# Properties

 Label 207.6.a.a.1.2 Level $207$ Weight $6$ Character 207.1 Self dual yes Analytic conductor $33.199$ Analytic rank $0$ Dimension $2$ CM no Inner twists $1$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$207 = 3^{2} \cdot 23$$ Weight: $$k$$ $$=$$ $$6$$ Character orbit: $$[\chi]$$ $$=$$ 207.a (trivial)

## Newform invariants

 Self dual: yes Analytic conductor: $$33.1994507013$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(\sqrt{29})$$ Defining polynomial: $$x^{2} - x - 7$$ x^2 - x - 7 Coefficient ring: $$\Z[a_1, \ldots, a_{5}]$$ Coefficient ring index: $$2$$ Twist minimal: no (minimal twist has level 69) Fricke sign: $$-1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

 Embedding label 1.2 Root $$-2.19258$$ of defining polynomial Character $$\chi$$ $$=$$ 207.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+10.7703 q^{2} +84.0000 q^{4} -41.6148 q^{5} +0.236813 q^{7} +560.057 q^{8} +O(q^{10})$$ $$q+10.7703 q^{2} +84.0000 q^{4} -41.6148 q^{5} +0.236813 q^{7} +560.057 q^{8} -448.205 q^{10} +421.598 q^{11} +254.502 q^{13} +2.55055 q^{14} +3344.00 q^{16} +975.007 q^{17} +2039.79 q^{19} -3495.65 q^{20} +4540.75 q^{22} -529.000 q^{23} -1393.21 q^{25} +2741.07 q^{26} +19.8923 q^{28} -2671.55 q^{29} +9039.14 q^{31} +18094.2 q^{32} +10501.1 q^{34} -9.85493 q^{35} -12665.3 q^{37} +21969.2 q^{38} -23306.7 q^{40} -10146.4 q^{41} +19523.2 q^{43} +35414.2 q^{44} -5697.50 q^{46} -27679.7 q^{47} -16806.9 q^{49} -15005.3 q^{50} +21378.2 q^{52} -10852.8 q^{53} -17544.7 q^{55} +132.629 q^{56} -28773.4 q^{58} -11907.7 q^{59} +39861.9 q^{61} +97354.5 q^{62} +87872.0 q^{64} -10591.1 q^{65} -28550.5 q^{67} +81900.6 q^{68} -106.141 q^{70} -52179.8 q^{71} +56918.0 q^{73} -136410. q^{74} +171342. q^{76} +99.8398 q^{77} +23178.3 q^{79} -139160. q^{80} -109281. q^{82} +18344.6 q^{83} -40574.8 q^{85} +210272. q^{86} +236119. q^{88} -47362.4 q^{89} +60.2694 q^{91} -44436.0 q^{92} -298120. q^{94} -84885.4 q^{95} -140379. q^{97} -181016. q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q + 168 q^{4} - 94 q^{5} - 118 q^{7}+O(q^{10})$$ 2 * q + 168 * q^4 - 94 * q^5 - 118 * q^7 $$2 q + 168 q^{4} - 94 q^{5} - 118 q^{7} + 116 q^{10} - 320 q^{11} - 288 q^{13} + 1276 q^{14} + 6688 q^{16} + 1810 q^{17} + 730 q^{19} - 7896 q^{20} + 12528 q^{22} - 1058 q^{23} - 1774 q^{25} + 8584 q^{26} - 9912 q^{28} - 8208 q^{29} + 1772 q^{31} + 1508 q^{34} + 6184 q^{35} - 23112 q^{37} + 36076 q^{38} + 6032 q^{40} - 5516 q^{41} + 10322 q^{43} - 26880 q^{44} - 42952 q^{47} - 19634 q^{49} - 10904 q^{50} - 24192 q^{52} + 25350 q^{53} + 21304 q^{55} + 66352 q^{56} + 30856 q^{58} - 18344 q^{59} + 37224 q^{61} + 175624 q^{62} + 175744 q^{64} + 17828 q^{65} - 7482 q^{67} + 152040 q^{68} - 66816 q^{70} - 126848 q^{71} + 137660 q^{73} - 23896 q^{74} + 61320 q^{76} + 87784 q^{77} + 62286 q^{79} - 314336 q^{80} - 159152 q^{82} - 83120 q^{83} - 84316 q^{85} + 309372 q^{86} + 651456 q^{88} - 69770 q^{89} + 64204 q^{91} - 88872 q^{92} - 133632 q^{94} - 16272 q^{95} - 170104 q^{97} - 150568 q^{98}+O(q^{100})$$ 2 * q + 168 * q^4 - 94 * q^5 - 118 * q^7 + 116 * q^10 - 320 * q^11 - 288 * q^13 + 1276 * q^14 + 6688 * q^16 + 1810 * q^17 + 730 * q^19 - 7896 * q^20 + 12528 * q^22 - 1058 * q^23 - 1774 * q^25 + 8584 * q^26 - 9912 * q^28 - 8208 * q^29 + 1772 * q^31 + 1508 * q^34 + 6184 * q^35 - 23112 * q^37 + 36076 * q^38 + 6032 * q^40 - 5516 * q^41 + 10322 * q^43 - 26880 * q^44 - 42952 * q^47 - 19634 * q^49 - 10904 * q^50 - 24192 * q^52 + 25350 * q^53 + 21304 * q^55 + 66352 * q^56 + 30856 * q^58 - 18344 * q^59 + 37224 * q^61 + 175624 * q^62 + 175744 * q^64 + 17828 * q^65 - 7482 * q^67 + 152040 * q^68 - 66816 * q^70 - 126848 * q^71 + 137660 * q^73 - 23896 * q^74 + 61320 * q^76 + 87784 * q^77 + 62286 * q^79 - 314336 * q^80 - 159152 * q^82 - 83120 * q^83 - 84316 * q^85 + 309372 * q^86 + 651456 * q^88 - 69770 * q^89 + 64204 * q^91 - 88872 * q^92 - 133632 * q^94 - 16272 * q^95 - 170104 * q^97 - 150568 * 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 10.7703 1.90394 0.951972 0.306186i $$-0.0990530\pi$$
0.951972 + 0.306186i $$0.0990530\pi$$
$$3$$ 0 0
$$4$$ 84.0000 2.62500
$$5$$ −41.6148 −0.744429 −0.372214 0.928147i $$-0.621401\pi$$
−0.372214 + 0.928147i $$0.621401\pi$$
$$6$$ 0 0
$$7$$ 0.236813 0.00182667 0.000913335 1.00000i $$-0.499709\pi$$
0.000913335 1.00000i $$0.499709\pi$$
$$8$$ 560.057 3.09391
$$9$$ 0 0
$$10$$ −448.205 −1.41735
$$11$$ 421.598 1.05055 0.525275 0.850933i $$-0.323963\pi$$
0.525275 + 0.850933i $$0.323963\pi$$
$$12$$ 0 0
$$13$$ 254.502 0.417670 0.208835 0.977951i $$-0.433033\pi$$
0.208835 + 0.977951i $$0.433033\pi$$
$$14$$ 2.55055 0.00347788
$$15$$ 0 0
$$16$$ 3344.00 3.26562
$$17$$ 975.007 0.818249 0.409125 0.912479i $$-0.365834\pi$$
0.409125 + 0.912479i $$0.365834\pi$$
$$18$$ 0 0
$$19$$ 2039.79 1.29629 0.648143 0.761519i $$-0.275546\pi$$
0.648143 + 0.761519i $$0.275546\pi$$
$$20$$ −3495.65 −1.95413
$$21$$ 0 0
$$22$$ 4540.75 2.00019
$$23$$ −529.000 −0.208514
$$24$$ 0 0
$$25$$ −1393.21 −0.445826
$$26$$ 2741.07 0.795220
$$27$$ 0 0
$$28$$ 19.8923 0.00479501
$$29$$ −2671.55 −0.589885 −0.294943 0.955515i $$-0.595301\pi$$
−0.294943 + 0.955515i $$0.595301\pi$$
$$30$$ 0 0
$$31$$ 9039.14 1.68936 0.844681 0.535270i $$-0.179790\pi$$
0.844681 + 0.535270i $$0.179790\pi$$
$$32$$ 18094.2 3.12366
$$33$$ 0 0
$$34$$ 10501.1 1.55790
$$35$$ −9.85493 −0.00135983
$$36$$ 0 0
$$37$$ −12665.3 −1.52094 −0.760471 0.649372i $$-0.775032\pi$$
−0.760471 + 0.649372i $$0.775032\pi$$
$$38$$ 21969.2 2.46805
$$39$$ 0 0
$$40$$ −23306.7 −2.30319
$$41$$ −10146.4 −0.942658 −0.471329 0.881957i $$-0.656226\pi$$
−0.471329 + 0.881957i $$0.656226\pi$$
$$42$$ 0 0
$$43$$ 19523.2 1.61020 0.805102 0.593137i $$-0.202111\pi$$
0.805102 + 0.593137i $$0.202111\pi$$
$$44$$ 35414.2 2.75769
$$45$$ 0 0
$$46$$ −5697.50 −0.397000
$$47$$ −27679.7 −1.82775 −0.913875 0.405995i $$-0.866925\pi$$
−0.913875 + 0.405995i $$0.866925\pi$$
$$48$$ 0 0
$$49$$ −16806.9 −0.999997
$$50$$ −15005.3 −0.848827
$$51$$ 0 0
$$52$$ 21378.2 1.09638
$$53$$ −10852.8 −0.530703 −0.265351 0.964152i $$-0.585488\pi$$
−0.265351 + 0.964152i $$0.585488\pi$$
$$54$$ 0 0
$$55$$ −17544.7 −0.782059
$$56$$ 132.629 0.00565155
$$57$$ 0 0
$$58$$ −28773.4 −1.12311
$$59$$ −11907.7 −0.445345 −0.222672 0.974893i $$-0.571478\pi$$
−0.222672 + 0.974893i $$0.571478\pi$$
$$60$$ 0 0
$$61$$ 39861.9 1.37162 0.685809 0.727782i $$-0.259449\pi$$
0.685809 + 0.727782i $$0.259449\pi$$
$$62$$ 97354.5 3.21645
$$63$$ 0 0
$$64$$ 87872.0 2.68164
$$65$$ −10591.1 −0.310925
$$66$$ 0 0
$$67$$ −28550.5 −0.777009 −0.388504 0.921447i $$-0.627008\pi$$
−0.388504 + 0.921447i $$0.627008\pi$$
$$68$$ 81900.6 2.14790
$$69$$ 0 0
$$70$$ −106.141 −0.00258903
$$71$$ −52179.8 −1.22845 −0.614223 0.789132i $$-0.710531\pi$$
−0.614223 + 0.789132i $$0.710531\pi$$
$$72$$ 0 0
$$73$$ 56918.0 1.25009 0.625047 0.780587i $$-0.285080\pi$$
0.625047 + 0.780587i $$0.285080\pi$$
$$74$$ −136410. −2.89579
$$75$$ 0 0
$$76$$ 171342. 3.40275
$$77$$ 99.8398 0.00191901
$$78$$ 0 0
$$79$$ 23178.3 0.417844 0.208922 0.977932i $$-0.433004\pi$$
0.208922 + 0.977932i $$0.433004\pi$$
$$80$$ −139160. −2.43103
$$81$$ 0 0
$$82$$ −109281. −1.79477
$$83$$ 18344.6 0.292289 0.146144 0.989263i $$-0.453314\pi$$
0.146144 + 0.989263i $$0.453314\pi$$
$$84$$ 0 0
$$85$$ −40574.8 −0.609128
$$86$$ 210272. 3.06574
$$87$$ 0 0
$$88$$ 236119. 3.25030
$$89$$ −47362.4 −0.633810 −0.316905 0.948457i $$-0.602644\pi$$
−0.316905 + 0.948457i $$0.602644\pi$$
$$90$$ 0 0
$$91$$ 60.2694 0.000762945 0
$$92$$ −44436.0 −0.547350
$$93$$ 0 0
$$94$$ −298120. −3.47993
$$95$$ −84885.4 −0.964992
$$96$$ 0 0
$$97$$ −140379. −1.51486 −0.757432 0.652915i $$-0.773546\pi$$
−0.757432 + 0.652915i $$0.773546\pi$$
$$98$$ −181016. −1.90394
$$99$$ 0 0
$$100$$ −117029. −1.17029
$$101$$ −87080.3 −0.849408 −0.424704 0.905332i $$-0.639622\pi$$
−0.424704 + 0.905332i $$0.639622\pi$$
$$102$$ 0 0
$$103$$ 17988.9 0.167075 0.0835375 0.996505i $$-0.473378\pi$$
0.0835375 + 0.996505i $$0.473378\pi$$
$$104$$ 142536. 1.29223
$$105$$ 0 0
$$106$$ −116888. −1.01043
$$107$$ 127485. 1.07646 0.538231 0.842797i $$-0.319093\pi$$
0.538231 + 0.842797i $$0.319093\pi$$
$$108$$ 0 0
$$109$$ −136418. −1.09978 −0.549890 0.835237i $$-0.685330\pi$$
−0.549890 + 0.835237i $$0.685330\pi$$
$$110$$ −188962. −1.48900
$$111$$ 0 0
$$112$$ 791.902 0.00596522
$$113$$ 104012. 0.766279 0.383139 0.923691i $$-0.374843\pi$$
0.383139 + 0.923691i $$0.374843\pi$$
$$114$$ 0 0
$$115$$ 22014.2 0.155224
$$116$$ −224410. −1.54845
$$117$$ 0 0
$$118$$ −128249. −0.847912
$$119$$ 230.894 0.00149467
$$120$$ 0 0
$$121$$ 16693.7 0.103655
$$122$$ 429325. 2.61148
$$123$$ 0 0
$$124$$ 759288. 4.43458
$$125$$ 188024. 1.07631
$$126$$ 0 0
$$127$$ 203763. 1.12103 0.560513 0.828145i $$-0.310604\pi$$
0.560513 + 0.828145i $$0.310604\pi$$
$$128$$ 367397. 1.98203
$$129$$ 0 0
$$130$$ −114069. −0.591984
$$131$$ −60674.1 −0.308905 −0.154453 0.988000i $$-0.549361\pi$$
−0.154453 + 0.988000i $$0.549361\pi$$
$$132$$ 0 0
$$133$$ 483.048 0.00236789
$$134$$ −307498. −1.47938
$$135$$ 0 0
$$136$$ 546060. 2.53159
$$137$$ −94446.5 −0.429917 −0.214958 0.976623i $$-0.568962\pi$$
−0.214958 + 0.976623i $$0.568962\pi$$
$$138$$ 0 0
$$139$$ 403508. 1.77139 0.885697 0.464263i $$-0.153681\pi$$
0.885697 + 0.464263i $$0.153681\pi$$
$$140$$ −827.814 −0.00356954
$$141$$ 0 0
$$142$$ −561993. −2.33889
$$143$$ 107298. 0.438783
$$144$$ 0 0
$$145$$ 111176. 0.439128
$$146$$ 613026. 2.38011
$$147$$ 0 0
$$148$$ −1.06389e6 −3.99247
$$149$$ −384528. −1.41893 −0.709467 0.704738i $$-0.751064\pi$$
−0.709467 + 0.704738i $$0.751064\pi$$
$$150$$ 0 0
$$151$$ −442508. −1.57935 −0.789675 0.613525i $$-0.789751\pi$$
−0.789675 + 0.613525i $$0.789751\pi$$
$$152$$ 1.14240e6 4.01059
$$153$$ 0 0
$$154$$ 1075.31 0.00365368
$$155$$ −376162. −1.25761
$$156$$ 0 0
$$157$$ 240724. 0.779416 0.389708 0.920938i $$-0.372576\pi$$
0.389708 + 0.920938i $$0.372576\pi$$
$$158$$ 249638. 0.795552
$$159$$ 0 0
$$160$$ −752985. −2.32534
$$161$$ −125.274 −0.000380887 0
$$162$$ 0 0
$$163$$ −178188. −0.525301 −0.262651 0.964891i $$-0.584597\pi$$
−0.262651 + 0.964891i $$0.584597\pi$$
$$164$$ −852301. −2.47448
$$165$$ 0 0
$$166$$ 197577. 0.556502
$$167$$ −25525.2 −0.0708236 −0.0354118 0.999373i $$-0.511274\pi$$
−0.0354118 + 0.999373i $$0.511274\pi$$
$$168$$ 0 0
$$169$$ −306522. −0.825552
$$170$$ −437004. −1.15975
$$171$$ 0 0
$$172$$ 1.63995e6 4.22678
$$173$$ −701865. −1.78295 −0.891474 0.453072i $$-0.850328\pi$$
−0.891474 + 0.453072i $$0.850328\pi$$
$$174$$ 0 0
$$175$$ −329.929 −0.000814377 0
$$176$$ 1.40982e6 3.43070
$$177$$ 0 0
$$178$$ −510109. −1.20674
$$179$$ 292917. 0.683302 0.341651 0.939827i $$-0.389014\pi$$
0.341651 + 0.939827i $$0.389014\pi$$
$$180$$ 0 0
$$181$$ −38932.7 −0.0883321 −0.0441660 0.999024i $$-0.514063\pi$$
−0.0441660 + 0.999024i $$0.514063\pi$$
$$182$$ 649.121 0.00145260
$$183$$ 0 0
$$184$$ −296270. −0.645124
$$185$$ 527066. 1.13223
$$186$$ 0 0
$$187$$ 411061. 0.859611
$$188$$ −2.32510e6 −4.79784
$$189$$ 0 0
$$190$$ −914243. −1.83729
$$191$$ −37244.8 −0.0738724 −0.0369362 0.999318i $$-0.511760\pi$$
−0.0369362 + 0.999318i $$0.511760\pi$$
$$192$$ 0 0
$$193$$ −42454.3 −0.0820406 −0.0410203 0.999158i $$-0.513061\pi$$
−0.0410203 + 0.999158i $$0.513061\pi$$
$$194$$ −1.51193e6 −2.88421
$$195$$ 0 0
$$196$$ −1.41178e6 −2.62499
$$197$$ −87335.1 −0.160333 −0.0801666 0.996781i $$-0.525545\pi$$
−0.0801666 + 0.996781i $$0.525545\pi$$
$$198$$ 0 0
$$199$$ 1.08779e6 1.94721 0.973604 0.228245i $$-0.0732989\pi$$
0.973604 + 0.228245i $$0.0732989\pi$$
$$200$$ −780275. −1.37934
$$201$$ 0 0
$$202$$ −937883. −1.61722
$$203$$ −632.657 −0.00107753
$$204$$ 0 0
$$205$$ 422243. 0.701742
$$206$$ 193746. 0.318101
$$207$$ 0 0
$$208$$ 851055. 1.36395
$$209$$ 859969. 1.36181
$$210$$ 0 0
$$211$$ −1.02777e6 −1.58923 −0.794617 0.607111i $$-0.792328\pi$$
−0.794617 + 0.607111i $$0.792328\pi$$
$$212$$ −911634. −1.39310
$$213$$ 0 0
$$214$$ 1.37305e6 2.04952
$$215$$ −812456. −1.19868
$$216$$ 0 0
$$217$$ 2140.58 0.00308591
$$218$$ −1.46927e6 −2.09392
$$219$$ 0 0
$$220$$ −1.47376e6 −2.05291
$$221$$ 248141. 0.341758
$$222$$ 0 0
$$223$$ −209627. −0.282284 −0.141142 0.989989i $$-0.545077\pi$$
−0.141142 + 0.989989i $$0.545077\pi$$
$$224$$ 4284.93 0.00570589
$$225$$ 0 0
$$226$$ 1.12024e6 1.45895
$$227$$ 347103. 0.447088 0.223544 0.974694i $$-0.428237\pi$$
0.223544 + 0.974694i $$0.428237\pi$$
$$228$$ 0 0
$$229$$ −474094. −0.597414 −0.298707 0.954345i $$-0.596555\pi$$
−0.298707 + 0.954345i $$0.596555\pi$$
$$230$$ 237101. 0.295538
$$231$$ 0 0
$$232$$ −1.49622e6 −1.82505
$$233$$ −67426.2 −0.0813652 −0.0406826 0.999172i $$-0.512953\pi$$
−0.0406826 + 0.999172i $$0.512953\pi$$
$$234$$ 0 0
$$235$$ 1.15189e6 1.36063
$$236$$ −1.00024e6 −1.16903
$$237$$ 0 0
$$238$$ 2486.81 0.00284577
$$239$$ 631686. 0.715331 0.357665 0.933850i $$-0.383573\pi$$
0.357665 + 0.933850i $$0.383573\pi$$
$$240$$ 0 0
$$241$$ −582036. −0.645516 −0.322758 0.946482i $$-0.604610\pi$$
−0.322758 + 0.946482i $$0.604610\pi$$
$$242$$ 179797. 0.197353
$$243$$ 0 0
$$244$$ 3.34840e6 3.60050
$$245$$ 699418. 0.744426
$$246$$ 0 0
$$247$$ 519130. 0.541419
$$248$$ 5.06243e6 5.22673
$$249$$ 0 0
$$250$$ 2.02508e6 2.04924
$$251$$ 1.28835e6 1.29077 0.645386 0.763856i $$-0.276696\pi$$
0.645386 + 0.763856i $$0.276696\pi$$
$$252$$ 0 0
$$253$$ −223025. −0.219055
$$254$$ 2.19459e6 2.13437
$$255$$ 0 0
$$256$$ 1.14509e6 1.09204
$$257$$ 204908. 0.193520 0.0967601 0.995308i $$-0.469152\pi$$
0.0967601 + 0.995308i $$0.469152\pi$$
$$258$$ 0 0
$$259$$ −2999.32 −0.00277826
$$260$$ −889650. −0.816179
$$261$$ 0 0
$$262$$ −653480. −0.588138
$$263$$ −418862. −0.373407 −0.186703 0.982416i $$-0.559780\pi$$
−0.186703 + 0.982416i $$0.559780\pi$$
$$264$$ 0 0
$$265$$ 451637. 0.395071
$$266$$ 5202.58 0.00450832
$$267$$ 0 0
$$268$$ −2.39824e6 −2.03965
$$269$$ 1.48662e6 1.25262 0.626308 0.779576i $$-0.284565\pi$$
0.626308 + 0.779576i $$0.284565\pi$$
$$270$$ 0 0
$$271$$ −658640. −0.544785 −0.272392 0.962186i $$-0.587815\pi$$
−0.272392 + 0.962186i $$0.587815\pi$$
$$272$$ 3.26042e6 2.67209
$$273$$ 0 0
$$274$$ −1.01722e6 −0.818537
$$275$$ −587372. −0.468362
$$276$$ 0 0
$$277$$ 236526. 0.185216 0.0926082 0.995703i $$-0.470480\pi$$
0.0926082 + 0.995703i $$0.470480\pi$$
$$278$$ 4.34592e6 3.37263
$$279$$ 0 0
$$280$$ −5519.32 −0.00420718
$$281$$ 1.66253e6 1.25604 0.628020 0.778197i $$-0.283866\pi$$
0.628020 + 0.778197i $$0.283866\pi$$
$$282$$ 0 0
$$283$$ 966812. 0.717589 0.358795 0.933417i $$-0.383188\pi$$
0.358795 + 0.933417i $$0.383188\pi$$
$$284$$ −4.38310e6 −3.22467
$$285$$ 0 0
$$286$$ 1.15563e6 0.835418
$$287$$ −2402.81 −0.00172193
$$288$$ 0 0
$$289$$ −469218. −0.330469
$$290$$ 1.19740e6 0.836074
$$291$$ 0 0
$$292$$ 4.78111e6 3.28150
$$293$$ 82436.0 0.0560981 0.0280490 0.999607i $$-0.491071\pi$$
0.0280490 + 0.999607i $$0.491071\pi$$
$$294$$ 0 0
$$295$$ 495535. 0.331528
$$296$$ −7.09332e6 −4.70565
$$297$$ 0 0
$$298$$ −4.14149e6 −2.70157
$$299$$ −134632. −0.0870902
$$300$$ 0 0
$$301$$ 4623.35 0.00294131
$$302$$ −4.76595e6 −3.00699
$$303$$ 0 0
$$304$$ 6.82105e6 4.23318
$$305$$ −1.65884e6 −1.02107
$$306$$ 0 0
$$307$$ 471104. 0.285280 0.142640 0.989775i $$-0.454441\pi$$
0.142640 + 0.989775i $$0.454441\pi$$
$$308$$ 8386.54 0.00503740
$$309$$ 0 0
$$310$$ −4.05139e6 −2.39442
$$311$$ −974141. −0.571112 −0.285556 0.958362i $$-0.592178\pi$$
−0.285556 + 0.958362i $$0.592178\pi$$
$$312$$ 0 0
$$313$$ 203897. 0.117639 0.0588194 0.998269i $$-0.481266\pi$$
0.0588194 + 0.998269i $$0.481266\pi$$
$$314$$ 2.59267e6 1.48396
$$315$$ 0 0
$$316$$ 1.94698e6 1.09684
$$317$$ 1.11600e6 0.623757 0.311879 0.950122i $$-0.399042\pi$$
0.311879 + 0.950122i $$0.399042\pi$$
$$318$$ 0 0
$$319$$ −1.12632e6 −0.619704
$$320$$ −3.65678e6 −1.99629
$$321$$ 0 0
$$322$$ −1349.24 −0.000725187 0
$$323$$ 1.98881e6 1.06068
$$324$$ 0 0
$$325$$ −354574. −0.186208
$$326$$ −1.91914e6 −1.00014
$$327$$ 0 0
$$328$$ −5.68259e6 −2.91650
$$329$$ −6554.91 −0.00333870
$$330$$ 0 0
$$331$$ 2.08998e6 1.04851 0.524254 0.851562i $$-0.324344\pi$$
0.524254 + 0.851562i $$0.324344\pi$$
$$332$$ 1.54094e6 0.767258
$$333$$ 0 0
$$334$$ −274915. −0.134844
$$335$$ 1.18812e6 0.578428
$$336$$ 0 0
$$337$$ 901699. 0.432501 0.216250 0.976338i $$-0.430617\pi$$
0.216250 + 0.976338i $$0.430617\pi$$
$$338$$ −3.30134e6 −1.57180
$$339$$ 0 0
$$340$$ −3.40828e6 −1.59896
$$341$$ 3.81088e6 1.77476
$$342$$ 0 0
$$343$$ −7960.21 −0.00365333
$$344$$ 1.09341e7 4.98182
$$345$$ 0 0
$$346$$ −7.55932e6 −3.39463
$$347$$ 1.53207e6 0.683053 0.341526 0.939872i $$-0.389056\pi$$
0.341526 + 0.939872i $$0.389056\pi$$
$$348$$ 0 0
$$349$$ 1.28353e6 0.564084 0.282042 0.959402i $$-0.408988\pi$$
0.282042 + 0.959402i $$0.408988\pi$$
$$350$$ −3553.44 −0.00155053
$$351$$ 0 0
$$352$$ 7.62846e6 3.28156
$$353$$ 4.45978e6 1.90492 0.952460 0.304663i $$-0.0985440\pi$$
0.952460 + 0.304663i $$0.0985440\pi$$
$$354$$ 0 0
$$355$$ 2.17145e6 0.914491
$$356$$ −3.97844e6 −1.66375
$$357$$ 0 0
$$358$$ 3.15482e6 1.30097
$$359$$ −4.67506e6 −1.91448 −0.957240 0.289296i $$-0.906579\pi$$
−0.957240 + 0.289296i $$0.906579\pi$$
$$360$$ 0 0
$$361$$ 1.68463e6 0.680356
$$362$$ −419318. −0.168179
$$363$$ 0 0
$$364$$ 5062.63 0.00200273
$$365$$ −2.36863e6 −0.930606
$$366$$ 0 0
$$367$$ 2.43229e6 0.942650 0.471325 0.881960i $$-0.343776\pi$$
0.471325 + 0.881960i $$0.343776\pi$$
$$368$$ −1.76898e6 −0.680930
$$369$$ 0 0
$$370$$ 5.67668e6 2.15571
$$371$$ −2570.08 −0.000969419 0
$$372$$ 0 0
$$373$$ 1.37458e6 0.511561 0.255780 0.966735i $$-0.417668\pi$$
0.255780 + 0.966735i $$0.417668\pi$$
$$374$$ 4.42726e6 1.63665
$$375$$ 0 0
$$376$$ −1.55022e7 −5.65489
$$377$$ −679914. −0.246377
$$378$$ 0 0
$$379$$ 2.01997e6 0.722350 0.361175 0.932498i $$-0.382376\pi$$
0.361175 + 0.932498i $$0.382376\pi$$
$$380$$ −7.13037e6 −2.53310
$$381$$ 0 0
$$382$$ −401139. −0.140649
$$383$$ −2.00834e6 −0.699584 −0.349792 0.936827i $$-0.613748\pi$$
−0.349792 + 0.936827i $$0.613748\pi$$
$$384$$ 0 0
$$385$$ −4154.82 −0.00142857
$$386$$ −457247. −0.156201
$$387$$ 0 0
$$388$$ −1.17919e7 −3.97652
$$389$$ −3.25055e6 −1.08914 −0.544569 0.838716i $$-0.683307\pi$$
−0.544569 + 0.838716i $$0.683307\pi$$
$$390$$ 0 0
$$391$$ −515779. −0.170617
$$392$$ −9.41285e6 −3.09390
$$393$$ 0 0
$$394$$ −940628. −0.305265
$$395$$ −964563. −0.311055
$$396$$ 0 0
$$397$$ 5.43707e6 1.73137 0.865683 0.500592i $$-0.166884\pi$$
0.865683 + 0.500592i $$0.166884\pi$$
$$398$$ 1.17159e7 3.70737
$$399$$ 0 0
$$400$$ −4.65888e6 −1.45590
$$401$$ −3.27208e6 −1.01616 −0.508081 0.861309i $$-0.669645\pi$$
−0.508081 + 0.861309i $$0.669645\pi$$
$$402$$ 0 0
$$403$$ 2.30048e6 0.705596
$$404$$ −7.31474e6 −2.22970
$$405$$ 0 0
$$406$$ −6813.92 −0.00205155
$$407$$ −5.33968e6 −1.59783
$$408$$ 0 0
$$409$$ −1.56299e6 −0.462007 −0.231003 0.972953i $$-0.574201\pi$$
−0.231003 + 0.972953i $$0.574201\pi$$
$$410$$ 4.54769e6 1.33608
$$411$$ 0 0
$$412$$ 1.51107e6 0.438572
$$413$$ −2819.89 −0.000813498 0
$$414$$ 0 0
$$415$$ −763406. −0.217588
$$416$$ 4.60500e6 1.30466
$$417$$ 0 0
$$418$$ 9.26215e6 2.59281
$$419$$ 4.76111e6 1.32487 0.662434 0.749120i $$-0.269523\pi$$
0.662434 + 0.749120i $$0.269523\pi$$
$$420$$ 0 0
$$421$$ −4.56989e6 −1.25661 −0.628305 0.777967i $$-0.716251\pi$$
−0.628305 + 0.777967i $$0.716251\pi$$
$$422$$ −1.10694e7 −3.02581
$$423$$ 0 0
$$424$$ −6.07818e6 −1.64195
$$425$$ −1.35839e6 −0.364796
$$426$$ 0 0
$$427$$ 9439.80 0.00250549
$$428$$ 1.07087e7 2.82571
$$429$$ 0 0
$$430$$ −8.75042e6 −2.28222
$$431$$ 3.28891e6 0.852824 0.426412 0.904529i $$-0.359777\pi$$
0.426412 + 0.904529i $$0.359777\pi$$
$$432$$ 0 0
$$433$$ 2.11805e6 0.542895 0.271447 0.962453i $$-0.412498\pi$$
0.271447 + 0.962453i $$0.412498\pi$$
$$434$$ 23054.8 0.00587540
$$435$$ 0 0
$$436$$ −1.14591e7 −2.88692
$$437$$ −1.07905e6 −0.270294
$$438$$ 0 0
$$439$$ 758443. 0.187829 0.0939143 0.995580i $$-0.470062\pi$$
0.0939143 + 0.995580i $$0.470062\pi$$
$$440$$ −9.82605e6 −2.41962
$$441$$ 0 0
$$442$$ 2.67257e6 0.650688
$$443$$ −650377. −0.157455 −0.0787274 0.996896i $$-0.525086\pi$$
−0.0787274 + 0.996896i $$0.525086\pi$$
$$444$$ 0 0
$$445$$ 1.97098e6 0.471826
$$446$$ −2.25776e6 −0.537452
$$447$$ 0 0
$$448$$ 20809.2 0.00489847
$$449$$ 7.58111e6 1.77467 0.887333 0.461129i $$-0.152555\pi$$
0.887333 + 0.461129i $$0.152555\pi$$
$$450$$ 0 0
$$451$$ −4.27772e6 −0.990309
$$452$$ 8.73699e6 2.01148
$$453$$ 0 0
$$454$$ 3.73841e6 0.851231
$$455$$ −2508.10 −0.000567958 0
$$456$$ 0 0
$$457$$ −8.04537e6 −1.80200 −0.901002 0.433815i $$-0.857167\pi$$
−0.901002 + 0.433815i $$0.857167\pi$$
$$458$$ −5.10614e6 −1.13744
$$459$$ 0 0
$$460$$ 1.84920e6 0.407463
$$461$$ −5.63578e6 −1.23510 −0.617550 0.786532i $$-0.711875\pi$$
−0.617550 + 0.786532i $$0.711875\pi$$
$$462$$ 0 0
$$463$$ 1.39156e6 0.301682 0.150841 0.988558i $$-0.451802\pi$$
0.150841 + 0.988558i $$0.451802\pi$$
$$464$$ −8.93365e6 −1.92634
$$465$$ 0 0
$$466$$ −726202. −0.154915
$$467$$ −4.05063e6 −0.859469 −0.429734 0.902955i $$-0.641393\pi$$
−0.429734 + 0.902955i $$0.641393\pi$$
$$468$$ 0 0
$$469$$ −6761.12 −0.00141934
$$470$$ 1.24062e7 2.59056
$$471$$ 0 0
$$472$$ −6.66897e6 −1.37786
$$473$$ 8.23095e6 1.69160
$$474$$ 0 0
$$475$$ −2.84184e6 −0.577917
$$476$$ 19395.1 0.00392351
$$477$$ 0 0
$$478$$ 6.80347e6 1.36195
$$479$$ −6.55529e6 −1.30543 −0.652714 0.757605i $$-0.726370\pi$$
−0.652714 + 0.757605i $$0.726370\pi$$
$$480$$ 0 0
$$481$$ −3.22336e6 −0.635252
$$482$$ −6.26872e6 −1.22903
$$483$$ 0 0
$$484$$ 1.40227e6 0.272094
$$485$$ 5.84186e6 1.12771
$$486$$ 0 0
$$487$$ −1.98924e6 −0.380071 −0.190035 0.981777i $$-0.560860\pi$$
−0.190035 + 0.981777i $$0.560860\pi$$
$$488$$ 2.23249e7 4.24366
$$489$$ 0 0
$$490$$ 7.53296e6 1.41735
$$491$$ −7.99205e6 −1.49608 −0.748040 0.663654i $$-0.769005\pi$$
−0.748040 + 0.663654i $$0.769005\pi$$
$$492$$ 0 0
$$493$$ −2.60478e6 −0.482673
$$494$$ 5.59120e6 1.03083
$$495$$ 0 0
$$496$$ 3.02269e7 5.51682
$$497$$ −12356.8 −0.00224397
$$498$$ 0 0
$$499$$ −1.00308e7 −1.80338 −0.901688 0.432387i $$-0.857671\pi$$
−0.901688 + 0.432387i $$0.857671\pi$$
$$500$$ 1.57940e7 2.82533
$$501$$ 0 0
$$502$$ 1.38760e7 2.45756
$$503$$ 4.82601e6 0.850488 0.425244 0.905079i $$-0.360188\pi$$
0.425244 + 0.905079i $$0.360188\pi$$
$$504$$ 0 0
$$505$$ 3.62383e6 0.632324
$$506$$ −2.40206e6 −0.417068
$$507$$ 0 0
$$508$$ 1.71161e7 2.94270
$$509$$ −138289. −0.0236589 −0.0118294 0.999930i $$-0.503766\pi$$
−0.0118294 + 0.999930i $$0.503766\pi$$
$$510$$ 0 0
$$511$$ 13478.9 0.00228351
$$512$$ 576256. 0.0971494
$$513$$ 0 0
$$514$$ 2.20693e6 0.368451
$$515$$ −748605. −0.124375
$$516$$ 0 0
$$517$$ −1.16697e7 −1.92014
$$518$$ −32303.6 −0.00528965
$$519$$ 0 0
$$520$$ −5.93160e6 −0.961975
$$521$$ −4.62831e6 −0.747012 −0.373506 0.927628i $$-0.621845\pi$$
−0.373506 + 0.927628i $$0.621845\pi$$
$$522$$ 0 0
$$523$$ −1.54914e6 −0.247649 −0.123825 0.992304i $$-0.539516\pi$$
−0.123825 + 0.992304i $$0.539516\pi$$
$$524$$ −5.09662e6 −0.810876
$$525$$ 0 0
$$526$$ −4.51129e6 −0.710945
$$527$$ 8.81323e6 1.38232
$$528$$ 0 0
$$529$$ 279841. 0.0434783
$$530$$ 4.86428e6 0.752192
$$531$$ 0 0
$$532$$ 40576.0 0.00621570
$$533$$ −2.58229e6 −0.393720
$$534$$ 0 0
$$535$$ −5.30526e6 −0.801349
$$536$$ −1.59899e7 −2.40399
$$537$$ 0 0
$$538$$ 1.60113e7 2.38491
$$539$$ −7.08577e6 −1.05055
$$540$$ 0 0
$$541$$ −6.52702e6 −0.958787 −0.479393 0.877600i $$-0.659143\pi$$
−0.479393 + 0.877600i $$0.659143\pi$$
$$542$$ −7.09377e6 −1.03724
$$543$$ 0 0
$$544$$ 1.76419e7 2.55593
$$545$$ 5.67701e6 0.818707
$$546$$ 0 0
$$547$$ 1.06849e7 1.52686 0.763432 0.645888i $$-0.223513\pi$$
0.763432 + 0.645888i $$0.223513\pi$$
$$548$$ −7.93351e6 −1.12853
$$549$$ 0 0
$$550$$ −6.32619e6 −0.891735
$$551$$ −5.44938e6 −0.764660
$$552$$ 0 0
$$553$$ 5488.93 0.000763264 0
$$554$$ 2.54746e6 0.352642
$$555$$ 0 0
$$556$$ 3.38947e7 4.64991
$$557$$ 3.07804e6 0.420374 0.210187 0.977661i $$-0.432593\pi$$
0.210187 + 0.977661i $$0.432593\pi$$
$$558$$ 0 0
$$559$$ 4.96871e6 0.672533
$$560$$ −32954.9 −0.00444068
$$561$$ 0 0
$$562$$ 1.79060e7 2.39143
$$563$$ −1.10366e7 −1.46745 −0.733724 0.679448i $$-0.762219\pi$$
−0.733724 + 0.679448i $$0.762219\pi$$
$$564$$ 0 0
$$565$$ −4.32844e6 −0.570440
$$566$$ 1.04129e7 1.36625
$$567$$ 0 0
$$568$$ −2.92237e7 −3.80070
$$569$$ 9.26308e6 1.19943 0.599715 0.800214i $$-0.295281\pi$$
0.599715 + 0.800214i $$0.295281\pi$$
$$570$$ 0 0
$$571$$ −1.31913e7 −1.69315 −0.846576 0.532267i $$-0.821340\pi$$
−0.846576 + 0.532267i $$0.821340\pi$$
$$572$$ 9.01300e6 1.15181
$$573$$ 0 0
$$574$$ −25879.0 −0.00327845
$$575$$ 737006. 0.0929611
$$576$$ 0 0
$$577$$ −1.29741e6 −0.162232 −0.0811160 0.996705i $$-0.525848\pi$$
−0.0811160 + 0.996705i $$0.525848\pi$$
$$578$$ −5.05363e6 −0.629193
$$579$$ 0 0
$$580$$ 9.33878e6 1.15271
$$581$$ 4344.23 0.000533916 0
$$582$$ 0 0
$$583$$ −4.57551e6 −0.557530
$$584$$ 3.18773e7 3.86767
$$585$$ 0 0
$$586$$ 887863. 0.106808
$$587$$ −4.51203e6 −0.540477 −0.270238 0.962793i $$-0.587103\pi$$
−0.270238 + 0.962793i $$0.587103\pi$$
$$588$$ 0 0
$$589$$ 1.84379e7 2.18990
$$590$$ 5.33708e6 0.631210
$$591$$ 0 0
$$592$$ −4.23529e7 −4.96683
$$593$$ −9.27288e6 −1.08287 −0.541437 0.840741i $$-0.682120\pi$$
−0.541437 + 0.840741i $$0.682120\pi$$
$$594$$ 0 0
$$595$$ −9608.63 −0.00111268
$$596$$ −3.23004e7 −3.72470
$$597$$ 0 0
$$598$$ −1.45003e6 −0.165815
$$599$$ 6.32225e6 0.719954 0.359977 0.932961i $$-0.382785\pi$$
0.359977 + 0.932961i $$0.382785\pi$$
$$600$$ 0 0
$$601$$ 3.18785e6 0.360008 0.180004 0.983666i $$-0.442389\pi$$
0.180004 + 0.983666i $$0.442389\pi$$
$$602$$ 49795.0 0.00560009
$$603$$ 0 0
$$604$$ −3.71706e7 −4.14579
$$605$$ −694706. −0.0771636
$$606$$ 0 0
$$607$$ −5.70410e6 −0.628369 −0.314185 0.949362i $$-0.601731\pi$$
−0.314185 + 0.949362i $$0.601731\pi$$
$$608$$ 3.69082e7 4.04915
$$609$$ 0 0
$$610$$ −1.78663e7 −1.94406
$$611$$ −7.04455e6 −0.763396
$$612$$ 0 0
$$613$$ 1.17835e7 1.26655 0.633276 0.773926i $$-0.281710\pi$$
0.633276 + 0.773926i $$0.281710\pi$$
$$614$$ 5.07394e6 0.543156
$$615$$ 0 0
$$616$$ 55916.0 0.00593723
$$617$$ −1.41628e6 −0.149774 −0.0748868 0.997192i $$-0.523860\pi$$
−0.0748868 + 0.997192i $$0.523860\pi$$
$$618$$ 0 0
$$619$$ −4.37752e6 −0.459200 −0.229600 0.973285i $$-0.573742\pi$$
−0.229600 + 0.973285i $$0.573742\pi$$
$$620$$ −3.15976e7 −3.30123
$$621$$ 0 0
$$622$$ −1.04918e7 −1.08736
$$623$$ −11216.0 −0.00115776
$$624$$ 0 0
$$625$$ −3.47084e6 −0.355414
$$626$$ 2.19604e6 0.223978
$$627$$ 0 0
$$628$$ 2.02208e7 2.04597
$$629$$ −1.23488e7 −1.24451
$$630$$ 0 0
$$631$$ −1.61975e7 −1.61948 −0.809739 0.586790i $$-0.800391\pi$$
−0.809739 + 0.586790i $$0.800391\pi$$
$$632$$ 1.29812e7 1.29277
$$633$$ 0 0
$$634$$ 1.20197e7 1.18760
$$635$$ −8.47956e6 −0.834525
$$636$$ 0 0
$$637$$ −4.27740e6 −0.417668
$$638$$ −1.21308e7 −1.17988
$$639$$ 0 0
$$640$$ −1.52892e7 −1.47548
$$641$$ 1.56439e7 1.50383 0.751915 0.659260i $$-0.229130\pi$$
0.751915 + 0.659260i $$0.229130\pi$$
$$642$$ 0 0
$$643$$ −1.57570e7 −1.50295 −0.751476 0.659760i $$-0.770658\pi$$
−0.751476 + 0.659760i $$0.770658\pi$$
$$644$$ −10523.0 −0.000999829 0
$$645$$ 0 0
$$646$$ 2.14201e7 2.01948
$$647$$ 660291. 0.0620119 0.0310059 0.999519i $$-0.490129\pi$$
0.0310059 + 0.999519i $$0.490129\pi$$
$$648$$ 0 0
$$649$$ −5.02024e6 −0.467857
$$650$$ −3.81888e6 −0.354529
$$651$$ 0 0
$$652$$ −1.49678e7 −1.37892
$$653$$ −1.24310e7 −1.14084 −0.570419 0.821354i $$-0.693219\pi$$
−0.570419 + 0.821354i $$0.693219\pi$$
$$654$$ 0 0
$$655$$ 2.52494e6 0.229958
$$656$$ −3.39297e7 −3.07837
$$657$$ 0 0
$$658$$ −70598.6 −0.00635669
$$659$$ 13723.9 0.00123101 0.000615507 1.00000i $$-0.499804\pi$$
0.000615507 1.00000i $$0.499804\pi$$
$$660$$ 0 0
$$661$$ 6.54194e6 0.582375 0.291187 0.956666i $$-0.405950\pi$$
0.291187 + 0.956666i $$0.405950\pi$$
$$662$$ 2.25098e7 1.99630
$$663$$ 0 0
$$664$$ 1.02740e7 0.904315
$$665$$ −20101.9 −0.00176272
$$666$$ 0 0
$$667$$ 1.41325e6 0.123000
$$668$$ −2.14412e6 −0.185912
$$669$$ 0 0
$$670$$ 1.27965e7 1.10129
$$671$$ 1.68057e7 1.44095
$$672$$ 0 0
$$673$$ 1.54266e7 1.31290 0.656451 0.754369i $$-0.272057\pi$$
0.656451 + 0.754369i $$0.272057\pi$$
$$674$$ 9.71159e6 0.823456
$$675$$ 0 0
$$676$$ −2.57478e7 −2.16707
$$677$$ −5.30462e6 −0.444818 −0.222409 0.974953i $$-0.571392\pi$$
−0.222409 + 0.974953i $$0.571392\pi$$
$$678$$ 0 0
$$679$$ −33243.6 −0.00276716
$$680$$ −2.27242e7 −1.88459
$$681$$ 0 0
$$682$$ 4.10444e7 3.37904
$$683$$ −1.52230e7 −1.24867 −0.624337 0.781155i $$-0.714631\pi$$
−0.624337 + 0.781155i $$0.714631\pi$$
$$684$$ 0 0
$$685$$ 3.93038e6 0.320043
$$686$$ −85734.1 −0.00695574
$$687$$ 0 0
$$688$$ 6.52857e7 5.25832
$$689$$ −2.76206e6 −0.221659
$$690$$ 0 0
$$691$$ 1.04711e7 0.834248 0.417124 0.908850i $$-0.363038\pi$$
0.417124 + 0.908850i $$0.363038\pi$$
$$692$$ −5.89567e7 −4.68024
$$693$$ 0 0
$$694$$ 1.65009e7 1.30049
$$695$$ −1.67919e7 −1.31868
$$696$$ 0 0
$$697$$ −9.89286e6 −0.771329
$$698$$ 1.38241e7 1.07398
$$699$$ 0 0
$$700$$ −27714.0 −0.00213774
$$701$$ 2.28874e7 1.75914 0.879572 0.475765i $$-0.157829\pi$$
0.879572 + 0.475765i $$0.157829\pi$$
$$702$$ 0 0
$$703$$ −2.58346e7 −1.97158
$$704$$ 3.70466e7 2.81720
$$705$$ 0 0
$$706$$ 4.80333e7 3.62686
$$707$$ −20621.7 −0.00155159
$$708$$ 0 0
$$709$$ 1.85127e7 1.38310 0.691550 0.722329i $$-0.256928\pi$$
0.691550 + 0.722329i $$0.256928\pi$$
$$710$$ 2.33873e7 1.74114
$$711$$ 0 0
$$712$$ −2.65257e7 −1.96095
$$713$$ −4.78170e6 −0.352256
$$714$$ 0 0
$$715$$ −4.46517e6 −0.326643
$$716$$ 2.46051e7 1.79367
$$717$$ 0 0
$$718$$ −5.03519e7 −3.64506
$$719$$ −1.25679e7 −0.906652 −0.453326 0.891345i $$-0.649763\pi$$
−0.453326 + 0.891345i $$0.649763\pi$$
$$720$$ 0 0
$$721$$ 4260.00 0.000305191 0
$$722$$ 1.81440e7 1.29536
$$723$$ 0 0
$$724$$ −3.27035e6 −0.231872
$$725$$ 3.72201e6 0.262986
$$726$$ 0 0
$$727$$ 3.64050e6 0.255462 0.127731 0.991809i $$-0.459231\pi$$
0.127731 + 0.991809i $$0.459231\pi$$
$$728$$ 33754.3 0.00236048
$$729$$ 0 0
$$730$$ −2.55110e7 −1.77182
$$731$$ 1.90353e7 1.31755
$$732$$ 0 0
$$733$$ −4.38735e6 −0.301608 −0.150804 0.988564i $$-0.548186\pi$$
−0.150804 + 0.988564i $$0.548186\pi$$
$$734$$ 2.61966e7 1.79475
$$735$$ 0 0
$$736$$ −9.57181e6 −0.651327
$$737$$ −1.20368e7 −0.816287
$$738$$ 0 0
$$739$$ 1.95857e7 1.31925 0.659625 0.751595i $$-0.270715\pi$$
0.659625 + 0.751595i $$0.270715\pi$$
$$740$$ 4.42736e7 2.97211
$$741$$ 0 0
$$742$$ −27680.6 −0.00184572
$$743$$ 2.94833e7 1.95931 0.979657 0.200678i $$-0.0643146\pi$$
0.979657 + 0.200678i $$0.0643146\pi$$
$$744$$ 0 0
$$745$$ 1.60021e7 1.05630
$$746$$ 1.48047e7 0.973983
$$747$$ 0 0
$$748$$ 3.45291e7 2.25648
$$749$$ 30190.0 0.00196634
$$750$$ 0 0
$$751$$ 1.27147e7 0.822634 0.411317 0.911492i $$-0.365069\pi$$
0.411317 + 0.911492i $$0.365069\pi$$
$$752$$ −9.25609e7 −5.96875
$$753$$ 0 0
$$754$$ −7.32290e6 −0.469089
$$755$$ 1.84149e7 1.17571
$$756$$ 0 0
$$757$$ 1.63980e7 1.04004 0.520022 0.854153i $$-0.325924\pi$$
0.520022 + 0.854153i $$0.325924\pi$$
$$758$$ 2.17558e7 1.37531
$$759$$ 0 0
$$760$$ −4.75407e7 −2.98560
$$761$$ −8.50863e6 −0.532596 −0.266298 0.963891i $$-0.585801\pi$$
−0.266298 + 0.963891i $$0.585801\pi$$
$$762$$ 0 0
$$763$$ −32305.5 −0.00200893
$$764$$ −3.12856e6 −0.193915
$$765$$ 0 0
$$766$$ −2.16305e7 −1.33197
$$767$$ −3.03053e6 −0.186007
$$768$$ 0 0
$$769$$ 1.70141e7 1.03751 0.518755 0.854923i $$-0.326396\pi$$
0.518755 + 0.854923i $$0.326396\pi$$
$$770$$ −44748.7 −0.00271991
$$771$$ 0 0
$$772$$ −3.56616e6 −0.215356
$$773$$ −3.63916e6 −0.219055 −0.109527 0.993984i $$-0.534934\pi$$
−0.109527 + 0.993984i $$0.534934\pi$$
$$774$$ 0 0
$$775$$ −1.25934e7 −0.753161
$$776$$ −7.86204e7 −4.68685
$$777$$ 0 0
$$778$$ −3.50095e7 −2.07366
$$779$$ −2.06966e7 −1.22195
$$780$$ 0 0
$$781$$ −2.19989e7 −1.29054
$$782$$ −5.55511e6 −0.324845
$$783$$ 0 0
$$784$$ −5.62024e7 −3.26561
$$785$$ −1.00177e7 −0.580220
$$786$$ 0 0
$$787$$ −5.30127e6 −0.305101 −0.152550 0.988296i $$-0.548749\pi$$
−0.152550 + 0.988296i $$0.548749\pi$$
$$788$$ −7.33615e6 −0.420875
$$789$$ 0 0
$$790$$ −1.03887e7 −0.592232
$$791$$ 24631.3 0.00139974
$$792$$ 0 0
$$793$$ 1.01449e7 0.572883
$$794$$ 5.85591e7 3.29642
$$795$$ 0 0
$$796$$ 9.13743e7 5.11142
$$797$$ −1.41955e7 −0.791598 −0.395799 0.918337i $$-0.629532\pi$$
−0.395799 + 0.918337i $$0.629532\pi$$
$$798$$ 0 0
$$799$$ −2.69879e7 −1.49555
$$800$$ −2.52089e7 −1.39261
$$801$$ 0 0
$$802$$ −3.52414e7 −1.93472
$$803$$ 2.39965e7 1.31329
$$804$$ 0 0
$$805$$ 5213.26 0.000283543 0
$$806$$ 2.47769e7 1.34341
$$807$$ 0 0
$$808$$ −4.87699e7 −2.62799
$$809$$ 1.58542e7 0.851675 0.425838 0.904800i $$-0.359979\pi$$
0.425838 + 0.904800i $$0.359979\pi$$
$$810$$ 0 0
$$811$$ −1.40129e7 −0.748127 −0.374063 0.927403i $$-0.622036\pi$$
−0.374063 + 0.927403i $$0.622036\pi$$
$$812$$ −53143.1 −0.00282851
$$813$$ 0 0
$$814$$ −5.75101e7 −3.04217
$$815$$ 7.41524e6 0.391049
$$816$$ 0 0
$$817$$ 3.98232e7 2.08728
$$818$$ −1.68339e7 −0.879634
$$819$$ 0 0
$$820$$ 3.54684e7 1.84207
$$821$$ −1.16279e7 −0.602065 −0.301033 0.953614i $$-0.597331\pi$$
−0.301033 + 0.953614i $$0.597331\pi$$
$$822$$ 0 0
$$823$$ −2.76237e7 −1.42161 −0.710807 0.703387i $$-0.751670\pi$$
−0.710807 + 0.703387i $$0.751670\pi$$
$$824$$ 1.00748e7 0.516914
$$825$$ 0 0
$$826$$ −30371.1 −0.00154885
$$827$$ 2.78146e7 1.41420 0.707098 0.707116i $$-0.250004\pi$$
0.707098 + 0.707116i $$0.250004\pi$$
$$828$$ 0 0
$$829$$ −1.23659e7 −0.624943 −0.312471 0.949927i $$-0.601157\pi$$
−0.312471 + 0.949927i $$0.601157\pi$$
$$830$$ −8.22214e6 −0.414276
$$831$$ 0 0
$$832$$ 2.23636e7 1.12004
$$833$$ −1.63869e7 −0.818246
$$834$$ 0 0
$$835$$ 1.06223e6 0.0527231
$$836$$ 7.22374e7 3.57476
$$837$$ 0 0
$$838$$ 5.12787e7 2.52247
$$839$$ 3.49502e7 1.71413 0.857067 0.515205i $$-0.172284\pi$$
0.857067 + 0.515205i $$0.172284\pi$$
$$840$$ 0 0
$$841$$ −1.33740e7 −0.652035
$$842$$ −4.92192e7 −2.39251
$$843$$ 0 0
$$844$$ −8.63323e7 −4.17174
$$845$$ 1.27558e7 0.614565
$$846$$ 0 0
$$847$$ 3953.28 0.000189343 0
$$848$$ −3.62917e7 −1.73308
$$849$$ 0 0
$$850$$ −1.46303e7 −0.694552
$$851$$ 6.69997e6 0.317138
$$852$$ 0 0
$$853$$ −9.99950e6 −0.470550 −0.235275 0.971929i $$-0.575599\pi$$
−0.235275 + 0.971929i $$0.575599\pi$$
$$854$$ 101670. 0.00477032
$$855$$ 0 0
$$856$$ 7.13987e7 3.33047
$$857$$ −9.71240e6 −0.451725 −0.225863 0.974159i $$-0.572520\pi$$
−0.225863 + 0.974159i $$0.572520\pi$$
$$858$$ 0 0
$$859$$ 3.69393e7 1.70807 0.854035 0.520216i $$-0.174149\pi$$
0.854035 + 0.520216i $$0.174149\pi$$
$$860$$ −6.82463e7 −3.14654
$$861$$ 0 0
$$862$$ 3.54227e7 1.62373
$$863$$ 3.31284e7 1.51416 0.757082 0.653319i $$-0.226624\pi$$
0.757082 + 0.653319i $$0.226624\pi$$
$$864$$ 0 0
$$865$$ 2.92080e7 1.32728
$$866$$ 2.28121e7 1.03364
$$867$$ 0 0
$$868$$ 179809. 0.00810051
$$869$$ 9.77194e6 0.438966
$$870$$ 0 0
$$871$$ −7.26615e6 −0.324533
$$872$$ −7.64019e7 −3.40262
$$873$$ 0 0
$$874$$ −1.16217e7 −0.514625
$$875$$ 44526.6 0.00196607
$$876$$ 0 0
$$877$$ 1.38007e7 0.605902 0.302951 0.953006i $$-0.402028\pi$$
0.302951 + 0.953006i $$0.402028\pi$$
$$878$$ 8.16869e6 0.357615
$$879$$ 0 0
$$880$$ −5.86696e7 −2.55391
$$881$$ 7.74868e6 0.336347 0.168174 0.985757i $$-0.446213\pi$$
0.168174 + 0.985757i $$0.446213\pi$$
$$882$$ 0 0
$$883$$ 3.79838e7 1.63944 0.819722 0.572761i $$-0.194128\pi$$
0.819722 + 0.572761i $$0.194128\pi$$
$$884$$ 2.08439e7 0.897115
$$885$$ 0 0
$$886$$ −7.00477e6 −0.299785
$$887$$ 1.51721e7 0.647495 0.323747 0.946144i $$-0.395057\pi$$
0.323747 + 0.946144i $$0.395057\pi$$
$$888$$ 0 0
$$889$$ 48253.7 0.00204775
$$890$$ 2.12281e7 0.898330
$$891$$ 0 0
$$892$$ −1.76087e7 −0.740995
$$893$$ −5.64607e7 −2.36929
$$894$$ 0 0
$$895$$ −1.21897e7 −0.508670
$$896$$ 87004.5 0.00362052
$$897$$ 0 0
$$898$$ 8.16510e7 3.37886
$$899$$ −2.41485e7 −0.996530
$$900$$ 0 0
$$901$$ −1.05815e7 −0.434247
$$902$$ −4.60724e7 −1.88549
$$903$$ 0 0
$$904$$ 5.82526e7 2.37080
$$905$$ 1.62018e6 0.0657569
$$906$$ 0 0
$$907$$ 8.48315e6 0.342404 0.171202 0.985236i $$-0.445235\pi$$
0.171202 + 0.985236i $$0.445235\pi$$
$$908$$ 2.91566e7 1.17361
$$909$$ 0 0
$$910$$ −27013.1 −0.00108136
$$911$$ −2.96302e7 −1.18288 −0.591438 0.806351i $$-0.701439\pi$$
−0.591438 + 0.806351i $$0.701439\pi$$
$$912$$ 0 0
$$913$$ 7.73403e6 0.307064
$$914$$ −8.66513e7 −3.43091
$$915$$ 0 0
$$916$$ −3.98239e7 −1.56821
$$917$$ −14368.4 −0.000564268 0
$$918$$ 0 0
$$919$$ −1.27080e7 −0.496352 −0.248176 0.968715i $$-0.579831\pi$$
−0.248176 + 0.968715i $$0.579831\pi$$
$$920$$ 1.23292e7 0.480249
$$921$$ 0 0
$$922$$ −6.06992e7 −2.35156
$$923$$ −1.32799e7 −0.513085
$$924$$ 0 0
$$925$$ 1.76454e7 0.678075
$$926$$ 1.49875e7 0.574385
$$927$$ 0 0
$$928$$ −4.83394e7 −1.84260
$$929$$ 4.50533e7 1.71272 0.856362 0.516376i $$-0.172719\pi$$
0.856362 + 0.516376i $$0.172719\pi$$
$$930$$ 0 0
$$931$$ −3.42826e7 −1.29628
$$932$$ −5.66380e6 −0.213584
$$933$$ 0 0
$$934$$ −4.36266e7 −1.63638
$$935$$ −1.71062e7 −0.639919
$$936$$ 0 0
$$937$$ −2.49632e7 −0.928864 −0.464432 0.885609i $$-0.653741\pi$$
−0.464432 + 0.885609i $$0.653741\pi$$
$$938$$ −72819.4 −0.00270234
$$939$$ 0 0
$$940$$ 9.67585e7 3.57165
$$941$$ 3.36141e7 1.23751 0.618754 0.785585i $$-0.287638\pi$$
0.618754 + 0.785585i $$0.287638\pi$$
$$942$$ 0 0
$$943$$ 5.36747e6 0.196558
$$944$$ −3.98192e7 −1.45433
$$945$$ 0 0
$$946$$ 8.86501e7 3.22071
$$947$$ 5.33926e6 0.193467 0.0967333 0.995310i $$-0.469161\pi$$
0.0967333 + 0.995310i $$0.469161\pi$$
$$948$$ 0 0
$$949$$ 1.44858e7 0.522127
$$950$$ −3.06076e7 −1.10032
$$951$$ 0 0
$$952$$ 129314. 0.00462438
$$953$$ 3.69391e7 1.31751 0.658755 0.752358i $$-0.271084\pi$$
0.658755 + 0.752358i $$0.271084\pi$$
$$954$$ 0 0
$$955$$ 1.54994e6 0.0549928
$$956$$ 5.30617e7 1.87774
$$957$$ 0 0
$$958$$ −7.06026e7 −2.48546
$$959$$ −22366.2 −0.000785317 0
$$960$$ 0 0
$$961$$ 5.30769e7 1.85395
$$962$$ −3.47166e7 −1.20948
$$963$$ 0 0
$$964$$ −4.88910e7 −1.69448
$$965$$ 1.76673e6 0.0610734
$$966$$ 0 0
$$967$$ −4.47688e7 −1.53960 −0.769802 0.638283i $$-0.779645\pi$$
−0.769802 + 0.638283i $$0.779645\pi$$
$$968$$ 9.34943e6 0.320698
$$969$$ 0 0
$$970$$ 6.29187e7 2.14709
$$971$$ 4.07416e7 1.38672 0.693361 0.720590i $$-0.256129\pi$$
0.693361 + 0.720590i $$0.256129\pi$$
$$972$$ 0 0
$$973$$ 95555.9 0.00323575
$$974$$ −2.14247e7 −0.723633
$$975$$ 0 0
$$976$$ 1.33298e8 4.47919
$$977$$ −1.07576e7 −0.360561 −0.180281 0.983615i $$-0.557701\pi$$
−0.180281 + 0.983615i $$0.557701\pi$$
$$978$$ 0 0
$$979$$ −1.99679e7 −0.665849
$$980$$ 5.87511e7 1.95412
$$981$$ 0 0
$$982$$ −8.60770e7 −2.84845
$$983$$ 2.44766e7 0.807917 0.403958 0.914777i $$-0.367634\pi$$
0.403958 + 0.914777i $$0.367634\pi$$
$$984$$ 0 0
$$985$$ 3.63444e6 0.119357
$$986$$ −2.80543e7 −0.918982
$$987$$ 0 0
$$988$$ 4.36069e7 1.42123
$$989$$ −1.03278e7 −0.335751
$$990$$ 0 0
$$991$$ −2.09086e6 −0.0676301 −0.0338151 0.999428i $$-0.510766\pi$$
−0.0338151 + 0.999428i $$0.510766\pi$$
$$992$$ 1.63556e8 5.27699
$$993$$ 0 0
$$994$$ −133087. −0.00427239
$$995$$ −4.52682e7 −1.44956
$$996$$ 0 0
$$997$$ 1.49624e7 0.476721 0.238360 0.971177i $$-0.423390\pi$$
0.238360 + 0.971177i $$0.423390\pi$$
$$998$$ −1.08036e8 −3.43353
$$999$$ 0 0
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 207.6.a.a.1.2 2
3.2 odd 2 69.6.a.a.1.1 2
12.11 even 2 1104.6.a.h.1.1 2

By twisted newform
Twist Min Dim Char Parity Ord Type
69.6.a.a.1.1 2 3.2 odd 2
207.6.a.a.1.2 2 1.1 even 1 trivial
1104.6.a.h.1.1 2 12.11 even 2