# Properties

 Label 35.4.a.b.1.1 Level $35$ Weight $4$ Character 35.1 Self dual yes Analytic conductor $2.065$ 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] = [35,4,Mod(1,35)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(35, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("35.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$35 = 5 \cdot 7$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 35.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: $$2.06506685020$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(\zeta_{8})^+$$ comment: defining polynomial  gp: f.mod \\ as an extension of the character field Defining polynomial: $$x^{2} - 2$$ x^2 - 2 Coefficient ring: $$\Z[a_1, a_2]$$ Coefficient ring index: $$1$$ Twist minimal: yes Fricke sign: $$+1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

 Embedding label 1.1 Root $$-1.41421$$ of defining polynomial Character $$\chi$$ $$=$$ 35.1

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+2.58579 q^{2} +6.65685 q^{3} -1.31371 q^{4} -5.00000 q^{5} +17.2132 q^{6} -7.00000 q^{7} -24.0833 q^{8} +17.3137 q^{9} +O(q^{10})$$ $$q+2.58579 q^{2} +6.65685 q^{3} -1.31371 q^{4} -5.00000 q^{5} +17.2132 q^{6} -7.00000 q^{7} -24.0833 q^{8} +17.3137 q^{9} -12.9289 q^{10} +38.2548 q^{11} -8.74517 q^{12} +19.3431 q^{13} -18.1005 q^{14} -33.2843 q^{15} -51.7645 q^{16} -87.2254 q^{17} +44.7696 q^{18} -44.2254 q^{19} +6.56854 q^{20} -46.5980 q^{21} +98.9188 q^{22} +218.167 q^{23} -160.319 q^{24} +25.0000 q^{25} +50.0172 q^{26} -64.4802 q^{27} +9.19596 q^{28} -46.9411 q^{29} -86.0660 q^{30} +194.558 q^{31} +58.8141 q^{32} +254.657 q^{33} -225.546 q^{34} +35.0000 q^{35} -22.7452 q^{36} +366.853 q^{37} -114.357 q^{38} +128.765 q^{39} +120.416 q^{40} -339.362 q^{41} -120.492 q^{42} -226.167 q^{43} -50.2557 q^{44} -86.5685 q^{45} +564.132 q^{46} +11.6762 q^{47} -344.589 q^{48} +49.0000 q^{49} +64.6447 q^{50} -580.647 q^{51} -25.4113 q^{52} -209.019 q^{53} -166.732 q^{54} -191.274 q^{55} +168.583 q^{56} -294.402 q^{57} -121.380 q^{58} -616.000 q^{59} +43.7258 q^{60} +320.735 q^{61} +503.087 q^{62} -121.196 q^{63} +566.197 q^{64} -96.7157 q^{65} +658.488 q^{66} +14.5097 q^{67} +114.589 q^{68} +1452.30 q^{69} +90.5025 q^{70} -952.000 q^{71} -416.971 q^{72} +824.489 q^{73} +948.603 q^{74} +166.421 q^{75} +58.0993 q^{76} -267.784 q^{77} +332.958 q^{78} +156.275 q^{79} +258.823 q^{80} -896.706 q^{81} -877.519 q^{82} -1036.53 q^{83} +61.2162 q^{84} +436.127 q^{85} -584.818 q^{86} -312.480 q^{87} -921.301 q^{88} -170.225 q^{89} -223.848 q^{90} -135.402 q^{91} -286.607 q^{92} +1295.15 q^{93} +30.1921 q^{94} +221.127 q^{95} +391.517 q^{96} +1059.87 q^{97} +126.704 q^{98} +662.333 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q + 8 q^{2} + 2 q^{3} + 20 q^{4} - 10 q^{5} - 8 q^{6} - 14 q^{7} + 48 q^{8} + 12 q^{9}+O(q^{10})$$ 2 * q + 8 * q^2 + 2 * q^3 + 20 * q^4 - 10 * q^5 - 8 * q^6 - 14 * q^7 + 48 * q^8 + 12 * q^9 $$2 q + 8 q^{2} + 2 q^{3} + 20 q^{4} - 10 q^{5} - 8 q^{6} - 14 q^{7} + 48 q^{8} + 12 q^{9} - 40 q^{10} - 14 q^{11} - 108 q^{12} + 50 q^{13} - 56 q^{14} - 10 q^{15} + 168 q^{16} - 50 q^{17} + 16 q^{18} + 36 q^{19} - 100 q^{20} - 14 q^{21} - 184 q^{22} + 244 q^{23} - 496 q^{24} + 50 q^{25} + 216 q^{26} + 86 q^{27} - 140 q^{28} - 26 q^{29} + 40 q^{30} - 120 q^{31} + 672 q^{32} + 498 q^{33} - 24 q^{34} + 70 q^{35} - 136 q^{36} + 564 q^{37} + 320 q^{38} - 14 q^{39} - 240 q^{40} - 328 q^{41} + 56 q^{42} - 260 q^{43} - 1164 q^{44} - 60 q^{45} + 704 q^{46} - 350 q^{47} - 1368 q^{48} + 98 q^{49} + 200 q^{50} - 754 q^{51} + 628 q^{52} - 56 q^{53} + 648 q^{54} + 70 q^{55} - 336 q^{56} - 668 q^{57} - 8 q^{58} - 1232 q^{59} + 540 q^{60} + 336 q^{61} - 1200 q^{62} - 84 q^{63} + 2128 q^{64} - 250 q^{65} + 1976 q^{66} - 152 q^{67} + 908 q^{68} + 1332 q^{69} + 280 q^{70} - 1904 q^{71} - 800 q^{72} + 676 q^{73} + 2016 q^{74} + 50 q^{75} + 1768 q^{76} + 98 q^{77} - 440 q^{78} + 1014 q^{79} - 840 q^{80} - 1454 q^{81} - 816 q^{82} - 376 q^{83} + 756 q^{84} + 250 q^{85} - 768 q^{86} - 410 q^{87} - 4688 q^{88} - 216 q^{89} - 80 q^{90} - 350 q^{91} + 264 q^{92} + 2760 q^{93} - 1928 q^{94} - 180 q^{95} - 2464 q^{96} + 2742 q^{97} + 392 q^{98} + 940 q^{99}+O(q^{100})$$ 2 * q + 8 * q^2 + 2 * q^3 + 20 * q^4 - 10 * q^5 - 8 * q^6 - 14 * q^7 + 48 * q^8 + 12 * q^9 - 40 * q^10 - 14 * q^11 - 108 * q^12 + 50 * q^13 - 56 * q^14 - 10 * q^15 + 168 * q^16 - 50 * q^17 + 16 * q^18 + 36 * q^19 - 100 * q^20 - 14 * q^21 - 184 * q^22 + 244 * q^23 - 496 * q^24 + 50 * q^25 + 216 * q^26 + 86 * q^27 - 140 * q^28 - 26 * q^29 + 40 * q^30 - 120 * q^31 + 672 * q^32 + 498 * q^33 - 24 * q^34 + 70 * q^35 - 136 * q^36 + 564 * q^37 + 320 * q^38 - 14 * q^39 - 240 * q^40 - 328 * q^41 + 56 * q^42 - 260 * q^43 - 1164 * q^44 - 60 * q^45 + 704 * q^46 - 350 * q^47 - 1368 * q^48 + 98 * q^49 + 200 * q^50 - 754 * q^51 + 628 * q^52 - 56 * q^53 + 648 * q^54 + 70 * q^55 - 336 * q^56 - 668 * q^57 - 8 * q^58 - 1232 * q^59 + 540 * q^60 + 336 * q^61 - 1200 * q^62 - 84 * q^63 + 2128 * q^64 - 250 * q^65 + 1976 * q^66 - 152 * q^67 + 908 * q^68 + 1332 * q^69 + 280 * q^70 - 1904 * q^71 - 800 * q^72 + 676 * q^73 + 2016 * q^74 + 50 * q^75 + 1768 * q^76 + 98 * q^77 - 440 * q^78 + 1014 * q^79 - 840 * q^80 - 1454 * q^81 - 816 * q^82 - 376 * q^83 + 756 * q^84 + 250 * q^85 - 768 * q^86 - 410 * q^87 - 4688 * q^88 - 216 * q^89 - 80 * q^90 - 350 * q^91 + 264 * q^92 + 2760 * q^93 - 1928 * q^94 - 180 * q^95 - 2464 * q^96 + 2742 * q^97 + 392 * q^98 + 940 * 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 2.58579 0.914214 0.457107 0.889412i $$-0.348886\pi$$
0.457107 + 0.889412i $$0.348886\pi$$
$$3$$ 6.65685 1.28111 0.640556 0.767911i $$-0.278704\pi$$
0.640556 + 0.767911i $$0.278704\pi$$
$$4$$ −1.31371 −0.164214
$$5$$ −5.00000 −0.447214
$$6$$ 17.2132 1.17121
$$7$$ −7.00000 −0.377964
$$8$$ −24.0833 −1.06434
$$9$$ 17.3137 0.641248
$$10$$ −12.9289 −0.408849
$$11$$ 38.2548 1.04857 0.524285 0.851543i $$-0.324333\pi$$
0.524285 + 0.851543i $$0.324333\pi$$
$$12$$ −8.74517 −0.210376
$$13$$ 19.3431 0.412679 0.206339 0.978480i $$-0.433845\pi$$
0.206339 + 0.978480i $$0.433845\pi$$
$$14$$ −18.1005 −0.345540
$$15$$ −33.2843 −0.572931
$$16$$ −51.7645 −0.808820
$$17$$ −87.2254 −1.24443 −0.622214 0.782847i $$-0.713767\pi$$
−0.622214 + 0.782847i $$0.713767\pi$$
$$18$$ 44.7696 0.586238
$$19$$ −44.2254 −0.534000 −0.267000 0.963697i $$-0.586032\pi$$
−0.267000 + 0.963697i $$0.586032\pi$$
$$20$$ 6.56854 0.0734385
$$21$$ −46.5980 −0.484215
$$22$$ 98.9188 0.958617
$$23$$ 218.167 1.97786 0.988932 0.148371i $$-0.0474028\pi$$
0.988932 + 0.148371i $$0.0474028\pi$$
$$24$$ −160.319 −1.36354
$$25$$ 25.0000 0.200000
$$26$$ 50.0172 0.377276
$$27$$ −64.4802 −0.459601
$$28$$ 9.19596 0.0620669
$$29$$ −46.9411 −0.300578 −0.150289 0.988642i $$-0.548020\pi$$
−0.150289 + 0.988642i $$0.548020\pi$$
$$30$$ −86.0660 −0.523781
$$31$$ 194.558 1.12722 0.563609 0.826042i $$-0.309413\pi$$
0.563609 + 0.826042i $$0.309413\pi$$
$$32$$ 58.8141 0.324905
$$33$$ 254.657 1.34334
$$34$$ −225.546 −1.13767
$$35$$ 35.0000 0.169031
$$36$$ −22.7452 −0.105302
$$37$$ 366.853 1.63001 0.815003 0.579457i $$-0.196735\pi$$
0.815003 + 0.579457i $$0.196735\pi$$
$$38$$ −114.357 −0.488190
$$39$$ 128.765 0.528688
$$40$$ 120.416 0.475987
$$41$$ −339.362 −1.29267 −0.646336 0.763053i $$-0.723699\pi$$
−0.646336 + 0.763053i $$0.723699\pi$$
$$42$$ −120.492 −0.442676
$$43$$ −226.167 −0.802095 −0.401047 0.916057i $$-0.631354\pi$$
−0.401047 + 0.916057i $$0.631354\pi$$
$$44$$ −50.2557 −0.172189
$$45$$ −86.5685 −0.286775
$$46$$ 564.132 1.80819
$$47$$ 11.6762 0.0362372 0.0181186 0.999836i $$-0.494232\pi$$
0.0181186 + 0.999836i $$0.494232\pi$$
$$48$$ −344.589 −1.03619
$$49$$ 49.0000 0.142857
$$50$$ 64.6447 0.182843
$$51$$ −580.647 −1.59425
$$52$$ −25.4113 −0.0677674
$$53$$ −209.019 −0.541717 −0.270859 0.962619i $$-0.587308\pi$$
−0.270859 + 0.962619i $$0.587308\pi$$
$$54$$ −166.732 −0.420173
$$55$$ −191.274 −0.468935
$$56$$ 168.583 0.402283
$$57$$ −294.402 −0.684114
$$58$$ −121.380 −0.274792
$$59$$ −616.000 −1.35926 −0.679630 0.733555i $$-0.737860\pi$$
−0.679630 + 0.733555i $$0.737860\pi$$
$$60$$ 43.7258 0.0940830
$$61$$ 320.735 0.673212 0.336606 0.941646i $$-0.390721\pi$$
0.336606 + 0.941646i $$0.390721\pi$$
$$62$$ 503.087 1.03052
$$63$$ −121.196 −0.242369
$$64$$ 566.197 1.10585
$$65$$ −96.7157 −0.184556
$$66$$ 658.488 1.22810
$$67$$ 14.5097 0.0264573 0.0132286 0.999912i $$-0.495789\pi$$
0.0132286 + 0.999912i $$0.495789\pi$$
$$68$$ 114.589 0.204352
$$69$$ 1452.30 2.53387
$$70$$ 90.5025 0.154530
$$71$$ −952.000 −1.59129 −0.795645 0.605763i $$-0.792868\pi$$
−0.795645 + 0.605763i $$0.792868\pi$$
$$72$$ −416.971 −0.682506
$$73$$ 824.489 1.32191 0.660953 0.750427i $$-0.270152\pi$$
0.660953 + 0.750427i $$0.270152\pi$$
$$74$$ 948.603 1.49017
$$75$$ 166.421 0.256222
$$76$$ 58.0993 0.0876901
$$77$$ −267.784 −0.396322
$$78$$ 332.958 0.483334
$$79$$ 156.275 0.222561 0.111280 0.993789i $$-0.464505\pi$$
0.111280 + 0.993789i $$0.464505\pi$$
$$80$$ 258.823 0.361715
$$81$$ −896.706 −1.23005
$$82$$ −877.519 −1.18178
$$83$$ −1036.53 −1.37077 −0.685384 0.728182i $$-0.740366\pi$$
−0.685384 + 0.728182i $$0.740366\pi$$
$$84$$ 61.2162 0.0795147
$$85$$ 436.127 0.556525
$$86$$ −584.818 −0.733286
$$87$$ −312.480 −0.385074
$$88$$ −921.301 −1.11603
$$89$$ −170.225 −0.202740 −0.101370 0.994849i $$-0.532323\pi$$
−0.101370 + 0.994849i $$0.532323\pi$$
$$90$$ −223.848 −0.262174
$$91$$ −135.402 −0.155978
$$92$$ −286.607 −0.324792
$$93$$ 1295.15 1.44409
$$94$$ 30.1921 0.0331285
$$95$$ 221.127 0.238812
$$96$$ 391.517 0.416240
$$97$$ 1059.87 1.10942 0.554710 0.832044i $$-0.312829\pi$$
0.554710 + 0.832044i $$0.312829\pi$$
$$98$$ 126.704 0.130602
$$99$$ 662.333 0.672394
$$100$$ −32.8427 −0.0328427
$$101$$ −241.833 −0.238251 −0.119125 0.992879i $$-0.538009\pi$$
−0.119125 + 0.992879i $$0.538009\pi$$
$$102$$ −1501.43 −1.45749
$$103$$ −1679.58 −1.60673 −0.803367 0.595484i $$-0.796960\pi$$
−0.803367 + 0.595484i $$0.796960\pi$$
$$104$$ −465.846 −0.439230
$$105$$ 232.990 0.216547
$$106$$ −540.479 −0.495245
$$107$$ 1506.88 1.36146 0.680728 0.732537i $$-0.261664\pi$$
0.680728 + 0.732537i $$0.261664\pi$$
$$108$$ 84.7082 0.0754727
$$109$$ −1252.41 −1.10054 −0.550271 0.834986i $$-0.685476\pi$$
−0.550271 + 0.834986i $$0.685476\pi$$
$$110$$ −494.594 −0.428706
$$111$$ 2442.09 2.08822
$$112$$ 362.352 0.305705
$$113$$ 1370.20 1.14069 0.570345 0.821405i $$-0.306810\pi$$
0.570345 + 0.821405i $$0.306810\pi$$
$$114$$ −761.261 −0.625426
$$115$$ −1090.83 −0.884528
$$116$$ 61.6670 0.0493589
$$117$$ 334.902 0.264630
$$118$$ −1592.84 −1.24265
$$119$$ 610.578 0.470349
$$120$$ 801.594 0.609793
$$121$$ 132.432 0.0994984
$$122$$ 829.352 0.615459
$$123$$ −2259.09 −1.65606
$$124$$ −255.593 −0.185104
$$125$$ −125.000 −0.0894427
$$126$$ −313.387 −0.221577
$$127$$ 1213.49 0.847873 0.423936 0.905692i $$-0.360648\pi$$
0.423936 + 0.905692i $$0.360648\pi$$
$$128$$ 993.551 0.686081
$$129$$ −1505.56 −1.02757
$$130$$ −250.086 −0.168723
$$131$$ −1982.42 −1.32217 −0.661087 0.750309i $$-0.729904\pi$$
−0.661087 + 0.750309i $$0.729904\pi$$
$$132$$ −334.545 −0.220594
$$133$$ 309.578 0.201833
$$134$$ 37.5189 0.0241876
$$135$$ 322.401 0.205540
$$136$$ 2100.67 1.32449
$$137$$ 2210.95 1.37879 0.689394 0.724386i $$-0.257877\pi$$
0.689394 + 0.724386i $$0.257877\pi$$
$$138$$ 3755.34 2.31649
$$139$$ 528.039 0.322213 0.161107 0.986937i $$-0.448494\pi$$
0.161107 + 0.986937i $$0.448494\pi$$
$$140$$ −45.9798 −0.0277572
$$141$$ 77.7267 0.0464239
$$142$$ −2461.67 −1.45478
$$143$$ 739.969 0.432722
$$144$$ −896.235 −0.518655
$$145$$ 234.706 0.134422
$$146$$ 2131.95 1.20851
$$147$$ 326.186 0.183016
$$148$$ −481.938 −0.267669
$$149$$ −328.372 −0.180545 −0.0902727 0.995917i $$-0.528774\pi$$
−0.0902727 + 0.995917i $$0.528774\pi$$
$$150$$ 430.330 0.234242
$$151$$ 1029.43 0.554793 0.277396 0.960756i $$-0.410528\pi$$
0.277396 + 0.960756i $$0.410528\pi$$
$$152$$ 1065.09 0.568358
$$153$$ −1510.20 −0.797987
$$154$$ −692.432 −0.362323
$$155$$ −972.792 −0.504107
$$156$$ −169.159 −0.0868177
$$157$$ 525.098 0.266926 0.133463 0.991054i $$-0.457390\pi$$
0.133463 + 0.991054i $$0.457390\pi$$
$$158$$ 404.094 0.203468
$$159$$ −1391.41 −0.694001
$$160$$ −294.071 −0.145302
$$161$$ −1527.17 −0.747562
$$162$$ −2318.69 −1.12453
$$163$$ 1002.63 0.481790 0.240895 0.970551i $$-0.422559\pi$$
0.240895 + 0.970551i $$0.422559\pi$$
$$164$$ 445.823 0.212274
$$165$$ −1273.28 −0.600758
$$166$$ −2680.24 −1.25317
$$167$$ −359.422 −0.166544 −0.0832722 0.996527i $$-0.526537\pi$$
−0.0832722 + 0.996527i $$0.526537\pi$$
$$168$$ 1122.23 0.515369
$$169$$ −1822.84 −0.829696
$$170$$ 1127.73 0.508783
$$171$$ −765.706 −0.342427
$$172$$ 297.117 0.131715
$$173$$ 3293.65 1.44747 0.723733 0.690080i $$-0.242425\pi$$
0.723733 + 0.690080i $$0.242425\pi$$
$$174$$ −808.007 −0.352039
$$175$$ −175.000 −0.0755929
$$176$$ −1980.24 −0.848104
$$177$$ −4100.62 −1.74137
$$178$$ −440.167 −0.185348
$$179$$ 2978.82 1.24384 0.621921 0.783080i $$-0.286353\pi$$
0.621921 + 0.783080i $$0.286353\pi$$
$$180$$ 113.726 0.0470923
$$181$$ 1462.31 0.600514 0.300257 0.953858i $$-0.402928\pi$$
0.300257 + 0.953858i $$0.402928\pi$$
$$182$$ −350.121 −0.142597
$$183$$ 2135.09 0.862460
$$184$$ −5254.16 −2.10512
$$185$$ −1834.26 −0.728961
$$186$$ 3348.97 1.32021
$$187$$ −3336.79 −1.30487
$$188$$ −15.3391 −0.00595064
$$189$$ 451.362 0.173713
$$190$$ 571.787 0.218325
$$191$$ −374.923 −0.142034 −0.0710169 0.997475i $$-0.522624\pi$$
−0.0710169 + 0.997475i $$0.522624\pi$$
$$192$$ 3769.09 1.41672
$$193$$ 733.028 0.273391 0.136696 0.990613i $$-0.456352\pi$$
0.136696 + 0.990613i $$0.456352\pi$$
$$194$$ 2740.61 1.01425
$$195$$ −643.823 −0.236436
$$196$$ −64.3717 −0.0234591
$$197$$ −2093.24 −0.757043 −0.378521 0.925593i $$-0.623567\pi$$
−0.378521 + 0.925593i $$0.623567\pi$$
$$198$$ 1712.65 0.614711
$$199$$ 2865.04 1.02059 0.510295 0.860000i $$-0.329536\pi$$
0.510295 + 0.860000i $$0.329536\pi$$
$$200$$ −602.082 −0.212868
$$201$$ 96.5887 0.0338948
$$202$$ −625.330 −0.217812
$$203$$ 328.588 0.113608
$$204$$ 762.801 0.261798
$$205$$ 1696.81 0.578100
$$206$$ −4343.03 −1.46890
$$207$$ 3777.27 1.26830
$$208$$ −1001.29 −0.333783
$$209$$ −1691.84 −0.559936
$$210$$ 602.462 0.197971
$$211$$ 5643.65 1.84135 0.920674 0.390331i $$-0.127640\pi$$
0.920674 + 0.390331i $$0.127640\pi$$
$$212$$ 274.590 0.0889573
$$213$$ −6337.33 −2.03862
$$214$$ 3896.47 1.24466
$$215$$ 1130.83 0.358708
$$216$$ 1552.89 0.489172
$$217$$ −1361.91 −0.426048
$$218$$ −3238.46 −1.00613
$$219$$ 5488.51 1.69351
$$220$$ 251.279 0.0770054
$$221$$ −1687.21 −0.513549
$$222$$ 6314.71 1.90908
$$223$$ −6369.16 −1.91260 −0.956302 0.292381i $$-0.905552\pi$$
−0.956302 + 0.292381i $$0.905552\pi$$
$$224$$ −411.699 −0.122803
$$225$$ 432.843 0.128250
$$226$$ 3543.05 1.04283
$$227$$ −1015.67 −0.296972 −0.148486 0.988914i $$-0.547440\pi$$
−0.148486 + 0.988914i $$0.547440\pi$$
$$228$$ 386.758 0.112341
$$229$$ 4108.35 1.18554 0.592768 0.805373i $$-0.298035\pi$$
0.592768 + 0.805373i $$0.298035\pi$$
$$230$$ −2820.66 −0.808647
$$231$$ −1782.60 −0.507733
$$232$$ 1130.50 0.319917
$$233$$ 608.431 0.171071 0.0855357 0.996335i $$-0.472740\pi$$
0.0855357 + 0.996335i $$0.472740\pi$$
$$234$$ 865.984 0.241928
$$235$$ −58.3810 −0.0162058
$$236$$ 809.244 0.223209
$$237$$ 1040.30 0.285126
$$238$$ 1578.82 0.430000
$$239$$ −5054.44 −1.36797 −0.683985 0.729496i $$-0.739755\pi$$
−0.683985 + 0.729496i $$0.739755\pi$$
$$240$$ 1722.94 0.463398
$$241$$ 4.86782 0.00130109 0.000650547 1.00000i $$-0.499793\pi$$
0.000650547 1.00000i $$0.499793\pi$$
$$242$$ 342.442 0.0909628
$$243$$ −4228.27 −1.11623
$$244$$ −421.352 −0.110551
$$245$$ −245.000 −0.0638877
$$246$$ −5841.52 −1.51399
$$247$$ −855.458 −0.220370
$$248$$ −4685.60 −1.19974
$$249$$ −6900.02 −1.75611
$$250$$ −323.223 −0.0817697
$$251$$ −547.921 −0.137787 −0.0688934 0.997624i $$-0.521947\pi$$
−0.0688934 + 0.997624i $$0.521947\pi$$
$$252$$ 159.216 0.0398003
$$253$$ 8345.92 2.07393
$$254$$ 3137.83 0.775137
$$255$$ 2903.23 0.712971
$$256$$ −1960.46 −0.478629
$$257$$ −1774.61 −0.430729 −0.215364 0.976534i $$-0.569094\pi$$
−0.215364 + 0.976534i $$0.569094\pi$$
$$258$$ −3893.05 −0.939421
$$259$$ −2567.97 −0.616084
$$260$$ 127.056 0.0303065
$$261$$ −812.725 −0.192745
$$262$$ −5126.11 −1.20875
$$263$$ −1199.09 −0.281138 −0.140569 0.990071i $$-0.544893\pi$$
−0.140569 + 0.990071i $$0.544893\pi$$
$$264$$ −6132.97 −1.42977
$$265$$ 1045.10 0.242263
$$266$$ 800.502 0.184519
$$267$$ −1133.17 −0.259733
$$268$$ −19.0615 −0.00434464
$$269$$ 3250.29 0.736706 0.368353 0.929686i $$-0.379922\pi$$
0.368353 + 0.929686i $$0.379922\pi$$
$$270$$ 833.661 0.187907
$$271$$ −896.143 −0.200874 −0.100437 0.994943i $$-0.532024\pi$$
−0.100437 + 0.994943i $$0.532024\pi$$
$$272$$ 4515.18 1.00652
$$273$$ −901.352 −0.199825
$$274$$ 5717.04 1.26051
$$275$$ 956.371 0.209714
$$276$$ −1907.90 −0.416095
$$277$$ −386.562 −0.0838492 −0.0419246 0.999121i $$-0.513349\pi$$
−0.0419246 + 0.999121i $$0.513349\pi$$
$$278$$ 1365.40 0.294572
$$279$$ 3368.53 0.722826
$$280$$ −842.914 −0.179906
$$281$$ −3335.10 −0.708025 −0.354013 0.935241i $$-0.615183\pi$$
−0.354013 + 0.935241i $$0.615183\pi$$
$$282$$ 200.985 0.0424414
$$283$$ 5412.26 1.13684 0.568419 0.822739i $$-0.307555\pi$$
0.568419 + 0.822739i $$0.307555\pi$$
$$284$$ 1250.65 0.261311
$$285$$ 1472.01 0.305945
$$286$$ 1913.40 0.395601
$$287$$ 2375.54 0.488584
$$288$$ 1018.29 0.208345
$$289$$ 2695.27 0.548600
$$290$$ 606.899 0.122891
$$291$$ 7055.42 1.42129
$$292$$ −1083.14 −0.217075
$$293$$ 282.211 0.0562695 0.0281347 0.999604i $$-0.491043\pi$$
0.0281347 + 0.999604i $$0.491043\pi$$
$$294$$ 843.447 0.167316
$$295$$ 3080.00 0.607880
$$296$$ −8835.01 −1.73488
$$297$$ −2466.68 −0.481924
$$298$$ −849.099 −0.165057
$$299$$ 4220.03 0.816222
$$300$$ −218.629 −0.0420752
$$301$$ 1583.17 0.303163
$$302$$ 2661.88 0.507199
$$303$$ −1609.85 −0.305226
$$304$$ 2289.31 0.431910
$$305$$ −1603.68 −0.301069
$$306$$ −3905.04 −0.729531
$$307$$ 1919.67 0.356878 0.178439 0.983951i $$-0.442895\pi$$
0.178439 + 0.983951i $$0.442895\pi$$
$$308$$ 351.790 0.0650815
$$309$$ −11180.7 −2.05841
$$310$$ −2515.43 −0.460861
$$311$$ 1213.31 0.221223 0.110612 0.993864i $$-0.464719\pi$$
0.110612 + 0.993864i $$0.464719\pi$$
$$312$$ −3101.07 −0.562703
$$313$$ −1434.00 −0.258960 −0.129480 0.991582i $$-0.541331\pi$$
−0.129480 + 0.991582i $$0.541331\pi$$
$$314$$ 1357.79 0.244028
$$315$$ 605.980 0.108391
$$316$$ −205.300 −0.0365475
$$317$$ 6496.95 1.15112 0.575560 0.817760i $$-0.304784\pi$$
0.575560 + 0.817760i $$0.304784\pi$$
$$318$$ −3597.89 −0.634465
$$319$$ −1795.72 −0.315176
$$320$$ −2830.98 −0.494553
$$321$$ 10031.1 1.74418
$$322$$ −3948.92 −0.683432
$$323$$ 3857.58 0.664524
$$324$$ 1178.01 0.201991
$$325$$ 483.579 0.0825357
$$326$$ 2592.58 0.440459
$$327$$ −8337.11 −1.40992
$$328$$ 8172.96 1.37584
$$329$$ −81.7333 −0.0136964
$$330$$ −3292.44 −0.549221
$$331$$ −9683.88 −1.60808 −0.804039 0.594576i $$-0.797320\pi$$
−0.804039 + 0.594576i $$0.797320\pi$$
$$332$$ 1361.70 0.225099
$$333$$ 6351.58 1.04524
$$334$$ −929.389 −0.152257
$$335$$ −72.5483 −0.0118321
$$336$$ 2412.12 0.391643
$$337$$ 29.1319 0.00470895 0.00235447 0.999997i $$-0.499251\pi$$
0.00235447 + 0.999997i $$0.499251\pi$$
$$338$$ −4713.48 −0.758520
$$339$$ 9121.24 1.46135
$$340$$ −572.944 −0.0913889
$$341$$ 7442.80 1.18197
$$342$$ −1979.95 −0.313051
$$343$$ −343.000 −0.0539949
$$344$$ 5446.83 0.853701
$$345$$ −7261.51 −1.13318
$$346$$ 8516.68 1.32329
$$347$$ −7848.58 −1.21422 −0.607110 0.794618i $$-0.707671\pi$$
−0.607110 + 0.794618i $$0.707671\pi$$
$$348$$ 410.508 0.0632343
$$349$$ −10269.6 −1.57513 −0.787567 0.616229i $$-0.788659\pi$$
−0.787567 + 0.616229i $$0.788659\pi$$
$$350$$ −452.513 −0.0691080
$$351$$ −1247.25 −0.189668
$$352$$ 2249.93 0.340686
$$353$$ 2799.93 0.422168 0.211084 0.977468i $$-0.432301\pi$$
0.211084 + 0.977468i $$0.432301\pi$$
$$354$$ −10603.3 −1.59198
$$355$$ 4760.00 0.711647
$$356$$ 223.627 0.0332927
$$357$$ 4064.53 0.602570
$$358$$ 7702.60 1.13714
$$359$$ −3163.29 −0.465048 −0.232524 0.972591i $$-0.574698\pi$$
−0.232524 + 0.972591i $$0.574698\pi$$
$$360$$ 2084.85 0.305226
$$361$$ −4903.11 −0.714844
$$362$$ 3781.23 0.548998
$$363$$ 881.583 0.127469
$$364$$ 177.879 0.0256137
$$365$$ −4122.45 −0.591175
$$366$$ 5520.88 0.788472
$$367$$ 3182.85 0.452706 0.226353 0.974045i $$-0.427320\pi$$
0.226353 + 0.974045i $$0.427320\pi$$
$$368$$ −11293.3 −1.59974
$$369$$ −5875.62 −0.828923
$$370$$ −4743.02 −0.666426
$$371$$ 1463.14 0.204750
$$372$$ −1701.45 −0.237139
$$373$$ −2615.14 −0.363021 −0.181510 0.983389i $$-0.558099\pi$$
−0.181510 + 0.983389i $$0.558099\pi$$
$$374$$ −8628.23 −1.19293
$$375$$ −832.107 −0.114586
$$376$$ −281.201 −0.0385687
$$377$$ −907.989 −0.124042
$$378$$ 1167.12 0.158811
$$379$$ −672.434 −0.0911362 −0.0455681 0.998961i $$-0.514510\pi$$
−0.0455681 + 0.998961i $$0.514510\pi$$
$$380$$ −290.496 −0.0392162
$$381$$ 8078.03 1.08622
$$382$$ −969.470 −0.129849
$$383$$ 1169.86 0.156075 0.0780377 0.996950i $$-0.475135\pi$$
0.0780377 + 0.996950i $$0.475135\pi$$
$$384$$ 6613.92 0.878946
$$385$$ 1338.92 0.177241
$$386$$ 1895.45 0.249938
$$387$$ −3915.78 −0.514342
$$388$$ −1392.36 −0.182182
$$389$$ −1122.22 −0.146269 −0.0731347 0.997322i $$-0.523300\pi$$
−0.0731347 + 0.997322i $$0.523300\pi$$
$$390$$ −1664.79 −0.216153
$$391$$ −19029.7 −2.46131
$$392$$ −1180.08 −0.152049
$$393$$ −13196.7 −1.69385
$$394$$ −5412.68 −0.692099
$$395$$ −781.375 −0.0995323
$$396$$ −870.113 −0.110416
$$397$$ −1985.93 −0.251060 −0.125530 0.992090i $$-0.540063\pi$$
−0.125530 + 0.992090i $$0.540063\pi$$
$$398$$ 7408.38 0.933037
$$399$$ 2060.81 0.258571
$$400$$ −1294.11 −0.161764
$$401$$ −4172.38 −0.519597 −0.259799 0.965663i $$-0.583656\pi$$
−0.259799 + 0.965663i $$0.583656\pi$$
$$402$$ 249.758 0.0309870
$$403$$ 3763.37 0.465178
$$404$$ 317.699 0.0391240
$$405$$ 4483.53 0.550095
$$406$$ 849.658 0.103862
$$407$$ 14033.9 1.70918
$$408$$ 13983.9 1.69682
$$409$$ −11700.8 −1.41459 −0.707295 0.706919i $$-0.750085\pi$$
−0.707295 + 0.706919i $$0.750085\pi$$
$$410$$ 4387.59 0.528507
$$411$$ 14718.0 1.76638
$$412$$ 2206.47 0.263848
$$413$$ 4312.00 0.513752
$$414$$ 9767.22 1.15950
$$415$$ 5182.64 0.613026
$$416$$ 1137.65 0.134082
$$417$$ 3515.08 0.412791
$$418$$ −4374.72 −0.511901
$$419$$ 2733.20 0.318677 0.159339 0.987224i $$-0.449064\pi$$
0.159339 + 0.987224i $$0.449064\pi$$
$$420$$ −306.081 −0.0355600
$$421$$ 13549.4 1.56854 0.784272 0.620417i $$-0.213037\pi$$
0.784272 + 0.620417i $$0.213037\pi$$
$$422$$ 14593.3 1.68339
$$423$$ 202.158 0.0232370
$$424$$ 5033.87 0.576571
$$425$$ −2180.63 −0.248885
$$426$$ −16387.0 −1.86374
$$427$$ −2245.15 −0.254450
$$428$$ −1979.60 −0.223569
$$429$$ 4925.86 0.554366
$$430$$ 2924.09 0.327935
$$431$$ −6429.25 −0.718530 −0.359265 0.933236i $$-0.616973\pi$$
−0.359265 + 0.933236i $$0.616973\pi$$
$$432$$ 3337.79 0.371735
$$433$$ 8022.03 0.890333 0.445166 0.895448i $$-0.353145\pi$$
0.445166 + 0.895448i $$0.353145\pi$$
$$434$$ −3521.61 −0.389499
$$435$$ 1562.40 0.172210
$$436$$ 1645.30 0.180724
$$437$$ −9648.50 −1.05618
$$438$$ 14192.1 1.54823
$$439$$ −5569.88 −0.605549 −0.302774 0.953062i $$-0.597913\pi$$
−0.302774 + 0.953062i $$0.597913\pi$$
$$440$$ 4606.51 0.499106
$$441$$ 848.372 0.0916069
$$442$$ −4362.77 −0.469493
$$443$$ −5486.21 −0.588392 −0.294196 0.955745i $$-0.595052\pi$$
−0.294196 + 0.955745i $$0.595052\pi$$
$$444$$ −3208.19 −0.342914
$$445$$ 851.127 0.0906681
$$446$$ −16469.3 −1.74853
$$447$$ −2185.92 −0.231299
$$448$$ −3963.38 −0.417973
$$449$$ −7232.67 −0.760203 −0.380101 0.924945i $$-0.624111\pi$$
−0.380101 + 0.924945i $$0.624111\pi$$
$$450$$ 1119.24 0.117248
$$451$$ −12982.3 −1.35546
$$452$$ −1800.05 −0.187317
$$453$$ 6852.76 0.710752
$$454$$ −2626.32 −0.271496
$$455$$ 677.010 0.0697554
$$456$$ 7090.16 0.728130
$$457$$ −2900.51 −0.296893 −0.148446 0.988920i $$-0.547427\pi$$
−0.148446 + 0.988920i $$0.547427\pi$$
$$458$$ 10623.3 1.08383
$$459$$ 5624.31 0.571940
$$460$$ 1433.04 0.145251
$$461$$ 6073.57 0.613611 0.306805 0.951772i $$-0.400740\pi$$
0.306805 + 0.951772i $$0.400740\pi$$
$$462$$ −4609.42 −0.464176
$$463$$ −18922.8 −1.89939 −0.949693 0.313183i $$-0.898605\pi$$
−0.949693 + 0.313183i $$0.898605\pi$$
$$464$$ 2429.88 0.243113
$$465$$ −6475.74 −0.645817
$$466$$ 1573.27 0.156396
$$467$$ −6776.71 −0.671496 −0.335748 0.941952i $$-0.608989\pi$$
−0.335748 + 0.941952i $$0.608989\pi$$
$$468$$ −439.963 −0.0434558
$$469$$ −101.568 −0.00999991
$$470$$ −150.961 −0.0148155
$$471$$ 3495.50 0.341962
$$472$$ 14835.3 1.44672
$$473$$ −8651.96 −0.841052
$$474$$ 2689.99 0.260666
$$475$$ −1105.63 −0.106800
$$476$$ −802.121 −0.0772377
$$477$$ −3618.90 −0.347375
$$478$$ −13069.7 −1.25062
$$479$$ 2397.32 0.228677 0.114338 0.993442i $$-0.463525\pi$$
0.114338 + 0.993442i $$0.463525\pi$$
$$480$$ −1957.59 −0.186148
$$481$$ 7096.09 0.672669
$$482$$ 12.5871 0.00118948
$$483$$ −10166.1 −0.957711
$$484$$ −173.977 −0.0163390
$$485$$ −5299.37 −0.496148
$$486$$ −10933.4 −1.02047
$$487$$ 5586.17 0.519781 0.259890 0.965638i $$-0.416314\pi$$
0.259890 + 0.965638i $$0.416314\pi$$
$$488$$ −7724.35 −0.716526
$$489$$ 6674.33 0.617227
$$490$$ −633.518 −0.0584070
$$491$$ 537.392 0.0493934 0.0246967 0.999695i $$-0.492138\pi$$
0.0246967 + 0.999695i $$0.492138\pi$$
$$492$$ 2967.78 0.271947
$$493$$ 4094.46 0.374047
$$494$$ −2212.03 −0.201466
$$495$$ −3311.67 −0.300704
$$496$$ −10071.2 −0.911716
$$497$$ 6664.00 0.601451
$$498$$ −17842.0 −1.60546
$$499$$ 598.965 0.0537342 0.0268671 0.999639i $$-0.491447\pi$$
0.0268671 + 0.999639i $$0.491447\pi$$
$$500$$ 164.214 0.0146877
$$501$$ −2392.62 −0.213362
$$502$$ −1416.81 −0.125966
$$503$$ 4426.76 0.392405 0.196202 0.980563i $$-0.437139\pi$$
0.196202 + 0.980563i $$0.437139\pi$$
$$504$$ 2918.79 0.257963
$$505$$ 1209.17 0.106549
$$506$$ 21580.8 1.89601
$$507$$ −12134.4 −1.06293
$$508$$ −1594.17 −0.139232
$$509$$ 17727.7 1.54374 0.771872 0.635779i $$-0.219321\pi$$
0.771872 + 0.635779i $$0.219321\pi$$
$$510$$ 7507.14 0.651808
$$511$$ −5771.43 −0.499634
$$512$$ −13017.7 −1.12365
$$513$$ 2851.66 0.245427
$$514$$ −4588.77 −0.393778
$$515$$ 8397.88 0.718553
$$516$$ 1977.86 0.168741
$$517$$ 446.671 0.0379972
$$518$$ −6640.22 −0.563233
$$519$$ 21925.4 1.85437
$$520$$ 2329.23 0.196430
$$521$$ 8662.79 0.728453 0.364226 0.931310i $$-0.381333\pi$$
0.364226 + 0.931310i $$0.381333\pi$$
$$522$$ −2101.53 −0.176210
$$523$$ −7770.40 −0.649667 −0.324833 0.945771i $$-0.605308\pi$$
−0.324833 + 0.945771i $$0.605308\pi$$
$$524$$ 2604.32 0.217119
$$525$$ −1164.95 −0.0968430
$$526$$ −3100.60 −0.257020
$$527$$ −16970.4 −1.40274
$$528$$ −13182.2 −1.08652
$$529$$ 35429.6 2.91194
$$530$$ 2702.40 0.221480
$$531$$ −10665.2 −0.871624
$$532$$ −406.695 −0.0331437
$$533$$ −6564.34 −0.533458
$$534$$ −2930.12 −0.237451
$$535$$ −7534.41 −0.608861
$$536$$ −349.440 −0.0281595
$$537$$ 19829.6 1.59350
$$538$$ 8404.56 0.673506
$$539$$ 1874.49 0.149796
$$540$$ −423.541 −0.0337524
$$541$$ 21641.0 1.71981 0.859906 0.510453i $$-0.170522\pi$$
0.859906 + 0.510453i $$0.170522\pi$$
$$542$$ −2317.23 −0.183642
$$543$$ 9734.41 0.769325
$$544$$ −5130.09 −0.404321
$$545$$ 6262.05 0.492177
$$546$$ −2330.70 −0.182683
$$547$$ 7489.29 0.585409 0.292705 0.956203i $$-0.405445\pi$$
0.292705 + 0.956203i $$0.405445\pi$$
$$548$$ −2904.54 −0.226416
$$549$$ 5553.11 0.431696
$$550$$ 2472.97 0.191723
$$551$$ 2075.99 0.160508
$$552$$ −34976.2 −2.69689
$$553$$ −1093.93 −0.0841201
$$554$$ −999.566 −0.0766561
$$555$$ −12210.4 −0.933881
$$556$$ −693.689 −0.0529118
$$557$$ 25297.9 1.92443 0.962214 0.272295i $$-0.0877826\pi$$
0.962214 + 0.272295i $$0.0877826\pi$$
$$558$$ 8710.29 0.660817
$$559$$ −4374.77 −0.331007
$$560$$ −1811.76 −0.136716
$$561$$ −22212.5 −1.67168
$$562$$ −8623.85 −0.647286
$$563$$ 15661.3 1.17237 0.586186 0.810177i $$-0.300629\pi$$
0.586186 + 0.810177i $$0.300629\pi$$
$$564$$ −102.110 −0.00762343
$$565$$ −6851.02 −0.510132
$$566$$ 13994.9 1.03931
$$567$$ 6276.94 0.464915
$$568$$ 22927.3 1.69367
$$569$$ −9982.75 −0.735498 −0.367749 0.929925i $$-0.619871\pi$$
−0.367749 + 0.929925i $$0.619871\pi$$
$$570$$ 3806.30 0.279699
$$571$$ −11583.6 −0.848966 −0.424483 0.905436i $$-0.639544\pi$$
−0.424483 + 0.905436i $$0.639544\pi$$
$$572$$ −972.103 −0.0710589
$$573$$ −2495.81 −0.181961
$$574$$ 6142.63 0.446670
$$575$$ 5454.16 0.395573
$$576$$ 9802.97 0.709127
$$577$$ −595.378 −0.0429565 −0.0214783 0.999769i $$-0.506837\pi$$
−0.0214783 + 0.999769i $$0.506837\pi$$
$$578$$ 6969.39 0.501537
$$579$$ 4879.66 0.350245
$$580$$ −308.335 −0.0220740
$$581$$ 7255.70 0.518102
$$582$$ 18243.8 1.29936
$$583$$ −7996.00 −0.568028
$$584$$ −19856.4 −1.40696
$$585$$ −1674.51 −0.118346
$$586$$ 729.738 0.0514423
$$587$$ −15750.3 −1.10747 −0.553736 0.832693i $$-0.686798\pi$$
−0.553736 + 0.832693i $$0.686798\pi$$
$$588$$ −428.513 −0.0300537
$$589$$ −8604.42 −0.601934
$$590$$ 7964.22 0.555732
$$591$$ −13934.4 −0.969856
$$592$$ −18990.0 −1.31838
$$593$$ −417.878 −0.0289379 −0.0144690 0.999895i $$-0.504606\pi$$
−0.0144690 + 0.999895i $$0.504606\pi$$
$$594$$ −6378.31 −0.440581
$$595$$ −3052.89 −0.210347
$$596$$ 431.385 0.0296480
$$597$$ 19072.2 1.30749
$$598$$ 10912.1 0.746201
$$599$$ −19997.3 −1.36406 −0.682028 0.731326i $$-0.738902\pi$$
−0.682028 + 0.731326i $$0.738902\pi$$
$$600$$ −4007.97 −0.272708
$$601$$ −15992.6 −1.08545 −0.542723 0.839912i $$-0.682607\pi$$
−0.542723 + 0.839912i $$0.682607\pi$$
$$602$$ 4093.73 0.277156
$$603$$ 251.216 0.0169657
$$604$$ −1352.37 −0.0911045
$$605$$ −662.162 −0.0444970
$$606$$ −4162.73 −0.279042
$$607$$ 14159.2 0.946793 0.473396 0.880850i $$-0.343028\pi$$
0.473396 + 0.880850i $$0.343028\pi$$
$$608$$ −2601.08 −0.173499
$$609$$ 2187.36 0.145544
$$610$$ −4146.76 −0.275242
$$611$$ 225.854 0.0149543
$$612$$ 1983.96 0.131040
$$613$$ −4629.41 −0.305025 −0.152512 0.988302i $$-0.548736\pi$$
−0.152512 + 0.988302i $$0.548736\pi$$
$$614$$ 4963.87 0.326263
$$615$$ 11295.4 0.740611
$$616$$ 6449.11 0.421821
$$617$$ −23165.3 −1.51151 −0.755753 0.654857i $$-0.772729\pi$$
−0.755753 + 0.654857i $$0.772729\pi$$
$$618$$ −28910.9 −1.88182
$$619$$ 12370.6 0.803258 0.401629 0.915803i $$-0.368444\pi$$
0.401629 + 0.915803i $$0.368444\pi$$
$$620$$ 1277.97 0.0827812
$$621$$ −14067.4 −0.909028
$$622$$ 3137.36 0.202245
$$623$$ 1191.58 0.0766285
$$624$$ −6665.43 −0.427613
$$625$$ 625.000 0.0400000
$$626$$ −3708.02 −0.236745
$$627$$ −11262.3 −0.717341
$$628$$ −689.826 −0.0438329
$$629$$ −31998.9 −2.02842
$$630$$ 1566.93 0.0990923
$$631$$ 13980.2 0.882002 0.441001 0.897507i $$-0.354623\pi$$
0.441001 + 0.897507i $$0.354623\pi$$
$$632$$ −3763.61 −0.236880
$$633$$ 37568.9 2.35897
$$634$$ 16799.7 1.05237
$$635$$ −6067.45 −0.379180
$$636$$ 1827.91 0.113964
$$637$$ 947.814 0.0589541
$$638$$ −4643.36 −0.288139
$$639$$ −16482.7 −1.02041
$$640$$ −4967.75 −0.306825
$$641$$ −16060.9 −0.989655 −0.494828 0.868991i $$-0.664769\pi$$
−0.494828 + 0.868991i $$0.664769\pi$$
$$642$$ 25938.3 1.59455
$$643$$ −4502.17 −0.276125 −0.138063 0.990424i $$-0.544087\pi$$
−0.138063 + 0.990424i $$0.544087\pi$$
$$644$$ 2006.25 0.122760
$$645$$ 7527.79 0.459545
$$646$$ 9974.87 0.607517
$$647$$ 29414.8 1.78735 0.893675 0.448715i $$-0.148118\pi$$
0.893675 + 0.448715i $$0.148118\pi$$
$$648$$ 21595.6 1.30919
$$649$$ −23565.0 −1.42528
$$650$$ 1250.43 0.0754553
$$651$$ −9066.03 −0.545815
$$652$$ −1317.16 −0.0791164
$$653$$ 13013.6 0.779882 0.389941 0.920840i $$-0.372495\pi$$
0.389941 + 0.920840i $$0.372495\pi$$
$$654$$ −21558.0 −1.28897
$$655$$ 9912.09 0.591294
$$656$$ 17566.9 1.04554
$$657$$ 14275.0 0.847671
$$658$$ −211.345 −0.0125214
$$659$$ 23474.2 1.38759 0.693797 0.720171i $$-0.255937\pi$$
0.693797 + 0.720171i $$0.255937\pi$$
$$660$$ 1672.72 0.0986526
$$661$$ −9266.36 −0.545264 −0.272632 0.962118i $$-0.587894\pi$$
−0.272632 + 0.962118i $$0.587894\pi$$
$$662$$ −25040.4 −1.47013
$$663$$ −11231.5 −0.657914
$$664$$ 24963.0 1.45896
$$665$$ −1547.89 −0.0902625
$$666$$ 16423.8 0.955572
$$667$$ −10241.0 −0.594501
$$668$$ 472.176 0.0273489
$$669$$ −42398.6 −2.45026
$$670$$ −187.595 −0.0108170
$$671$$ 12269.7 0.705909
$$672$$ −2740.62 −0.157324
$$673$$ −25067.2 −1.43576 −0.717882 0.696164i $$-0.754888\pi$$
−0.717882 + 0.696164i $$0.754888\pi$$
$$674$$ 75.3288 0.00430498
$$675$$ −1612.01 −0.0919202
$$676$$ 2394.68 0.136247
$$677$$ −22409.6 −1.27219 −0.636093 0.771613i $$-0.719450\pi$$
−0.636093 + 0.771613i $$0.719450\pi$$
$$678$$ 23585.6 1.33599
$$679$$ −7419.11 −0.419322
$$680$$ −10503.4 −0.592332
$$681$$ −6761.20 −0.380455
$$682$$ 19245.5 1.08057
$$683$$ −8757.53 −0.490626 −0.245313 0.969444i $$-0.578891\pi$$
−0.245313 + 0.969444i $$0.578891\pi$$
$$684$$ 1005.91 0.0562311
$$685$$ −11054.7 −0.616613
$$686$$ −886.925 −0.0493629
$$687$$ 27348.7 1.51880
$$688$$ 11707.4 0.648750
$$689$$ −4043.09 −0.223555
$$690$$ −18776.7 −1.03597
$$691$$ 8468.42 0.466214 0.233107 0.972451i $$-0.425111\pi$$
0.233107 + 0.972451i $$0.425111\pi$$
$$692$$ −4326.90 −0.237694
$$693$$ −4636.33 −0.254141
$$694$$ −20294.8 −1.11006
$$695$$ −2640.19 −0.144098
$$696$$ 7525.54 0.409849
$$697$$ 29601.0 1.60864
$$698$$ −26555.1 −1.44001
$$699$$ 4050.23 0.219162
$$700$$ 229.899 0.0124134
$$701$$ 15996.9 0.861906 0.430953 0.902374i $$-0.358177\pi$$
0.430953 + 0.902374i $$0.358177\pi$$
$$702$$ −3225.12 −0.173397
$$703$$ −16224.2 −0.870423
$$704$$ 21659.8 1.15956
$$705$$ −388.633 −0.0207614
$$706$$ 7240.03 0.385952
$$707$$ 1692.83 0.0900503
$$708$$ 5387.02 0.285956
$$709$$ 19903.0 1.05426 0.527131 0.849784i $$-0.323268\pi$$
0.527131 + 0.849784i $$0.323268\pi$$
$$710$$ 12308.3 0.650597
$$711$$ 2705.70 0.142717
$$712$$ 4099.58 0.215784
$$713$$ 42446.1 2.22948
$$714$$ 10510.0 0.550878
$$715$$ −3699.84 −0.193519
$$716$$ −3913.30 −0.204256
$$717$$ −33646.7 −1.75252
$$718$$ −8179.59 −0.425153
$$719$$ −11073.1 −0.574347 −0.287174 0.957879i $$-0.592716\pi$$
−0.287174 + 0.957879i $$0.592716\pi$$
$$720$$ 4481.18 0.231949
$$721$$ 11757.0 0.607288
$$722$$ −12678.4 −0.653520
$$723$$ 32.4043 0.00166685
$$724$$ −1921.06 −0.0986125
$$725$$ −1173.53 −0.0601155
$$726$$ 2279.58 0.116533
$$727$$ 31652.7 1.61476 0.807382 0.590029i $$-0.200884\pi$$
0.807382 + 0.590029i $$0.200884\pi$$
$$728$$ 3260.92 0.166013
$$729$$ −3935.94 −0.199967
$$730$$ −10659.8 −0.540460
$$731$$ 19727.5 0.998149
$$732$$ −2804.88 −0.141628
$$733$$ 16958.3 0.854528 0.427264 0.904127i $$-0.359477\pi$$
0.427264 + 0.904127i $$0.359477\pi$$
$$734$$ 8230.16 0.413870
$$735$$ −1630.93 −0.0818473
$$736$$ 12831.3 0.642618
$$737$$ 555.065 0.0277423
$$738$$ −15193.1 −0.757813
$$739$$ −11616.6 −0.578245 −0.289123 0.957292i $$-0.593364\pi$$
−0.289123 + 0.957292i $$0.593364\pi$$
$$740$$ 2409.69 0.119705
$$741$$ −5694.66 −0.282319
$$742$$ 3783.36 0.187185
$$743$$ 15928.0 0.786464 0.393232 0.919439i $$-0.371357\pi$$
0.393232 + 0.919439i $$0.371357\pi$$
$$744$$ −31191.4 −1.53700
$$745$$ 1641.86 0.0807423
$$746$$ −6762.19 −0.331879
$$747$$ −17946.1 −0.879003
$$748$$ 4383.57 0.214277
$$749$$ −10548.2 −0.514582
$$750$$ −2151.65 −0.104756
$$751$$ 25571.9 1.24252 0.621260 0.783604i $$-0.286621\pi$$
0.621260 + 0.783604i $$0.286621\pi$$
$$752$$ −604.412 −0.0293094
$$753$$ −3647.43 −0.176520
$$754$$ −2347.87 −0.113401
$$755$$ −5147.14 −0.248111
$$756$$ −592.958 −0.0285260
$$757$$ 6202.41 0.297794 0.148897 0.988853i $$-0.452428\pi$$
0.148897 + 0.988853i $$0.452428\pi$$
$$758$$ −1738.77 −0.0833179
$$759$$ 55557.6 2.65693
$$760$$ −5325.46 −0.254177
$$761$$ −29199.1 −1.39089 −0.695444 0.718580i $$-0.744792\pi$$
−0.695444 + 0.718580i $$0.744792\pi$$
$$762$$ 20888.1 0.993037
$$763$$ 8766.87 0.415966
$$764$$ 492.539 0.0233239
$$765$$ 7550.98 0.356871
$$766$$ 3025.00 0.142686
$$767$$ −11915.4 −0.560938
$$768$$ −13050.5 −0.613177
$$769$$ 21838.2 1.02407 0.512033 0.858966i $$-0.328892\pi$$
0.512033 + 0.858966i $$0.328892\pi$$
$$770$$ 3462.16 0.162036
$$771$$ −11813.3 −0.551812
$$772$$ −962.985 −0.0448945
$$773$$ −25544.8 −1.18859 −0.594296 0.804246i $$-0.702569\pi$$
−0.594296 + 0.804246i $$0.702569\pi$$
$$774$$ −10125.4 −0.470218
$$775$$ 4863.96 0.225443
$$776$$ −25525.2 −1.18080
$$777$$ −17094.6 −0.789273
$$778$$ −2901.82 −0.133721
$$779$$ 15008.4 0.690286
$$780$$ 845.795 0.0388261
$$781$$ −36418.6 −1.66858
$$782$$ −49206.6 −2.25016
$$783$$ 3026.77 0.138146
$$784$$ −2536.46 −0.115546
$$785$$ −2625.49 −0.119373
$$786$$ −34123.8 −1.54854
$$787$$ −37223.2 −1.68598 −0.842989 0.537931i $$-0.819206\pi$$
−0.842989 + 0.537931i $$0.819206\pi$$
$$788$$ 2749.91 0.124317
$$789$$ −7982.19 −0.360169
$$790$$ −2020.47 −0.0909938
$$791$$ −9591.42 −0.431140
$$792$$ −15951.1 −0.715655
$$793$$ 6204.03 0.277820
$$794$$ −5135.18 −0.229522
$$795$$ 6957.06 0.310366
$$796$$ −3763.83 −0.167595
$$797$$ −40384.6 −1.79485 −0.897425 0.441168i $$-0.854564\pi$$
−0.897425 + 0.441168i $$0.854564\pi$$
$$798$$ 5328.83 0.236389
$$799$$ −1018.46 −0.0450945
$$800$$ 1470.35 0.0649811
$$801$$ −2947.23 −0.130007
$$802$$ −10788.9 −0.475023
$$803$$ 31540.7 1.38611
$$804$$ −126.889 −0.00556598
$$805$$ 7635.83 0.334320
$$806$$ 9731.28 0.425272
$$807$$ 21636.7 0.943803
$$808$$ 5824.14 0.253580
$$809$$ −1955.76 −0.0849948 −0.0424974 0.999097i $$-0.513531\pi$$
−0.0424974 + 0.999097i $$0.513531\pi$$
$$810$$ 11593.4 0.502904
$$811$$ −34301.8 −1.48520 −0.742600 0.669735i $$-0.766408\pi$$
−0.742600 + 0.669735i $$0.766408\pi$$
$$812$$ −431.669 −0.0186559
$$813$$ −5965.49 −0.257342
$$814$$ 36288.7 1.56255
$$815$$ −5013.13 −0.215463
$$816$$ 30056.9 1.28946
$$817$$ 10002.3 0.428319
$$818$$ −30255.8 −1.29324
$$819$$ −2344.31 −0.100021
$$820$$ −2229.12 −0.0949319
$$821$$ −13665.6 −0.580918 −0.290459 0.956887i $$-0.593808\pi$$
−0.290459 + 0.956887i $$0.593808\pi$$
$$822$$ 38057.5 1.61485
$$823$$ −21519.5 −0.911449 −0.455724 0.890121i $$-0.650620\pi$$
−0.455724 + 0.890121i $$0.650620\pi$$
$$824$$ 40449.7 1.71011
$$825$$ 6366.42 0.268667
$$826$$ 11149.9 0.469679
$$827$$ 35220.6 1.48094 0.740471 0.672088i $$-0.234602\pi$$
0.740471 + 0.672088i $$0.234602\pi$$
$$828$$ −4962.23 −0.208272
$$829$$ 31365.5 1.31408 0.657039 0.753857i $$-0.271809\pi$$
0.657039 + 0.753857i $$0.271809\pi$$
$$830$$ 13401.2 0.560437
$$831$$ −2573.28 −0.107420
$$832$$ 10952.0 0.456362
$$833$$ −4274.04 −0.177775
$$834$$ 9089.24 0.377380
$$835$$ 1797.11 0.0744810
$$836$$ 2222.58 0.0919491
$$837$$ −12545.2 −0.518070
$$838$$ 7067.48 0.291339
$$839$$ −28287.1 −1.16398 −0.581990 0.813196i $$-0.697726\pi$$
−0.581990 + 0.813196i $$0.697726\pi$$
$$840$$ −5611.16 −0.230480
$$841$$ −22185.5 −0.909653
$$842$$ 35035.8 1.43398
$$843$$ −22201.2 −0.907060
$$844$$ −7414.11 −0.302374
$$845$$ 9114.21 0.371051
$$846$$ 522.738 0.0212436
$$847$$ −927.026 −0.0376068
$$848$$ 10819.8 0.438152
$$849$$ 36028.6 1.45642
$$850$$ −5638.66 −0.227534
$$851$$ 80035.0 3.22393
$$852$$ 8325.40 0.334769
$$853$$ 9405.41 0.377533 0.188766 0.982022i $$-0.439551\pi$$
0.188766 + 0.982022i $$0.439551\pi$$
$$854$$ −5805.47 −0.232622
$$855$$ 3828.53 0.153138
$$856$$ −36290.6 −1.44905
$$857$$ −27966.9 −1.11474 −0.557369 0.830265i $$-0.688189\pi$$
−0.557369 + 0.830265i $$0.688189\pi$$
$$858$$ 12737.2 0.506809
$$859$$ 6281.11 0.249486 0.124743 0.992189i $$-0.460189\pi$$
0.124743 + 0.992189i $$0.460189\pi$$
$$860$$ −1485.58 −0.0589047
$$861$$ 15813.6 0.625931
$$862$$ −16624.7 −0.656890
$$863$$ −4757.13 −0.187642 −0.0938208 0.995589i $$-0.529908\pi$$
−0.0938208 + 0.995589i $$0.529908\pi$$
$$864$$ −3792.35 −0.149327
$$865$$ −16468.3 −0.647327
$$866$$ 20743.3 0.813954
$$867$$ 17942.0 0.702818
$$868$$ 1789.15 0.0699629
$$869$$ 5978.28 0.233371
$$870$$ 4040.04 0.157437
$$871$$ 280.663 0.0109184
$$872$$ 30162.1 1.17135
$$873$$ 18350.3 0.711414
$$874$$ −24949.0 −0.965574
$$875$$ 875.000 0.0338062
$$876$$ −7210.30 −0.278097
$$877$$ −30240.5 −1.16437 −0.582184 0.813057i $$-0.697802\pi$$
−0.582184 + 0.813057i $$0.697802\pi$$
$$878$$ −14402.5 −0.553601
$$879$$ 1878.64 0.0720875
$$880$$ 9901.21 0.379284
$$881$$ 44875.5 1.71611 0.858056 0.513556i $$-0.171672\pi$$
0.858056 + 0.513556i $$0.171672\pi$$
$$882$$ 2193.71 0.0837483
$$883$$ 4892.13 0.186448 0.0932238 0.995645i $$-0.470283\pi$$
0.0932238 + 0.995645i $$0.470283\pi$$
$$884$$ 2216.51 0.0843317
$$885$$ 20503.1 0.778762
$$886$$ −14186.2 −0.537916
$$887$$ 1761.40 0.0666765 0.0333382 0.999444i $$-0.489386\pi$$
0.0333382 + 0.999444i $$0.489386\pi$$
$$888$$ −58813.4 −2.22258
$$889$$ −8494.43 −0.320466
$$890$$ 2200.83 0.0828900
$$891$$ −34303.3 −1.28979
$$892$$ 8367.22 0.314075
$$893$$ −516.384 −0.0193507
$$894$$ −5652.33 −0.211457
$$895$$ −14894.1 −0.556263
$$896$$ −6954.86 −0.259314
$$897$$ 28092.1 1.04567
$$898$$ −18702.2 −0.694988
$$899$$ −9132.79 −0.338816
$$900$$ −568.629 −0.0210603
$$901$$ 18231.8 0.674128
$$902$$ −33569.3 −1.23918
$$903$$ 10538.9 0.388386
$$904$$ −32999.0 −1.21408
$$905$$ −7311.57 −0.268558
$$906$$ 17719.8 0.649779
$$907$$ 23689.1 0.867238 0.433619 0.901096i $$-0.357236\pi$$
0.433619 + 0.901096i $$0.357236\pi$$
$$908$$ 1334.30 0.0487669
$$909$$ −4187.03 −0.152778
$$910$$ 1750.60 0.0637714
$$911$$ −13877.3 −0.504692 −0.252346 0.967637i $$-0.581202\pi$$
−0.252346 + 0.967637i $$0.581202\pi$$
$$912$$ 15239.6 0.553325
$$913$$ −39652.2 −1.43735
$$914$$ −7500.09 −0.271423
$$915$$ −10675.4 −0.385704
$$916$$ −5397.18 −0.194681
$$917$$ 13876.9 0.499735
$$918$$ 14543.3 0.522875
$$919$$ 14331.6 0.514426 0.257213 0.966355i $$-0.417196\pi$$
0.257213 + 0.966355i $$0.417196\pi$$
$$920$$ 26270.8 0.941438
$$921$$ 12779.0 0.457201
$$922$$ 15705.0 0.560971
$$923$$ −18414.7 −0.656692
$$924$$ 2341.81 0.0833767
$$925$$ 9171.32 0.326001
$$926$$ −48930.2 −1.73644
$$927$$ −29079.7 −1.03032
$$928$$ −2760.80 −0.0976592
$$929$$ 16668.4 0.588668 0.294334 0.955703i $$-0.404902\pi$$
0.294334 + 0.955703i $$0.404902\pi$$
$$930$$ −16744.9 −0.590415
$$931$$ −2167.04 −0.0762857
$$932$$ −799.300 −0.0280922
$$933$$ 8076.82 0.283412
$$934$$ −17523.1 −0.613891
$$935$$ 16684.0 0.583555
$$936$$ −8065.52 −0.281656
$$937$$ 30384.9 1.05937 0.529685 0.848194i $$-0.322310\pi$$
0.529685 + 0.848194i $$0.322310\pi$$
$$938$$ −262.632 −0.00914206
$$939$$ −9545.94 −0.331757
$$940$$ 76.6956 0.00266121
$$941$$ −1196.35 −0.0414452 −0.0207226 0.999785i $$-0.506597\pi$$
−0.0207226 + 0.999785i $$0.506597\pi$$
$$942$$ 9038.63 0.312627
$$943$$ −74037.5 −2.55673
$$944$$ 31886.9 1.09940
$$945$$ −2256.81 −0.0776867
$$946$$ −22372.1 −0.768901
$$947$$ 1788.41 0.0613681 0.0306840 0.999529i $$-0.490231\pi$$
0.0306840 + 0.999529i $$0.490231\pi$$
$$948$$ −1366.65 −0.0468215
$$949$$ 15948.2 0.545523
$$950$$ −2858.94 −0.0976380
$$951$$ 43249.2 1.47471
$$952$$ −14704.7 −0.500612
$$953$$ 8578.60 0.291593 0.145796 0.989315i $$-0.453426\pi$$
0.145796 + 0.989315i $$0.453426\pi$$
$$954$$ −9357.70 −0.317575
$$955$$ 1874.61 0.0635194
$$956$$ 6640.06 0.224639
$$957$$ −11953.9 −0.403776
$$958$$ 6198.95 0.209059
$$959$$ −15476.6 −0.521133
$$960$$ −18845.4 −0.633577
$$961$$ 8061.99 0.270618
$$962$$ 18349.0 0.614963
$$963$$ 26089.7 0.873031
$$964$$ −6.39489 −0.000213657 0
$$965$$ −3665.14 −0.122264
$$966$$ −26287.4 −0.875552
$$967$$ −55459.3 −1.84431 −0.922156 0.386818i $$-0.873574\pi$$
−0.922156 + 0.386818i $$0.873574\pi$$
$$968$$ −3189.40 −0.105900
$$969$$ 25679.3 0.851330
$$970$$ −13703.0 −0.453585
$$971$$ 22047.3 0.728662 0.364331 0.931270i $$-0.381298\pi$$
0.364331 + 0.931270i $$0.381298\pi$$
$$972$$ 5554.72 0.183300
$$973$$ −3696.27 −0.121785
$$974$$ 14444.6 0.475191
$$975$$ 3219.11 0.105738
$$976$$ −16602.7 −0.544507
$$977$$ 14402.3 0.471617 0.235809 0.971800i $$-0.424226\pi$$
0.235809 + 0.971800i $$0.424226\pi$$
$$978$$ 17258.4 0.564277
$$979$$ −6511.94 −0.212587
$$980$$ 321.859 0.0104912
$$981$$ −21683.9 −0.705721
$$982$$ 1389.58 0.0451561
$$983$$ 7817.11 0.253639 0.126819 0.991926i $$-0.459523\pi$$
0.126819 + 0.991926i $$0.459523\pi$$
$$984$$ 54406.2 1.76261
$$985$$ 10466.2 0.338560
$$986$$ 10587.4 0.341959
$$987$$ −544.087 −0.0175466
$$988$$ 1123.82 0.0361878
$$989$$ −49342.0 −1.58643
$$990$$ −8563.26 −0.274907
$$991$$ 24501.6 0.785386 0.392693 0.919670i $$-0.371543\pi$$
0.392693 + 0.919670i $$0.371543\pi$$
$$992$$ 11442.8 0.366239
$$993$$ −64464.2 −2.06013
$$994$$ 17231.7 0.549855
$$995$$ −14325.2 −0.456421
$$996$$ 9064.61 0.288377
$$997$$ −50696.0 −1.61039 −0.805195 0.593010i $$-0.797940\pi$$
−0.805195 + 0.593010i $$0.797940\pi$$
$$998$$ 1548.80 0.0491245
$$999$$ −23654.8 −0.749152
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 35.4.a.b.1.1 2
3.2 odd 2 315.4.a.f.1.2 2
4.3 odd 2 560.4.a.r.1.1 2
5.2 odd 4 175.4.b.c.99.3 4
5.3 odd 4 175.4.b.c.99.2 4
5.4 even 2 175.4.a.c.1.2 2
7.2 even 3 245.4.e.h.116.2 4
7.3 odd 6 245.4.e.i.226.2 4
7.4 even 3 245.4.e.h.226.2 4
7.5 odd 6 245.4.e.i.116.2 4
7.6 odd 2 245.4.a.k.1.1 2
8.3 odd 2 2240.4.a.bo.1.2 2
8.5 even 2 2240.4.a.bn.1.1 2
15.14 odd 2 1575.4.a.z.1.1 2
21.20 even 2 2205.4.a.u.1.2 2
35.34 odd 2 1225.4.a.m.1.2 2

By twisted newform
Twist Min Dim Char Parity Ord Type
35.4.a.b.1.1 2 1.1 even 1 trivial
175.4.a.c.1.2 2 5.4 even 2
175.4.b.c.99.2 4 5.3 odd 4
175.4.b.c.99.3 4 5.2 odd 4
245.4.a.k.1.1 2 7.6 odd 2
245.4.e.h.116.2 4 7.2 even 3
245.4.e.h.226.2 4 7.4 even 3
245.4.e.i.116.2 4 7.5 odd 6
245.4.e.i.226.2 4 7.3 odd 6
315.4.a.f.1.2 2 3.2 odd 2
560.4.a.r.1.1 2 4.3 odd 2
1225.4.a.m.1.2 2 35.34 odd 2
1575.4.a.z.1.1 2 15.14 odd 2
2205.4.a.u.1.2 2 21.20 even 2
2240.4.a.bn.1.1 2 8.5 even 2
2240.4.a.bo.1.2 2 8.3 odd 2