.229652
$$966$$ 8.03226e6 0.276946
$$967$$ −5.30202e7 −1.82337 −0.911686 0.410888i $$-0.865219\pi$$
−0.911686 + 0.410888i $$0.865219\pi$$
$$968$$ 5.77093e7 1.97951
$$969$$ −8.91630e6 −0.305053
$$970$$ −9.21409e6 −0.314429
$$971$$ −5.43523e7 −1.84999 −0.924996 0.379976i $$-0.875932\pi$$
−0.924996 + 0.379976i $$0.875932\pi$$
$$972$$ −8.41202e6 −0.285585
$$973$$ −9.88809e6 −0.334835
$$974$$ −1.62309e7 −0.548207
$$975$$ −4.26620e6 −0.143724
$$976$$ 858083. 0.0288340
$$977$$ 1.08929e7 0.365097 0.182549 0.983197i $$-0.441565\pi$$
0.182549 + 0.983197i $$0.441565\pi$$
$$978$$ −3.76922e6 −0.126010
$$979$$ −2.93282e6 −0.0977976
$$980$$ 1.17236e6 0.0389937
$$981$$ 2.90031e6 0.0962215
$$982$$ −2.33796e7 −0.773674
$$983$$ −3.42136e7 −1.12932 −0.564658 0.825325i $$-0.690992\pi$$
−0.564658 + 0.825325i $$0.690992\pi$$
$$984$$ 4.02632e7 1.32562
$$985$$ 1.29466e7 0.425173
$$986$$ 2.36348e7 0.774211
$$987$$ 2.86111e6 0.0934850
$$988$$ 6.48943e6 0.211502
$$989$$ −5.90047e7 −1.91821
$$990$$ 3.55409e6 0.115250
$$991$$ 4.22117e6 0.136537 0.0682683 0.997667i $$-0.478253\pi$$
0.0682683 + 0.997667i $$0.478253\pi$$
$$992$$ 2.25986e7 0.729125
$$993$$ −1.54796e7 −0.498181
$$994$$ 3.28591e6 0.105485
$$995$$ 3.71716e6 0.119029
$$996$$ −1.87790e7 −0.599824
$$997$$ 4.30323e7 1.37106 0.685530 0.728044i $$-0.259571\pi$$
0.685530 + 0.728044i $$0.259571\pi$$
$$998$$ 1.59830e7 0.507964
$$999$$ −2.56822e6 −0.0814177
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 35.6.a.b.1.1 2
3.2 odd 2 315.6.a.c.1.2 2
4.3 odd 2 560.6.a.l.1.1 2
5.2 odd 4 175.6.b.d.99.2 4
5.3 odd 4 175.6.b.d.99.3 4
5.4 even 2 175.6.a.d.1.2 2
7.6 odd 2 245.6.a.c.1.1 2

By twisted newform
Twist Min Dim Char Parity Ord Type
35.6.a.b.1.1 2 1.1 even 1 trivial
175.6.a.d.1.2 2 5.4 even 2
175.6.b.d.99.2 4 5.2 odd 4
175.6.b.d.99.3 4 5.3 odd 4
245.6.a.c.1.1 2 7.6 odd 2
315.6.a.c.1.2 2 3.2 odd 2
560.6.a.l.1.1 2 4.3 odd 2