# Properties

 Label 1815.4.a.i.1.1 Level $1815$ Weight $4$ Character 1815.1 Self dual yes Analytic conductor $107.088$ Analytic rank $1$ Dimension $2$ CM no Inner twists $1$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$1815 = 3 \cdot 5 \cdot 11^{2}$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 1815.a (trivial)

## Newform invariants

 Self dual: yes Analytic conductor: $$107.088466660$$ Analytic rank: $$1$$ Dimension: $$2$$ Coefficient field: $$\Q(\sqrt{41})$$ Defining polynomial: $$x^{2} - x - 10$$ x^2 - x - 10 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 $$3.70156$$ of defining polynomial Character $$\chi$$ $$=$$ 1815.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q-3.70156 q^{2} +3.00000 q^{3} +5.70156 q^{4} +5.00000 q^{5} -11.1047 q^{6} +9.10469 q^{7} +8.50781 q^{8} +9.00000 q^{9} +O(q^{10})$$ $$q-3.70156 q^{2} +3.00000 q^{3} +5.70156 q^{4} +5.00000 q^{5} -11.1047 q^{6} +9.10469 q^{7} +8.50781 q^{8} +9.00000 q^{9} -18.5078 q^{10} +17.1047 q^{12} -20.2984 q^{13} -33.7016 q^{14} +15.0000 q^{15} -77.1047 q^{16} +61.8062 q^{17} -33.3141 q^{18} +8.68594 q^{19} +28.5078 q^{20} +27.3141 q^{21} -127.748 q^{23} +25.5234 q^{24} +25.0000 q^{25} +75.1359 q^{26} +27.0000 q^{27} +51.9109 q^{28} +85.9109 q^{29} -55.5234 q^{30} -158.733 q^{31} +217.345 q^{32} -228.780 q^{34} +45.5234 q^{35} +51.3141 q^{36} +138.423 q^{37} -32.1515 q^{38} -60.8953 q^{39} +42.5391 q^{40} -28.2094 q^{41} -101.105 q^{42} -265.884 q^{43} +45.0000 q^{45} +472.869 q^{46} -515.602 q^{47} -231.314 q^{48} -260.105 q^{49} -92.5391 q^{50} +185.419 q^{51} -115.733 q^{52} -466.702 q^{53} -99.9422 q^{54} +77.4609 q^{56} +26.0578 q^{57} -318.005 q^{58} +373.475 q^{59} +85.5234 q^{60} -84.8172 q^{61} +587.559 q^{62} +81.9422 q^{63} -187.680 q^{64} -101.492 q^{65} -88.7657 q^{67} +352.392 q^{68} -383.245 q^{69} -168.508 q^{70} -536.695 q^{71} +76.5703 q^{72} -322.450 q^{73} -512.383 q^{74} +75.0000 q^{75} +49.5234 q^{76} +225.408 q^{78} -265.592 q^{79} -385.523 q^{80} +81.0000 q^{81} +104.419 q^{82} +520.758 q^{83} +155.733 q^{84} +309.031 q^{85} +984.187 q^{86} +257.733 q^{87} -464.713 q^{89} -166.570 q^{90} -184.811 q^{91} -728.366 q^{92} -476.198 q^{93} +1908.53 q^{94} +43.4297 q^{95} +652.036 q^{96} -204.481 q^{97} +962.794 q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q - q^{2} + 6 q^{3} + 5 q^{4} + 10 q^{5} - 3 q^{6} - q^{7} - 15 q^{8} + 18 q^{9}+O(q^{10})$$ 2 * q - q^2 + 6 * q^3 + 5 * q^4 + 10 * q^5 - 3 * q^6 - q^7 - 15 * q^8 + 18 * q^9 $$2 q - q^{2} + 6 q^{3} + 5 q^{4} + 10 q^{5} - 3 q^{6} - q^{7} - 15 q^{8} + 18 q^{9} - 5 q^{10} + 15 q^{12} - 47 q^{13} - 61 q^{14} + 30 q^{15} - 135 q^{16} + 98 q^{17} - 9 q^{18} + 75 q^{19} + 25 q^{20} - 3 q^{21} - 57 q^{23} - 45 q^{24} + 50 q^{25} + 3 q^{26} + 54 q^{27} + 59 q^{28} + 127 q^{29} - 15 q^{30} - 183 q^{31} + 249 q^{32} - 131 q^{34} - 5 q^{35} + 45 q^{36} - 229 q^{37} + 147 q^{38} - 141 q^{39} - 75 q^{40} - 18 q^{41} - 183 q^{42} - 186 q^{43} + 90 q^{45} + 664 q^{46} - 615 q^{47} - 405 q^{48} - 501 q^{49} - 25 q^{50} + 294 q^{51} - 97 q^{52} - 927 q^{53} - 27 q^{54} + 315 q^{56} + 225 q^{57} - 207 q^{58} - 380 q^{59} + 75 q^{60} - 509 q^{61} + 522 q^{62} - 9 q^{63} + 361 q^{64} - 235 q^{65} - 1138 q^{67} + 327 q^{68} - 171 q^{69} - 305 q^{70} - 273 q^{71} - 135 q^{72} - 440 q^{73} - 1505 q^{74} + 150 q^{75} + 3 q^{76} + 9 q^{78} - 973 q^{79} - 675 q^{80} + 162 q^{81} + 132 q^{82} - 15 q^{83} + 177 q^{84} + 490 q^{85} + 1200 q^{86} + 381 q^{87} - 1288 q^{89} - 45 q^{90} + 85 q^{91} - 778 q^{92} - 549 q^{93} + 1640 q^{94} + 375 q^{95} + 747 q^{96} - 76 q^{97} + 312 q^{98}+O(q^{100})$$ 2 * q - q^2 + 6 * q^3 + 5 * q^4 + 10 * q^5 - 3 * q^6 - q^7 - 15 * q^8 + 18 * q^9 - 5 * q^10 + 15 * q^12 - 47 * q^13 - 61 * q^14 + 30 * q^15 - 135 * q^16 + 98 * q^17 - 9 * q^18 + 75 * q^19 + 25 * q^20 - 3 * q^21 - 57 * q^23 - 45 * q^24 + 50 * q^25 + 3 * q^26 + 54 * q^27 + 59 * q^28 + 127 * q^29 - 15 * q^30 - 183 * q^31 + 249 * q^32 - 131 * q^34 - 5 * q^35 + 45 * q^36 - 229 * q^37 + 147 * q^38 - 141 * q^39 - 75 * q^40 - 18 * q^41 - 183 * q^42 - 186 * q^43 + 90 * q^45 + 664 * q^46 - 615 * q^47 - 405 * q^48 - 501 * q^49 - 25 * q^50 + 294 * q^51 - 97 * q^52 - 927 * q^53 - 27 * q^54 + 315 * q^56 + 225 * q^57 - 207 * q^58 - 380 * q^59 + 75 * q^60 - 509 * q^61 + 522 * q^62 - 9 * q^63 + 361 * q^64 - 235 * q^65 - 1138 * q^67 + 327 * q^68 - 171 * q^69 - 305 * q^70 - 273 * q^71 - 135 * q^72 - 440 * q^73 - 1505 * q^74 + 150 * q^75 + 3 * q^76 + 9 * q^78 - 973 * q^79 - 675 * q^80 + 162 * q^81 + 132 * q^82 - 15 * q^83 + 177 * q^84 + 490 * q^85 + 1200 * q^86 + 381 * q^87 - 1288 * q^89 - 45 * q^90 + 85 * q^91 - 778 * q^92 - 549 * q^93 + 1640 * q^94 + 375 * q^95 + 747 * q^96 - 76 * q^97 + 312 * q^98

## Coefficient data

For each $$n$$ we display the coefficients of the $$q$$-expansion $$a_n$$, the Satake parameters $$\alpha_p$$, and the Satake angles $$\theta_p = \textrm{Arg}(\alpha_p)$$.

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −3.70156 −1.30870 −0.654350 0.756192i $$-0.727058\pi$$
−0.654350 + 0.756192i $$0.727058\pi$$
$$3$$ 3.00000 0.577350
$$4$$ 5.70156 0.712695
$$5$$ 5.00000 0.447214
$$6$$ −11.1047 −0.755578
$$7$$ 9.10469 0.491607 0.245803 0.969320i $$-0.420948\pi$$
0.245803 + 0.969320i $$0.420948\pi$$
$$8$$ 8.50781 0.375996
$$9$$ 9.00000 0.333333
$$10$$ −18.5078 −0.585268
$$11$$ 0 0
$$12$$ 17.1047 0.411475
$$13$$ −20.2984 −0.433060 −0.216530 0.976276i $$-0.569474\pi$$
−0.216530 + 0.976276i $$0.569474\pi$$
$$14$$ −33.7016 −0.643366
$$15$$ 15.0000 0.258199
$$16$$ −77.1047 −1.20476
$$17$$ 61.8062 0.881777 0.440889 0.897562i $$-0.354663\pi$$
0.440889 + 0.897562i $$0.354663\pi$$
$$18$$ −33.3141 −0.436233
$$19$$ 8.68594 0.104879 0.0524393 0.998624i $$-0.483300\pi$$
0.0524393 + 0.998624i $$0.483300\pi$$
$$20$$ 28.5078 0.318727
$$21$$ 27.3141 0.283829
$$22$$ 0 0
$$23$$ −127.748 −1.15815 −0.579074 0.815275i $$-0.696586\pi$$
−0.579074 + 0.815275i $$0.696586\pi$$
$$24$$ 25.5234 0.217081
$$25$$ 25.0000 0.200000
$$26$$ 75.1359 0.566745
$$27$$ 27.0000 0.192450
$$28$$ 51.9109 0.350366
$$29$$ 85.9109 0.550112 0.275056 0.961428i $$-0.411304\pi$$
0.275056 + 0.961428i $$0.411304\pi$$
$$30$$ −55.5234 −0.337905
$$31$$ −158.733 −0.919653 −0.459827 0.888009i $$-0.652088\pi$$
−0.459827 + 0.888009i $$0.652088\pi$$
$$32$$ 217.345 1.20067
$$33$$ 0 0
$$34$$ −228.780 −1.15398
$$35$$ 45.5234 0.219853
$$36$$ 51.3141 0.237565
$$37$$ 138.423 0.615045 0.307523 0.951541i $$-0.400500\pi$$
0.307523 + 0.951541i $$0.400500\pi$$
$$38$$ −32.1515 −0.137254
$$39$$ −60.8953 −0.250027
$$40$$ 42.5391 0.168150
$$41$$ −28.2094 −0.107453 −0.0537264 0.998556i $$-0.517110\pi$$
−0.0537264 + 0.998556i $$0.517110\pi$$
$$42$$ −101.105 −0.371447
$$43$$ −265.884 −0.942953 −0.471477 0.881879i $$-0.656279\pi$$
−0.471477 + 0.881879i $$0.656279\pi$$
$$44$$ 0 0
$$45$$ 45.0000 0.149071
$$46$$ 472.869 1.51567
$$47$$ −515.602 −1.60017 −0.800087 0.599883i $$-0.795214\pi$$
−0.800087 + 0.599883i $$0.795214\pi$$
$$48$$ −231.314 −0.695569
$$49$$ −260.105 −0.758323
$$50$$ −92.5391 −0.261740
$$51$$ 185.419 0.509094
$$52$$ −115.733 −0.308639
$$53$$ −466.702 −1.20955 −0.604777 0.796395i $$-0.706738\pi$$
−0.604777 + 0.796395i $$0.706738\pi$$
$$54$$ −99.9422 −0.251859
$$55$$ 0 0
$$56$$ 77.4609 0.184842
$$57$$ 26.0578 0.0605516
$$58$$ −318.005 −0.719932
$$59$$ 373.475 0.824107 0.412053 0.911160i $$-0.364812\pi$$
0.412053 + 0.911160i $$0.364812\pi$$
$$60$$ 85.5234 0.184017
$$61$$ −84.8172 −0.178028 −0.0890142 0.996030i $$-0.528372\pi$$
−0.0890142 + 0.996030i $$0.528372\pi$$
$$62$$ 587.559 1.20355
$$63$$ 81.9422 0.163869
$$64$$ −187.680 −0.366562
$$65$$ −101.492 −0.193670
$$66$$ 0 0
$$67$$ −88.7657 −0.161858 −0.0809288 0.996720i $$-0.525789\pi$$
−0.0809288 + 0.996720i $$0.525789\pi$$
$$68$$ 352.392 0.628439
$$69$$ −383.245 −0.668657
$$70$$ −168.508 −0.287722
$$71$$ −536.695 −0.897099 −0.448549 0.893758i $$-0.648059\pi$$
−0.448549 + 0.893758i $$0.648059\pi$$
$$72$$ 76.5703 0.125332
$$73$$ −322.450 −0.516985 −0.258493 0.966013i $$-0.583226\pi$$
−0.258493 + 0.966013i $$0.583226\pi$$
$$74$$ −512.383 −0.804909
$$75$$ 75.0000 0.115470
$$76$$ 49.5234 0.0747464
$$77$$ 0 0
$$78$$ 225.408 0.327210
$$79$$ −265.592 −0.378246 −0.189123 0.981953i $$-0.560565\pi$$
−0.189123 + 0.981953i $$0.560565\pi$$
$$80$$ −385.523 −0.538785
$$81$$ 81.0000 0.111111
$$82$$ 104.419 0.140623
$$83$$ 520.758 0.688682 0.344341 0.938845i $$-0.388102\pi$$
0.344341 + 0.938845i $$0.388102\pi$$
$$84$$ 155.733 0.202284
$$85$$ 309.031 0.394343
$$86$$ 984.187 1.23404
$$87$$ 257.733 0.317608
$$88$$ 0 0
$$89$$ −464.713 −0.553477 −0.276738 0.960945i $$-0.589254\pi$$
−0.276738 + 0.960945i $$0.589254\pi$$
$$90$$ −166.570 −0.195089
$$91$$ −184.811 −0.212895
$$92$$ −728.366 −0.825406
$$93$$ −476.198 −0.530962
$$94$$ 1908.53 2.09415
$$95$$ 43.4297 0.0469031
$$96$$ 652.036 0.693210
$$97$$ −204.481 −0.214040 −0.107020 0.994257i $$-0.534131\pi$$
−0.107020 + 0.994257i $$0.534131\pi$$
$$98$$ 962.794 0.992417
$$99$$ 0 0
$$100$$ 142.539 0.142539
$$101$$ −27.2516 −0.0268479 −0.0134239 0.999910i $$-0.504273\pi$$
−0.0134239 + 0.999910i $$0.504273\pi$$
$$102$$ −686.339 −0.666252
$$103$$ 1062.80 1.01671 0.508353 0.861149i $$-0.330255\pi$$
0.508353 + 0.861149i $$0.330255\pi$$
$$104$$ −172.695 −0.162828
$$105$$ 136.570 0.126932
$$106$$ 1727.52 1.58294
$$107$$ −1702.96 −1.53861 −0.769306 0.638881i $$-0.779398\pi$$
−0.769306 + 0.638881i $$0.779398\pi$$
$$108$$ 153.942 0.137158
$$109$$ −556.334 −0.488873 −0.244437 0.969665i $$-0.578603\pi$$
−0.244437 + 0.969665i $$0.578603\pi$$
$$110$$ 0 0
$$111$$ 415.270 0.355096
$$112$$ −702.014 −0.592269
$$113$$ −2088.31 −1.73851 −0.869256 0.494363i $$-0.835401\pi$$
−0.869256 + 0.494363i $$0.835401\pi$$
$$114$$ −96.4546 −0.0792439
$$115$$ −638.742 −0.517939
$$116$$ 489.827 0.392063
$$117$$ −182.686 −0.144353
$$118$$ −1382.44 −1.07851
$$119$$ 562.727 0.433488
$$120$$ 127.617 0.0970817
$$121$$ 0 0
$$122$$ 313.956 0.232986
$$123$$ −84.6281 −0.0620379
$$124$$ −905.025 −0.655433
$$125$$ 125.000 0.0894427
$$126$$ −303.314 −0.214455
$$127$$ 2179.16 1.52259 0.761296 0.648405i $$-0.224564\pi$$
0.761296 + 0.648405i $$0.224564\pi$$
$$128$$ −1044.05 −0.720955
$$129$$ −797.653 −0.544414
$$130$$ 375.680 0.253456
$$131$$ 1951.11 1.30129 0.650645 0.759382i $$-0.274499\pi$$
0.650645 + 0.759382i $$0.274499\pi$$
$$132$$ 0 0
$$133$$ 79.0828 0.0515590
$$134$$ 328.572 0.211823
$$135$$ 135.000 0.0860663
$$136$$ 525.836 0.331545
$$137$$ −613.425 −0.382543 −0.191272 0.981537i $$-0.561261\pi$$
−0.191272 + 0.981537i $$0.561261\pi$$
$$138$$ 1418.61 0.875071
$$139$$ 2130.63 1.30013 0.650064 0.759880i $$-0.274742\pi$$
0.650064 + 0.759880i $$0.274742\pi$$
$$140$$ 259.555 0.156688
$$141$$ −1546.80 −0.923861
$$142$$ 1986.61 1.17403
$$143$$ 0 0
$$144$$ −693.942 −0.401587
$$145$$ 429.555 0.246018
$$146$$ 1193.57 0.676578
$$147$$ −780.314 −0.437818
$$148$$ 789.230 0.438340
$$149$$ 570.900 0.313892 0.156946 0.987607i $$-0.449835\pi$$
0.156946 + 0.987607i $$0.449835\pi$$
$$150$$ −277.617 −0.151116
$$151$$ −2154.78 −1.16128 −0.580641 0.814159i $$-0.697198\pi$$
−0.580641 + 0.814159i $$0.697198\pi$$
$$152$$ 73.8983 0.0394339
$$153$$ 556.256 0.293926
$$154$$ 0 0
$$155$$ −793.664 −0.411281
$$156$$ −347.198 −0.178193
$$157$$ −157.105 −0.0798619 −0.0399310 0.999202i $$-0.512714\pi$$
−0.0399310 + 0.999202i $$0.512714\pi$$
$$158$$ 983.106 0.495011
$$159$$ −1400.10 −0.698337
$$160$$ 1086.73 0.536958
$$161$$ −1163.11 −0.569353
$$162$$ −299.827 −0.145411
$$163$$ 1736.66 0.834512 0.417256 0.908789i $$-0.362992\pi$$
0.417256 + 0.908789i $$0.362992\pi$$
$$164$$ −160.837 −0.0765811
$$165$$ 0 0
$$166$$ −1927.62 −0.901278
$$167$$ 1466.55 0.679549 0.339775 0.940507i $$-0.389649\pi$$
0.339775 + 0.940507i $$0.389649\pi$$
$$168$$ 232.383 0.106719
$$169$$ −1784.97 −0.812459
$$170$$ −1143.90 −0.516076
$$171$$ 78.1735 0.0349595
$$172$$ −1515.96 −0.672038
$$173$$ 143.781 0.0631878 0.0315939 0.999501i $$-0.489942\pi$$
0.0315939 + 0.999501i $$0.489942\pi$$
$$174$$ −954.014 −0.415653
$$175$$ 227.617 0.0983214
$$176$$ 0 0
$$177$$ 1120.42 0.475798
$$178$$ 1720.16 0.724335
$$179$$ −1412.93 −0.589984 −0.294992 0.955500i $$-0.595317\pi$$
−0.294992 + 0.955500i $$0.595317\pi$$
$$180$$ 256.570 0.106242
$$181$$ −2239.25 −0.919570 −0.459785 0.888030i $$-0.652073\pi$$
−0.459785 + 0.888030i $$0.652073\pi$$
$$182$$ 684.089 0.278616
$$183$$ −254.452 −0.102785
$$184$$ −1086.86 −0.435458
$$185$$ 692.117 0.275057
$$186$$ 1762.68 0.694870
$$187$$ 0 0
$$188$$ −2939.73 −1.14044
$$189$$ 245.827 0.0946098
$$190$$ −160.758 −0.0613821
$$191$$ 1745.94 0.661425 0.330712 0.943732i $$-0.392711\pi$$
0.330712 + 0.943732i $$0.392711\pi$$
$$192$$ −563.039 −0.211635
$$193$$ 3985.04 1.48627 0.743134 0.669143i $$-0.233338\pi$$
0.743134 + 0.669143i $$0.233338\pi$$
$$194$$ 756.900 0.280115
$$195$$ −304.477 −0.111815
$$196$$ −1483.00 −0.540453
$$197$$ −2262.00 −0.818076 −0.409038 0.912517i $$-0.634136\pi$$
−0.409038 + 0.912517i $$0.634136\pi$$
$$198$$ 0 0
$$199$$ 2340.15 0.833613 0.416806 0.908995i $$-0.363149\pi$$
0.416806 + 0.908995i $$0.363149\pi$$
$$200$$ 212.695 0.0751991
$$201$$ −266.297 −0.0934485
$$202$$ 100.873 0.0351358
$$203$$ 782.192 0.270439
$$204$$ 1057.18 0.362829
$$205$$ −141.047 −0.0480543
$$206$$ −3934.01 −1.33056
$$207$$ −1149.74 −0.386049
$$208$$ 1565.10 0.521733
$$209$$ 0 0
$$210$$ −505.523 −0.166116
$$211$$ −1524.44 −0.497377 −0.248689 0.968583i $$-0.580000\pi$$
−0.248689 + 0.968583i $$0.580000\pi$$
$$212$$ −2660.93 −0.862044
$$213$$ −1610.09 −0.517940
$$214$$ 6303.62 2.01358
$$215$$ −1329.42 −0.421701
$$216$$ 229.711 0.0723604
$$217$$ −1445.21 −0.452108
$$218$$ 2059.31 0.639788
$$219$$ −967.350 −0.298482
$$220$$ 0 0
$$221$$ −1254.57 −0.381862
$$222$$ −1537.15 −0.464715
$$223$$ 5083.42 1.52651 0.763253 0.646100i $$-0.223601\pi$$
0.763253 + 0.646100i $$0.223601\pi$$
$$224$$ 1978.86 0.590260
$$225$$ 225.000 0.0666667
$$226$$ 7730.01 2.27519
$$227$$ −3910.66 −1.14343 −0.571717 0.820451i $$-0.693723\pi$$
−0.571717 + 0.820451i $$0.693723\pi$$
$$228$$ 148.570 0.0431549
$$229$$ 2733.31 0.788743 0.394371 0.918951i $$-0.370962\pi$$
0.394371 + 0.918951i $$0.370962\pi$$
$$230$$ 2364.34 0.677827
$$231$$ 0 0
$$232$$ 730.914 0.206840
$$233$$ −4355.46 −1.22462 −0.612308 0.790619i $$-0.709759\pi$$
−0.612308 + 0.790619i $$0.709759\pi$$
$$234$$ 676.223 0.188915
$$235$$ −2578.01 −0.715620
$$236$$ 2129.39 0.587337
$$237$$ −796.777 −0.218381
$$238$$ −2082.97 −0.567305
$$239$$ −4731.48 −1.28056 −0.640281 0.768141i $$-0.721182\pi$$
−0.640281 + 0.768141i $$0.721182\pi$$
$$240$$ −1156.57 −0.311068
$$241$$ 1833.12 0.489966 0.244983 0.969527i $$-0.421218\pi$$
0.244983 + 0.969527i $$0.421218\pi$$
$$242$$ 0 0
$$243$$ 243.000 0.0641500
$$244$$ −483.591 −0.126880
$$245$$ −1300.52 −0.339132
$$246$$ 313.256 0.0811890
$$247$$ −176.311 −0.0454186
$$248$$ −1350.47 −0.345786
$$249$$ 1562.27 0.397611
$$250$$ −462.695 −0.117054
$$251$$ −3168.31 −0.796741 −0.398370 0.917225i $$-0.630424\pi$$
−0.398370 + 0.917225i $$0.630424\pi$$
$$252$$ 467.198 0.116789
$$253$$ 0 0
$$254$$ −8066.29 −1.99262
$$255$$ 927.094 0.227674
$$256$$ 5366.07 1.31008
$$257$$ 5378.55 1.30547 0.652733 0.757588i $$-0.273622\pi$$
0.652733 + 0.757588i $$0.273622\pi$$
$$258$$ 2952.56 0.712475
$$259$$ 1260.30 0.302360
$$260$$ −578.664 −0.138028
$$261$$ 773.198 0.183371
$$262$$ −7222.14 −1.70300
$$263$$ 4584.03 1.07477 0.537383 0.843338i $$-0.319413\pi$$
0.537383 + 0.843338i $$0.319413\pi$$
$$264$$ 0 0
$$265$$ −2333.51 −0.540929
$$266$$ −292.730 −0.0674752
$$267$$ −1394.14 −0.319550
$$268$$ −506.103 −0.115355
$$269$$ −1741.03 −0.394618 −0.197309 0.980341i $$-0.563220\pi$$
−0.197309 + 0.980341i $$0.563220\pi$$
$$270$$ −499.711 −0.112635
$$271$$ 1340.58 0.300495 0.150248 0.988648i $$-0.451993\pi$$
0.150248 + 0.988648i $$0.451993\pi$$
$$272$$ −4765.55 −1.06233
$$273$$ −554.433 −0.122915
$$274$$ 2270.63 0.500634
$$275$$ 0 0
$$276$$ −2185.10 −0.476548
$$277$$ −5220.77 −1.13244 −0.566220 0.824254i $$-0.691595\pi$$
−0.566220 + 0.824254i $$0.691595\pi$$
$$278$$ −7886.66 −1.70148
$$279$$ −1428.60 −0.306551
$$280$$ 387.305 0.0826639
$$281$$ 2494.68 0.529609 0.264804 0.964302i $$-0.414693\pi$$
0.264804 + 0.964302i $$0.414693\pi$$
$$282$$ 5725.59 1.20906
$$283$$ 4329.43 0.909391 0.454696 0.890647i $$-0.349748\pi$$
0.454696 + 0.890647i $$0.349748\pi$$
$$284$$ −3060.00 −0.639358
$$285$$ 130.289 0.0270795
$$286$$ 0 0
$$287$$ −256.837 −0.0528245
$$288$$ 1956.11 0.400225
$$289$$ −1092.99 −0.222468
$$290$$ −1590.02 −0.321963
$$291$$ −613.444 −0.123576
$$292$$ −1838.47 −0.368453
$$293$$ −4330.93 −0.863534 −0.431767 0.901985i $$-0.642110\pi$$
−0.431767 + 0.901985i $$0.642110\pi$$
$$294$$ 2888.38 0.572972
$$295$$ 1867.37 0.368552
$$296$$ 1177.68 0.231254
$$297$$ 0 0
$$298$$ −2113.22 −0.410791
$$299$$ 2593.09 0.501547
$$300$$ 427.617 0.0822950
$$301$$ −2420.79 −0.463562
$$302$$ 7976.06 1.51977
$$303$$ −81.7547 −0.0155006
$$304$$ −669.727 −0.126353
$$305$$ −424.086 −0.0796167
$$306$$ −2059.02 −0.384661
$$307$$ −2052.56 −0.381582 −0.190791 0.981631i $$-0.561105\pi$$
−0.190791 + 0.981631i $$0.561105\pi$$
$$308$$ 0 0
$$309$$ 3188.39 0.586995
$$310$$ 2937.80 0.538244
$$311$$ 2627.76 0.479121 0.239561 0.970881i $$-0.422997\pi$$
0.239561 + 0.970881i $$0.422997\pi$$
$$312$$ −518.086 −0.0940091
$$313$$ 6878.40 1.24214 0.621070 0.783755i $$-0.286698\pi$$
0.621070 + 0.783755i $$0.286698\pi$$
$$314$$ 581.533 0.104515
$$315$$ 409.711 0.0732844
$$316$$ −1514.29 −0.269574
$$317$$ −3026.05 −0.536151 −0.268076 0.963398i $$-0.586388\pi$$
−0.268076 + 0.963398i $$0.586388\pi$$
$$318$$ 5182.57 0.913913
$$319$$ 0 0
$$320$$ −938.398 −0.163931
$$321$$ −5108.88 −0.888318
$$322$$ 4305.32 0.745112
$$323$$ 536.845 0.0924795
$$324$$ 461.827 0.0791884
$$325$$ −507.461 −0.0866119
$$326$$ −6428.34 −1.09213
$$327$$ −1669.00 −0.282251
$$328$$ −240.000 −0.0404018
$$329$$ −4694.39 −0.786657
$$330$$ 0 0
$$331$$ −4326.50 −0.718447 −0.359223 0.933252i $$-0.616958\pi$$
−0.359223 + 0.933252i $$0.616958\pi$$
$$332$$ 2969.13 0.490820
$$333$$ 1245.81 0.205015
$$334$$ −5428.51 −0.889326
$$335$$ −443.828 −0.0723849
$$336$$ −2106.04 −0.341946
$$337$$ −1759.36 −0.284387 −0.142194 0.989839i $$-0.545416\pi$$
−0.142194 + 0.989839i $$0.545416\pi$$
$$338$$ 6607.19 1.06327
$$339$$ −6264.93 −1.00373
$$340$$ 1761.96 0.281046
$$341$$ 0 0
$$342$$ −289.364 −0.0457515
$$343$$ −5491.08 −0.864403
$$344$$ −2262.09 −0.354546
$$345$$ −1916.23 −0.299032
$$346$$ −532.215 −0.0826939
$$347$$ −11730.7 −1.81481 −0.907404 0.420260i $$-0.861939\pi$$
−0.907404 + 0.420260i $$0.861939\pi$$
$$348$$ 1469.48 0.226357
$$349$$ −3152.38 −0.483504 −0.241752 0.970338i $$-0.577722\pi$$
−0.241752 + 0.970338i $$0.577722\pi$$
$$350$$ −842.539 −0.128673
$$351$$ −548.058 −0.0833423
$$352$$ 0 0
$$353$$ −6881.03 −1.03751 −0.518754 0.854923i $$-0.673604\pi$$
−0.518754 + 0.854923i $$0.673604\pi$$
$$354$$ −4147.32 −0.622677
$$355$$ −2683.48 −0.401195
$$356$$ −2649.59 −0.394460
$$357$$ 1688.18 0.250274
$$358$$ 5230.04 0.772112
$$359$$ −2858.96 −0.420307 −0.210154 0.977668i $$-0.567396\pi$$
−0.210154 + 0.977668i $$0.567396\pi$$
$$360$$ 382.851 0.0560501
$$361$$ −6783.55 −0.989001
$$362$$ 8288.72 1.20344
$$363$$ 0 0
$$364$$ −1053.71 −0.151729
$$365$$ −1612.25 −0.231203
$$366$$ 941.868 0.134514
$$367$$ −10973.4 −1.56079 −0.780393 0.625289i $$-0.784981\pi$$
−0.780393 + 0.625289i $$0.784981\pi$$
$$368$$ 9850.00 1.39529
$$369$$ −253.884 −0.0358176
$$370$$ −2561.91 −0.359966
$$371$$ −4249.17 −0.594625
$$372$$ −2715.07 −0.378414
$$373$$ 10443.4 1.44970 0.724852 0.688905i $$-0.241908\pi$$
0.724852 + 0.688905i $$0.241908\pi$$
$$374$$ 0 0
$$375$$ 375.000 0.0516398
$$376$$ −4386.64 −0.601659
$$377$$ −1743.86 −0.238231
$$378$$ −909.942 −0.123816
$$379$$ −7405.86 −1.00373 −0.501865 0.864946i $$-0.667352\pi$$
−0.501865 + 0.864946i $$0.667352\pi$$
$$380$$ 247.617 0.0334276
$$381$$ 6537.48 0.879069
$$382$$ −6462.72 −0.865607
$$383$$ 14155.0 1.88848 0.944238 0.329264i $$-0.106801\pi$$
0.944238 + 0.329264i $$0.106801\pi$$
$$384$$ −3132.16 −0.416244
$$385$$ 0 0
$$386$$ −14750.9 −1.94508
$$387$$ −2392.96 −0.314318
$$388$$ −1165.86 −0.152546
$$389$$ −13031.6 −1.69853 −0.849263 0.527970i $$-0.822953\pi$$
−0.849263 + 0.527970i $$0.822953\pi$$
$$390$$ 1127.04 0.146333
$$391$$ −7895.65 −1.02123
$$392$$ −2212.92 −0.285126
$$393$$ 5853.32 0.751300
$$394$$ 8372.94 1.07062
$$395$$ −1327.96 −0.169157
$$396$$ 0 0
$$397$$ 2281.02 0.288366 0.144183 0.989551i $$-0.453945\pi$$
0.144183 + 0.989551i $$0.453945\pi$$
$$398$$ −8662.22 −1.09095
$$399$$ 237.248 0.0297676
$$400$$ −1927.62 −0.240952
$$401$$ −13017.7 −1.62114 −0.810568 0.585645i $$-0.800841\pi$$
−0.810568 + 0.585645i $$0.800841\pi$$
$$402$$ 985.715 0.122296
$$403$$ 3222.03 0.398265
$$404$$ −155.377 −0.0191343
$$405$$ 405.000 0.0496904
$$406$$ −2895.33 −0.353924
$$407$$ 0 0
$$408$$ 1577.51 0.191417
$$409$$ −3548.46 −0.428998 −0.214499 0.976724i $$-0.568812\pi$$
−0.214499 + 0.976724i $$0.568812\pi$$
$$410$$ 522.094 0.0628887
$$411$$ −1840.27 −0.220861
$$412$$ 6059.61 0.724601
$$413$$ 3400.37 0.405136
$$414$$ 4255.82 0.505222
$$415$$ 2603.79 0.307988
$$416$$ −4411.77 −0.519964
$$417$$ 6391.89 0.750629
$$418$$ 0 0
$$419$$ −14801.3 −1.72575 −0.862876 0.505416i $$-0.831339\pi$$
−0.862876 + 0.505416i $$0.831339\pi$$
$$420$$ 778.664 0.0904641
$$421$$ 11542.8 1.33625 0.668123 0.744051i $$-0.267098\pi$$
0.668123 + 0.744051i $$0.267098\pi$$
$$422$$ 5642.80 0.650918
$$423$$ −4640.41 −0.533392
$$424$$ −3970.61 −0.454787
$$425$$ 1545.16 0.176355
$$426$$ 5959.83 0.677828
$$427$$ −772.234 −0.0875200
$$428$$ −9709.54 −1.09656
$$429$$ 0 0
$$430$$ 4920.94 0.551881
$$431$$ −12712.6 −1.42076 −0.710378 0.703820i $$-0.751476\pi$$
−0.710378 + 0.703820i $$0.751476\pi$$
$$432$$ −2081.83 −0.231856
$$433$$ −16385.4 −1.81855 −0.909273 0.416200i $$-0.863361\pi$$
−0.909273 + 0.416200i $$0.863361\pi$$
$$434$$ 5349.54 0.591674
$$435$$ 1288.66 0.142038
$$436$$ −3171.97 −0.348418
$$437$$ −1109.62 −0.121465
$$438$$ 3580.71 0.390623
$$439$$ −6603.62 −0.717935 −0.358968 0.933350i $$-0.616871\pi$$
−0.358968 + 0.933350i $$0.616871\pi$$
$$440$$ 0 0
$$441$$ −2340.94 −0.252774
$$442$$ 4643.87 0.499743
$$443$$ −11641.0 −1.24849 −0.624244 0.781230i $$-0.714593\pi$$
−0.624244 + 0.781230i $$0.714593\pi$$
$$444$$ 2367.69 0.253076
$$445$$ −2323.56 −0.247522
$$446$$ −18816.6 −1.99774
$$447$$ 1712.70 0.181226
$$448$$ −1708.76 −0.180204
$$449$$ 13886.8 1.45960 0.729799 0.683662i $$-0.239614\pi$$
0.729799 + 0.683662i $$0.239614\pi$$
$$450$$ −832.851 −0.0872467
$$451$$ 0 0
$$452$$ −11906.6 −1.23903
$$453$$ −6464.35 −0.670467
$$454$$ 14475.6 1.49641
$$455$$ −924.055 −0.0952096
$$456$$ 221.695 0.0227672
$$457$$ −3625.85 −0.371138 −0.185569 0.982631i $$-0.559413\pi$$
−0.185569 + 0.982631i $$0.559413\pi$$
$$458$$ −10117.5 −1.03223
$$459$$ 1668.77 0.169698
$$460$$ −3641.83 −0.369133
$$461$$ −18329.1 −1.85178 −0.925890 0.377794i $$-0.876683\pi$$
−0.925890 + 0.377794i $$0.876683\pi$$
$$462$$ 0 0
$$463$$ 10760.7 1.08011 0.540056 0.841629i $$-0.318403\pi$$
0.540056 + 0.841629i $$0.318403\pi$$
$$464$$ −6624.14 −0.662754
$$465$$ −2380.99 −0.237453
$$466$$ 16122.0 1.60265
$$467$$ −7964.29 −0.789172 −0.394586 0.918859i $$-0.629112\pi$$
−0.394586 + 0.918859i $$0.629112\pi$$
$$468$$ −1041.60 −0.102880
$$469$$ −808.184 −0.0795703
$$470$$ 9542.66 0.936532
$$471$$ −471.314 −0.0461083
$$472$$ 3177.45 0.309861
$$473$$ 0 0
$$474$$ 2949.32 0.285795
$$475$$ 217.149 0.0209757
$$476$$ 3208.42 0.308945
$$477$$ −4200.31 −0.403185
$$478$$ 17513.9 1.67587
$$479$$ −822.463 −0.0784536 −0.0392268 0.999230i $$-0.512489\pi$$
−0.0392268 + 0.999230i $$0.512489\pi$$
$$480$$ 3260.18 0.310013
$$481$$ −2809.78 −0.266351
$$482$$ −6785.41 −0.641218
$$483$$ −3489.33 −0.328716
$$484$$ 0 0
$$485$$ −1022.41 −0.0957218
$$486$$ −899.480 −0.0839531
$$487$$ 6709.58 0.624312 0.312156 0.950031i $$-0.398949\pi$$
0.312156 + 0.950031i $$0.398949\pi$$
$$488$$ −721.609 −0.0669379
$$489$$ 5209.97 0.481806
$$490$$ 4813.97 0.443822
$$491$$ −12689.3 −1.16631 −0.583156 0.812360i $$-0.698182\pi$$
−0.583156 + 0.812360i $$0.698182\pi$$
$$492$$ −482.512 −0.0442141
$$493$$ 5309.83 0.485077
$$494$$ 652.626 0.0594394
$$495$$ 0 0
$$496$$ 12239.0 1.10796
$$497$$ −4886.44 −0.441020
$$498$$ −5782.85 −0.520353
$$499$$ −9810.79 −0.880143 −0.440072 0.897963i $$-0.645047\pi$$
−0.440072 + 0.897963i $$0.645047\pi$$
$$500$$ 712.695 0.0637454
$$501$$ 4399.64 0.392338
$$502$$ 11727.7 1.04269
$$503$$ 12865.7 1.14047 0.570233 0.821483i $$-0.306853\pi$$
0.570233 + 0.821483i $$0.306853\pi$$
$$504$$ 697.149 0.0616140
$$505$$ −136.258 −0.0120067
$$506$$ 0 0
$$507$$ −5354.92 −0.469074
$$508$$ 12424.6 1.08514
$$509$$ 2551.78 0.222211 0.111106 0.993809i $$-0.464561\pi$$
0.111106 + 0.993809i $$0.464561\pi$$
$$510$$ −3431.70 −0.297957
$$511$$ −2935.81 −0.254153
$$512$$ −11510.4 −0.993541
$$513$$ 234.520 0.0201839
$$514$$ −19909.0 −1.70846
$$515$$ 5313.99 0.454684
$$516$$ −4547.87 −0.388001
$$517$$ 0 0
$$518$$ −4665.09 −0.395699
$$519$$ 431.344 0.0364815
$$520$$ −863.476 −0.0728191
$$521$$ 9761.13 0.820812 0.410406 0.911903i $$-0.365387\pi$$
0.410406 + 0.911903i $$0.365387\pi$$
$$522$$ −2862.04 −0.239977
$$523$$ −4548.79 −0.380315 −0.190157 0.981754i $$-0.560900\pi$$
−0.190157 + 0.981754i $$0.560900\pi$$
$$524$$ 11124.4 0.927423
$$525$$ 682.851 0.0567659
$$526$$ −16968.1 −1.40655
$$527$$ −9810.68 −0.810930
$$528$$ 0 0
$$529$$ 4152.66 0.341305
$$530$$ 8637.62 0.707914
$$531$$ 3361.27 0.274702
$$532$$ 450.895 0.0367458
$$533$$ 572.606 0.0465334
$$534$$ 5160.49 0.418195
$$535$$ −8514.80 −0.688088
$$536$$ −755.202 −0.0608577
$$537$$ −4238.78 −0.340628
$$538$$ 6444.52 0.516437
$$539$$ 0 0
$$540$$ 769.711 0.0613390
$$541$$ 9184.79 0.729917 0.364958 0.931024i $$-0.381083\pi$$
0.364958 + 0.931024i $$0.381083\pi$$
$$542$$ −4962.23 −0.393258
$$543$$ −6717.75 −0.530914
$$544$$ 13433.3 1.05873
$$545$$ −2781.67 −0.218631
$$546$$ 2052.27 0.160859
$$547$$ −20966.6 −1.63888 −0.819439 0.573167i $$-0.805715\pi$$
−0.819439 + 0.573167i $$0.805715\pi$$
$$548$$ −3497.48 −0.272637
$$549$$ −763.355 −0.0593428
$$550$$ 0 0
$$551$$ 746.217 0.0576950
$$552$$ −3260.58 −0.251412
$$553$$ −2418.13 −0.185948
$$554$$ 19325.0 1.48202
$$555$$ 2076.35 0.158804
$$556$$ 12147.9 0.926595
$$557$$ 4422.49 0.336422 0.168211 0.985751i $$-0.446201\pi$$
0.168211 + 0.985751i $$0.446201\pi$$
$$558$$ 5288.03 0.401183
$$559$$ 5397.04 0.408355
$$560$$ −3510.07 −0.264871
$$561$$ 0 0
$$562$$ −9234.21 −0.693099
$$563$$ 6066.46 0.454122 0.227061 0.973881i $$-0.427088\pi$$
0.227061 + 0.973881i $$0.427088\pi$$
$$564$$ −8819.20 −0.658432
$$565$$ −10441.6 −0.777486
$$566$$ −16025.6 −1.19012
$$567$$ 737.480 0.0546230
$$568$$ −4566.10 −0.337305
$$569$$ −17341.9 −1.27770 −0.638850 0.769331i $$-0.720590\pi$$
−0.638850 + 0.769331i $$0.720590\pi$$
$$570$$ −482.273 −0.0354390
$$571$$ −621.014 −0.0455142 −0.0227571 0.999741i $$-0.507244\pi$$
−0.0227571 + 0.999741i $$0.507244\pi$$
$$572$$ 0 0
$$573$$ 5237.83 0.381874
$$574$$ 950.700 0.0691314
$$575$$ −3193.71 −0.231629
$$576$$ −1689.12 −0.122187
$$577$$ 4458.77 0.321700 0.160850 0.986979i $$-0.448576\pi$$
0.160850 + 0.986979i $$0.448576\pi$$
$$578$$ 4045.76 0.291144
$$579$$ 11955.1 0.858097
$$580$$ 2449.13 0.175336
$$581$$ 4741.34 0.338561
$$582$$ 2270.70 0.161724
$$583$$ 0 0
$$584$$ −2743.34 −0.194384
$$585$$ −913.430 −0.0645567
$$586$$ 16031.2 1.13011
$$587$$ 1326.96 0.0933038 0.0466519 0.998911i $$-0.485145\pi$$
0.0466519 + 0.998911i $$0.485145\pi$$
$$588$$ −4449.01 −0.312031
$$589$$ −1378.74 −0.0964519
$$590$$ −6912.20 −0.482324
$$591$$ −6786.01 −0.472317
$$592$$ −10673.1 −0.740982
$$593$$ 13296.2 0.920756 0.460378 0.887723i $$-0.347714\pi$$
0.460378 + 0.887723i $$0.347714\pi$$
$$594$$ 0 0
$$595$$ 2813.63 0.193862
$$596$$ 3255.02 0.223710
$$597$$ 7020.45 0.481287
$$598$$ −9598.50 −0.656374
$$599$$ −7420.72 −0.506181 −0.253091 0.967443i $$-0.581447\pi$$
−0.253091 + 0.967443i $$0.581447\pi$$
$$600$$ 638.086 0.0434162
$$601$$ −5189.31 −0.352207 −0.176104 0.984372i $$-0.556349\pi$$
−0.176104 + 0.984372i $$0.556349\pi$$
$$602$$ 8960.72 0.606664
$$603$$ −798.891 −0.0539525
$$604$$ −12285.6 −0.827641
$$605$$ 0 0
$$606$$ 302.620 0.0202857
$$607$$ 26545.6 1.77505 0.887523 0.460763i $$-0.152424\pi$$
0.887523 + 0.460763i $$0.152424\pi$$
$$608$$ 1887.85 0.125925
$$609$$ 2346.58 0.156138
$$610$$ 1569.78 0.104194
$$611$$ 10465.9 0.692971
$$612$$ 3171.53 0.209480
$$613$$ 26097.9 1.71955 0.859776 0.510671i $$-0.170603\pi$$
0.859776 + 0.510671i $$0.170603\pi$$
$$614$$ 7597.67 0.499377
$$615$$ −423.141 −0.0277442
$$616$$ 0 0
$$617$$ 12275.1 0.800933 0.400466 0.916311i $$-0.368848\pi$$
0.400466 + 0.916311i $$0.368848\pi$$
$$618$$ −11802.0 −0.768200
$$619$$ 6067.21 0.393961 0.196980 0.980407i $$-0.436886\pi$$
0.196980 + 0.980407i $$0.436886\pi$$
$$620$$ −4525.12 −0.293118
$$621$$ −3449.21 −0.222886
$$622$$ −9726.82 −0.627026
$$623$$ −4231.06 −0.272093
$$624$$ 4695.31 0.301223
$$625$$ 625.000 0.0400000
$$626$$ −25460.8 −1.62559
$$627$$ 0 0
$$628$$ −895.742 −0.0569172
$$629$$ 8555.43 0.542333
$$630$$ −1516.57 −0.0959073
$$631$$ 3074.16 0.193947 0.0969733 0.995287i $$-0.469084\pi$$
0.0969733 + 0.995287i $$0.469084\pi$$
$$632$$ −2259.61 −0.142219
$$633$$ −4573.31 −0.287161
$$634$$ 11201.1 0.701661
$$635$$ 10895.8 0.680924
$$636$$ −7982.78 −0.497701
$$637$$ 5279.72 0.328399
$$638$$ 0 0
$$639$$ −4830.26 −0.299033
$$640$$ −5220.27 −0.322421
$$641$$ −10825.9 −0.667080 −0.333540 0.942736i $$-0.608243\pi$$
−0.333540 + 0.942736i $$0.608243\pi$$
$$642$$ 18910.8 1.16254
$$643$$ −117.142 −0.00718450 −0.00359225 0.999994i $$-0.501143\pi$$
−0.00359225 + 0.999994i $$0.501143\pi$$
$$644$$ −6631.54 −0.405775
$$645$$ −3988.27 −0.243469
$$646$$ −1987.17 −0.121028
$$647$$ 23811.6 1.44688 0.723439 0.690388i $$-0.242560\pi$$
0.723439 + 0.690388i $$0.242560\pi$$
$$648$$ 689.133 0.0417773
$$649$$ 0 0
$$650$$ 1878.40 0.113349
$$651$$ −4335.64 −0.261025
$$652$$ 9901.65 0.594753
$$653$$ −17773.3 −1.06512 −0.532560 0.846392i $$-0.678770\pi$$
−0.532560 + 0.846392i $$0.678770\pi$$
$$654$$ 6177.92 0.369382
$$655$$ 9755.53 0.581954
$$656$$ 2175.07 0.129455
$$657$$ −2902.05 −0.172328
$$658$$ 17376.6 1.02950
$$659$$ 13015.6 0.769370 0.384685 0.923048i $$-0.374310\pi$$
0.384685 + 0.923048i $$0.374310\pi$$
$$660$$ 0 0
$$661$$ 15769.6 0.927935 0.463968 0.885852i $$-0.346425\pi$$
0.463968 + 0.885852i $$0.346425\pi$$
$$662$$ 16014.8 0.940231
$$663$$ −3763.71 −0.220468
$$664$$ 4430.51 0.258941
$$665$$ 395.414 0.0230579
$$666$$ −4611.45 −0.268303
$$667$$ −10975.0 −0.637111
$$668$$ 8361.60 0.484311
$$669$$ 15250.3 0.881329
$$670$$ 1642.86 0.0947301
$$671$$ 0 0
$$672$$ 5936.58 0.340787
$$673$$ 31519.1 1.80531 0.902653 0.430370i $$-0.141617\pi$$
0.902653 + 0.430370i $$0.141617\pi$$
$$674$$ 6512.38 0.372177
$$675$$ 675.000 0.0384900
$$676$$ −10177.1 −0.579036
$$677$$ −12418.6 −0.705000 −0.352500 0.935812i $$-0.614668\pi$$
−0.352500 + 0.935812i $$0.614668\pi$$
$$678$$ 23190.0 1.31358
$$679$$ −1861.74 −0.105224
$$680$$ 2629.18 0.148271
$$681$$ −11732.0 −0.660162
$$682$$ 0 0
$$683$$ 23543.0 1.31896 0.659478 0.751724i $$-0.270777\pi$$
0.659478 + 0.751724i $$0.270777\pi$$
$$684$$ 445.711 0.0249155
$$685$$ −3067.12 −0.171079
$$686$$ 20325.6 1.13124
$$687$$ 8199.92 0.455381
$$688$$ 20500.9 1.13603
$$689$$ 9473.31 0.523809
$$690$$ 7093.03 0.391344
$$691$$ −9642.84 −0.530870 −0.265435 0.964129i $$-0.585516\pi$$
−0.265435 + 0.964129i $$0.585516\pi$$
$$692$$ 819.778 0.0450336
$$693$$ 0 0
$$694$$ 43422.0 2.37504
$$695$$ 10653.2 0.581435
$$696$$ 2192.74 0.119419
$$697$$ −1743.52 −0.0947494
$$698$$ 11668.7 0.632762
$$699$$ −13066.4 −0.707032
$$700$$ 1297.77 0.0700732
$$701$$ −30593.3 −1.64835 −0.824176 0.566334i $$-0.808361\pi$$
−0.824176 + 0.566334i $$0.808361\pi$$
$$702$$ 2028.67 0.109070
$$703$$ 1202.34 0.0645050
$$704$$ 0 0
$$705$$ −7734.02 −0.413163
$$706$$ 25470.6 1.35779
$$707$$ −248.117 −0.0131986
$$708$$ 6388.17 0.339099
$$709$$ −30248.4 −1.60226 −0.801130 0.598491i $$-0.795767\pi$$
−0.801130 + 0.598491i $$0.795767\pi$$
$$710$$ 9933.05 0.525044
$$711$$ −2390.33 −0.126082
$$712$$ −3953.69 −0.208105
$$713$$ 20277.9 1.06509
$$714$$ −6248.90 −0.327534
$$715$$ 0 0
$$716$$ −8055.90 −0.420479
$$717$$ −14194.4 −0.739332
$$718$$ 10582.6 0.550056
$$719$$ 30471.8 1.58054 0.790269 0.612761i $$-0.209941\pi$$
0.790269 + 0.612761i $$0.209941\pi$$
$$720$$ −3469.71 −0.179595
$$721$$ 9676.45 0.499819
$$722$$ 25109.7 1.29430
$$723$$ 5499.37 0.282882
$$724$$ −12767.2 −0.655373
$$725$$ 2147.77 0.110022
$$726$$ 0 0
$$727$$ 25149.9 1.28302 0.641511 0.767114i $$-0.278308\pi$$
0.641511 + 0.767114i $$0.278308\pi$$
$$728$$ −1572.34 −0.0800476
$$729$$ 729.000 0.0370370
$$730$$ 5967.84 0.302575
$$731$$ −16433.3 −0.831475
$$732$$ −1450.77 −0.0732542
$$733$$ 9974.73 0.502626 0.251313 0.967906i $$-0.419138\pi$$
0.251313 + 0.967906i $$0.419138\pi$$
$$734$$ 40618.8 2.04260
$$735$$ −3901.57 −0.195798
$$736$$ −27765.5 −1.39056
$$737$$ 0 0
$$738$$ 939.769 0.0468745
$$739$$ 11579.9 0.576418 0.288209 0.957568i $$-0.406940\pi$$
0.288209 + 0.957568i $$0.406940\pi$$
$$740$$ 3946.15 0.196031
$$741$$ −528.933 −0.0262225
$$742$$ 15728.6 0.778186
$$743$$ 20323.7 1.00351 0.501753 0.865011i $$-0.332689\pi$$
0.501753 + 0.865011i $$0.332689\pi$$
$$744$$ −4051.41 −0.199639
$$745$$ 2854.50 0.140377
$$746$$ −38656.9 −1.89723
$$747$$ 4686.82 0.229561
$$748$$ 0 0
$$749$$ −15504.9 −0.756392
$$750$$ −1388.09 −0.0675810
$$751$$ 8023.94 0.389877 0.194939 0.980815i $$-0.437549\pi$$
0.194939 + 0.980815i $$0.437549\pi$$
$$752$$ 39755.3 1.92783
$$753$$ −9504.93 −0.459998
$$754$$ 6455.00 0.311773
$$755$$ −10773.9 −0.519342
$$756$$ 1401.60 0.0674279
$$757$$ 542.713 0.0260571 0.0130285 0.999915i $$-0.495853\pi$$
0.0130285 + 0.999915i $$0.495853\pi$$
$$758$$ 27413.2 1.31358
$$759$$ 0 0
$$760$$ 369.492 0.0176354
$$761$$ −16292.2 −0.776073 −0.388037 0.921644i $$-0.626847\pi$$
−0.388037 + 0.921644i $$0.626847\pi$$
$$762$$ −24198.9 −1.15044
$$763$$ −5065.25 −0.240333
$$764$$ 9954.61 0.471394
$$765$$ 2781.28 0.131448
$$766$$ −52395.6 −2.47145
$$767$$ −7580.96 −0.356887
$$768$$ 16098.2 0.756373
$$769$$ 7107.01 0.333271 0.166636 0.986019i $$-0.446710\pi$$
0.166636 + 0.986019i $$0.446710\pi$$
$$770$$ 0 0
$$771$$ 16135.7 0.753711
$$772$$ 22721.0 1.05926
$$773$$ −19776.7 −0.920204 −0.460102 0.887866i $$-0.652187\pi$$
−0.460102 + 0.887866i $$0.652187\pi$$
$$774$$ 8857.69 0.411348
$$775$$ −3968.32 −0.183931
$$776$$ −1739.69 −0.0804783
$$777$$ 3780.91 0.174568
$$778$$ 48237.1 2.22286
$$779$$ −245.025 −0.0112695
$$780$$ −1735.99 −0.0796904
$$781$$ 0 0
$$782$$ 29226.2 1.33648
$$783$$ 2319.60 0.105869
$$784$$ 20055.3 0.913597
$$785$$ −785.523 −0.0357153
$$786$$ −21666.4 −0.983226
$$787$$ −19943.8 −0.903327 −0.451664 0.892188i $$-0.649169\pi$$
−0.451664 + 0.892188i $$0.649169\pi$$
$$788$$ −12896.9 −0.583039
$$789$$ 13752.1 0.620517
$$790$$ 4915.53 0.221376
$$791$$ −19013.4 −0.854664
$$792$$ 0 0
$$793$$ 1721.66 0.0770969
$$794$$ −8443.34 −0.377384
$$795$$ −7000.52 −0.312306
$$796$$ 13342.5 0.594112
$$797$$ −24333.8 −1.08149 −0.540744 0.841187i $$-0.681857\pi$$
−0.540744 + 0.841187i $$0.681857\pi$$
$$798$$ −878.189 −0.0389568
$$799$$ −31867.4 −1.41100
$$800$$ 5433.63 0.240135
$$801$$ −4182.41 −0.184492
$$802$$ 48186.0 2.12158
$$803$$ 0 0
$$804$$ −1518.31 −0.0666003
$$805$$ −5815.55 −0.254622
$$806$$ −11926.5 −0.521209
$$807$$ −5223.08 −0.227833
$$808$$ −231.851 −0.0100947
$$809$$ 15308.7 0.665298 0.332649 0.943051i $$-0.392058\pi$$
0.332649 + 0.943051i $$0.392058\pi$$
$$810$$ −1499.13 −0.0650298
$$811$$ −22639.1 −0.980229 −0.490115 0.871658i $$-0.663045\pi$$
−0.490115 + 0.871658i $$0.663045\pi$$
$$812$$ 4459.72 0.192741
$$813$$ 4021.73 0.173491
$$814$$ 0 0
$$815$$ 8683.28 0.373205
$$816$$ −14296.7 −0.613337
$$817$$ −2309.46 −0.0988955
$$818$$ 13134.8 0.561429
$$819$$ −1663.30 −0.0709650
$$820$$ −804.187 −0.0342481
$$821$$ 35341.0 1.50232 0.751162 0.660118i $$-0.229494\pi$$
0.751162 + 0.660118i $$0.229494\pi$$
$$822$$ 6811.89 0.289041
$$823$$ 28121.5 1.19107 0.595536 0.803329i $$-0.296940\pi$$
0.595536 + 0.803329i $$0.296940\pi$$
$$824$$ 9042.09 0.382277
$$825$$ 0 0
$$826$$ −12586.7 −0.530202
$$827$$ 5952.92 0.250306 0.125153 0.992137i $$-0.460058\pi$$
0.125153 + 0.992137i $$0.460058\pi$$
$$828$$ −6555.29 −0.275135
$$829$$ 18696.9 0.783316 0.391658 0.920111i $$-0.371902\pi$$
0.391658 + 0.920111i $$0.371902\pi$$
$$830$$ −9638.09 −0.403064
$$831$$ −15662.3 −0.653814
$$832$$ 3809.60 0.158743
$$833$$ −16076.1 −0.668672
$$834$$ −23660.0 −0.982348
$$835$$ 7332.73 0.303904
$$836$$ 0 0
$$837$$ −4285.79 −0.176987
$$838$$ 54787.9 2.25849
$$839$$ −25774.1 −1.06057 −0.530287 0.847818i $$-0.677916\pi$$
−0.530287 + 0.847818i $$0.677916\pi$$
$$840$$ 1161.91 0.0477260
$$841$$ −17008.3 −0.697376
$$842$$ −42726.2 −1.74874
$$843$$ 7484.04 0.305770
$$844$$ −8691.68 −0.354478
$$845$$ −8924.87 −0.363343
$$846$$ 17176.8 0.698049
$$847$$ 0 0
$$848$$ 35984.9 1.45722
$$849$$ 12988.3 0.525037
$$850$$ −5719.49 −0.230796
$$851$$ −17683.4 −0.712313
$$852$$ −9180.00 −0.369134
$$853$$ 18664.1 0.749174 0.374587 0.927192i $$-0.377785\pi$$
0.374587 + 0.927192i $$0.377785\pi$$
$$854$$ 2858.47 0.114537
$$855$$ 390.867 0.0156344
$$856$$ −14488.5 −0.578511
$$857$$ −37192.5 −1.48246 −0.741232 0.671249i $$-0.765758\pi$$
−0.741232 + 0.671249i $$0.765758\pi$$
$$858$$ 0 0
$$859$$ 46306.0 1.83928 0.919640 0.392763i $$-0.128481\pi$$
0.919640 + 0.392763i $$0.128481\pi$$
$$860$$ −7579.78 −0.300545
$$861$$ −770.512 −0.0304983
$$862$$ 47056.6 1.85934
$$863$$ −19587.1 −0.772599 −0.386299 0.922373i $$-0.626247\pi$$
−0.386299 + 0.922373i $$0.626247\pi$$
$$864$$ 5868.32 0.231070
$$865$$ 718.907 0.0282584
$$866$$ 60651.4 2.37993
$$867$$ −3278.96 −0.128442
$$868$$ −8239.97 −0.322215
$$869$$ 0 0
$$870$$ −4770.07 −0.185886
$$871$$ 1801.80 0.0700939
$$872$$ −4733.19 −0.183814
$$873$$ −1840.33 −0.0713468
$$874$$ 4107.31 0.158961
$$875$$ 1138.09 0.0439707
$$876$$ −5515.41 −0.212726
$$877$$ −26580.8 −1.02345 −0.511727 0.859148i $$-0.670994\pi$$
−0.511727 + 0.859148i $$0.670994\pi$$
$$878$$ 24443.7 0.939562
$$879$$ −12992.8 −0.498561
$$880$$ 0 0
$$881$$ −731.459 −0.0279722 −0.0139861 0.999902i $$-0.504452\pi$$
−0.0139861 + 0.999902i $$0.504452\pi$$
$$882$$ 8665.14 0.330806
$$883$$ −45291.1 −1.72612 −0.863062 0.505099i $$-0.831456\pi$$
−0.863062 + 0.505099i $$0.831456\pi$$
$$884$$ −7153.01 −0.272151
$$885$$ 5602.12 0.212783
$$886$$ 43089.8 1.63390
$$887$$ 37730.7 1.42827 0.714134 0.700009i $$-0.246821\pi$$
0.714134 + 0.700009i $$0.246821\pi$$
$$888$$ 3533.04 0.133515
$$889$$ 19840.6 0.748516
$$890$$ 8600.81 0.323932
$$891$$ 0 0
$$892$$ 28983.4 1.08793
$$893$$ −4478.48 −0.167824
$$894$$ −6339.67 −0.237170
$$895$$ −7064.64 −0.263849
$$896$$ −9505.79 −0.354426
$$897$$ 7779.28 0.289568
$$898$$ −51402.9 −1.91017
$$899$$ −13636.9 −0.505913
$$900$$ 1282.85 0.0475130
$$901$$ −28845.1 −1.06656
$$902$$ 0 0
$$903$$ −7262.38 −0.267638
$$904$$ −17767.0 −0.653673
$$905$$ −11196.2 −0.411244
$$906$$ 23928.2 0.877440
$$907$$ 25846.2 0.946208 0.473104 0.881007i $$-0.343134\pi$$
0.473104 + 0.881007i $$0.343134\pi$$
$$908$$ −22296.9 −0.814920
$$909$$ −245.264 −0.00894928
$$910$$ 3420.45 0.124601
$$911$$ −30349.8 −1.10377 −0.551885 0.833920i $$-0.686091\pi$$
−0.551885 + 0.833920i $$0.686091\pi$$
$$912$$ −2009.18 −0.0729502
$$913$$ 0 0
$$914$$ 13421.3 0.485708
$$915$$ −1272.26 −0.0459667
$$916$$ 15584.1 0.562133
$$917$$ 17764.2 0.639723
$$918$$ −6177.05 −0.222084
$$919$$ −41031.3 −1.47279 −0.736397 0.676550i $$-0.763474\pi$$
−0.736397 + 0.676550i $$0.763474\pi$$
$$920$$ −5434.30 −0.194743
$$921$$ −6157.68 −0.220307
$$922$$ 67846.2 2.42342
$$923$$ 10894.1 0.388497
$$924$$ 0 0
$$925$$ 3460.59 0.123009
$$926$$ −39831.4 −1.41354
$$927$$ 9565.18 0.338902
$$928$$ 18672.3 0.660506
$$929$$ −3859.82 −0.136315 −0.0681575 0.997675i $$-0.521712\pi$$
−0.0681575 + 0.997675i $$0.521712\pi$$
$$930$$ 8813.39 0.310755
$$931$$ −2259.25 −0.0795317
$$932$$ −24832.9 −0.872778
$$933$$ 7883.29 0.276621
$$934$$ 29480.3 1.03279
$$935$$ 0 0
$$936$$ −1554.26 −0.0542762
$$937$$ −22026.5 −0.767955 −0.383977 0.923343i $$-0.625446\pi$$
−0.383977 + 0.923343i $$0.625446\pi$$
$$938$$ 2991.54 0.104134
$$939$$ 20635.2 0.717150
$$940$$ −14698.7 −0.510019
$$941$$ 24778.0 0.858386 0.429193 0.903213i $$-0.358798\pi$$
0.429193 + 0.903213i $$0.358798\pi$$
$$942$$ 1744.60 0.0603419
$$943$$ 3603.70 0.124446
$$944$$ −28796.7 −0.992851
$$945$$ 1229.13 0.0423108
$$946$$ 0 0
$$947$$ 34055.7 1.16860 0.584299 0.811539i $$-0.301370\pi$$
0.584299 + 0.811539i $$0.301370\pi$$
$$948$$ −4542.87 −0.155639
$$949$$ 6545.23 0.223885
$$950$$ −803.789 −0.0274509
$$951$$ −9078.15 −0.309547
$$952$$ 4787.57 0.162990
$$953$$ 30211.9 1.02693 0.513463 0.858112i $$-0.328363\pi$$
0.513463 + 0.858112i $$0.328363\pi$$
$$954$$ 15547.7 0.527648
$$955$$ 8729.72 0.295798
$$956$$ −26976.8 −0.912650
$$957$$ 0 0
$$958$$ 3044.40 0.102672
$$959$$ −5585.04 −0.188061
$$960$$ −2815.19 −0.0946459
$$961$$ −4594.90 −0.154238
$$962$$ 10400.6 0.348574
$$963$$ −15326.6 −0.512871
$$964$$ 10451.7 0.349196
$$965$$ 19925.2 0.664679
$$966$$ 12916.0 0.430191
$$967$$ −34883.2 −1.16005 −0.580024 0.814599i $$-0.696957\pi$$
−0.580024 + 0.814599i $$0.696957\pi$$
$$968$$ 0 0
$$969$$ 1610.54 0.0533931
$$970$$ 3784.50 0.125271
$$971$$ 19753.0 0.652835 0.326418 0.945226i $$-0.394158\pi$$
0.326418 + 0.945226i $$0.394158\pi$$
$$972$$ 1385.48 0.0457194
$$973$$ 19398.7 0.639152
$$974$$ −24835.9 −0.817038
$$975$$ −1522.38 −0.0500054
$$976$$ 6539.80 0.214482
$$977$$ −2208.90 −0.0723326 −0.0361663 0.999346i $$-0.511515\pi$$
−0.0361663 + 0.999346i $$0.511515\pi$$
$$978$$ −19285.0 −0.630539
$$979$$ 0 0
$$980$$ −7415.02 −0.241698
$$981$$ −5007.01 −0.162958
$$982$$ 46970.2 1.52635
$$983$$ −40306.0 −1.30779 −0.653897 0.756583i $$-0.726867\pi$$
−0.653897 + 0.756583i $$0.726867\pi$$
$$984$$ −720.000 −0.0233260
$$985$$ −11310.0 −0.365855
$$986$$ −19654.7 −0.634820
$$987$$ −14083.2 −0.454177
$$988$$ −1005.25 −0.0323696
$$989$$ 33966.3 1.09208
$$990$$ 0 0
$$991$$ −15199.4 −0.487211 −0.243605 0.969874i $$-0.578330\pi$$
−0.243605 + 0.969874i $$0.578330\pi$$
$$992$$ −34499.8 −1.10420
$$993$$ −12979.5 −0.414796
$$994$$ 18087.5 0.577163
$$995$$ 11700.8 0.372803
$$996$$ 8907.40 0.283375
$$997$$ 48073.6 1.52709 0.763543 0.645757i $$-0.223458\pi$$
0.763543 + 0.645757i $$0.223458\pi$$
$$998$$ 36315.3 1.15184
$$999$$ 3737.43 0.118365
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 1815.4.a.i.1.1 2
11.10 odd 2 1815.4.a.o.1.2 yes 2

By twisted newform
Twist Min Dim Char Parity Ord Type
1815.4.a.i.1.1 2 1.1 even 1 trivial
1815.4.a.o.1.2 yes 2 11.10 odd 2