# Properties

 Label 3675.2.a.bj.1.1 Level $3675$ Weight $2$ Character 3675.1 Self dual yes Analytic conductor $29.345$ Analytic rank $0$ Dimension $3$ CM no Inner twists $1$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$3675 = 3 \cdot 5^{2} \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 3675.a (trivial)

## Newform invariants

 Self dual: yes Analytic conductor: $$29.3450227428$$ Analytic rank: $$0$$ Dimension: $$3$$ Coefficient field: 3.3.148.1 Defining polynomial: $$x^{3} - x^{2} - 3x + 1$$ x^3 - x^2 - 3*x + 1 Coefficient ring: $$\Z[a_1, a_2]$$ Coefficient ring index: $$2$$ Twist minimal: no (minimal twist has level 105) Fricke sign: $$-1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

 Embedding label 1.1 Root $$0.311108$$ of defining polynomial Character $$\chi$$ $$=$$ 3675.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q-1.90321 q^{2} +1.00000 q^{3} +1.62222 q^{4} -1.90321 q^{6} +0.719004 q^{8} +1.00000 q^{9} +O(q^{10})$$ $$q-1.90321 q^{2} +1.00000 q^{3} +1.62222 q^{4} -1.90321 q^{6} +0.719004 q^{8} +1.00000 q^{9} +2.00000 q^{11} +1.62222 q^{12} +6.42864 q^{13} -4.61285 q^{16} -4.42864 q^{17} -1.90321 q^{18} +2.42864 q^{19} -3.80642 q^{22} +1.37778 q^{23} +0.719004 q^{24} -12.2351 q^{26} +1.00000 q^{27} +0.755569 q^{29} -5.18421 q^{31} +7.34122 q^{32} +2.00000 q^{33} +8.42864 q^{34} +1.62222 q^{36} +7.61285 q^{37} -4.62222 q^{38} +6.42864 q^{39} +8.23506 q^{41} +10.1017 q^{43} +3.24443 q^{44} -2.62222 q^{46} -2.75557 q^{47} -4.61285 q^{48} -4.42864 q^{51} +10.4286 q^{52} +9.18421 q^{53} -1.90321 q^{54} +2.42864 q^{57} -1.43801 q^{58} -14.1017 q^{59} -6.85728 q^{61} +9.86665 q^{62} -4.74620 q^{64} -3.80642 q^{66} +2.75557 q^{67} -7.18421 q^{68} +1.37778 q^{69} +2.00000 q^{71} +0.719004 q^{72} +1.57136 q^{73} -14.4889 q^{74} +3.93978 q^{76} -12.2351 q^{78} -4.85728 q^{79} +1.00000 q^{81} -15.6731 q^{82} -11.6128 q^{83} -19.2257 q^{86} +0.755569 q^{87} +1.43801 q^{88} -4.62222 q^{89} +2.23506 q^{92} -5.18421 q^{93} +5.24443 q^{94} +7.34122 q^{96} +11.9398 q^{97} +2.00000 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$3 q + q^{2} + 3 q^{3} + 5 q^{4} + q^{6} + 9 q^{8} + 3 q^{9}+O(q^{10})$$ 3 * q + q^2 + 3 * q^3 + 5 * q^4 + q^6 + 9 * q^8 + 3 * q^9 $$3 q + q^{2} + 3 q^{3} + 5 q^{4} + q^{6} + 9 q^{8} + 3 q^{9} + 6 q^{11} + 5 q^{12} + 6 q^{13} + 13 q^{16} + q^{18} - 6 q^{19} + 2 q^{22} + 4 q^{23} + 9 q^{24} - 10 q^{26} + 3 q^{27} + 2 q^{29} - 2 q^{31} + 29 q^{32} + 6 q^{33} + 12 q^{34} + 5 q^{36} - 4 q^{37} - 14 q^{38} + 6 q^{39} - 2 q^{41} + 4 q^{43} + 10 q^{44} - 8 q^{46} - 8 q^{47} + 13 q^{48} + 18 q^{52} + 14 q^{53} + q^{54} - 6 q^{57} - 18 q^{58} - 16 q^{59} + 6 q^{61} + 30 q^{62} + 13 q^{64} + 2 q^{66} + 8 q^{67} - 8 q^{68} + 4 q^{69} + 6 q^{71} + 9 q^{72} + 18 q^{73} - 44 q^{74} - 2 q^{76} - 10 q^{78} + 12 q^{79} + 3 q^{81} - 34 q^{82} - 8 q^{83} - 4 q^{86} + 2 q^{87} + 18 q^{88} - 14 q^{89} - 20 q^{92} - 2 q^{93} + 16 q^{94} + 29 q^{96} + 22 q^{97} + 6 q^{99}+O(q^{100})$$ 3 * q + q^2 + 3 * q^3 + 5 * q^4 + q^6 + 9 * q^8 + 3 * q^9 + 6 * q^11 + 5 * q^12 + 6 * q^13 + 13 * q^16 + q^18 - 6 * q^19 + 2 * q^22 + 4 * q^23 + 9 * q^24 - 10 * q^26 + 3 * q^27 + 2 * q^29 - 2 * q^31 + 29 * q^32 + 6 * q^33 + 12 * q^34 + 5 * q^36 - 4 * q^37 - 14 * q^38 + 6 * q^39 - 2 * q^41 + 4 * q^43 + 10 * q^44 - 8 * q^46 - 8 * q^47 + 13 * q^48 + 18 * q^52 + 14 * q^53 + q^54 - 6 * q^57 - 18 * q^58 - 16 * q^59 + 6 * q^61 + 30 * q^62 + 13 * q^64 + 2 * q^66 + 8 * q^67 - 8 * q^68 + 4 * q^69 + 6 * q^71 + 9 * q^72 + 18 * q^73 - 44 * q^74 - 2 * q^76 - 10 * q^78 + 12 * q^79 + 3 * q^81 - 34 * q^82 - 8 * q^83 - 4 * q^86 + 2 * q^87 + 18 * q^88 - 14 * q^89 - 20 * q^92 - 2 * q^93 + 16 * q^94 + 29 * q^96 + 22 * q^97 + 6 * 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −1.90321 −1.34577 −0.672887 0.739745i $$-0.734946\pi$$
−0.672887 + 0.739745i $$0.734946\pi$$
$$3$$ 1.00000 0.577350
$$4$$ 1.62222 0.811108
$$5$$ 0 0
$$6$$ −1.90321 −0.776983
$$7$$ 0 0
$$8$$ 0.719004 0.254206
$$9$$ 1.00000 0.333333
$$10$$ 0 0
$$11$$ 2.00000 0.603023 0.301511 0.953463i $$-0.402509\pi$$
0.301511 + 0.953463i $$0.402509\pi$$
$$12$$ 1.62222 0.468293
$$13$$ 6.42864 1.78298 0.891492 0.453037i $$-0.149659\pi$$
0.891492 + 0.453037i $$0.149659\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ −4.61285 −1.15321
$$17$$ −4.42864 −1.07410 −0.537051 0.843550i $$-0.680462\pi$$
−0.537051 + 0.843550i $$0.680462\pi$$
$$18$$ −1.90321 −0.448591
$$19$$ 2.42864 0.557168 0.278584 0.960412i $$-0.410135\pi$$
0.278584 + 0.960412i $$0.410135\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ −3.80642 −0.811532
$$23$$ 1.37778 0.287288 0.143644 0.989629i $$-0.454118\pi$$
0.143644 + 0.989629i $$0.454118\pi$$
$$24$$ 0.719004 0.146766
$$25$$ 0 0
$$26$$ −12.2351 −2.39949
$$27$$ 1.00000 0.192450
$$28$$ 0 0
$$29$$ 0.755569 0.140306 0.0701528 0.997536i $$-0.477651\pi$$
0.0701528 + 0.997536i $$0.477651\pi$$
$$30$$ 0 0
$$31$$ −5.18421 −0.931111 −0.465556 0.885019i $$-0.654145\pi$$
−0.465556 + 0.885019i $$0.654145\pi$$
$$32$$ 7.34122 1.29776
$$33$$ 2.00000 0.348155
$$34$$ 8.42864 1.44550
$$35$$ 0 0
$$36$$ 1.62222 0.270369
$$37$$ 7.61285 1.25154 0.625772 0.780006i $$-0.284784\pi$$
0.625772 + 0.780006i $$0.284784\pi$$
$$38$$ −4.62222 −0.749822
$$39$$ 6.42864 1.02941
$$40$$ 0 0
$$41$$ 8.23506 1.28610 0.643050 0.765824i $$-0.277669\pi$$
0.643050 + 0.765824i $$0.277669\pi$$
$$42$$ 0 0
$$43$$ 10.1017 1.54050 0.770248 0.637744i $$-0.220132\pi$$
0.770248 + 0.637744i $$0.220132\pi$$
$$44$$ 3.24443 0.489116
$$45$$ 0 0
$$46$$ −2.62222 −0.386625
$$47$$ −2.75557 −0.401941 −0.200971 0.979597i $$-0.564410\pi$$
−0.200971 + 0.979597i $$0.564410\pi$$
$$48$$ −4.61285 −0.665807
$$49$$ 0 0
$$50$$ 0 0
$$51$$ −4.42864 −0.620134
$$52$$ 10.4286 1.44619
$$53$$ 9.18421 1.26155 0.630774 0.775967i $$-0.282737\pi$$
0.630774 + 0.775967i $$0.282737\pi$$
$$54$$ −1.90321 −0.258994
$$55$$ 0 0
$$56$$ 0 0
$$57$$ 2.42864 0.321681
$$58$$ −1.43801 −0.188820
$$59$$ −14.1017 −1.83589 −0.917943 0.396712i $$-0.870151\pi$$
−0.917943 + 0.396712i $$0.870151\pi$$
$$60$$ 0 0
$$61$$ −6.85728 −0.877985 −0.438992 0.898491i $$-0.644664\pi$$
−0.438992 + 0.898491i $$0.644664\pi$$
$$62$$ 9.86665 1.25307
$$63$$ 0 0
$$64$$ −4.74620 −0.593275
$$65$$ 0 0
$$66$$ −3.80642 −0.468538
$$67$$ 2.75557 0.336646 0.168323 0.985732i $$-0.446165\pi$$
0.168323 + 0.985732i $$0.446165\pi$$
$$68$$ −7.18421 −0.871213
$$69$$ 1.37778 0.165866
$$70$$ 0 0
$$71$$ 2.00000 0.237356 0.118678 0.992933i $$-0.462134\pi$$
0.118678 + 0.992933i $$0.462134\pi$$
$$72$$ 0.719004 0.0847354
$$73$$ 1.57136 0.183914 0.0919569 0.995763i $$-0.470688\pi$$
0.0919569 + 0.995763i $$0.470688\pi$$
$$74$$ −14.4889 −1.68430
$$75$$ 0 0
$$76$$ 3.93978 0.451923
$$77$$ 0 0
$$78$$ −12.2351 −1.38535
$$79$$ −4.85728 −0.546487 −0.273243 0.961945i $$-0.588096\pi$$
−0.273243 + 0.961945i $$0.588096\pi$$
$$80$$ 0 0
$$81$$ 1.00000 0.111111
$$82$$ −15.6731 −1.73080
$$83$$ −11.6128 −1.27468 −0.637338 0.770585i $$-0.719964\pi$$
−0.637338 + 0.770585i $$0.719964\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ −19.2257 −2.07316
$$87$$ 0.755569 0.0810055
$$88$$ 1.43801 0.153292
$$89$$ −4.62222 −0.489954 −0.244977 0.969529i $$-0.578780\pi$$
−0.244977 + 0.969529i $$0.578780\pi$$
$$90$$ 0 0
$$91$$ 0 0
$$92$$ 2.23506 0.233021
$$93$$ −5.18421 −0.537577
$$94$$ 5.24443 0.540922
$$95$$ 0 0
$$96$$ 7.34122 0.749260
$$97$$ 11.9398 1.21230 0.606150 0.795350i $$-0.292713\pi$$
0.606150 + 0.795350i $$0.292713\pi$$
$$98$$ 0 0
$$99$$ 2.00000 0.201008
$$100$$ 0 0
$$101$$ −1.47949 −0.147215 −0.0736076 0.997287i $$-0.523451\pi$$
−0.0736076 + 0.997287i $$0.523451\pi$$
$$102$$ 8.42864 0.834560
$$103$$ 8.85728 0.872734 0.436367 0.899769i $$-0.356265\pi$$
0.436367 + 0.899769i $$0.356265\pi$$
$$104$$ 4.62222 0.453246
$$105$$ 0 0
$$106$$ −17.4795 −1.69776
$$107$$ 1.76494 0.170623 0.0853114 0.996354i $$-0.472811\pi$$
0.0853114 + 0.996354i $$0.472811\pi$$
$$108$$ 1.62222 0.156098
$$109$$ 5.61285 0.537613 0.268807 0.963194i $$-0.413371\pi$$
0.268807 + 0.963194i $$0.413371\pi$$
$$110$$ 0 0
$$111$$ 7.61285 0.722580
$$112$$ 0 0
$$113$$ −11.2859 −1.06169 −0.530845 0.847469i $$-0.678125\pi$$
−0.530845 + 0.847469i $$0.678125\pi$$
$$114$$ −4.62222 −0.432910
$$115$$ 0 0
$$116$$ 1.22570 0.113803
$$117$$ 6.42864 0.594328
$$118$$ 26.8385 2.47069
$$119$$ 0 0
$$120$$ 0 0
$$121$$ −7.00000 −0.636364
$$122$$ 13.0509 1.18157
$$123$$ 8.23506 0.742531
$$124$$ −8.40990 −0.755232
$$125$$ 0 0
$$126$$ 0 0
$$127$$ −12.8573 −1.14090 −0.570450 0.821333i $$-0.693231\pi$$
−0.570450 + 0.821333i $$0.693231\pi$$
$$128$$ −5.64941 −0.499342
$$129$$ 10.1017 0.889406
$$130$$ 0 0
$$131$$ 2.10171 0.183627 0.0918136 0.995776i $$-0.470734\pi$$
0.0918136 + 0.995776i $$0.470734\pi$$
$$132$$ 3.24443 0.282391
$$133$$ 0 0
$$134$$ −5.24443 −0.453050
$$135$$ 0 0
$$136$$ −3.18421 −0.273044
$$137$$ 15.9398 1.36183 0.680914 0.732364i $$-0.261583\pi$$
0.680914 + 0.732364i $$0.261583\pi$$
$$138$$ −2.62222 −0.223218
$$139$$ −11.6731 −0.990097 −0.495048 0.868865i $$-0.664850\pi$$
−0.495048 + 0.868865i $$0.664850\pi$$
$$140$$ 0 0
$$141$$ −2.75557 −0.232061
$$142$$ −3.80642 −0.319428
$$143$$ 12.8573 1.07518
$$144$$ −4.61285 −0.384404
$$145$$ 0 0
$$146$$ −2.99063 −0.247506
$$147$$ 0 0
$$148$$ 12.3497 1.01514
$$149$$ −21.2257 −1.73888 −0.869438 0.494041i $$-0.835519\pi$$
−0.869438 + 0.494041i $$0.835519\pi$$
$$150$$ 0 0
$$151$$ 16.8573 1.37183 0.685913 0.727684i $$-0.259403\pi$$
0.685913 + 0.727684i $$0.259403\pi$$
$$152$$ 1.74620 0.141636
$$153$$ −4.42864 −0.358034
$$154$$ 0 0
$$155$$ 0 0
$$156$$ 10.4286 0.834959
$$157$$ 10.4286 0.832296 0.416148 0.909297i $$-0.363380\pi$$
0.416148 + 0.909297i $$0.363380\pi$$
$$158$$ 9.24443 0.735447
$$159$$ 9.18421 0.728355
$$160$$ 0 0
$$161$$ 0 0
$$162$$ −1.90321 −0.149530
$$163$$ 20.8573 1.63367 0.816834 0.576873i $$-0.195727\pi$$
0.816834 + 0.576873i $$0.195727\pi$$
$$164$$ 13.3590 1.04317
$$165$$ 0 0
$$166$$ 22.1017 1.71543
$$167$$ −15.3461 −1.18752 −0.593760 0.804642i $$-0.702357\pi$$
−0.593760 + 0.804642i $$0.702357\pi$$
$$168$$ 0 0
$$169$$ 28.3274 2.17903
$$170$$ 0 0
$$171$$ 2.42864 0.185723
$$172$$ 16.3872 1.24951
$$173$$ −2.06022 −0.156636 −0.0783179 0.996928i $$-0.524955\pi$$
−0.0783179 + 0.996928i $$0.524955\pi$$
$$174$$ −1.43801 −0.109015
$$175$$ 0 0
$$176$$ −9.22570 −0.695413
$$177$$ −14.1017 −1.05995
$$178$$ 8.79706 0.659367
$$179$$ 10.0000 0.747435 0.373718 0.927543i $$-0.378083\pi$$
0.373718 + 0.927543i $$0.378083\pi$$
$$180$$ 0 0
$$181$$ 12.1017 0.899513 0.449757 0.893151i $$-0.351511\pi$$
0.449757 + 0.893151i $$0.351511\pi$$
$$182$$ 0 0
$$183$$ −6.85728 −0.506905
$$184$$ 0.990632 0.0730304
$$185$$ 0 0
$$186$$ 9.86665 0.723458
$$187$$ −8.85728 −0.647708
$$188$$ −4.47013 −0.326017
$$189$$ 0 0
$$190$$ 0 0
$$191$$ 0.488863 0.0353729 0.0176864 0.999844i $$-0.494370\pi$$
0.0176864 + 0.999844i $$0.494370\pi$$
$$192$$ −4.74620 −0.342528
$$193$$ −22.9590 −1.65262 −0.826312 0.563212i $$-0.809565\pi$$
−0.826312 + 0.563212i $$0.809565\pi$$
$$194$$ −22.7239 −1.63148
$$195$$ 0 0
$$196$$ 0 0
$$197$$ −1.18421 −0.0843713 −0.0421857 0.999110i $$-0.513432\pi$$
−0.0421857 + 0.999110i $$0.513432\pi$$
$$198$$ −3.80642 −0.270511
$$199$$ −8.79706 −0.623607 −0.311803 0.950147i $$-0.600933\pi$$
−0.311803 + 0.950147i $$0.600933\pi$$
$$200$$ 0 0
$$201$$ 2.75557 0.194363
$$202$$ 2.81579 0.198118
$$203$$ 0 0
$$204$$ −7.18421 −0.502995
$$205$$ 0 0
$$206$$ −16.8573 −1.17450
$$207$$ 1.37778 0.0957626
$$208$$ −29.6543 −2.05616
$$209$$ 4.85728 0.335985
$$210$$ 0 0
$$211$$ 23.2257 1.59892 0.799461 0.600717i $$-0.205118\pi$$
0.799461 + 0.600717i $$0.205118\pi$$
$$212$$ 14.8988 1.02325
$$213$$ 2.00000 0.137038
$$214$$ −3.35905 −0.229620
$$215$$ 0 0
$$216$$ 0.719004 0.0489220
$$217$$ 0 0
$$218$$ −10.6824 −0.723506
$$219$$ 1.57136 0.106183
$$220$$ 0 0
$$221$$ −28.4701 −1.91511
$$222$$ −14.4889 −0.972429
$$223$$ 15.2257 1.01959 0.509794 0.860297i $$-0.329722\pi$$
0.509794 + 0.860297i $$0.329722\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 21.4795 1.42879
$$227$$ 14.3684 0.953665 0.476833 0.878994i $$-0.341785\pi$$
0.476833 + 0.878994i $$0.341785\pi$$
$$228$$ 3.93978 0.260918
$$229$$ 5.61285 0.370907 0.185454 0.982653i $$-0.440625\pi$$
0.185454 + 0.982653i $$0.440625\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0.543257 0.0356666
$$233$$ 23.2859 1.52551 0.762756 0.646687i $$-0.223846\pi$$
0.762756 + 0.646687i $$0.223846\pi$$
$$234$$ −12.2351 −0.799831
$$235$$ 0 0
$$236$$ −22.8760 −1.48910
$$237$$ −4.85728 −0.315514
$$238$$ 0 0
$$239$$ −8.48886 −0.549099 −0.274549 0.961573i $$-0.588529\pi$$
−0.274549 + 0.961573i $$0.588529\pi$$
$$240$$ 0 0
$$241$$ 7.24443 0.466655 0.233327 0.972398i $$-0.425039\pi$$
0.233327 + 0.972398i $$0.425039\pi$$
$$242$$ 13.3225 0.856402
$$243$$ 1.00000 0.0641500
$$244$$ −11.1240 −0.712140
$$245$$ 0 0
$$246$$ −15.6731 −0.999278
$$247$$ 15.6128 0.993422
$$248$$ −3.72746 −0.236694
$$249$$ −11.6128 −0.735934
$$250$$ 0 0
$$251$$ −27.6128 −1.74291 −0.871454 0.490478i $$-0.836822\pi$$
−0.871454 + 0.490478i $$0.836822\pi$$
$$252$$ 0 0
$$253$$ 2.75557 0.173241
$$254$$ 24.4701 1.53539
$$255$$ 0 0
$$256$$ 20.2444 1.26528
$$257$$ 0.428639 0.0267378 0.0133689 0.999911i $$-0.495744\pi$$
0.0133689 + 0.999911i $$0.495744\pi$$
$$258$$ −19.2257 −1.19694
$$259$$ 0 0
$$260$$ 0 0
$$261$$ 0.755569 0.0467685
$$262$$ −4.00000 −0.247121
$$263$$ −9.37778 −0.578259 −0.289129 0.957290i $$-0.593366\pi$$
−0.289129 + 0.957290i $$0.593366\pi$$
$$264$$ 1.43801 0.0885032
$$265$$ 0 0
$$266$$ 0 0
$$267$$ −4.62222 −0.282875
$$268$$ 4.47013 0.273056
$$269$$ −1.74620 −0.106468 −0.0532339 0.998582i $$-0.516953\pi$$
−0.0532339 + 0.998582i $$0.516953\pi$$
$$270$$ 0 0
$$271$$ 2.69535 0.163731 0.0818653 0.996643i $$-0.473912\pi$$
0.0818653 + 0.996643i $$0.473912\pi$$
$$272$$ 20.4286 1.23867
$$273$$ 0 0
$$274$$ −30.3368 −1.83271
$$275$$ 0 0
$$276$$ 2.23506 0.134535
$$277$$ −5.12399 −0.307870 −0.153935 0.988081i $$-0.549195\pi$$
−0.153935 + 0.988081i $$0.549195\pi$$
$$278$$ 22.2163 1.33245
$$279$$ −5.18421 −0.310370
$$280$$ 0 0
$$281$$ 23.9813 1.43060 0.715301 0.698816i $$-0.246290\pi$$
0.715301 + 0.698816i $$0.246290\pi$$
$$282$$ 5.24443 0.312301
$$283$$ −2.36842 −0.140788 −0.0703939 0.997519i $$-0.522426\pi$$
−0.0703939 + 0.997519i $$0.522426\pi$$
$$284$$ 3.24443 0.192522
$$285$$ 0 0
$$286$$ −24.4701 −1.44695
$$287$$ 0 0
$$288$$ 7.34122 0.432585
$$289$$ 2.61285 0.153697
$$290$$ 0 0
$$291$$ 11.9398 0.699922
$$292$$ 2.54909 0.149174
$$293$$ −8.42864 −0.492406 −0.246203 0.969218i $$-0.579183\pi$$
−0.246203 + 0.969218i $$0.579183\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ 5.47367 0.318150
$$297$$ 2.00000 0.116052
$$298$$ 40.3970 2.34014
$$299$$ 8.85728 0.512230
$$300$$ 0 0
$$301$$ 0 0
$$302$$ −32.0830 −1.84617
$$303$$ −1.47949 −0.0849947
$$304$$ −11.2029 −0.642533
$$305$$ 0 0
$$306$$ 8.42864 0.481833
$$307$$ 22.5718 1.28824 0.644121 0.764923i $$-0.277223\pi$$
0.644121 + 0.764923i $$0.277223\pi$$
$$308$$ 0 0
$$309$$ 8.85728 0.503873
$$310$$ 0 0
$$311$$ 24.0830 1.36562 0.682810 0.730596i $$-0.260758\pi$$
0.682810 + 0.730596i $$0.260758\pi$$
$$312$$ 4.62222 0.261681
$$313$$ −9.65433 −0.545695 −0.272848 0.962057i $$-0.587965\pi$$
−0.272848 + 0.962057i $$0.587965\pi$$
$$314$$ −19.8479 −1.12008
$$315$$ 0 0
$$316$$ −7.87955 −0.443260
$$317$$ −6.04149 −0.339324 −0.169662 0.985502i $$-0.554268\pi$$
−0.169662 + 0.985502i $$0.554268\pi$$
$$318$$ −17.4795 −0.980201
$$319$$ 1.51114 0.0846075
$$320$$ 0 0
$$321$$ 1.76494 0.0985092
$$322$$ 0 0
$$323$$ −10.7556 −0.598456
$$324$$ 1.62222 0.0901231
$$325$$ 0 0
$$326$$ −39.6958 −2.19855
$$327$$ 5.61285 0.310391
$$328$$ 5.92104 0.326935
$$329$$ 0 0
$$330$$ 0 0
$$331$$ 13.5111 0.742639 0.371320 0.928505i $$-0.378905\pi$$
0.371320 + 0.928505i $$0.378905\pi$$
$$332$$ −18.8385 −1.03390
$$333$$ 7.61285 0.417181
$$334$$ 29.2070 1.59813
$$335$$ 0 0
$$336$$ 0 0
$$337$$ 10.4889 0.571365 0.285682 0.958324i $$-0.407780\pi$$
0.285682 + 0.958324i $$0.407780\pi$$
$$338$$ −53.9131 −2.93248
$$339$$ −11.2859 −0.612967
$$340$$ 0 0
$$341$$ −10.3684 −0.561481
$$342$$ −4.62222 −0.249941
$$343$$ 0 0
$$344$$ 7.26317 0.391604
$$345$$ 0 0
$$346$$ 3.92104 0.210796
$$347$$ −16.7239 −0.897787 −0.448894 0.893585i $$-0.648182\pi$$
−0.448894 + 0.893585i $$0.648182\pi$$
$$348$$ 1.22570 0.0657042
$$349$$ 16.3684 0.876181 0.438091 0.898931i $$-0.355655\pi$$
0.438091 + 0.898931i $$0.355655\pi$$
$$350$$ 0 0
$$351$$ 6.42864 0.343135
$$352$$ 14.6824 0.782577
$$353$$ −0.549086 −0.0292249 −0.0146124 0.999893i $$-0.504651\pi$$
−0.0146124 + 0.999893i $$0.504651\pi$$
$$354$$ 26.8385 1.42645
$$355$$ 0 0
$$356$$ −7.49823 −0.397405
$$357$$ 0 0
$$358$$ −19.0321 −1.00588
$$359$$ −0.285442 −0.0150651 −0.00753253 0.999972i $$-0.502398\pi$$
−0.00753253 + 0.999972i $$0.502398\pi$$
$$360$$ 0 0
$$361$$ −13.1017 −0.689564
$$362$$ −23.0321 −1.21054
$$363$$ −7.00000 −0.367405
$$364$$ 0 0
$$365$$ 0 0
$$366$$ 13.0509 0.682179
$$367$$ −1.71456 −0.0894992 −0.0447496 0.998998i $$-0.514249\pi$$
−0.0447496 + 0.998998i $$0.514249\pi$$
$$368$$ −6.35551 −0.331304
$$369$$ 8.23506 0.428700
$$370$$ 0 0
$$371$$ 0 0
$$372$$ −8.40990 −0.436033
$$373$$ 16.0000 0.828449 0.414224 0.910175i $$-0.364053\pi$$
0.414224 + 0.910175i $$0.364053\pi$$
$$374$$ 16.8573 0.871669
$$375$$ 0 0
$$376$$ −1.98126 −0.102176
$$377$$ 4.85728 0.250163
$$378$$ 0 0
$$379$$ −4.85728 −0.249502 −0.124751 0.992188i $$-0.539813\pi$$
−0.124751 + 0.992188i $$0.539813\pi$$
$$380$$ 0 0
$$381$$ −12.8573 −0.658698
$$382$$ −0.930409 −0.0476039
$$383$$ 8.38715 0.428563 0.214282 0.976772i $$-0.431259\pi$$
0.214282 + 0.976772i $$0.431259\pi$$
$$384$$ −5.64941 −0.288295
$$385$$ 0 0
$$386$$ 43.6958 2.22406
$$387$$ 10.1017 0.513499
$$388$$ 19.3689 0.983307
$$389$$ 8.95899 0.454239 0.227119 0.973867i $$-0.427069\pi$$
0.227119 + 0.973867i $$0.427069\pi$$
$$390$$ 0 0
$$391$$ −6.10171 −0.308577
$$392$$ 0 0
$$393$$ 2.10171 0.106017
$$394$$ 2.25380 0.113545
$$395$$ 0 0
$$396$$ 3.24443 0.163039
$$397$$ 2.54909 0.127935 0.0639675 0.997952i $$-0.479625\pi$$
0.0639675 + 0.997952i $$0.479625\pi$$
$$398$$ 16.7427 0.839234
$$399$$ 0 0
$$400$$ 0 0
$$401$$ 0.958989 0.0478896 0.0239448 0.999713i $$-0.492377\pi$$
0.0239448 + 0.999713i $$0.492377\pi$$
$$402$$ −5.24443 −0.261568
$$403$$ −33.3274 −1.66016
$$404$$ −2.40006 −0.119407
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 15.2257 0.754710
$$408$$ −3.18421 −0.157642
$$409$$ 31.9813 1.58137 0.790686 0.612222i $$-0.209724\pi$$
0.790686 + 0.612222i $$0.209724\pi$$
$$410$$ 0 0
$$411$$ 15.9398 0.786251
$$412$$ 14.3684 0.707881
$$413$$ 0 0
$$414$$ −2.62222 −0.128875
$$415$$ 0 0
$$416$$ 47.1941 2.31388
$$417$$ −11.6731 −0.571633
$$418$$ −9.24443 −0.452160
$$419$$ 0.470127 0.0229672 0.0114836 0.999934i $$-0.496345\pi$$
0.0114836 + 0.999934i $$0.496345\pi$$
$$420$$ 0 0
$$421$$ −33.6128 −1.63819 −0.819095 0.573658i $$-0.805524\pi$$
−0.819095 + 0.573658i $$0.805524\pi$$
$$422$$ −44.2034 −2.15179
$$423$$ −2.75557 −0.133980
$$424$$ 6.60348 0.320693
$$425$$ 0 0
$$426$$ −3.80642 −0.184422
$$427$$ 0 0
$$428$$ 2.86311 0.138394
$$429$$ 12.8573 0.620755
$$430$$ 0 0
$$431$$ 11.7146 0.564270 0.282135 0.959375i $$-0.408957\pi$$
0.282135 + 0.959375i $$0.408957\pi$$
$$432$$ −4.61285 −0.221936
$$433$$ 0.0602231 0.00289414 0.00144707 0.999999i $$-0.499539\pi$$
0.00144707 + 0.999999i $$0.499539\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 9.10525 0.436062
$$437$$ 3.34614 0.160068
$$438$$ −2.99063 −0.142898
$$439$$ 22.4286 1.07046 0.535230 0.844706i $$-0.320225\pi$$
0.535230 + 0.844706i $$0.320225\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 54.1847 2.57730
$$443$$ −23.9496 −1.13788 −0.568940 0.822379i $$-0.692647\pi$$
−0.568940 + 0.822379i $$0.692647\pi$$
$$444$$ 12.3497 0.586090
$$445$$ 0 0
$$446$$ −28.9777 −1.37214
$$447$$ −21.2257 −1.00394
$$448$$ 0 0
$$449$$ 29.4291 1.38885 0.694423 0.719567i $$-0.255660\pi$$
0.694423 + 0.719567i $$0.255660\pi$$
$$450$$ 0 0
$$451$$ 16.4701 0.775548
$$452$$ −18.3082 −0.861145
$$453$$ 16.8573 0.792024
$$454$$ −27.3461 −1.28342
$$455$$ 0 0
$$456$$ 1.74620 0.0817733
$$457$$ −3.14272 −0.147010 −0.0735051 0.997295i $$-0.523419\pi$$
−0.0735051 + 0.997295i $$0.523419\pi$$
$$458$$ −10.6824 −0.499158
$$459$$ −4.42864 −0.206711
$$460$$ 0 0
$$461$$ 3.37778 0.157319 0.0786596 0.996902i $$-0.474936\pi$$
0.0786596 + 0.996902i $$0.474936\pi$$
$$462$$ 0 0
$$463$$ 20.8573 0.969320 0.484660 0.874703i $$-0.338943\pi$$
0.484660 + 0.874703i $$0.338943\pi$$
$$464$$ −3.48532 −0.161802
$$465$$ 0 0
$$466$$ −44.3180 −2.05299
$$467$$ 14.3684 0.664891 0.332446 0.943122i $$-0.392126\pi$$
0.332446 + 0.943122i $$0.392126\pi$$
$$468$$ 10.4286 0.482064
$$469$$ 0 0
$$470$$ 0 0
$$471$$ 10.4286 0.480526
$$472$$ −10.1392 −0.466694
$$473$$ 20.2034 0.928954
$$474$$ 9.24443 0.424611
$$475$$ 0 0
$$476$$ 0 0
$$477$$ 9.18421 0.420516
$$478$$ 16.1561 0.738963
$$479$$ −6.36842 −0.290980 −0.145490 0.989360i $$-0.546476\pi$$
−0.145490 + 0.989360i $$0.546476\pi$$
$$480$$ 0 0
$$481$$ 48.9403 2.23148
$$482$$ −13.7877 −0.628012
$$483$$ 0 0
$$484$$ −11.3555 −0.516160
$$485$$ 0 0
$$486$$ −1.90321 −0.0863314
$$487$$ 17.3274 0.785180 0.392590 0.919714i $$-0.371579\pi$$
0.392590 + 0.919714i $$0.371579\pi$$
$$488$$ −4.93041 −0.223189
$$489$$ 20.8573 0.943199
$$490$$ 0 0
$$491$$ 2.00000 0.0902587 0.0451294 0.998981i $$-0.485630\pi$$
0.0451294 + 0.998981i $$0.485630\pi$$
$$492$$ 13.3590 0.602272
$$493$$ −3.34614 −0.150703
$$494$$ −29.7146 −1.33692
$$495$$ 0 0
$$496$$ 23.9140 1.07377
$$497$$ 0 0
$$498$$ 22.1017 0.990401
$$499$$ 23.3461 1.04512 0.522558 0.852603i $$-0.324978\pi$$
0.522558 + 0.852603i $$0.324978\pi$$
$$500$$ 0 0
$$501$$ −15.3461 −0.685615
$$502$$ 52.5531 2.34556
$$503$$ −0.387152 −0.0172623 −0.00863113 0.999963i $$-0.502747\pi$$
−0.00863113 + 0.999963i $$0.502747\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ −5.24443 −0.233143
$$507$$ 28.3274 1.25806
$$508$$ −20.8573 −0.925392
$$509$$ 29.9496 1.32749 0.663747 0.747957i $$-0.268965\pi$$
0.663747 + 0.747957i $$0.268965\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ −27.2306 −1.20343
$$513$$ 2.42864 0.107227
$$514$$ −0.815792 −0.0359830
$$515$$ 0 0
$$516$$ 16.3872 0.721404
$$517$$ −5.51114 −0.242380
$$518$$ 0 0
$$519$$ −2.06022 −0.0904338
$$520$$ 0 0
$$521$$ 18.5205 0.811398 0.405699 0.914007i $$-0.367028\pi$$
0.405699 + 0.914007i $$0.367028\pi$$
$$522$$ −1.43801 −0.0629399
$$523$$ 4.00000 0.174908 0.0874539 0.996169i $$-0.472127\pi$$
0.0874539 + 0.996169i $$0.472127\pi$$
$$524$$ 3.40943 0.148942
$$525$$ 0 0
$$526$$ 17.8479 0.778206
$$527$$ 22.9590 1.00011
$$528$$ −9.22570 −0.401497
$$529$$ −21.1017 −0.917466
$$530$$ 0 0
$$531$$ −14.1017 −0.611962
$$532$$ 0 0
$$533$$ 52.9403 2.29310
$$534$$ 8.79706 0.380686
$$535$$ 0 0
$$536$$ 1.98126 0.0855776
$$537$$ 10.0000 0.431532
$$538$$ 3.32339 0.143282
$$539$$ 0 0
$$540$$ 0 0
$$541$$ 14.5906 0.627298 0.313649 0.949539i $$-0.398449\pi$$
0.313649 + 0.949539i $$0.398449\pi$$
$$542$$ −5.12981 −0.220344
$$543$$ 12.1017 0.519334
$$544$$ −32.5116 −1.39392
$$545$$ 0 0
$$546$$ 0 0
$$547$$ −18.7556 −0.801930 −0.400965 0.916093i $$-0.631325\pi$$
−0.400965 + 0.916093i $$0.631325\pi$$
$$548$$ 25.8578 1.10459
$$549$$ −6.85728 −0.292662
$$550$$ 0 0
$$551$$ 1.83500 0.0781738
$$552$$ 0.990632 0.0421641
$$553$$ 0 0
$$554$$ 9.75203 0.414324
$$555$$ 0 0
$$556$$ −18.9362 −0.803075
$$557$$ 31.8765 1.35065 0.675325 0.737520i $$-0.264003\pi$$
0.675325 + 0.737520i $$0.264003\pi$$
$$558$$ 9.86665 0.417688
$$559$$ 64.9403 2.74668
$$560$$ 0 0
$$561$$ −8.85728 −0.373955
$$562$$ −45.6414 −1.92527
$$563$$ 2.01874 0.0850796 0.0425398 0.999095i $$-0.486455\pi$$
0.0425398 + 0.999095i $$0.486455\pi$$
$$564$$ −4.47013 −0.188226
$$565$$ 0 0
$$566$$ 4.50760 0.189468
$$567$$ 0 0
$$568$$ 1.43801 0.0603375
$$569$$ −28.9590 −1.21402 −0.607012 0.794693i $$-0.707632\pi$$
−0.607012 + 0.794693i $$0.707632\pi$$
$$570$$ 0 0
$$571$$ 8.97773 0.375706 0.187853 0.982197i $$-0.439847\pi$$
0.187853 + 0.982197i $$0.439847\pi$$
$$572$$ 20.8573 0.872087
$$573$$ 0.488863 0.0204225
$$574$$ 0 0
$$575$$ 0 0
$$576$$ −4.74620 −0.197758
$$577$$ −28.6766 −1.19382 −0.596911 0.802307i $$-0.703606\pi$$
−0.596911 + 0.802307i $$0.703606\pi$$
$$578$$ −4.97280 −0.206841
$$579$$ −22.9590 −0.954143
$$580$$ 0 0
$$581$$ 0 0
$$582$$ −22.7239 −0.941937
$$583$$ 18.3684 0.760742
$$584$$ 1.12981 0.0467520
$$585$$ 0 0
$$586$$ 16.0415 0.662668
$$587$$ −45.2070 −1.86589 −0.932945 0.360018i $$-0.882771\pi$$
−0.932945 + 0.360018i $$0.882771\pi$$
$$588$$ 0 0
$$589$$ −12.5906 −0.518786
$$590$$ 0 0
$$591$$ −1.18421 −0.0487118
$$592$$ −35.1169 −1.44330
$$593$$ 18.2636 0.749998 0.374999 0.927025i $$-0.377643\pi$$
0.374999 + 0.927025i $$0.377643\pi$$
$$594$$ −3.80642 −0.156179
$$595$$ 0 0
$$596$$ −34.4327 −1.41042
$$597$$ −8.79706 −0.360040
$$598$$ −16.8573 −0.689345
$$599$$ −22.7368 −0.929002 −0.464501 0.885573i $$-0.653766\pi$$
−0.464501 + 0.885573i $$0.653766\pi$$
$$600$$ 0 0
$$601$$ −0.488863 −0.0199411 −0.00997056 0.999950i $$-0.503174\pi$$
−0.00997056 + 0.999950i $$0.503174\pi$$
$$602$$ 0 0
$$603$$ 2.75557 0.112215
$$604$$ 27.3461 1.11270
$$605$$ 0 0
$$606$$ 2.81579 0.114384
$$607$$ −20.2034 −0.820032 −0.410016 0.912078i $$-0.634477\pi$$
−0.410016 + 0.912078i $$0.634477\pi$$
$$608$$ 17.8292 0.723069
$$609$$ 0 0
$$610$$ 0 0
$$611$$ −17.7146 −0.716654
$$612$$ −7.18421 −0.290404
$$613$$ −10.3684 −0.418776 −0.209388 0.977833i $$-0.567147\pi$$
−0.209388 + 0.977833i $$0.567147\pi$$
$$614$$ −42.9590 −1.73368
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 39.2859 1.58159 0.790796 0.612080i $$-0.209667\pi$$
0.790796 + 0.612080i $$0.209667\pi$$
$$618$$ −16.8573 −0.678099
$$619$$ −42.8988 −1.72425 −0.862123 0.506698i $$-0.830866\pi$$
−0.862123 + 0.506698i $$0.830866\pi$$
$$620$$ 0 0
$$621$$ 1.37778 0.0552886
$$622$$ −45.8350 −1.83782
$$623$$ 0 0
$$624$$ −29.6543 −1.18712
$$625$$ 0 0
$$626$$ 18.3742 0.734383
$$627$$ 4.85728 0.193981
$$628$$ 16.9175 0.675082
$$629$$ −33.7146 −1.34429
$$630$$ 0 0
$$631$$ 15.3461 0.610920 0.305460 0.952205i $$-0.401190\pi$$
0.305460 + 0.952205i $$0.401190\pi$$
$$632$$ −3.49240 −0.138920
$$633$$ 23.2257 0.923139
$$634$$ 11.4982 0.456653
$$635$$ 0 0
$$636$$ 14.8988 0.590775
$$637$$ 0 0
$$638$$ −2.87601 −0.113863
$$639$$ 2.00000 0.0791188
$$640$$ 0 0
$$641$$ 30.6735 1.21153 0.605766 0.795643i $$-0.292867\pi$$
0.605766 + 0.795643i $$0.292867\pi$$
$$642$$ −3.35905 −0.132571
$$643$$ −49.0607 −1.93477 −0.967383 0.253320i $$-0.918477\pi$$
−0.967383 + 0.253320i $$0.918477\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 20.4701 0.805386
$$647$$ −15.3461 −0.603319 −0.301660 0.953416i $$-0.597541\pi$$
−0.301660 + 0.953416i $$0.597541\pi$$
$$648$$ 0.719004 0.0282451
$$649$$ −28.2034 −1.10708
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 33.8350 1.32508
$$653$$ 19.4697 0.761906 0.380953 0.924594i $$-0.375596\pi$$
0.380953 + 0.924594i $$0.375596\pi$$
$$654$$ −10.6824 −0.417716
$$655$$ 0 0
$$656$$ −37.9871 −1.48315
$$657$$ 1.57136 0.0613046
$$658$$ 0 0
$$659$$ 30.9403 1.20526 0.602631 0.798020i $$-0.294119\pi$$
0.602631 + 0.798020i $$0.294119\pi$$
$$660$$ 0 0
$$661$$ −47.7975 −1.85911 −0.929554 0.368685i $$-0.879808\pi$$
−0.929554 + 0.368685i $$0.879808\pi$$
$$662$$ −25.7146 −0.999425
$$663$$ −28.4701 −1.10569
$$664$$ −8.34968 −0.324030
$$665$$ 0 0
$$666$$ −14.4889 −0.561432
$$667$$ 1.04101 0.0403081
$$668$$ −24.8948 −0.963207
$$669$$ 15.2257 0.588659
$$670$$ 0 0
$$671$$ −13.7146 −0.529445
$$672$$ 0 0
$$673$$ −27.8163 −1.07224 −0.536119 0.844142i $$-0.680110\pi$$
−0.536119 + 0.844142i $$0.680110\pi$$
$$674$$ −19.9625 −0.768928
$$675$$ 0 0
$$676$$ 45.9532 1.76743
$$677$$ −19.0005 −0.730248 −0.365124 0.930959i $$-0.618973\pi$$
−0.365124 + 0.930959i $$0.618973\pi$$
$$678$$ 21.4795 0.824915
$$679$$ 0 0
$$680$$ 0 0
$$681$$ 14.3684 0.550599
$$682$$ 19.7333 0.755627
$$683$$ −4.52051 −0.172972 −0.0864862 0.996253i $$-0.527564\pi$$
−0.0864862 + 0.996253i $$0.527564\pi$$
$$684$$ 3.93978 0.150641
$$685$$ 0 0
$$686$$ 0 0
$$687$$ 5.61285 0.214143
$$688$$ −46.5977 −1.77652
$$689$$ 59.0420 2.24932
$$690$$ 0 0
$$691$$ 1.18421 0.0450494 0.0225247 0.999746i $$-0.492830\pi$$
0.0225247 + 0.999746i $$0.492830\pi$$
$$692$$ −3.34213 −0.127049
$$693$$ 0 0
$$694$$ 31.8292 1.20822
$$695$$ 0 0
$$696$$ 0.543257 0.0205921
$$697$$ −36.4701 −1.38140
$$698$$ −31.1526 −1.17914
$$699$$ 23.2859 0.880754
$$700$$ 0 0
$$701$$ −26.6735 −1.00745 −0.503723 0.863865i $$-0.668037\pi$$
−0.503723 + 0.863865i $$0.668037\pi$$
$$702$$ −12.2351 −0.461783
$$703$$ 18.4889 0.697321
$$704$$ −9.49240 −0.357758
$$705$$ 0 0
$$706$$ 1.04503 0.0393301
$$707$$ 0 0
$$708$$ −22.8760 −0.859733
$$709$$ −18.2034 −0.683644 −0.341822 0.939765i $$-0.611044\pi$$
−0.341822 + 0.939765i $$0.611044\pi$$
$$710$$ 0 0
$$711$$ −4.85728 −0.182162
$$712$$ −3.32339 −0.124549
$$713$$ −7.14272 −0.267497
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 16.2222 0.606250
$$717$$ −8.48886 −0.317022
$$718$$ 0.543257 0.0202742
$$719$$ −4.85728 −0.181146 −0.0905730 0.995890i $$-0.528870\pi$$
−0.0905730 + 0.995890i $$0.528870\pi$$
$$720$$ 0 0
$$721$$ 0 0
$$722$$ 24.9353 0.927997
$$723$$ 7.24443 0.269423
$$724$$ 19.6316 0.729602
$$725$$ 0 0
$$726$$ 13.3225 0.494444
$$727$$ 21.0607 0.781098 0.390549 0.920582i $$-0.372285\pi$$
0.390549 + 0.920582i $$0.372285\pi$$
$$728$$ 0 0
$$729$$ 1.00000 0.0370370
$$730$$ 0 0
$$731$$ −44.7368 −1.65465
$$732$$ −11.1240 −0.411154
$$733$$ 9.45091 0.349077 0.174539 0.984650i $$-0.444157\pi$$
0.174539 + 0.984650i $$0.444157\pi$$
$$734$$ 3.26317 0.120446
$$735$$ 0 0
$$736$$ 10.1146 0.372830
$$737$$ 5.51114 0.203005
$$738$$ −15.6731 −0.576934
$$739$$ −8.20342 −0.301768 −0.150884 0.988551i $$-0.548212\pi$$
−0.150884 + 0.988551i $$0.548212\pi$$
$$740$$ 0 0
$$741$$ 15.6128 0.573552
$$742$$ 0 0
$$743$$ −8.33677 −0.305847 −0.152923 0.988238i $$-0.548869\pi$$
−0.152923 + 0.988238i $$0.548869\pi$$
$$744$$ −3.72746 −0.136655
$$745$$ 0 0
$$746$$ −30.4514 −1.11490
$$747$$ −11.6128 −0.424892
$$748$$ −14.3684 −0.525361
$$749$$ 0 0
$$750$$ 0 0
$$751$$ −25.9180 −0.945760 −0.472880 0.881127i $$-0.656786\pi$$
−0.472880 + 0.881127i $$0.656786\pi$$
$$752$$ 12.7110 0.463523
$$753$$ −27.6128 −1.00627
$$754$$ −9.24443 −0.336662
$$755$$ 0 0
$$756$$ 0 0
$$757$$ −8.94025 −0.324939 −0.162470 0.986714i $$-0.551946\pi$$
−0.162470 + 0.986714i $$0.551946\pi$$
$$758$$ 9.24443 0.335773
$$759$$ 2.75557 0.100021
$$760$$ 0 0
$$761$$ 0.825636 0.0299293 0.0149646 0.999888i $$-0.495236\pi$$
0.0149646 + 0.999888i $$0.495236\pi$$
$$762$$ 24.4701 0.886459
$$763$$ 0 0
$$764$$ 0.793040 0.0286912
$$765$$ 0 0
$$766$$ −15.9625 −0.576750
$$767$$ −90.6548 −3.27336
$$768$$ 20.2444 0.730508
$$769$$ −21.2257 −0.765418 −0.382709 0.923869i $$-0.625009\pi$$
−0.382709 + 0.923869i $$0.625009\pi$$
$$770$$ 0 0
$$771$$ 0.428639 0.0154371
$$772$$ −37.2444 −1.34046
$$773$$ 29.4893 1.06066 0.530329 0.847792i $$-0.322068\pi$$
0.530329 + 0.847792i $$0.322068\pi$$
$$774$$ −19.2257 −0.691053
$$775$$ 0 0
$$776$$ 8.58474 0.308174
$$777$$ 0 0
$$778$$ −17.0509 −0.611303
$$779$$ 20.0000 0.716574
$$780$$ 0 0
$$781$$ 4.00000 0.143131
$$782$$ 11.6128 0.415275
$$783$$ 0.755569 0.0270018
$$784$$ 0 0
$$785$$ 0 0
$$786$$ −4.00000 −0.142675
$$787$$ −34.4514 −1.22806 −0.614030 0.789283i $$-0.710453\pi$$
−0.614030 + 0.789283i $$0.710453\pi$$
$$788$$ −1.92104 −0.0684343
$$789$$ −9.37778 −0.333858
$$790$$ 0 0
$$791$$ 0 0
$$792$$ 1.43801 0.0510974
$$793$$ −44.0830 −1.56543
$$794$$ −4.85145 −0.172172
$$795$$ 0 0
$$796$$ −14.2707 −0.505812
$$797$$ 18.9175 0.670092 0.335046 0.942202i $$-0.391248\pi$$
0.335046 + 0.942202i $$0.391248\pi$$
$$798$$ 0 0
$$799$$ 12.2034 0.431726
$$800$$ 0 0
$$801$$ −4.62222 −0.163318
$$802$$ −1.82516 −0.0644486
$$803$$ 3.14272 0.110904
$$804$$ 4.47013 0.157649
$$805$$ 0 0
$$806$$ 63.4291 2.23420
$$807$$ −1.74620 −0.0614692
$$808$$ −1.06376 −0.0374230
$$809$$ 21.2257 0.746256 0.373128 0.927780i $$-0.378285\pi$$
0.373128 + 0.927780i $$0.378285\pi$$
$$810$$ 0 0
$$811$$ 21.5081 0.755251 0.377625 0.925958i $$-0.376741\pi$$
0.377625 + 0.925958i $$0.376741\pi$$
$$812$$ 0 0
$$813$$ 2.69535 0.0945299
$$814$$ −28.9777 −1.01567
$$815$$ 0 0
$$816$$ 20.4286 0.715145
$$817$$ 24.5334 0.858315
$$818$$ −60.8671 −2.12817
$$819$$ 0 0
$$820$$ 0 0
$$821$$ −46.2034 −1.61251 −0.806255 0.591568i $$-0.798509\pi$$
−0.806255 + 0.591568i $$0.798509\pi$$
$$822$$ −30.3368 −1.05812
$$823$$ 17.8350 0.621689 0.310845 0.950461i $$-0.399388\pi$$
0.310845 + 0.950461i $$0.399388\pi$$
$$824$$ 6.36842 0.221854
$$825$$ 0 0
$$826$$ 0 0
$$827$$ −35.2128 −1.22447 −0.612234 0.790676i $$-0.709729\pi$$
−0.612234 + 0.790676i $$0.709729\pi$$
$$828$$ 2.23506 0.0776738
$$829$$ −14.3872 −0.499686 −0.249843 0.968286i $$-0.580379\pi$$
−0.249843 + 0.968286i $$0.580379\pi$$
$$830$$ 0 0
$$831$$ −5.12399 −0.177749
$$832$$ −30.5116 −1.05780
$$833$$ 0 0
$$834$$ 22.2163 0.769289
$$835$$ 0 0
$$836$$ 7.87955 0.272520
$$837$$ −5.18421 −0.179192
$$838$$ −0.894751 −0.0309087
$$839$$ −1.51114 −0.0521703 −0.0260851 0.999660i $$-0.508304\pi$$
−0.0260851 + 0.999660i $$0.508304\pi$$
$$840$$ 0 0
$$841$$ −28.4291 −0.980314
$$842$$ 63.9724 2.20463
$$843$$ 23.9813 0.825959
$$844$$ 37.6771 1.29690
$$845$$ 0 0
$$846$$ 5.24443 0.180307
$$847$$ 0 0
$$848$$ −42.3654 −1.45483
$$849$$ −2.36842 −0.0812838
$$850$$ 0 0
$$851$$ 10.4889 0.359554
$$852$$ 3.24443 0.111152
$$853$$ −15.4064 −0.527504 −0.263752 0.964591i $$-0.584960\pi$$
−0.263752 + 0.964591i $$0.584960\pi$$
$$854$$ 0 0
$$855$$ 0 0
$$856$$ 1.26900 0.0433734
$$857$$ 19.8578 0.678328 0.339164 0.940727i $$-0.389856\pi$$
0.339164 + 0.940727i $$0.389856\pi$$
$$858$$ −24.4701 −0.835396
$$859$$ −2.42864 −0.0828641 −0.0414321 0.999141i $$-0.513192\pi$$
−0.0414321 + 0.999141i $$0.513192\pi$$
$$860$$ 0 0
$$861$$ 0 0
$$862$$ −22.2953 −0.759380
$$863$$ 39.2958 1.33764 0.668822 0.743423i $$-0.266799\pi$$
0.668822 + 0.743423i $$0.266799\pi$$
$$864$$ 7.34122 0.249753
$$865$$ 0 0
$$866$$ −0.114617 −0.00389485
$$867$$ 2.61285 0.0887370
$$868$$ 0 0
$$869$$ −9.71456 −0.329544
$$870$$ 0 0
$$871$$ 17.7146 0.600235
$$872$$ 4.03566 0.136665
$$873$$ 11.9398 0.404100
$$874$$ −6.36842 −0.215415
$$875$$ 0 0
$$876$$ 2.54909 0.0861256
$$877$$ 56.2864 1.90066 0.950328 0.311249i $$-0.100747\pi$$
0.950328 + 0.311249i $$0.100747\pi$$
$$878$$ −42.6865 −1.44060
$$879$$ −8.42864 −0.284291
$$880$$ 0 0
$$881$$ 2.33677 0.0787279 0.0393640 0.999225i $$-0.487467\pi$$
0.0393640 + 0.999225i $$0.487467\pi$$
$$882$$ 0 0
$$883$$ −33.7146 −1.13459 −0.567293 0.823516i $$-0.692009\pi$$
−0.567293 + 0.823516i $$0.692009\pi$$
$$884$$ −46.1847 −1.55336
$$885$$ 0 0
$$886$$ 45.5812 1.53133
$$887$$ 47.8992 1.60830 0.804150 0.594427i $$-0.202621\pi$$
0.804150 + 0.594427i $$0.202621\pi$$
$$888$$ 5.47367 0.183684
$$889$$ 0 0
$$890$$ 0 0
$$891$$ 2.00000 0.0670025
$$892$$ 24.6994 0.826996
$$893$$ −6.69228 −0.223949
$$894$$ 40.3970 1.35108
$$895$$ 0 0
$$896$$ 0 0
$$897$$ 8.85728 0.295736
$$898$$ −56.0098 −1.86907
$$899$$ −3.91703 −0.130640
$$900$$ 0 0
$$901$$ −40.6735 −1.35503
$$902$$ −31.3461 −1.04371
$$903$$ 0 0
$$904$$ −8.11462 −0.269888
$$905$$ 0 0
$$906$$ −32.0830 −1.06589
$$907$$ −23.7591 −0.788908 −0.394454 0.918916i $$-0.629066\pi$$
−0.394454 + 0.918916i $$0.629066\pi$$
$$908$$ 23.3087 0.773525
$$909$$ −1.47949 −0.0490717
$$910$$ 0 0
$$911$$ 22.9403 0.760045 0.380022 0.924977i $$-0.375916\pi$$
0.380022 + 0.924977i $$0.375916\pi$$
$$912$$ −11.2029 −0.370967
$$913$$ −23.2257 −0.768658
$$914$$ 5.98126 0.197843
$$915$$ 0 0
$$916$$ 9.10525 0.300846
$$917$$ 0 0
$$918$$ 8.42864 0.278187
$$919$$ 16.9777 0.560043 0.280022 0.959994i $$-0.409658\pi$$
0.280022 + 0.959994i $$0.409658\pi$$
$$920$$ 0 0
$$921$$ 22.5718 0.743767
$$922$$ −6.42864 −0.211716
$$923$$ 12.8573 0.423202
$$924$$ 0 0
$$925$$ 0 0
$$926$$ −39.6958 −1.30449
$$927$$ 8.85728 0.290911
$$928$$ 5.54680 0.182082
$$929$$ −39.3403 −1.29071 −0.645357 0.763881i $$-0.723291\pi$$
−0.645357 + 0.763881i $$0.723291\pi$$
$$930$$ 0 0
$$931$$ 0 0
$$932$$ 37.7748 1.23735
$$933$$ 24.0830 0.788441
$$934$$ −27.3461 −0.894793
$$935$$ 0 0
$$936$$ 4.62222 0.151082
$$937$$ −17.7748 −0.580677 −0.290338 0.956924i $$-0.593768\pi$$
−0.290338 + 0.956924i $$0.593768\pi$$
$$938$$ 0 0
$$939$$ −9.65433 −0.315057
$$940$$ 0 0
$$941$$ −35.5812 −1.15991 −0.579957 0.814647i $$-0.696931\pi$$
−0.579957 + 0.814647i $$0.696931\pi$$
$$942$$ −19.8479 −0.646680
$$943$$ 11.3461 0.369481
$$944$$ 65.0490 2.11717
$$945$$ 0 0
$$946$$ −38.4514 −1.25016
$$947$$ −30.5018 −0.991174 −0.495587 0.868558i $$-0.665047\pi$$
−0.495587 + 0.868558i $$0.665047\pi$$
$$948$$ −7.87955 −0.255916
$$949$$ 10.1017 0.327915
$$950$$ 0 0
$$951$$ −6.04149 −0.195909
$$952$$ 0 0
$$953$$ 51.1655 1.65741 0.828706 0.559684i $$-0.189077\pi$$
0.828706 + 0.559684i $$0.189077\pi$$
$$954$$ −17.4795 −0.565920
$$955$$ 0 0
$$956$$ −13.7708 −0.445378
$$957$$ 1.51114 0.0488481
$$958$$ 12.1204 0.391594
$$959$$ 0 0
$$960$$ 0 0
$$961$$ −4.12399 −0.133032
$$962$$ −93.1437 −3.00307
$$963$$ 1.76494 0.0568743
$$964$$ 11.7520 0.378507
$$965$$ 0 0
$$966$$ 0 0
$$967$$ −47.8992 −1.54034 −0.770168 0.637841i $$-0.779828\pi$$
−0.770168 + 0.637841i $$0.779828\pi$$
$$968$$ −5.03303 −0.161768
$$969$$ −10.7556 −0.345519
$$970$$ 0 0
$$971$$ −40.6735 −1.30528 −0.652638 0.757670i $$-0.726338\pi$$
−0.652638 + 0.757670i $$0.726338\pi$$
$$972$$ 1.62222 0.0520326
$$973$$ 0 0
$$974$$ −32.9777 −1.05667
$$975$$ 0 0
$$976$$ 31.6316 1.01250
$$977$$ 27.4893 0.879462 0.439731 0.898130i $$-0.355074\pi$$
0.439731 + 0.898130i $$0.355074\pi$$
$$978$$ −39.6958 −1.26933
$$979$$ −9.24443 −0.295453
$$980$$ 0 0
$$981$$ 5.61285 0.179204
$$982$$ −3.80642 −0.121468
$$983$$ 24.0000 0.765481 0.382741 0.923856i $$-0.374980\pi$$
0.382741 + 0.923856i $$0.374980\pi$$
$$984$$ 5.92104 0.188756
$$985$$ 0 0
$$986$$ 6.36842 0.202812
$$987$$ 0 0
$$988$$ 25.3274 0.805772
$$989$$ 13.9180 0.442566
$$990$$ 0 0
$$991$$ −34.6923 −1.10204 −0.551018 0.834493i $$-0.685761\pi$$
−0.551018 + 0.834493i $$0.685761\pi$$
$$992$$ −38.0584 −1.20836
$$993$$ 13.5111 0.428763
$$994$$ 0 0
$$995$$ 0 0
$$996$$ −18.8385 −0.596922
$$997$$ −28.6766 −0.908197 −0.454099 0.890951i $$-0.650039\pi$$
−0.454099 + 0.890951i $$0.650039\pi$$
$$998$$ −44.4327 −1.40649
$$999$$ 7.61285 0.240860
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 3675.2.a.bj.1.1 3
5.2 odd 4 735.2.d.b.589.2 6
5.3 odd 4 735.2.d.b.589.5 6
5.4 even 2 3675.2.a.bi.1.3 3
7.6 odd 2 525.2.a.k.1.1 3
15.2 even 4 2205.2.d.l.1324.5 6
15.8 even 4 2205.2.d.l.1324.2 6
21.20 even 2 1575.2.a.w.1.3 3
28.27 even 2 8400.2.a.dj.1.1 3
35.2 odd 12 735.2.q.f.214.2 12
35.3 even 12 735.2.q.e.79.2 12
35.12 even 12 735.2.q.e.214.2 12
35.13 even 4 105.2.d.b.64.5 yes 6
35.17 even 12 735.2.q.e.79.5 12
35.18 odd 12 735.2.q.f.79.2 12
35.23 odd 12 735.2.q.f.214.5 12
35.27 even 4 105.2.d.b.64.2 6
35.32 odd 12 735.2.q.f.79.5 12
35.33 even 12 735.2.q.e.214.5 12
35.34 odd 2 525.2.a.j.1.3 3
105.62 odd 4 315.2.d.e.64.5 6
105.83 odd 4 315.2.d.e.64.2 6
105.104 even 2 1575.2.a.x.1.1 3
140.27 odd 4 1680.2.t.k.1009.2 6
140.83 odd 4 1680.2.t.k.1009.5 6
140.139 even 2 8400.2.a.dg.1.3 3
420.83 even 4 5040.2.t.v.1009.3 6
420.167 even 4 5040.2.t.v.1009.4 6

By twisted newform
Twist Min Dim Char Parity Ord Type
105.2.d.b.64.2 6 35.27 even 4
105.2.d.b.64.5 yes 6 35.13 even 4
315.2.d.e.64.2 6 105.83 odd 4
315.2.d.e.64.5 6 105.62 odd 4
525.2.a.j.1.3 3 35.34 odd 2
525.2.a.k.1.1 3 7.6 odd 2
735.2.d.b.589.2 6 5.2 odd 4
735.2.d.b.589.5 6 5.3 odd 4
735.2.q.e.79.2 12 35.3 even 12
735.2.q.e.79.5 12 35.17 even 12
735.2.q.e.214.2 12 35.12 even 12
735.2.q.e.214.5 12 35.33 even 12
735.2.q.f.79.2 12 35.18 odd 12
735.2.q.f.79.5 12 35.32 odd 12
735.2.q.f.214.2 12 35.2 odd 12
735.2.q.f.214.5 12 35.23 odd 12
1575.2.a.w.1.3 3 21.20 even 2
1575.2.a.x.1.1 3 105.104 even 2
1680.2.t.k.1009.2 6 140.27 odd 4
1680.2.t.k.1009.5 6 140.83 odd 4
2205.2.d.l.1324.2 6 15.8 even 4
2205.2.d.l.1324.5 6 15.2 even 4
3675.2.a.bi.1.3 3 5.4 even 2
3675.2.a.bj.1.1 3 1.1 even 1 trivial
5040.2.t.v.1009.3 6 420.83 even 4
5040.2.t.v.1009.4 6 420.167 even 4
8400.2.a.dg.1.3 3 140.139 even 2
8400.2.a.dj.1.1 3 28.27 even 2