# Properties

 Label 1850.2.a.bc.1.1 Level $1850$ Weight $2$ Character 1850.1 Self dual yes Analytic conductor $14.772$ Analytic rank $0$ Dimension $3$ CM no Inner twists $1$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$1850 = 2 \cdot 5^{2} \cdot 37$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1850.a (trivial)

## Newform invariants

 Self dual: yes Analytic conductor: $$14.7723243739$$ Analytic rank: $$0$$ Dimension: $$3$$ Coefficient field: 3.3.1524.1 Defining polynomial: $$x^{3} - x^{2} - 7x + 1$$ x^3 - x^2 - 7*x + 1 Coefficient ring: $$\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$1$$ Twist minimal: yes Fricke sign: $$-1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

 Embedding label 1.1 Root $$-2.27307$$ of defining polynomial Character $$\chi$$ $$=$$ 1850.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+1.00000 q^{2} -2.27307 q^{3} +1.00000 q^{4} -2.27307 q^{6} -1.27307 q^{7} +1.00000 q^{8} +2.16686 q^{9} +O(q^{10})$$ $$q+1.00000 q^{2} -2.27307 q^{3} +1.00000 q^{4} -2.27307 q^{6} -1.27307 q^{7} +1.00000 q^{8} +2.16686 q^{9} -4.43993 q^{11} -2.27307 q^{12} +5.27307 q^{13} -1.27307 q^{14} +1.00000 q^{16} +0.273073 q^{17} +2.16686 q^{18} -5.71301 q^{19} +2.89379 q^{21} -4.43993 q^{22} +6.54615 q^{23} -2.27307 q^{24} +5.27307 q^{26} +1.89379 q^{27} -1.27307 q^{28} +0.546146 q^{29} -5.98608 q^{31} +1.00000 q^{32} +10.0923 q^{33} +0.273073 q^{34} +2.16686 q^{36} +1.00000 q^{37} -5.71301 q^{38} -11.9861 q^{39} +11.8799 q^{41} +2.89379 q^{42} +10.3793 q^{43} -4.43993 q^{44} +6.54615 q^{46} -2.27307 q^{48} -5.37929 q^{49} -0.620715 q^{51} +5.27307 q^{52} -2.33372 q^{53} +1.89379 q^{54} -1.27307 q^{56} +12.9861 q^{57} +0.546146 q^{58} +2.37929 q^{59} +11.8192 q^{61} -5.98608 q^{62} -2.75857 q^{63} +1.00000 q^{64} +10.0923 q^{66} -7.15294 q^{67} +0.273073 q^{68} -14.8799 q^{69} +5.60679 q^{71} +2.16686 q^{72} +9.71301 q^{73} +1.00000 q^{74} -5.71301 q^{76} +5.65236 q^{77} -11.9861 q^{78} +11.4260 q^{79} -10.8053 q^{81} +11.8799 q^{82} -3.89379 q^{83} +2.89379 q^{84} +10.3793 q^{86} -1.24143 q^{87} -4.43993 q^{88} +13.8659 q^{89} -6.71301 q^{91} +6.54615 q^{92} +13.6068 q^{93} -2.27307 q^{96} -0.879866 q^{97} -5.37929 q^{98} -9.62071 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$3 q + 3 q^{2} + q^{3} + 3 q^{4} + q^{6} + 4 q^{7} + 3 q^{8} + 6 q^{9}+O(q^{10})$$ 3 * q + 3 * q^2 + q^3 + 3 * q^4 + q^6 + 4 * q^7 + 3 * q^8 + 6 * q^9 $$3 q + 3 q^{2} + q^{3} + 3 q^{4} + q^{6} + 4 q^{7} + 3 q^{8} + 6 q^{9} - 5 q^{11} + q^{12} + 8 q^{13} + 4 q^{14} + 3 q^{16} - 7 q^{17} + 6 q^{18} - q^{19} + 16 q^{21} - 5 q^{22} + 4 q^{23} + q^{24} + 8 q^{26} + 13 q^{27} + 4 q^{28} - 14 q^{29} + 6 q^{31} + 3 q^{32} - q^{33} - 7 q^{34} + 6 q^{36} + 3 q^{37} - q^{38} - 12 q^{39} + 19 q^{41} + 16 q^{42} + 16 q^{43} - 5 q^{44} + 4 q^{46} + q^{48} - q^{49} - 17 q^{51} + 8 q^{52} - 6 q^{53} + 13 q^{54} + 4 q^{56} + 15 q^{57} - 14 q^{58} - 8 q^{59} + 12 q^{61} + 6 q^{62} + 22 q^{63} + 3 q^{64} - q^{66} + 3 q^{67} - 7 q^{68} - 28 q^{69} + 8 q^{71} + 6 q^{72} + 13 q^{73} + 3 q^{74} - q^{76} - 6 q^{77} - 12 q^{78} + 2 q^{79} + 15 q^{81} + 19 q^{82} - 19 q^{83} + 16 q^{84} + 16 q^{86} - 34 q^{87} - 5 q^{88} + q^{89} - 4 q^{91} + 4 q^{92} + 32 q^{93} + q^{96} + 14 q^{97} - q^{98} - 44 q^{99}+O(q^{100})$$ 3 * q + 3 * q^2 + q^3 + 3 * q^4 + q^6 + 4 * q^7 + 3 * q^8 + 6 * q^9 - 5 * q^11 + q^12 + 8 * q^13 + 4 * q^14 + 3 * q^16 - 7 * q^17 + 6 * q^18 - q^19 + 16 * q^21 - 5 * q^22 + 4 * q^23 + q^24 + 8 * q^26 + 13 * q^27 + 4 * q^28 - 14 * q^29 + 6 * q^31 + 3 * q^32 - q^33 - 7 * q^34 + 6 * q^36 + 3 * q^37 - q^38 - 12 * q^39 + 19 * q^41 + 16 * q^42 + 16 * q^43 - 5 * q^44 + 4 * q^46 + q^48 - q^49 - 17 * q^51 + 8 * q^52 - 6 * q^53 + 13 * q^54 + 4 * q^56 + 15 * q^57 - 14 * q^58 - 8 * q^59 + 12 * q^61 + 6 * q^62 + 22 * q^63 + 3 * q^64 - q^66 + 3 * q^67 - 7 * q^68 - 28 * q^69 + 8 * q^71 + 6 * q^72 + 13 * q^73 + 3 * q^74 - q^76 - 6 * q^77 - 12 * q^78 + 2 * q^79 + 15 * q^81 + 19 * q^82 - 19 * q^83 + 16 * q^84 + 16 * q^86 - 34 * q^87 - 5 * q^88 + q^89 - 4 * q^91 + 4 * q^92 + 32 * q^93 + q^96 + 14 * q^97 - q^98 - 44 * 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 1.00000 0.707107
$$3$$ −2.27307 −1.31236 −0.656180 0.754605i $$-0.727829\pi$$
−0.656180 + 0.754605i $$0.727829\pi$$
$$4$$ 1.00000 0.500000
$$5$$ 0 0
$$6$$ −2.27307 −0.927978
$$7$$ −1.27307 −0.481176 −0.240588 0.970627i $$-0.577340\pi$$
−0.240588 + 0.970627i $$0.577340\pi$$
$$8$$ 1.00000 0.353553
$$9$$ 2.16686 0.722287
$$10$$ 0 0
$$11$$ −4.43993 −1.33869 −0.669345 0.742952i $$-0.733425\pi$$
−0.669345 + 0.742952i $$0.733425\pi$$
$$12$$ −2.27307 −0.656180
$$13$$ 5.27307 1.46249 0.731244 0.682116i $$-0.238940\pi$$
0.731244 + 0.682116i $$0.238940\pi$$
$$14$$ −1.27307 −0.340243
$$15$$ 0 0
$$16$$ 1.00000 0.250000
$$17$$ 0.273073 0.0662299 0.0331149 0.999452i $$-0.489457\pi$$
0.0331149 + 0.999452i $$0.489457\pi$$
$$18$$ 2.16686 0.510734
$$19$$ −5.71301 −1.31065 −0.655327 0.755346i $$-0.727469\pi$$
−0.655327 + 0.755346i $$0.727469\pi$$
$$20$$ 0 0
$$21$$ 2.89379 0.631476
$$22$$ −4.43993 −0.946597
$$23$$ 6.54615 1.36497 0.682483 0.730902i $$-0.260900\pi$$
0.682483 + 0.730902i $$0.260900\pi$$
$$24$$ −2.27307 −0.463989
$$25$$ 0 0
$$26$$ 5.27307 1.03413
$$27$$ 1.89379 0.364460
$$28$$ −1.27307 −0.240588
$$29$$ 0.546146 0.101417 0.0507084 0.998714i $$-0.483852\pi$$
0.0507084 + 0.998714i $$0.483852\pi$$
$$30$$ 0 0
$$31$$ −5.98608 −1.07513 −0.537566 0.843222i $$-0.680656\pi$$
−0.537566 + 0.843222i $$0.680656\pi$$
$$32$$ 1.00000 0.176777
$$33$$ 10.0923 1.75684
$$34$$ 0.273073 0.0468316
$$35$$ 0 0
$$36$$ 2.16686 0.361143
$$37$$ 1.00000 0.164399
$$38$$ −5.71301 −0.926772
$$39$$ −11.9861 −1.91931
$$40$$ 0 0
$$41$$ 11.8799 1.85532 0.927662 0.373422i $$-0.121816\pi$$
0.927662 + 0.373422i $$0.121816\pi$$
$$42$$ 2.89379 0.446521
$$43$$ 10.3793 1.58283 0.791413 0.611282i $$-0.209346\pi$$
0.791413 + 0.611282i $$0.209346\pi$$
$$44$$ −4.43993 −0.669345
$$45$$ 0 0
$$46$$ 6.54615 0.965177
$$47$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$48$$ −2.27307 −0.328090
$$49$$ −5.37929 −0.768469
$$50$$ 0 0
$$51$$ −0.620715 −0.0869174
$$52$$ 5.27307 0.731244
$$53$$ −2.33372 −0.320561 −0.160281 0.987071i $$-0.551240\pi$$
−0.160281 + 0.987071i $$0.551240\pi$$
$$54$$ 1.89379 0.257712
$$55$$ 0 0
$$56$$ −1.27307 −0.170122
$$57$$ 12.9861 1.72005
$$58$$ 0.546146 0.0717124
$$59$$ 2.37929 0.309757 0.154878 0.987934i $$-0.450501\pi$$
0.154878 + 0.987934i $$0.450501\pi$$
$$60$$ 0 0
$$61$$ 11.8192 1.51330 0.756648 0.653823i $$-0.226836\pi$$
0.756648 + 0.653823i $$0.226836\pi$$
$$62$$ −5.98608 −0.760233
$$63$$ −2.75857 −0.347547
$$64$$ 1.00000 0.125000
$$65$$ 0 0
$$66$$ 10.0923 1.24228
$$67$$ −7.15294 −0.873871 −0.436935 0.899493i $$-0.643936\pi$$
−0.436935 + 0.899493i $$0.643936\pi$$
$$68$$ 0.273073 0.0331149
$$69$$ −14.8799 −1.79133
$$70$$ 0 0
$$71$$ 5.60679 0.665404 0.332702 0.943032i $$-0.392040\pi$$
0.332702 + 0.943032i $$0.392040\pi$$
$$72$$ 2.16686 0.255367
$$73$$ 9.71301 1.13682 0.568411 0.822745i $$-0.307558\pi$$
0.568411 + 0.822745i $$0.307558\pi$$
$$74$$ 1.00000 0.116248
$$75$$ 0 0
$$76$$ −5.71301 −0.655327
$$77$$ 5.65236 0.644146
$$78$$ −11.9861 −1.35716
$$79$$ 11.4260 1.28553 0.642763 0.766065i $$-0.277788\pi$$
0.642763 + 0.766065i $$0.277788\pi$$
$$80$$ 0 0
$$81$$ −10.8053 −1.20059
$$82$$ 11.8799 1.31191
$$83$$ −3.89379 −0.427399 −0.213699 0.976899i $$-0.568551\pi$$
−0.213699 + 0.976899i $$0.568551\pi$$
$$84$$ 2.89379 0.315738
$$85$$ 0 0
$$86$$ 10.3793 1.11923
$$87$$ −1.24143 −0.133095
$$88$$ −4.43993 −0.473298
$$89$$ 13.8659 1.46979 0.734894 0.678182i $$-0.237232\pi$$
0.734894 + 0.678182i $$0.237232\pi$$
$$90$$ 0 0
$$91$$ −6.71301 −0.703714
$$92$$ 6.54615 0.682483
$$93$$ 13.6068 1.41096
$$94$$ 0 0
$$95$$ 0 0
$$96$$ −2.27307 −0.231995
$$97$$ −0.879866 −0.0893369 −0.0446684 0.999002i $$-0.514223\pi$$
−0.0446684 + 0.999002i $$0.514223\pi$$
$$98$$ −5.37929 −0.543390
$$99$$ −9.62071 −0.966918
$$100$$ 0 0
$$101$$ 3.66628 0.364808 0.182404 0.983224i $$-0.441612\pi$$
0.182404 + 0.983224i $$0.441612\pi$$
$$102$$ −0.620715 −0.0614599
$$103$$ 12.3198 1.21391 0.606953 0.794738i $$-0.292392\pi$$
0.606953 + 0.794738i $$0.292392\pi$$
$$104$$ 5.27307 0.517067
$$105$$ 0 0
$$106$$ −2.33372 −0.226671
$$107$$ −7.36536 −0.712037 −0.356018 0.934479i $$-0.615866\pi$$
−0.356018 + 0.934479i $$0.615866\pi$$
$$108$$ 1.89379 0.182230
$$109$$ 4.33372 0.415095 0.207548 0.978225i $$-0.433452\pi$$
0.207548 + 0.978225i $$0.433452\pi$$
$$110$$ 0 0
$$111$$ −2.27307 −0.215751
$$112$$ −1.27307 −0.120294
$$113$$ −2.10621 −0.198136 −0.0990679 0.995081i $$-0.531586\pi$$
−0.0990679 + 0.995081i $$0.531586\pi$$
$$114$$ 12.9861 1.21626
$$115$$ 0 0
$$116$$ 0.546146 0.0507084
$$117$$ 11.4260 1.05634
$$118$$ 2.37929 0.219031
$$119$$ −0.347642 −0.0318683
$$120$$ 0 0
$$121$$ 8.71301 0.792091
$$122$$ 11.8192 1.07006
$$123$$ −27.0038 −2.43485
$$124$$ −5.98608 −0.537566
$$125$$ 0 0
$$126$$ −2.75857 −0.245753
$$127$$ 13.6068 1.20741 0.603704 0.797209i $$-0.293691\pi$$
0.603704 + 0.797209i $$0.293691\pi$$
$$128$$ 1.00000 0.0883883
$$129$$ −23.5929 −2.07724
$$130$$ 0 0
$$131$$ 4.16686 0.364060 0.182030 0.983293i $$-0.441733\pi$$
0.182030 + 0.983293i $$0.441733\pi$$
$$132$$ 10.0923 0.878421
$$133$$ 7.27307 0.630655
$$134$$ −7.15294 −0.617920
$$135$$ 0 0
$$136$$ 0.273073 0.0234158
$$137$$ −1.21243 −0.103584 −0.0517922 0.998658i $$-0.516493\pi$$
−0.0517922 + 0.998658i $$0.516493\pi$$
$$138$$ −14.8799 −1.26666
$$139$$ 7.53222 0.638875 0.319437 0.947607i $$-0.396506\pi$$
0.319437 + 0.947607i $$0.396506\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 5.60679 0.470512
$$143$$ −23.4121 −1.95782
$$144$$ 2.16686 0.180572
$$145$$ 0 0
$$146$$ 9.71301 0.803854
$$147$$ 12.2275 1.00851
$$148$$ 1.00000 0.0821995
$$149$$ −13.9861 −1.14578 −0.572892 0.819631i $$-0.694179\pi$$
−0.572892 + 0.819631i $$0.694179\pi$$
$$150$$ 0 0
$$151$$ 13.7597 1.11975 0.559876 0.828577i $$-0.310849\pi$$
0.559876 + 0.828577i $$0.310849\pi$$
$$152$$ −5.71301 −0.463386
$$153$$ 0.591711 0.0478370
$$154$$ 5.65236 0.455480
$$155$$ 0 0
$$156$$ −11.9861 −0.959654
$$157$$ −2.56007 −0.204316 −0.102158 0.994768i $$-0.532575\pi$$
−0.102158 + 0.994768i $$0.532575\pi$$
$$158$$ 11.4260 0.909005
$$159$$ 5.30472 0.420691
$$160$$ 0 0
$$161$$ −8.33372 −0.656789
$$162$$ −10.8053 −0.848944
$$163$$ 21.7130 1.70069 0.850347 0.526222i $$-0.176392\pi$$
0.850347 + 0.526222i $$0.176392\pi$$
$$164$$ 11.8799 0.927662
$$165$$ 0 0
$$166$$ −3.89379 −0.302217
$$167$$ −16.8659 −1.30513 −0.652563 0.757734i $$-0.726306\pi$$
−0.652563 + 0.757734i $$0.726306\pi$$
$$168$$ 2.89379 0.223261
$$169$$ 14.8053 1.13887
$$170$$ 0 0
$$171$$ −12.3793 −0.946668
$$172$$ 10.3793 0.791413
$$173$$ −10.7586 −0.817959 −0.408980 0.912544i $$-0.634115\pi$$
−0.408980 + 0.912544i $$0.634115\pi$$
$$174$$ −1.24143 −0.0941125
$$175$$ 0 0
$$176$$ −4.43993 −0.334673
$$177$$ −5.40829 −0.406512
$$178$$ 13.8659 1.03930
$$179$$ 1.66744 0.124630 0.0623152 0.998057i $$-0.480152\pi$$
0.0623152 + 0.998057i $$0.480152\pi$$
$$180$$ 0 0
$$181$$ 5.97216 0.443907 0.221953 0.975057i $$-0.428757\pi$$
0.221953 + 0.975057i $$0.428757\pi$$
$$182$$ −6.71301 −0.497601
$$183$$ −26.8659 −1.98599
$$184$$ 6.54615 0.482588
$$185$$ 0 0
$$186$$ 13.6068 0.997698
$$187$$ −1.21243 −0.0886613
$$188$$ 0 0
$$189$$ −2.41093 −0.175369
$$190$$ 0 0
$$191$$ −24.8520 −1.79823 −0.899115 0.437713i $$-0.855789\pi$$
−0.899115 + 0.437713i $$0.855789\pi$$
$$192$$ −2.27307 −0.164045
$$193$$ −7.65352 −0.550912 −0.275456 0.961314i $$-0.588829\pi$$
−0.275456 + 0.961314i $$0.588829\pi$$
$$194$$ −0.879866 −0.0631707
$$195$$ 0 0
$$196$$ −5.37929 −0.384235
$$197$$ 14.5322 1.03538 0.517689 0.855569i $$-0.326792\pi$$
0.517689 + 0.855569i $$0.326792\pi$$
$$198$$ −9.62071 −0.683714
$$199$$ −12.8799 −0.913030 −0.456515 0.889716i $$-0.650902\pi$$
−0.456515 + 0.889716i $$0.650902\pi$$
$$200$$ 0 0
$$201$$ 16.2592 1.14683
$$202$$ 3.66628 0.257959
$$203$$ −0.695283 −0.0487993
$$204$$ −0.620715 −0.0434587
$$205$$ 0 0
$$206$$ 12.3198 0.858361
$$207$$ 14.1846 0.985897
$$208$$ 5.27307 0.365622
$$209$$ 25.3654 1.75456
$$210$$ 0 0
$$211$$ −19.1529 −1.31854 −0.659271 0.751905i $$-0.729135\pi$$
−0.659271 + 0.751905i $$0.729135\pi$$
$$212$$ −2.33372 −0.160281
$$213$$ −12.7446 −0.873249
$$214$$ −7.36536 −0.503486
$$215$$ 0 0
$$216$$ 1.89379 0.128856
$$217$$ 7.62071 0.517328
$$218$$ 4.33372 0.293517
$$219$$ −22.0784 −1.49192
$$220$$ 0 0
$$221$$ 1.43993 0.0968604
$$222$$ −2.27307 −0.152559
$$223$$ −2.75857 −0.184728 −0.0923638 0.995725i $$-0.529442\pi$$
−0.0923638 + 0.995725i $$0.529442\pi$$
$$224$$ −1.27307 −0.0850608
$$225$$ 0 0
$$226$$ −2.10621 −0.140103
$$227$$ 17.2592 1.14553 0.572765 0.819720i $$-0.305871\pi$$
0.572765 + 0.819720i $$0.305871\pi$$
$$228$$ 12.9861 0.860024
$$229$$ −22.3059 −1.47401 −0.737007 0.675885i $$-0.763762\pi$$
−0.737007 + 0.675885i $$0.763762\pi$$
$$230$$ 0 0
$$231$$ −12.8482 −0.845351
$$232$$ 0.546146 0.0358562
$$233$$ 24.3514 1.59532 0.797658 0.603110i $$-0.206072\pi$$
0.797658 + 0.603110i $$0.206072\pi$$
$$234$$ 11.4260 0.746942
$$235$$ 0 0
$$236$$ 2.37929 0.154878
$$237$$ −25.9722 −1.68707
$$238$$ −0.347642 −0.0225343
$$239$$ 1.78757 0.115629 0.0578143 0.998327i $$-0.481587\pi$$
0.0578143 + 0.998327i $$0.481587\pi$$
$$240$$ 0 0
$$241$$ −3.72693 −0.240072 −0.120036 0.992770i $$-0.538301\pi$$
−0.120036 + 0.992770i $$0.538301\pi$$
$$242$$ 8.71301 0.560093
$$243$$ 18.8799 1.21114
$$244$$ 11.8192 0.756648
$$245$$ 0 0
$$246$$ −27.0038 −1.72170
$$247$$ −30.1251 −1.91681
$$248$$ −5.98608 −0.380116
$$249$$ 8.85086 0.560901
$$250$$ 0 0
$$251$$ −9.00000 −0.568075 −0.284037 0.958813i $$-0.591674\pi$$
−0.284037 + 0.958813i $$0.591674\pi$$
$$252$$ −2.75857 −0.173774
$$253$$ −29.0644 −1.82727
$$254$$ 13.6068 0.853766
$$255$$ 0 0
$$256$$ 1.00000 0.0625000
$$257$$ 3.42601 0.213709 0.106854 0.994275i $$-0.465922\pi$$
0.106854 + 0.994275i $$0.465922\pi$$
$$258$$ −23.5929 −1.46883
$$259$$ −1.27307 −0.0791049
$$260$$ 0 0
$$261$$ 1.18342 0.0732519
$$262$$ 4.16686 0.257429
$$263$$ −2.57399 −0.158719 −0.0793595 0.996846i $$-0.525287\pi$$
−0.0793595 + 0.996846i $$0.525287\pi$$
$$264$$ 10.0923 0.621138
$$265$$ 0 0
$$266$$ 7.27307 0.445941
$$267$$ −31.5183 −1.92889
$$268$$ −7.15294 −0.436935
$$269$$ −27.7319 −1.69084 −0.845422 0.534100i $$-0.820651\pi$$
−0.845422 + 0.534100i $$0.820651\pi$$
$$270$$ 0 0
$$271$$ 26.4588 1.60726 0.803629 0.595130i $$-0.202899\pi$$
0.803629 + 0.595130i $$0.202899\pi$$
$$272$$ 0.273073 0.0165575
$$273$$ 15.2592 0.923526
$$274$$ −1.21243 −0.0732453
$$275$$ 0 0
$$276$$ −14.8799 −0.895663
$$277$$ −0.573988 −0.0344876 −0.0172438 0.999851i $$-0.505489\pi$$
−0.0172438 + 0.999851i $$0.505489\pi$$
$$278$$ 7.53222 0.451753
$$279$$ −12.9710 −0.776553
$$280$$ 0 0
$$281$$ −29.2592 −1.74545 −0.872727 0.488208i $$-0.837651\pi$$
−0.872727 + 0.488208i $$0.837651\pi$$
$$282$$ 0 0
$$283$$ 21.0177 1.24937 0.624687 0.780875i $$-0.285227\pi$$
0.624687 + 0.780875i $$0.285227\pi$$
$$284$$ 5.60679 0.332702
$$285$$ 0 0
$$286$$ −23.4121 −1.38439
$$287$$ −15.1239 −0.892738
$$288$$ 2.16686 0.127683
$$289$$ −16.9254 −0.995614
$$290$$ 0 0
$$291$$ 2.00000 0.117242
$$292$$ 9.71301 0.568411
$$293$$ 17.9582 1.04913 0.524566 0.851370i $$-0.324228\pi$$
0.524566 + 0.851370i $$0.324228\pi$$
$$294$$ 12.2275 0.713123
$$295$$ 0 0
$$296$$ 1.00000 0.0581238
$$297$$ −8.40829 −0.487898
$$298$$ −13.9861 −0.810192
$$299$$ 34.5183 1.99625
$$300$$ 0 0
$$301$$ −13.2136 −0.761618
$$302$$ 13.7597 0.791784
$$303$$ −8.33372 −0.478760
$$304$$ −5.71301 −0.327663
$$305$$ 0 0
$$306$$ 0.591711 0.0338259
$$307$$ 23.1985 1.32401 0.662004 0.749500i $$-0.269706\pi$$
0.662004 + 0.749500i $$0.269706\pi$$
$$308$$ 5.65236 0.322073
$$309$$ −28.0038 −1.59308
$$310$$ 0 0
$$311$$ −6.98492 −0.396078 −0.198039 0.980194i $$-0.563457\pi$$
−0.198039 + 0.980194i $$0.563457\pi$$
$$312$$ −11.9861 −0.678578
$$313$$ 24.1669 1.36599 0.682996 0.730422i $$-0.260677\pi$$
0.682996 + 0.730422i $$0.260677\pi$$
$$314$$ −2.56007 −0.144473
$$315$$ 0 0
$$316$$ 11.4260 0.642763
$$317$$ −32.2920 −1.81370 −0.906848 0.421457i $$-0.861519\pi$$
−0.906848 + 0.421457i $$0.861519\pi$$
$$318$$ 5.30472 0.297474
$$319$$ −2.42485 −0.135766
$$320$$ 0 0
$$321$$ 16.7420 0.934448
$$322$$ −8.33372 −0.464420
$$323$$ −1.56007 −0.0868044
$$324$$ −10.8053 −0.600294
$$325$$ 0 0
$$326$$ 21.7130 1.20257
$$327$$ −9.85086 −0.544754
$$328$$ 11.8799 0.655956
$$329$$ 0 0
$$330$$ 0 0
$$331$$ −27.9254 −1.53492 −0.767460 0.641097i $$-0.778480\pi$$
−0.767460 + 0.641097i $$0.778480\pi$$
$$332$$ −3.89379 −0.213699
$$333$$ 2.16686 0.118743
$$334$$ −16.8659 −0.922863
$$335$$ 0 0
$$336$$ 2.89379 0.157869
$$337$$ −8.33256 −0.453903 −0.226952 0.973906i $$-0.572876\pi$$
−0.226952 + 0.973906i $$0.572876\pi$$
$$338$$ 14.8053 0.805302
$$339$$ 4.78757 0.260025
$$340$$ 0 0
$$341$$ 26.5778 1.43927
$$342$$ −12.3793 −0.669395
$$343$$ 15.7597 0.850946
$$344$$ 10.3793 0.559614
$$345$$ 0 0
$$346$$ −10.7586 −0.578384
$$347$$ −1.99884 −0.107303 −0.0536516 0.998560i $$-0.517086\pi$$
−0.0536516 + 0.998560i $$0.517086\pi$$
$$348$$ −1.24143 −0.0665476
$$349$$ −21.9582 −1.17540 −0.587699 0.809080i $$-0.699966\pi$$
−0.587699 + 0.809080i $$0.699966\pi$$
$$350$$ 0 0
$$351$$ 9.98608 0.533017
$$352$$ −4.43993 −0.236649
$$353$$ 11.7597 0.625907 0.312954 0.949768i $$-0.398682\pi$$
0.312954 + 0.949768i $$0.398682\pi$$
$$354$$ −5.40829 −0.287447
$$355$$ 0 0
$$356$$ 13.8659 0.734894
$$357$$ 0.790215 0.0418226
$$358$$ 1.66744 0.0881270
$$359$$ 2.57399 0.135850 0.0679249 0.997690i $$-0.478362\pi$$
0.0679249 + 0.997690i $$0.478362\pi$$
$$360$$ 0 0
$$361$$ 13.6384 0.717812
$$362$$ 5.97216 0.313890
$$363$$ −19.8053 −1.03951
$$364$$ −6.71301 −0.351857
$$365$$ 0 0
$$366$$ −26.8659 −1.40431
$$367$$ −12.4867 −0.651798 −0.325899 0.945405i $$-0.605667\pi$$
−0.325899 + 0.945405i $$0.605667\pi$$
$$368$$ 6.54615 0.341241
$$369$$ 25.7420 1.34008
$$370$$ 0 0
$$371$$ 2.97100 0.154246
$$372$$ 13.6068 0.705479
$$373$$ −14.8659 −0.769729 −0.384865 0.922973i $$-0.625752\pi$$
−0.384865 + 0.922973i $$0.625752\pi$$
$$374$$ −1.21243 −0.0626930
$$375$$ 0 0
$$376$$ 0 0
$$377$$ 2.87987 0.148321
$$378$$ −2.41093 −0.124005
$$379$$ −2.39437 −0.122990 −0.0614952 0.998107i $$-0.519587\pi$$
−0.0614952 + 0.998107i $$0.519587\pi$$
$$380$$ 0 0
$$381$$ −30.9292 −1.58455
$$382$$ −24.8520 −1.27154
$$383$$ −14.7725 −0.754839 −0.377420 0.926042i $$-0.623189\pi$$
−0.377420 + 0.926042i $$0.623189\pi$$
$$384$$ −2.27307 −0.115997
$$385$$ 0 0
$$386$$ −7.65352 −0.389554
$$387$$ 22.4905 1.14325
$$388$$ −0.879866 −0.0446684
$$389$$ −12.6991 −0.643869 −0.321935 0.946762i $$-0.604333\pi$$
−0.321935 + 0.946762i $$0.604333\pi$$
$$390$$ 0 0
$$391$$ 1.78757 0.0904015
$$392$$ −5.37929 −0.271695
$$393$$ −9.47158 −0.477778
$$394$$ 14.5322 0.732123
$$395$$ 0 0
$$396$$ −9.62071 −0.483459
$$397$$ −4.98492 −0.250186 −0.125093 0.992145i $$-0.539923\pi$$
−0.125093 + 0.992145i $$0.539923\pi$$
$$398$$ −12.8799 −0.645609
$$399$$ −16.5322 −0.827646
$$400$$ 0 0
$$401$$ 27.1985 1.35823 0.679114 0.734033i $$-0.262364\pi$$
0.679114 + 0.734033i $$0.262364\pi$$
$$402$$ 16.2592 0.810933
$$403$$ −31.5650 −1.57237
$$404$$ 3.66628 0.182404
$$405$$ 0 0
$$406$$ −0.695283 −0.0345063
$$407$$ −4.43993 −0.220079
$$408$$ −0.620715 −0.0307299
$$409$$ 35.5499 1.75783 0.878916 0.476977i $$-0.158267\pi$$
0.878916 + 0.476977i $$0.158267\pi$$
$$410$$ 0 0
$$411$$ 2.75593 0.135940
$$412$$ 12.3198 0.606953
$$413$$ −3.02900 −0.149048
$$414$$ 14.1846 0.697134
$$415$$ 0 0
$$416$$ 5.27307 0.258534
$$417$$ −17.1213 −0.838433
$$418$$ 25.3654 1.24066
$$419$$ −29.5322 −1.44274 −0.721372 0.692548i $$-0.756488\pi$$
−0.721372 + 0.692548i $$0.756488\pi$$
$$420$$ 0 0
$$421$$ −30.4905 −1.48601 −0.743007 0.669284i $$-0.766601\pi$$
−0.743007 + 0.669284i $$0.766601\pi$$
$$422$$ −19.1529 −0.932350
$$423$$ 0 0
$$424$$ −2.33372 −0.113335
$$425$$ 0 0
$$426$$ −12.7446 −0.617480
$$427$$ −15.0467 −0.728162
$$428$$ −7.36536 −0.356018
$$429$$ 53.2174 2.56936
$$430$$ 0 0
$$431$$ 21.9722 1.05836 0.529181 0.848509i $$-0.322499\pi$$
0.529181 + 0.848509i $$0.322499\pi$$
$$432$$ 1.89379 0.0911149
$$433$$ 5.00000 0.240285 0.120142 0.992757i $$-0.461665\pi$$
0.120142 + 0.992757i $$0.461665\pi$$
$$434$$ 7.62071 0.365806
$$435$$ 0 0
$$436$$ 4.33372 0.207548
$$437$$ −37.3982 −1.78900
$$438$$ −22.0784 −1.05495
$$439$$ 29.5171 1.40878 0.704388 0.709815i $$-0.251221\pi$$
0.704388 + 0.709815i $$0.251221\pi$$
$$440$$ 0 0
$$441$$ −11.6562 −0.555055
$$442$$ 1.43993 0.0684906
$$443$$ −28.9861 −1.37717 −0.688585 0.725156i $$-0.741768\pi$$
−0.688585 + 0.725156i $$0.741768\pi$$
$$444$$ −2.27307 −0.107875
$$445$$ 0 0
$$446$$ −2.75857 −0.130622
$$447$$ 31.7914 1.50368
$$448$$ −1.27307 −0.0601470
$$449$$ 36.6245 1.72842 0.864209 0.503133i $$-0.167819\pi$$
0.864209 + 0.503133i $$0.167819\pi$$
$$450$$ 0 0
$$451$$ −52.7458 −2.48370
$$452$$ −2.10621 −0.0990679
$$453$$ −31.2769 −1.46952
$$454$$ 17.2592 0.810012
$$455$$ 0 0
$$456$$ 12.9861 0.608129
$$457$$ −19.7446 −0.923616 −0.461808 0.886980i $$-0.652799\pi$$
−0.461808 + 0.886980i $$0.652799\pi$$
$$458$$ −22.3059 −1.04229
$$459$$ 0.517142 0.0241381
$$460$$ 0 0
$$461$$ 34.9733 1.62887 0.814435 0.580255i $$-0.197047\pi$$
0.814435 + 0.580255i $$0.197047\pi$$
$$462$$ −12.8482 −0.597753
$$463$$ 24.1707 1.12331 0.561653 0.827373i $$-0.310166\pi$$
0.561653 + 0.827373i $$0.310166\pi$$
$$464$$ 0.546146 0.0253542
$$465$$ 0 0
$$466$$ 24.3514 1.12806
$$467$$ −7.63844 −0.353465 −0.176732 0.984259i $$-0.556553\pi$$
−0.176732 + 0.984259i $$0.556553\pi$$
$$468$$ 11.4260 0.528168
$$469$$ 9.10621 0.420486
$$470$$ 0 0
$$471$$ 5.81922 0.268135
$$472$$ 2.37929 0.109515
$$473$$ −46.0833 −2.11891
$$474$$ −25.9722 −1.19294
$$475$$ 0 0
$$476$$ −0.347642 −0.0159341
$$477$$ −5.05685 −0.231537
$$478$$ 1.78757 0.0817618
$$479$$ −4.01392 −0.183401 −0.0917004 0.995787i $$-0.529230\pi$$
−0.0917004 + 0.995787i $$0.529230\pi$$
$$480$$ 0 0
$$481$$ 5.27307 0.240431
$$482$$ −3.72693 −0.169757
$$483$$ 18.9432 0.861943
$$484$$ 8.71301 0.396046
$$485$$ 0 0
$$486$$ 18.8799 0.856408
$$487$$ −43.3842 −1.96593 −0.982964 0.183798i $$-0.941161\pi$$
−0.982964 + 0.183798i $$0.941161\pi$$
$$488$$ 11.8192 0.535031
$$489$$ −49.3552 −2.23192
$$490$$ 0 0
$$491$$ −20.7307 −0.935565 −0.467782 0.883844i $$-0.654947\pi$$
−0.467782 + 0.883844i $$0.654947\pi$$
$$492$$ −27.0038 −1.21743
$$493$$ 0.149138 0.00671682
$$494$$ −30.1251 −1.35539
$$495$$ 0 0
$$496$$ −5.98608 −0.268783
$$497$$ −7.13786 −0.320177
$$498$$ 8.85086 0.396617
$$499$$ 5.92659 0.265311 0.132655 0.991162i $$-0.457650\pi$$
0.132655 + 0.991162i $$0.457650\pi$$
$$500$$ 0 0
$$501$$ 38.3375 1.71279
$$502$$ −9.00000 −0.401690
$$503$$ −24.0000 −1.07011 −0.535054 0.844818i $$-0.679709\pi$$
−0.535054 + 0.844818i $$0.679709\pi$$
$$504$$ −2.75857 −0.122877
$$505$$ 0 0
$$506$$ −29.0644 −1.29207
$$507$$ −33.6535 −1.49461
$$508$$ 13.6068 0.603704
$$509$$ −9.07837 −0.402392 −0.201196 0.979551i $$-0.564483\pi$$
−0.201196 + 0.979551i $$0.564483\pi$$
$$510$$ 0 0
$$511$$ −12.3654 −0.547012
$$512$$ 1.00000 0.0441942
$$513$$ −10.8192 −0.477680
$$514$$ 3.42601 0.151115
$$515$$ 0 0
$$516$$ −23.5929 −1.03862
$$517$$ 0 0
$$518$$ −1.27307 −0.0559356
$$519$$ 24.4550 1.07346
$$520$$ 0 0
$$521$$ −7.16686 −0.313986 −0.156993 0.987600i $$-0.550180\pi$$
−0.156993 + 0.987600i $$0.550180\pi$$
$$522$$ 1.18342 0.0517970
$$523$$ 29.3970 1.28544 0.642721 0.766101i $$-0.277806\pi$$
0.642721 + 0.766101i $$0.277806\pi$$
$$524$$ 4.16686 0.182030
$$525$$ 0 0
$$526$$ −2.57399 −0.112231
$$527$$ −1.63464 −0.0712058
$$528$$ 10.0923 0.439211
$$529$$ 19.8520 0.863131
$$530$$ 0 0
$$531$$ 5.15558 0.223733
$$532$$ 7.27307 0.315328
$$533$$ 62.6434 2.71339
$$534$$ −31.5183 −1.36393
$$535$$ 0 0
$$536$$ −7.15294 −0.308960
$$537$$ −3.79021 −0.163560
$$538$$ −27.7319 −1.19561
$$539$$ 23.8837 1.02874
$$540$$ 0 0
$$541$$ 26.0038 1.11799 0.558995 0.829171i $$-0.311187\pi$$
0.558995 + 0.829171i $$0.311187\pi$$
$$542$$ 26.4588 1.13650
$$543$$ −13.5751 −0.582565
$$544$$ 0.273073 0.0117079
$$545$$ 0 0
$$546$$ 15.2592 0.653031
$$547$$ 8.77746 0.375297 0.187648 0.982236i $$-0.439913\pi$$
0.187648 + 0.982236i $$0.439913\pi$$
$$548$$ −1.21243 −0.0517922
$$549$$ 25.6106 1.09303
$$550$$ 0 0
$$551$$ −3.12013 −0.132922
$$552$$ −14.8799 −0.633329
$$553$$ −14.5461 −0.618565
$$554$$ −0.573988 −0.0243864
$$555$$ 0 0
$$556$$ 7.53222 0.319437
$$557$$ 21.6663 0.918030 0.459015 0.888429i $$-0.348202\pi$$
0.459015 + 0.888429i $$0.348202\pi$$
$$558$$ −12.9710 −0.549106
$$559$$ 54.7307 2.31486
$$560$$ 0 0
$$561$$ 2.75593 0.116355
$$562$$ −29.2592 −1.23422
$$563$$ −19.4437 −0.819456 −0.409728 0.912208i $$-0.634376\pi$$
−0.409728 + 0.912208i $$0.634376\pi$$
$$564$$ 0 0
$$565$$ 0 0
$$566$$ 21.0177 0.883441
$$567$$ 13.7559 0.577695
$$568$$ 5.60679 0.235256
$$569$$ 21.7446 0.911583 0.455792 0.890087i $$-0.349356\pi$$
0.455792 + 0.890087i $$0.349356\pi$$
$$570$$ 0 0
$$571$$ 1.54498 0.0646556 0.0323278 0.999477i $$-0.489708\pi$$
0.0323278 + 0.999477i $$0.489708\pi$$
$$572$$ −23.4121 −0.978909
$$573$$ 56.4905 2.35992
$$574$$ −15.1239 −0.631261
$$575$$ 0 0
$$576$$ 2.16686 0.0902858
$$577$$ 37.8837 1.57712 0.788559 0.614959i $$-0.210828\pi$$
0.788559 + 0.614959i $$0.210828\pi$$
$$578$$ −16.9254 −0.704005
$$579$$ 17.3970 0.722995
$$580$$ 0 0
$$581$$ 4.95708 0.205654
$$582$$ 2.00000 0.0829027
$$583$$ 10.3616 0.429132
$$584$$ 9.71301 0.401927
$$585$$ 0 0
$$586$$ 17.9582 0.741848
$$587$$ 38.8053 1.60167 0.800833 0.598888i $$-0.204390\pi$$
0.800833 + 0.598888i $$0.204390\pi$$
$$588$$ 12.2275 0.504254
$$589$$ 34.1985 1.40912
$$590$$ 0 0
$$591$$ −33.0328 −1.35879
$$592$$ 1.00000 0.0410997
$$593$$ −22.0923 −0.907222 −0.453611 0.891200i $$-0.649864\pi$$
−0.453611 + 0.891200i $$0.649864\pi$$
$$594$$ −8.40829 −0.344996
$$595$$ 0 0
$$596$$ −13.9861 −0.572892
$$597$$ 29.2769 1.19822
$$598$$ 34.5183 1.41156
$$599$$ −17.8471 −0.729211 −0.364606 0.931162i $$-0.618796\pi$$
−0.364606 + 0.931162i $$0.618796\pi$$
$$600$$ 0 0
$$601$$ 46.1100 1.88087 0.940433 0.339978i $$-0.110420\pi$$
0.940433 + 0.339978i $$0.110420\pi$$
$$602$$ −13.2136 −0.538546
$$603$$ −15.4994 −0.631185
$$604$$ 13.7597 0.559876
$$605$$ 0 0
$$606$$ −8.33372 −0.338534
$$607$$ 47.3842 1.92327 0.961634 0.274337i $$-0.0884583\pi$$
0.961634 + 0.274337i $$0.0884583\pi$$
$$608$$ −5.71301 −0.231693
$$609$$ 1.58043 0.0640422
$$610$$ 0 0
$$611$$ 0 0
$$612$$ 0.591711 0.0239185
$$613$$ 15.7876 0.637654 0.318827 0.947813i $$-0.396711\pi$$
0.318827 + 0.947813i $$0.396711\pi$$
$$614$$ 23.1985 0.936215
$$615$$ 0 0
$$616$$ 5.65236 0.227740
$$617$$ 26.1390 1.05232 0.526159 0.850386i $$-0.323632\pi$$
0.526159 + 0.850386i $$0.323632\pi$$
$$618$$ −28.0038 −1.12648
$$619$$ 31.3047 1.25824 0.629121 0.777307i $$-0.283415\pi$$
0.629121 + 0.777307i $$0.283415\pi$$
$$620$$ 0 0
$$621$$ 12.3970 0.497475
$$622$$ −6.98492 −0.280070
$$623$$ −17.6524 −0.707227
$$624$$ −11.9861 −0.479827
$$625$$ 0 0
$$626$$ 24.1669 0.965902
$$627$$ −57.6573 −2.30261
$$628$$ −2.56007 −0.102158
$$629$$ 0.273073 0.0108881
$$630$$ 0 0
$$631$$ −15.3047 −0.609271 −0.304636 0.952469i $$-0.598535\pi$$
−0.304636 + 0.952469i $$0.598535\pi$$
$$632$$ 11.4260 0.454502
$$633$$ 43.5360 1.73040
$$634$$ −32.2920 −1.28248
$$635$$ 0 0
$$636$$ 5.30472 0.210346
$$637$$ −28.3654 −1.12388
$$638$$ −2.42485 −0.0960008
$$639$$ 12.1491 0.480612
$$640$$ 0 0
$$641$$ −12.8520 −0.507624 −0.253812 0.967254i $$-0.581685\pi$$
−0.253812 + 0.967254i $$0.581685\pi$$
$$642$$ 16.7420 0.660754
$$643$$ −0.139018 −0.00548233 −0.00274117 0.999996i $$-0.500873\pi$$
−0.00274117 + 0.999996i $$0.500873\pi$$
$$644$$ −8.33372 −0.328395
$$645$$ 0 0
$$646$$ −1.56007 −0.0613800
$$647$$ 46.8659 1.84249 0.921245 0.388982i $$-0.127173\pi$$
0.921245 + 0.388982i $$0.127173\pi$$
$$648$$ −10.8053 −0.424472
$$649$$ −10.5639 −0.414668
$$650$$ 0 0
$$651$$ −17.3224 −0.678920
$$652$$ 21.7130 0.850347
$$653$$ −7.48550 −0.292930 −0.146465 0.989216i $$-0.546790\pi$$
−0.146465 + 0.989216i $$0.546790\pi$$
$$654$$ −9.85086 −0.385199
$$655$$ 0 0
$$656$$ 11.8799 0.463831
$$657$$ 21.0467 0.821111
$$658$$ 0 0
$$659$$ −22.7914 −0.887826 −0.443913 0.896070i $$-0.646410\pi$$
−0.443913 + 0.896070i $$0.646410\pi$$
$$660$$ 0 0
$$661$$ 16.4249 0.638853 0.319426 0.947611i $$-0.396510\pi$$
0.319426 + 0.947611i $$0.396510\pi$$
$$662$$ −27.9254 −1.08535
$$663$$ −3.27307 −0.127116
$$664$$ −3.89379 −0.151108
$$665$$ 0 0
$$666$$ 2.16686 0.0839641
$$667$$ 3.57515 0.138430
$$668$$ −16.8659 −0.652563
$$669$$ 6.27043 0.242429
$$670$$ 0 0
$$671$$ −52.4765 −2.02583
$$672$$ 2.89379 0.111630
$$673$$ 51.2035 1.97375 0.986874 0.161490i $$-0.0516300\pi$$
0.986874 + 0.161490i $$0.0516300\pi$$
$$674$$ −8.33256 −0.320958
$$675$$ 0 0
$$676$$ 14.8053 0.569435
$$677$$ −1.00116 −0.0384778 −0.0192389 0.999815i $$-0.506124\pi$$
−0.0192389 + 0.999815i $$0.506124\pi$$
$$678$$ 4.78757 0.183866
$$679$$ 1.12013 0.0429868
$$680$$ 0 0
$$681$$ −39.2313 −1.50335
$$682$$ 26.5778 1.01772
$$683$$ 28.3526 1.08488 0.542441 0.840094i $$-0.317500\pi$$
0.542441 + 0.840094i $$0.317500\pi$$
$$684$$ −12.3793 −0.473334
$$685$$ 0 0
$$686$$ 15.7597 0.601709
$$687$$ 50.7029 1.93444
$$688$$ 10.3793 0.395707
$$689$$ −12.3059 −0.468817
$$690$$ 0 0
$$691$$ 26.3842 1.00370 0.501852 0.864953i $$-0.332652\pi$$
0.501852 + 0.864953i $$0.332652\pi$$
$$692$$ −10.7586 −0.408980
$$693$$ 12.2479 0.465258
$$694$$ −1.99884 −0.0758749
$$695$$ 0 0
$$696$$ −1.24143 −0.0470562
$$697$$ 3.24407 0.122878
$$698$$ −21.9582 −0.831132
$$699$$ −55.3526 −2.09363
$$700$$ 0 0
$$701$$ 40.5801 1.53269 0.766345 0.642429i $$-0.222073\pi$$
0.766345 + 0.642429i $$0.222073\pi$$
$$702$$ 9.98608 0.376900
$$703$$ −5.71301 −0.215470
$$704$$ −4.43993 −0.167336
$$705$$ 0 0
$$706$$ 11.7597 0.442583
$$707$$ −4.66744 −0.175537
$$708$$ −5.40829 −0.203256
$$709$$ 14.5461 0.546292 0.273146 0.961973i $$-0.411936\pi$$
0.273146 + 0.961973i $$0.411936\pi$$
$$710$$ 0 0
$$711$$ 24.7586 0.928519
$$712$$ 13.8659 0.519648
$$713$$ −39.1857 −1.46752
$$714$$ 0.790215 0.0295730
$$715$$ 0 0
$$716$$ 1.66744 0.0623152
$$717$$ −4.06329 −0.151746
$$718$$ 2.57399 0.0960604
$$719$$ 21.6701 0.808158 0.404079 0.914724i $$-0.367592\pi$$
0.404079 + 0.914724i $$0.367592\pi$$
$$720$$ 0 0
$$721$$ −15.6840 −0.584103
$$722$$ 13.6384 0.507570
$$723$$ 8.47158 0.315061
$$724$$ 5.97216 0.221953
$$725$$ 0 0
$$726$$ −19.8053 −0.735044
$$727$$ 28.8799 1.07109 0.535547 0.844505i $$-0.320105\pi$$
0.535547 + 0.844505i $$0.320105\pi$$
$$728$$ −6.71301 −0.248801
$$729$$ −10.4994 −0.388867
$$730$$ 0 0
$$731$$ 2.83430 0.104830
$$732$$ −26.8659 −0.992994
$$733$$ −21.9165 −0.809503 −0.404752 0.914427i $$-0.632642\pi$$
−0.404752 + 0.914427i $$0.632642\pi$$
$$734$$ −12.4867 −0.460891
$$735$$ 0 0
$$736$$ 6.54615 0.241294
$$737$$ 31.7586 1.16984
$$738$$ 25.7420 0.947576
$$739$$ −29.7040 −1.09268 −0.546341 0.837563i $$-0.683980\pi$$
−0.546341 + 0.837563i $$0.683980\pi$$
$$740$$ 0 0
$$741$$ 68.4765 2.51555
$$742$$ 2.97100 0.109069
$$743$$ −39.5171 −1.44974 −0.724872 0.688884i $$-0.758101\pi$$
−0.724872 + 0.688884i $$0.758101\pi$$
$$744$$ 13.6068 0.498849
$$745$$ 0 0
$$746$$ −14.8659 −0.544281
$$747$$ −8.43729 −0.308704
$$748$$ −1.21243 −0.0443307
$$749$$ 9.37665 0.342615
$$750$$ 0 0
$$751$$ −11.6384 −0.424693 −0.212346 0.977194i $$-0.568110\pi$$
−0.212346 + 0.977194i $$0.568110\pi$$
$$752$$ 0 0
$$753$$ 20.4577 0.745518
$$754$$ 2.87987 0.104879
$$755$$ 0 0
$$756$$ −2.41093 −0.0876847
$$757$$ 21.0923 0.766612 0.383306 0.923621i $$-0.374785\pi$$
0.383306 + 0.923621i $$0.374785\pi$$
$$758$$ −2.39437 −0.0869674
$$759$$ 66.0656 2.39803
$$760$$ 0 0
$$761$$ −16.8988 −0.612579 −0.306290 0.951938i $$-0.599088\pi$$
−0.306290 + 0.951938i $$0.599088\pi$$
$$762$$ −30.9292 −1.12045
$$763$$ −5.51714 −0.199734
$$764$$ −24.8520 −0.899115
$$765$$ 0 0
$$766$$ −14.7725 −0.533752
$$767$$ 12.5461 0.453015
$$768$$ −2.27307 −0.0820225
$$769$$ 28.6524 1.03323 0.516615 0.856218i $$-0.327192\pi$$
0.516615 + 0.856218i $$0.327192\pi$$
$$770$$ 0 0
$$771$$ −7.78757 −0.280463
$$772$$ −7.65352 −0.275456
$$773$$ −10.3198 −0.371177 −0.185589 0.982628i $$-0.559419\pi$$
−0.185589 + 0.982628i $$0.559419\pi$$
$$774$$ 22.4905 0.808403
$$775$$ 0 0
$$776$$ −0.879866 −0.0315854
$$777$$ 2.89379 0.103814
$$778$$ −12.6991 −0.455284
$$779$$ −67.8697 −2.43169
$$780$$ 0 0
$$781$$ −24.8938 −0.890770
$$782$$ 1.78757 0.0639235
$$783$$ 1.03428 0.0369623
$$784$$ −5.37929 −0.192117
$$785$$ 0 0
$$786$$ −9.47158 −0.337840
$$787$$ 16.3337 0.582234 0.291117 0.956687i $$-0.405973\pi$$
0.291117 + 0.956687i $$0.405973\pi$$
$$788$$ 14.5322 0.517689
$$789$$ 5.85086 0.208296
$$790$$ 0 0
$$791$$ 2.68136 0.0953383
$$792$$ −9.62071 −0.341857
$$793$$ 62.3236 2.21318
$$794$$ −4.98492 −0.176908
$$795$$ 0 0
$$796$$ −12.8799 −0.456515
$$797$$ 2.96719 0.105103 0.0525517 0.998618i $$-0.483265\pi$$
0.0525517 + 0.998618i $$0.483265\pi$$
$$798$$ −16.5322 −0.585234
$$799$$ 0 0
$$800$$ 0 0
$$801$$ 30.0456 1.06161
$$802$$ 27.1985 0.960413
$$803$$ −43.1251 −1.52185
$$804$$ 16.2592 0.573416
$$805$$ 0 0
$$806$$ −31.5650 −1.11183
$$807$$ 63.0366 2.21899
$$808$$ 3.66628 0.128979
$$809$$ −7.87870 −0.277001 −0.138500 0.990362i $$-0.544228\pi$$
−0.138500 + 0.990362i $$0.544228\pi$$
$$810$$ 0 0
$$811$$ −48.6396 −1.70797 −0.853984 0.520300i $$-0.825820\pi$$
−0.853984 + 0.520300i $$0.825820\pi$$
$$812$$ −0.695283 −0.0243997
$$813$$ −60.1428 −2.10930
$$814$$ −4.43993 −0.155620
$$815$$ 0 0
$$816$$ −0.620715 −0.0217294
$$817$$ −59.2969 −2.07454
$$818$$ 35.5499 1.24297
$$819$$ −14.5461 −0.508283
$$820$$ 0 0
$$821$$ −7.68020 −0.268041 −0.134020 0.990979i $$-0.542789\pi$$
−0.134020 + 0.990979i $$0.542789\pi$$
$$822$$ 2.75593 0.0961241
$$823$$ −26.3654 −0.919039 −0.459519 0.888168i $$-0.651978\pi$$
−0.459519 + 0.888168i $$0.651978\pi$$
$$824$$ 12.3198 0.429181
$$825$$ 0 0
$$826$$ −3.02900 −0.105393
$$827$$ −17.8343 −0.620159 −0.310080 0.950711i $$-0.600356\pi$$
−0.310080 + 0.950711i $$0.600356\pi$$
$$828$$ 14.1846 0.492948
$$829$$ −5.17962 −0.179896 −0.0899478 0.995946i $$-0.528670\pi$$
−0.0899478 + 0.995946i $$0.528670\pi$$
$$830$$ 0 0
$$831$$ 1.30472 0.0452601
$$832$$ 5.27307 0.182811
$$833$$ −1.46894 −0.0508956
$$834$$ −17.1213 −0.592862
$$835$$ 0 0
$$836$$ 25.3654 0.877279
$$837$$ −11.3364 −0.391842
$$838$$ −29.5322 −1.02017
$$839$$ −6.15294 −0.212423 −0.106212 0.994344i $$-0.533872\pi$$
−0.106212 + 0.994344i $$0.533872\pi$$
$$840$$ 0 0
$$841$$ −28.7017 −0.989715
$$842$$ −30.4905 −1.05077
$$843$$ 66.5082 2.29066
$$844$$ −19.1529 −0.659271
$$845$$ 0 0
$$846$$ 0 0
$$847$$ −11.0923 −0.381136
$$848$$ −2.33372 −0.0801403
$$849$$ −47.7748 −1.63963
$$850$$ 0 0
$$851$$ 6.54615 0.224399
$$852$$ −12.7446 −0.436625
$$853$$ −30.8837 −1.05744 −0.528718 0.848797i $$-0.677327\pi$$
−0.528718 + 0.848797i $$0.677327\pi$$
$$854$$ −15.0467 −0.514888
$$855$$ 0 0
$$856$$ −7.36536 −0.251743
$$857$$ 15.1529 0.517615 0.258807 0.965929i $$-0.416671\pi$$
0.258807 + 0.965929i $$0.416671\pi$$
$$858$$ 53.2174 1.81681
$$859$$ −7.28583 −0.248589 −0.124295 0.992245i $$-0.539667\pi$$
−0.124295 + 0.992245i $$0.539667\pi$$
$$860$$ 0 0
$$861$$ 34.3778 1.17159
$$862$$ 21.9722 0.748375
$$863$$ −51.7357 −1.76110 −0.880552 0.473950i $$-0.842828\pi$$
−0.880552 + 0.473950i $$0.842828\pi$$
$$864$$ 1.89379 0.0644280
$$865$$ 0 0
$$866$$ 5.00000 0.169907
$$867$$ 38.4727 1.30660
$$868$$ 7.62071 0.258664
$$869$$ −50.7307 −1.72092
$$870$$ 0 0
$$871$$ −37.7180 −1.27802
$$872$$ 4.33372 0.146758
$$873$$ −1.90655 −0.0645268
$$874$$ −37.3982 −1.26501
$$875$$ 0 0
$$876$$ −22.0784 −0.745959
$$877$$ −50.4109 −1.70226 −0.851128 0.524958i $$-0.824081\pi$$
−0.851128 + 0.524958i $$0.824081\pi$$
$$878$$ 29.5171 0.996155
$$879$$ −40.8204 −1.37684
$$880$$ 0 0
$$881$$ −45.0822 −1.51886 −0.759428 0.650591i $$-0.774521\pi$$
−0.759428 + 0.650591i $$0.774521\pi$$
$$882$$ −11.6562 −0.392483
$$883$$ −17.9988 −0.605709 −0.302855 0.953037i $$-0.597940\pi$$
−0.302855 + 0.953037i $$0.597940\pi$$
$$884$$ 1.43993 0.0484302
$$885$$ 0 0
$$886$$ −28.9861 −0.973806
$$887$$ −38.2502 −1.28432 −0.642158 0.766572i $$-0.721961\pi$$
−0.642158 + 0.766572i $$0.721961\pi$$
$$888$$ −2.27307 −0.0762793
$$889$$ −17.3224 −0.580976
$$890$$ 0 0
$$891$$ 47.9748 1.60722
$$892$$ −2.75857 −0.0923638
$$893$$ 0 0
$$894$$ 31.7914 1.06326
$$895$$ 0 0
$$896$$ −1.27307 −0.0425304
$$897$$ −78.4626 −2.61979
$$898$$ 36.6245 1.22218
$$899$$ −3.26927 −0.109036
$$900$$ 0 0
$$901$$ −0.637276 −0.0212307
$$902$$ −52.7458 −1.75624
$$903$$ 30.0354 0.999517
$$904$$ −2.10621 −0.0700516
$$905$$ 0 0
$$906$$ −31.2769 −1.03910
$$907$$ 10.0734 0.334482 0.167241 0.985916i $$-0.446514\pi$$
0.167241 + 0.985916i $$0.446514\pi$$
$$908$$ 17.2592 0.572765
$$909$$ 7.94432 0.263496
$$910$$ 0 0
$$911$$ −5.56123 −0.184252 −0.0921259 0.995747i $$-0.529366\pi$$
−0.0921259 + 0.995747i $$0.529366\pi$$
$$912$$ 12.9861 0.430012
$$913$$ 17.2882 0.572154
$$914$$ −19.7446 −0.653095
$$915$$ 0 0
$$916$$ −22.3059 −0.737007
$$917$$ −5.30472 −0.175177
$$918$$ 0.517142 0.0170682
$$919$$ −3.75973 −0.124022 −0.0620111 0.998075i $$-0.519751\pi$$
−0.0620111 + 0.998075i $$0.519751\pi$$
$$920$$ 0 0
$$921$$ −52.7319 −1.73757
$$922$$ 34.9733 1.15178
$$923$$ 29.5650 0.973145
$$924$$ −12.8482 −0.422675
$$925$$ 0 0
$$926$$ 24.1707 0.794297
$$927$$ 26.6953 0.876788
$$928$$ 0.546146 0.0179281
$$929$$ 3.40597 0.111746 0.0558731 0.998438i $$-0.482206\pi$$
0.0558731 + 0.998438i $$0.482206\pi$$
$$930$$ 0 0
$$931$$ 30.7319 1.00720
$$932$$ 24.3514 0.797658
$$933$$ 15.8772 0.519797
$$934$$ −7.63844 −0.249937
$$935$$ 0 0
$$936$$ 11.4260 0.373471
$$937$$ 34.8053 1.13704 0.568520 0.822670i $$-0.307516\pi$$
0.568520 + 0.822670i $$0.307516\pi$$
$$938$$ 9.10621 0.297328
$$939$$ −54.9330 −1.79267
$$940$$ 0 0
$$941$$ −1.63844 −0.0534115 −0.0267058 0.999643i $$-0.508502\pi$$
−0.0267058 + 0.999643i $$0.508502\pi$$
$$942$$ 5.81922 0.189600
$$943$$ 77.7673 2.53245
$$944$$ 2.37929 0.0774391
$$945$$ 0 0
$$946$$ −46.0833 −1.49830
$$947$$ 30.8520 1.00256 0.501278 0.865286i $$-0.332863\pi$$
0.501278 + 0.865286i $$0.332863\pi$$
$$948$$ −25.9722 −0.843536
$$949$$ 51.2174 1.66259
$$950$$ 0 0
$$951$$ 73.4020 2.38022
$$952$$ −0.347642 −0.0112671
$$953$$ −34.0467 −1.10288 −0.551441 0.834214i $$-0.685922\pi$$
−0.551441 + 0.834214i $$0.685922\pi$$
$$954$$ −5.05685 −0.163721
$$955$$ 0 0
$$956$$ 1.78757 0.0578143
$$957$$ 5.51186 0.178173
$$958$$ −4.01392 −0.129684
$$959$$ 1.54351 0.0498424
$$960$$ 0 0
$$961$$ 4.83314 0.155908
$$962$$ 5.27307 0.170011
$$963$$ −15.9597 −0.514295
$$964$$ −3.72693 −0.120036
$$965$$ 0 0
$$966$$ 18.9432 0.609486
$$967$$ 58.2757 1.87402 0.937010 0.349302i $$-0.113581\pi$$
0.937010 + 0.349302i $$0.113581\pi$$
$$968$$ 8.71301 0.280047
$$969$$ 3.54615 0.113919
$$970$$ 0 0
$$971$$ 57.6611 1.85043 0.925217 0.379439i $$-0.123883\pi$$
0.925217 + 0.379439i $$0.123883\pi$$
$$972$$ 18.8799 0.605572
$$973$$ −9.58907 −0.307411
$$974$$ −43.3842 −1.39012
$$975$$ 0 0
$$976$$ 11.8192 0.378324
$$977$$ −3.78261 −0.121016 −0.0605082 0.998168i $$-0.519272\pi$$
−0.0605082 + 0.998168i $$0.519272\pi$$
$$978$$ −49.3552 −1.57821
$$979$$ −61.5639 −1.96759
$$980$$ 0 0
$$981$$ 9.39057 0.299818
$$982$$ −20.7307 −0.661544
$$983$$ 41.3047 1.31742 0.658708 0.752399i $$-0.271103\pi$$
0.658708 + 0.752399i $$0.271103\pi$$
$$984$$ −27.0038 −0.860850
$$985$$ 0 0
$$986$$ 0.149138 0.00474951
$$987$$ 0 0
$$988$$ −30.1251 −0.958407
$$989$$ 67.9443 2.16050
$$990$$ 0 0
$$991$$ −9.89263 −0.314250 −0.157125 0.987579i $$-0.550222\pi$$
−0.157125 + 0.987579i $$0.550222\pi$$
$$992$$ −5.98608 −0.190058
$$993$$ 63.4765 2.01437
$$994$$ −7.13786 −0.226399
$$995$$ 0 0
$$996$$ 8.85086 0.280450
$$997$$ −44.5221 −1.41003 −0.705015 0.709193i $$-0.749060\pi$$
−0.705015 + 0.709193i $$0.749060\pi$$
$$998$$ 5.92659 0.187603
$$999$$ 1.89379 0.0599168
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 1850.2.a.bc.1.1 yes 3
5.2 odd 4 1850.2.b.p.149.6 6
5.3 odd 4 1850.2.b.p.149.1 6
5.4 even 2 1850.2.a.y.1.3 3

By twisted newform
Twist Min Dim Char Parity Ord Type
1850.2.a.y.1.3 3 5.4 even 2
1850.2.a.bc.1.1 yes 3 1.1 even 1 trivial
1850.2.b.p.149.1 6 5.3 odd 4
1850.2.b.p.149.6 6 5.2 odd 4