# Properties

 Label 5700.2.f.n.3649.2 Level $5700$ Weight $2$ Character 5700.3649 Analytic conductor $45.515$ Analytic rank $0$ Dimension $4$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$5700 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 5700.f (of order $$2$$, degree $$1$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$45.5147291521$$ Analytic rank: $$0$$ Dimension: $$4$$ Coefficient field: $$\Q(i, \sqrt{13})$$ Defining polynomial: $$x^{4} + 7x^{2} + 9$$ x^4 + 7*x^2 + 9 Coefficient ring: $$\Z[a_1, \ldots, a_{7}]$$ Coefficient ring index: $$2^{2}$$ Twist minimal: no (minimal twist has level 1140) Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

## Embedding invariants

 Embedding label 3649.2 Root $$1.30278i$$ of defining polynomial Character $$\chi$$ $$=$$ 5700.3649 Dual form 5700.2.f.n.3649.3

## $q$-expansion

 $$f(q)$$ $$=$$ $$q-1.00000i q^{3} +2.60555i q^{7} -1.00000 q^{9} +O(q^{10})$$ $$q-1.00000i q^{3} +2.60555i q^{7} -1.00000 q^{9} -4.60555 q^{11} +4.60555i q^{13} -2.00000i q^{17} +1.00000 q^{19} +2.60555 q^{21} -2.00000i q^{23} +1.00000i q^{27} -2.60555 q^{29} +4.00000 q^{31} +4.60555i q^{33} -3.39445i q^{37} +4.60555 q^{39} +6.60555 q^{41} +10.6056i q^{43} -6.00000i q^{47} +0.211103 q^{49} -2.00000 q^{51} -1.00000i q^{57} -5.21110 q^{59} -7.21110 q^{61} -2.60555i q^{63} -4.00000i q^{67} -2.00000 q^{69} -9.21110 q^{71} +6.00000i q^{73} -12.0000i q^{77} -8.00000 q^{79} +1.00000 q^{81} -11.2111i q^{83} +2.60555i q^{87} -6.60555 q^{89} -12.0000 q^{91} -4.00000i q^{93} -16.6056i q^{97} +4.60555 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4 q - 4 q^{9}+O(q^{10})$$ 4 * q - 4 * q^9 $$4 q - 4 q^{9} - 4 q^{11} + 4 q^{19} - 4 q^{21} + 4 q^{29} + 16 q^{31} + 4 q^{39} + 12 q^{41} - 28 q^{49} - 8 q^{51} + 8 q^{59} - 8 q^{69} - 8 q^{71} - 32 q^{79} + 4 q^{81} - 12 q^{89} - 48 q^{91} + 4 q^{99}+O(q^{100})$$ 4 * q - 4 * q^9 - 4 * q^11 + 4 * q^19 - 4 * q^21 + 4 * q^29 + 16 * q^31 + 4 * q^39 + 12 * q^41 - 28 * q^49 - 8 * q^51 + 8 * q^59 - 8 * q^69 - 8 * q^71 - 32 * q^79 + 4 * q^81 - 12 * q^89 - 48 * q^91 + 4 * q^99

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/5700\mathbb{Z}\right)^\times$$.

 $$n$$ $$1901$$ $$2851$$ $$3877$$ $$4201$$ $$\chi(n)$$ $$1$$ $$1$$ $$-1$$ $$1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0 0
$$3$$ − 1.00000i − 0.577350i
$$4$$ 0 0
$$5$$ 0 0
$$6$$ 0 0
$$7$$ 2.60555i 0.984806i 0.870367 + 0.492403i $$0.163881\pi$$
−0.870367 + 0.492403i $$0.836119\pi$$
$$8$$ 0 0
$$9$$ −1.00000 −0.333333
$$10$$ 0 0
$$11$$ −4.60555 −1.38863 −0.694313 0.719673i $$-0.744292\pi$$
−0.694313 + 0.719673i $$0.744292\pi$$
$$12$$ 0 0
$$13$$ 4.60555i 1.27735i 0.769477 + 0.638675i $$0.220517\pi$$
−0.769477 + 0.638675i $$0.779483\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ − 2.00000i − 0.485071i −0.970143 0.242536i $$-0.922021\pi$$
0.970143 0.242536i $$-0.0779791\pi$$
$$18$$ 0 0
$$19$$ 1.00000 0.229416
$$20$$ 0 0
$$21$$ 2.60555 0.568578
$$22$$ 0 0
$$23$$ − 2.00000i − 0.417029i −0.978019 0.208514i $$-0.933137\pi$$
0.978019 0.208514i $$-0.0668628\pi$$
$$24$$ 0 0
$$25$$ 0 0
$$26$$ 0 0
$$27$$ 1.00000i 0.192450i
$$28$$ 0 0
$$29$$ −2.60555 −0.483839 −0.241919 0.970296i $$-0.577777\pi$$
−0.241919 + 0.970296i $$0.577777\pi$$
$$30$$ 0 0
$$31$$ 4.00000 0.718421 0.359211 0.933257i $$-0.383046\pi$$
0.359211 + 0.933257i $$0.383046\pi$$
$$32$$ 0 0
$$33$$ 4.60555i 0.801724i
$$34$$ 0 0
$$35$$ 0 0
$$36$$ 0 0
$$37$$ − 3.39445i − 0.558044i −0.960285 0.279022i $$-0.909990\pi$$
0.960285 0.279022i $$-0.0900102\pi$$
$$38$$ 0 0
$$39$$ 4.60555 0.737478
$$40$$ 0 0
$$41$$ 6.60555 1.03161 0.515807 0.856705i $$-0.327492\pi$$
0.515807 + 0.856705i $$0.327492\pi$$
$$42$$ 0 0
$$43$$ 10.6056i 1.61733i 0.588268 + 0.808666i $$0.299810\pi$$
−0.588268 + 0.808666i $$0.700190\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ − 6.00000i − 0.875190i −0.899172 0.437595i $$-0.855830\pi$$
0.899172 0.437595i $$-0.144170\pi$$
$$48$$ 0 0
$$49$$ 0.211103 0.0301575
$$50$$ 0 0
$$51$$ −2.00000 −0.280056
$$52$$ 0 0
$$53$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$54$$ 0 0
$$55$$ 0 0
$$56$$ 0 0
$$57$$ − 1.00000i − 0.132453i
$$58$$ 0 0
$$59$$ −5.21110 −0.678428 −0.339214 0.940709i $$-0.610161\pi$$
−0.339214 + 0.940709i $$0.610161\pi$$
$$60$$ 0 0
$$61$$ −7.21110 −0.923287 −0.461644 0.887066i $$-0.652740\pi$$
−0.461644 + 0.887066i $$0.652740\pi$$
$$62$$ 0 0
$$63$$ − 2.60555i − 0.328269i
$$64$$ 0 0
$$65$$ 0 0
$$66$$ 0 0
$$67$$ − 4.00000i − 0.488678i −0.969690 0.244339i $$-0.921429\pi$$
0.969690 0.244339i $$-0.0785709\pi$$
$$68$$ 0 0
$$69$$ −2.00000 −0.240772
$$70$$ 0 0
$$71$$ −9.21110 −1.09316 −0.546578 0.837408i $$-0.684070\pi$$
−0.546578 + 0.837408i $$0.684070\pi$$
$$72$$ 0 0
$$73$$ 6.00000i 0.702247i 0.936329 + 0.351123i $$0.114200\pi$$
−0.936329 + 0.351123i $$0.885800\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 0 0
$$77$$ − 12.0000i − 1.36753i
$$78$$ 0 0
$$79$$ −8.00000 −0.900070 −0.450035 0.893011i $$-0.648589\pi$$
−0.450035 + 0.893011i $$0.648589\pi$$
$$80$$ 0 0
$$81$$ 1.00000 0.111111
$$82$$ 0 0
$$83$$ − 11.2111i − 1.23058i −0.788301 0.615289i $$-0.789039\pi$$
0.788301 0.615289i $$-0.210961\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ 0 0
$$87$$ 2.60555i 0.279344i
$$88$$ 0 0
$$89$$ −6.60555 −0.700187 −0.350094 0.936715i $$-0.613850\pi$$
−0.350094 + 0.936715i $$0.613850\pi$$
$$90$$ 0 0
$$91$$ −12.0000 −1.25794
$$92$$ 0 0
$$93$$ − 4.00000i − 0.414781i
$$94$$ 0 0
$$95$$ 0 0
$$96$$ 0 0
$$97$$ − 16.6056i − 1.68604i −0.537884 0.843019i $$-0.680776\pi$$
0.537884 0.843019i $$-0.319224\pi$$
$$98$$ 0 0
$$99$$ 4.60555 0.462875
$$100$$ 0 0
$$101$$ −7.21110 −0.717532 −0.358766 0.933428i $$-0.616802\pi$$
−0.358766 + 0.933428i $$0.616802\pi$$
$$102$$ 0 0
$$103$$ 18.4222i 1.81519i 0.419843 + 0.907597i $$0.362085\pi$$
−0.419843 + 0.907597i $$0.637915\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ − 18.4222i − 1.78094i −0.455040 0.890471i $$-0.650375\pi$$
0.455040 0.890471i $$-0.349625\pi$$
$$108$$ 0 0
$$109$$ 11.2111 1.07383 0.536914 0.843637i $$-0.319590\pi$$
0.536914 + 0.843637i $$0.319590\pi$$
$$110$$ 0 0
$$111$$ −3.39445 −0.322187
$$112$$ 0 0
$$113$$ − 1.21110i − 0.113931i −0.998376 0.0569655i $$-0.981858\pi$$
0.998376 0.0569655i $$-0.0181425\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ 0 0
$$117$$ − 4.60555i − 0.425783i
$$118$$ 0 0
$$119$$ 5.21110 0.477701
$$120$$ 0 0
$$121$$ 10.2111 0.928282
$$122$$ 0 0
$$123$$ − 6.60555i − 0.595603i
$$124$$ 0 0
$$125$$ 0 0
$$126$$ 0 0
$$127$$ − 18.4222i − 1.63471i −0.576137 0.817353i $$-0.695441\pi$$
0.576137 0.817353i $$-0.304559\pi$$
$$128$$ 0 0
$$129$$ 10.6056 0.933767
$$130$$ 0 0
$$131$$ −15.3944 −1.34502 −0.672510 0.740088i $$-0.734784\pi$$
−0.672510 + 0.740088i $$0.734784\pi$$
$$132$$ 0 0
$$133$$ 2.60555i 0.225930i
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ 12.4222i 1.06130i 0.847591 + 0.530650i $$0.178052\pi$$
−0.847591 + 0.530650i $$0.821948\pi$$
$$138$$ 0 0
$$139$$ −9.21110 −0.781276 −0.390638 0.920544i $$-0.627745\pi$$
−0.390638 + 0.920544i $$0.627745\pi$$
$$140$$ 0 0
$$141$$ −6.00000 −0.505291
$$142$$ 0 0
$$143$$ − 21.2111i − 1.77376i
$$144$$ 0 0
$$145$$ 0 0
$$146$$ 0 0
$$147$$ − 0.211103i − 0.0174114i
$$148$$ 0 0
$$149$$ −16.4222 −1.34536 −0.672680 0.739934i $$-0.734857\pi$$
−0.672680 + 0.739934i $$0.734857\pi$$
$$150$$ 0 0
$$151$$ −12.0000 −0.976546 −0.488273 0.872691i $$-0.662373\pi$$
−0.488273 + 0.872691i $$0.662373\pi$$
$$152$$ 0 0
$$153$$ 2.00000i 0.161690i
$$154$$ 0 0
$$155$$ 0 0
$$156$$ 0 0
$$157$$ − 15.2111i − 1.21398i −0.794710 0.606989i $$-0.792377\pi$$
0.794710 0.606989i $$-0.207623\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 0 0
$$161$$ 5.21110 0.410692
$$162$$ 0 0
$$163$$ − 17.0278i − 1.33372i −0.745184 0.666858i $$-0.767639\pi$$
0.745184 0.666858i $$-0.232361\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ 6.78890i 0.525341i 0.964886 + 0.262670i $$0.0846032\pi$$
−0.964886 + 0.262670i $$0.915397\pi$$
$$168$$ 0 0
$$169$$ −8.21110 −0.631623
$$170$$ 0 0
$$171$$ −1.00000 −0.0764719
$$172$$ 0 0
$$173$$ − 9.21110i − 0.700307i −0.936692 0.350154i $$-0.886129\pi$$
0.936692 0.350154i $$-0.113871\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 0 0
$$177$$ 5.21110i 0.391690i
$$178$$ 0 0
$$179$$ 21.2111 1.58539 0.792696 0.609617i $$-0.208677\pi$$
0.792696 + 0.609617i $$0.208677\pi$$
$$180$$ 0 0
$$181$$ −0.788897 −0.0586383 −0.0293191 0.999570i $$-0.509334\pi$$
−0.0293191 + 0.999570i $$0.509334\pi$$
$$182$$ 0 0
$$183$$ 7.21110i 0.533060i
$$184$$ 0 0
$$185$$ 0 0
$$186$$ 0 0
$$187$$ 9.21110i 0.673583i
$$188$$ 0 0
$$189$$ −2.60555 −0.189526
$$190$$ 0 0
$$191$$ −5.81665 −0.420878 −0.210439 0.977607i $$-0.567489\pi$$
−0.210439 + 0.977607i $$0.567489\pi$$
$$192$$ 0 0
$$193$$ − 0.605551i − 0.0435885i −0.999762 0.0217943i $$-0.993062\pi$$
0.999762 0.0217943i $$-0.00693788\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ − 14.0000i − 0.997459i −0.866758 0.498729i $$-0.833800\pi$$
0.866758 0.498729i $$-0.166200\pi$$
$$198$$ 0 0
$$199$$ −17.2111 −1.22006 −0.610031 0.792377i $$-0.708843\pi$$
−0.610031 + 0.792377i $$0.708843\pi$$
$$200$$ 0 0
$$201$$ −4.00000 −0.282138
$$202$$ 0 0
$$203$$ − 6.78890i − 0.476487i
$$204$$ 0 0
$$205$$ 0 0
$$206$$ 0 0
$$207$$ 2.00000i 0.139010i
$$208$$ 0 0
$$209$$ −4.60555 −0.318573
$$210$$ 0 0
$$211$$ −4.00000 −0.275371 −0.137686 0.990476i $$-0.543966\pi$$
−0.137686 + 0.990476i $$0.543966\pi$$
$$212$$ 0 0
$$213$$ 9.21110i 0.631134i
$$214$$ 0 0
$$215$$ 0 0
$$216$$ 0 0
$$217$$ 10.4222i 0.707505i
$$218$$ 0 0
$$219$$ 6.00000 0.405442
$$220$$ 0 0
$$221$$ 9.21110 0.619606
$$222$$ 0 0
$$223$$ − 10.4222i − 0.697922i −0.937137 0.348961i $$-0.886534\pi$$
0.937137 0.348961i $$-0.113466\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ 13.2111i 0.876852i 0.898767 + 0.438426i $$0.144464\pi$$
−0.898767 + 0.438426i $$0.855536\pi$$
$$228$$ 0 0
$$229$$ 3.21110 0.212196 0.106098 0.994356i $$-0.466164\pi$$
0.106098 + 0.994356i $$0.466164\pi$$
$$230$$ 0 0
$$231$$ −12.0000 −0.789542
$$232$$ 0 0
$$233$$ − 16.4222i − 1.07585i −0.842991 0.537927i $$-0.819208\pi$$
0.842991 0.537927i $$-0.180792\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ 0 0
$$237$$ 8.00000i 0.519656i
$$238$$ 0 0
$$239$$ −25.8167 −1.66994 −0.834970 0.550295i $$-0.814515\pi$$
−0.834970 + 0.550295i $$0.814515\pi$$
$$240$$ 0 0
$$241$$ −10.0000 −0.644157 −0.322078 0.946713i $$-0.604381\pi$$
−0.322078 + 0.946713i $$0.604381\pi$$
$$242$$ 0 0
$$243$$ − 1.00000i − 0.0641500i
$$244$$ 0 0
$$245$$ 0 0
$$246$$ 0 0
$$247$$ 4.60555i 0.293044i
$$248$$ 0 0
$$249$$ −11.2111 −0.710475
$$250$$ 0 0
$$251$$ −6.18335 −0.390289 −0.195145 0.980774i $$-0.562518\pi$$
−0.195145 + 0.980774i $$0.562518\pi$$
$$252$$ 0 0
$$253$$ 9.21110i 0.579097i
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ − 2.78890i − 0.173967i −0.996210 0.0869833i $$-0.972277\pi$$
0.996210 0.0869833i $$-0.0277227\pi$$
$$258$$ 0 0
$$259$$ 8.84441 0.549565
$$260$$ 0 0
$$261$$ 2.60555 0.161280
$$262$$ 0 0
$$263$$ 7.21110i 0.444656i 0.974972 + 0.222328i $$0.0713655\pi$$
−0.974972 + 0.222328i $$0.928634\pi$$
$$264$$ 0 0
$$265$$ 0 0
$$266$$ 0 0
$$267$$ 6.60555i 0.404253i
$$268$$ 0 0
$$269$$ 17.3944 1.06056 0.530279 0.847823i $$-0.322087\pi$$
0.530279 + 0.847823i $$0.322087\pi$$
$$270$$ 0 0
$$271$$ 11.6333 0.706673 0.353337 0.935496i $$-0.385047\pi$$
0.353337 + 0.935496i $$0.385047\pi$$
$$272$$ 0 0
$$273$$ 12.0000i 0.726273i
$$274$$ 0 0
$$275$$ 0 0
$$276$$ 0 0
$$277$$ 2.00000i 0.120168i 0.998193 + 0.0600842i $$0.0191369\pi$$
−0.998193 + 0.0600842i $$0.980863\pi$$
$$278$$ 0 0
$$279$$ −4.00000 −0.239474
$$280$$ 0 0
$$281$$ 18.2389 1.08804 0.544020 0.839073i $$-0.316902\pi$$
0.544020 + 0.839073i $$0.316902\pi$$
$$282$$ 0 0
$$283$$ − 18.6056i − 1.10599i −0.833186 0.552993i $$-0.813486\pi$$
0.833186 0.552993i $$-0.186514\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 17.2111i 1.01594i
$$288$$ 0 0
$$289$$ 13.0000 0.764706
$$290$$ 0 0
$$291$$ −16.6056 −0.973435
$$292$$ 0 0
$$293$$ 19.6333i 1.14699i 0.819209 + 0.573495i $$0.194413\pi$$
−0.819209 + 0.573495i $$0.805587\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ 0 0
$$297$$ − 4.60555i − 0.267241i
$$298$$ 0 0
$$299$$ 9.21110 0.532692
$$300$$ 0 0
$$301$$ −27.6333 −1.59276
$$302$$ 0 0
$$303$$ 7.21110i 0.414267i
$$304$$ 0 0
$$305$$ 0 0
$$306$$ 0 0
$$307$$ 11.6333i 0.663948i 0.943289 + 0.331974i $$0.107715\pi$$
−0.943289 + 0.331974i $$0.892285\pi$$
$$308$$ 0 0
$$309$$ 18.4222 1.04800
$$310$$ 0 0
$$311$$ 16.6056 0.941614 0.470807 0.882236i $$-0.343963\pi$$
0.470807 + 0.882236i $$0.343963\pi$$
$$312$$ 0 0
$$313$$ 0.788897i 0.0445911i 0.999751 + 0.0222956i $$0.00709749\pi$$
−0.999751 + 0.0222956i $$0.992903\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ 6.42221i 0.360707i 0.983602 + 0.180353i $$0.0577242\pi$$
−0.983602 + 0.180353i $$0.942276\pi$$
$$318$$ 0 0
$$319$$ 12.0000 0.671871
$$320$$ 0 0
$$321$$ −18.4222 −1.02823
$$322$$ 0 0
$$323$$ − 2.00000i − 0.111283i
$$324$$ 0 0
$$325$$ 0 0
$$326$$ 0 0
$$327$$ − 11.2111i − 0.619975i
$$328$$ 0 0
$$329$$ 15.6333 0.861892
$$330$$ 0 0
$$331$$ −8.00000 −0.439720 −0.219860 0.975531i $$-0.570560\pi$$
−0.219860 + 0.975531i $$0.570560\pi$$
$$332$$ 0 0
$$333$$ 3.39445i 0.186015i
$$334$$ 0 0
$$335$$ 0 0
$$336$$ 0 0
$$337$$ − 3.02776i − 0.164932i −0.996594 0.0824662i $$-0.973720\pi$$
0.996594 0.0824662i $$-0.0262797\pi$$
$$338$$ 0 0
$$339$$ −1.21110 −0.0657781
$$340$$ 0 0
$$341$$ −18.4222 −0.997618
$$342$$ 0 0
$$343$$ 18.7889i 1.01451i
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ − 21.6333i − 1.16134i −0.814140 0.580668i $$-0.802791\pi$$
0.814140 0.580668i $$-0.197209\pi$$
$$348$$ 0 0
$$349$$ −34.8444 −1.86518 −0.932589 0.360939i $$-0.882456\pi$$
−0.932589 + 0.360939i $$0.882456\pi$$
$$350$$ 0 0
$$351$$ −4.60555 −0.245826
$$352$$ 0 0
$$353$$ 0.422205i 0.0224717i 0.999937 + 0.0112359i $$0.00357656\pi$$
−0.999937 + 0.0112359i $$0.996423\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ 0 0
$$357$$ − 5.21110i − 0.275801i
$$358$$ 0 0
$$359$$ 13.8167 0.729215 0.364608 0.931161i $$-0.381203\pi$$
0.364608 + 0.931161i $$0.381203\pi$$
$$360$$ 0 0
$$361$$ 1.00000 0.0526316
$$362$$ 0 0
$$363$$ − 10.2111i − 0.535944i
$$364$$ 0 0
$$365$$ 0 0
$$366$$ 0 0
$$367$$ − 25.0278i − 1.30644i −0.757169 0.653219i $$-0.773418\pi$$
0.757169 0.653219i $$-0.226582\pi$$
$$368$$ 0 0
$$369$$ −6.60555 −0.343871
$$370$$ 0 0
$$371$$ 0 0
$$372$$ 0 0
$$373$$ 16.6056i 0.859803i 0.902876 + 0.429901i $$0.141452\pi$$
−0.902876 + 0.429901i $$0.858548\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ − 12.0000i − 0.618031i
$$378$$ 0 0
$$379$$ −26.4222 −1.35722 −0.678609 0.734500i $$-0.737417\pi$$
−0.678609 + 0.734500i $$0.737417\pi$$
$$380$$ 0 0
$$381$$ −18.4222 −0.943798
$$382$$ 0 0
$$383$$ − 12.0000i − 0.613171i −0.951843 0.306586i $$-0.900813\pi$$
0.951843 0.306586i $$-0.0991866\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 0 0
$$387$$ − 10.6056i − 0.539110i
$$388$$ 0 0
$$389$$ −36.4222 −1.84668 −0.923340 0.383984i $$-0.874552\pi$$
−0.923340 + 0.383984i $$0.874552\pi$$
$$390$$ 0 0
$$391$$ −4.00000 −0.202289
$$392$$ 0 0
$$393$$ 15.3944i 0.776547i
$$394$$ 0 0
$$395$$ 0 0
$$396$$ 0 0
$$397$$ 7.57779i 0.380319i 0.981753 + 0.190159i $$0.0609005\pi$$
−0.981753 + 0.190159i $$0.939100\pi$$
$$398$$ 0 0
$$399$$ 2.60555 0.130441
$$400$$ 0 0
$$401$$ 25.3944 1.26814 0.634069 0.773276i $$-0.281383\pi$$
0.634069 + 0.773276i $$0.281383\pi$$
$$402$$ 0 0
$$403$$ 18.4222i 0.917675i
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 15.6333i 0.774914i
$$408$$ 0 0
$$409$$ 12.7889 0.632370 0.316185 0.948698i $$-0.397598\pi$$
0.316185 + 0.948698i $$0.397598\pi$$
$$410$$ 0 0
$$411$$ 12.4222 0.612742
$$412$$ 0 0
$$413$$ − 13.5778i − 0.668120i
$$414$$ 0 0
$$415$$ 0 0
$$416$$ 0 0
$$417$$ 9.21110i 0.451070i
$$418$$ 0 0
$$419$$ 7.02776 0.343328 0.171664 0.985156i $$-0.445086\pi$$
0.171664 + 0.985156i $$0.445086\pi$$
$$420$$ 0 0
$$421$$ −8.42221 −0.410473 −0.205237 0.978712i $$-0.565796\pi$$
−0.205237 + 0.978712i $$0.565796\pi$$
$$422$$ 0 0
$$423$$ 6.00000i 0.291730i
$$424$$ 0 0
$$425$$ 0 0
$$426$$ 0 0
$$427$$ − 18.7889i − 0.909258i
$$428$$ 0 0
$$429$$ −21.2111 −1.02408
$$430$$ 0 0
$$431$$ −9.21110 −0.443683 −0.221842 0.975083i $$-0.571207\pi$$
−0.221842 + 0.975083i $$0.571207\pi$$
$$432$$ 0 0
$$433$$ − 16.6056i − 0.798012i −0.916948 0.399006i $$-0.869355\pi$$
0.916948 0.399006i $$-0.130645\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ − 2.00000i − 0.0956730i
$$438$$ 0 0
$$439$$ −34.4222 −1.64288 −0.821441 0.570293i $$-0.806830\pi$$
−0.821441 + 0.570293i $$0.806830\pi$$
$$440$$ 0 0
$$441$$ −0.211103 −0.0100525
$$442$$ 0 0
$$443$$ 18.8444i 0.895325i 0.894203 + 0.447662i $$0.147743\pi$$
−0.894203 + 0.447662i $$0.852257\pi$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ 0 0
$$447$$ 16.4222i 0.776744i
$$448$$ 0 0
$$449$$ 18.2389 0.860745 0.430372 0.902651i $$-0.358382\pi$$
0.430372 + 0.902651i $$0.358382\pi$$
$$450$$ 0 0
$$451$$ −30.4222 −1.43253
$$452$$ 0 0
$$453$$ 12.0000i 0.563809i
$$454$$ 0 0
$$455$$ 0 0
$$456$$ 0 0
$$457$$ − 32.0555i − 1.49949i −0.661725 0.749747i $$-0.730175\pi$$
0.661725 0.749747i $$-0.269825\pi$$
$$458$$ 0 0
$$459$$ 2.00000 0.0933520
$$460$$ 0 0
$$461$$ −22.8444 −1.06397 −0.531985 0.846754i $$-0.678554\pi$$
−0.531985 + 0.846754i $$0.678554\pi$$
$$462$$ 0 0
$$463$$ 33.0278i 1.53493i 0.641091 + 0.767465i $$0.278482\pi$$
−0.641091 + 0.767465i $$0.721518\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ − 22.8444i − 1.05711i −0.848898 0.528557i $$-0.822733\pi$$
0.848898 0.528557i $$-0.177267\pi$$
$$468$$ 0 0
$$469$$ 10.4222 0.481253
$$470$$ 0 0
$$471$$ −15.2111 −0.700891
$$472$$ 0 0
$$473$$ − 48.8444i − 2.24587i
$$474$$ 0 0
$$475$$ 0 0
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 0 0
$$479$$ −28.6056 −1.30702 −0.653510 0.756917i $$-0.726704\pi$$
−0.653510 + 0.756917i $$0.726704\pi$$
$$480$$ 0 0
$$481$$ 15.6333 0.712817
$$482$$ 0 0
$$483$$ − 5.21110i − 0.237113i
$$484$$ 0 0
$$485$$ 0 0
$$486$$ 0 0
$$487$$ − 0.366692i − 0.0166164i −0.999965 0.00830821i $$-0.997355\pi$$
0.999965 0.00830821i $$-0.00264462\pi$$
$$488$$ 0 0
$$489$$ −17.0278 −0.770022
$$490$$ 0 0
$$491$$ −12.2389 −0.552332 −0.276166 0.961110i $$-0.589064\pi$$
−0.276166 + 0.961110i $$0.589064\pi$$
$$492$$ 0 0
$$493$$ 5.21110i 0.234696i
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ − 24.0000i − 1.07655i
$$498$$ 0 0
$$499$$ 27.6333 1.23704 0.618518 0.785770i $$-0.287733\pi$$
0.618518 + 0.785770i $$0.287733\pi$$
$$500$$ 0 0
$$501$$ 6.78890 0.303306
$$502$$ 0 0
$$503$$ 12.7889i 0.570229i 0.958494 + 0.285114i $$0.0920316\pi$$
−0.958494 + 0.285114i $$0.907968\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ 0 0
$$507$$ 8.21110i 0.364668i
$$508$$ 0 0
$$509$$ 35.4500 1.57129 0.785646 0.618676i $$-0.212331\pi$$
0.785646 + 0.618676i $$0.212331\pi$$
$$510$$ 0 0
$$511$$ −15.6333 −0.691577
$$512$$ 0 0
$$513$$ 1.00000i 0.0441511i
$$514$$ 0 0
$$515$$ 0 0
$$516$$ 0 0
$$517$$ 27.6333i 1.21531i
$$518$$ 0 0
$$519$$ −9.21110 −0.404323
$$520$$ 0 0
$$521$$ −4.18335 −0.183276 −0.0916379 0.995792i $$-0.529210\pi$$
−0.0916379 + 0.995792i $$0.529210\pi$$
$$522$$ 0 0
$$523$$ − 25.2111i − 1.10240i −0.834372 0.551202i $$-0.814169\pi$$
0.834372 0.551202i $$-0.185831\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ − 8.00000i − 0.348485i
$$528$$ 0 0
$$529$$ 19.0000 0.826087
$$530$$ 0 0
$$531$$ 5.21110 0.226143
$$532$$ 0 0
$$533$$ 30.4222i 1.31773i
$$534$$ 0 0
$$535$$ 0 0
$$536$$ 0 0
$$537$$ − 21.2111i − 0.915327i
$$538$$ 0 0
$$539$$ −0.972244 −0.0418775
$$540$$ 0 0
$$541$$ 2.00000 0.0859867 0.0429934 0.999075i $$-0.486311\pi$$
0.0429934 + 0.999075i $$0.486311\pi$$
$$542$$ 0 0
$$543$$ 0.788897i 0.0338548i
$$544$$ 0 0
$$545$$ 0 0
$$546$$ 0 0
$$547$$ 22.7889i 0.974383i 0.873295 + 0.487191i $$0.161979\pi$$
−0.873295 + 0.487191i $$0.838021\pi$$
$$548$$ 0 0
$$549$$ 7.21110 0.307762
$$550$$ 0 0
$$551$$ −2.60555 −0.111000
$$552$$ 0 0
$$553$$ − 20.8444i − 0.886394i
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ 4.42221i 0.187375i 0.995602 + 0.0936874i $$0.0298654\pi$$
−0.995602 + 0.0936874i $$0.970135\pi$$
$$558$$ 0 0
$$559$$ −48.8444 −2.06590
$$560$$ 0 0
$$561$$ 9.21110 0.388893
$$562$$ 0 0
$$563$$ 31.6333i 1.33318i 0.745422 + 0.666592i $$0.232248\pi$$
−0.745422 + 0.666592i $$0.767752\pi$$
$$564$$ 0 0
$$565$$ 0 0
$$566$$ 0 0
$$567$$ 2.60555i 0.109423i
$$568$$ 0 0
$$569$$ −39.4500 −1.65383 −0.826914 0.562328i $$-0.809906\pi$$
−0.826914 + 0.562328i $$0.809906\pi$$
$$570$$ 0 0
$$571$$ 7.63331 0.319444 0.159722 0.987162i $$-0.448940\pi$$
0.159722 + 0.987162i $$0.448940\pi$$
$$572$$ 0 0
$$573$$ 5.81665i 0.242994i
$$574$$ 0 0
$$575$$ 0 0
$$576$$ 0 0
$$577$$ 23.2111i 0.966291i 0.875540 + 0.483145i $$0.160506\pi$$
−0.875540 + 0.483145i $$0.839494\pi$$
$$578$$ 0 0
$$579$$ −0.605551 −0.0251659
$$580$$ 0 0
$$581$$ 29.2111 1.21188
$$582$$ 0 0
$$583$$ 0 0
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ − 12.4222i − 0.512719i −0.966581 0.256360i $$-0.917477\pi$$
0.966581 0.256360i $$-0.0825231\pi$$
$$588$$ 0 0
$$589$$ 4.00000 0.164817
$$590$$ 0 0
$$591$$ −14.0000 −0.575883
$$592$$ 0 0
$$593$$ − 3.57779i − 0.146922i −0.997298 0.0734612i $$-0.976595\pi$$
0.997298 0.0734612i $$-0.0234045\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 0 0
$$597$$ 17.2111i 0.704404i
$$598$$ 0 0
$$599$$ −36.8444 −1.50542 −0.752711 0.658351i $$-0.771254\pi$$
−0.752711 + 0.658351i $$0.771254\pi$$
$$600$$ 0 0
$$601$$ 4.78890 0.195343 0.0976716 0.995219i $$-0.468861\pi$$
0.0976716 + 0.995219i $$0.468861\pi$$
$$602$$ 0 0
$$603$$ 4.00000i 0.162893i
$$604$$ 0 0
$$605$$ 0 0
$$606$$ 0 0
$$607$$ 23.6333i 0.959246i 0.877475 + 0.479623i $$0.159227\pi$$
−0.877475 + 0.479623i $$0.840773\pi$$
$$608$$ 0 0
$$609$$ −6.78890 −0.275100
$$610$$ 0 0
$$611$$ 27.6333 1.11792
$$612$$ 0 0
$$613$$ 4.78890i 0.193422i 0.995313 + 0.0967109i $$0.0308322\pi$$
−0.995313 + 0.0967109i $$0.969168\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ − 34.0000i − 1.36879i −0.729112 0.684394i $$-0.760067\pi$$
0.729112 0.684394i $$-0.239933\pi$$
$$618$$ 0 0
$$619$$ 4.36669 0.175512 0.0877561 0.996142i $$-0.472030\pi$$
0.0877561 + 0.996142i $$0.472030\pi$$
$$620$$ 0 0
$$621$$ 2.00000 0.0802572
$$622$$ 0 0
$$623$$ − 17.2111i − 0.689548i
$$624$$ 0 0
$$625$$ 0 0
$$626$$ 0 0
$$627$$ 4.60555i 0.183928i
$$628$$ 0 0
$$629$$ −6.78890 −0.270691
$$630$$ 0 0
$$631$$ 36.8444 1.46675 0.733376 0.679823i $$-0.237943\pi$$
0.733376 + 0.679823i $$0.237943\pi$$
$$632$$ 0 0
$$633$$ 4.00000i 0.158986i
$$634$$ 0 0
$$635$$ 0 0
$$636$$ 0 0
$$637$$ 0.972244i 0.0385217i
$$638$$ 0 0
$$639$$ 9.21110 0.364386
$$640$$ 0 0
$$641$$ 35.4500 1.40019 0.700095 0.714050i $$-0.253141\pi$$
0.700095 + 0.714050i $$0.253141\pi$$
$$642$$ 0 0
$$643$$ 5.39445i 0.212736i 0.994327 + 0.106368i $$0.0339222\pi$$
−0.994327 + 0.106368i $$0.966078\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 2.36669i 0.0930443i 0.998917 + 0.0465221i $$0.0148138\pi$$
−0.998917 + 0.0465221i $$0.985186\pi$$
$$648$$ 0 0
$$649$$ 24.0000 0.942082
$$650$$ 0 0
$$651$$ 10.4222 0.408478
$$652$$ 0 0
$$653$$ 42.0000i 1.64359i 0.569785 + 0.821794i $$0.307026\pi$$
−0.569785 + 0.821794i $$0.692974\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ 0 0
$$657$$ − 6.00000i − 0.234082i
$$658$$ 0 0
$$659$$ −36.0000 −1.40236 −0.701180 0.712984i $$-0.747343\pi$$
−0.701180 + 0.712984i $$0.747343\pi$$
$$660$$ 0 0
$$661$$ −31.2111 −1.21397 −0.606986 0.794713i $$-0.707621\pi$$
−0.606986 + 0.794713i $$0.707621\pi$$
$$662$$ 0 0
$$663$$ − 9.21110i − 0.357730i
$$664$$ 0 0
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 5.21110i 0.201775i
$$668$$ 0 0
$$669$$ −10.4222 −0.402946
$$670$$ 0 0
$$671$$ 33.2111 1.28210
$$672$$ 0 0
$$673$$ 36.6056i 1.41104i 0.708690 + 0.705520i $$0.249287\pi$$
−0.708690 + 0.705520i $$0.750713\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ − 10.4222i − 0.400558i −0.979739 0.200279i $$-0.935815\pi$$
0.979739 0.200279i $$-0.0641848\pi$$
$$678$$ 0 0
$$679$$ 43.2666 1.66042
$$680$$ 0 0
$$681$$ 13.2111 0.506251
$$682$$ 0 0
$$683$$ − 48.0000i − 1.83667i −0.395805 0.918334i $$-0.629534\pi$$
0.395805 0.918334i $$-0.370466\pi$$
$$684$$ 0 0
$$685$$ 0 0
$$686$$ 0 0
$$687$$ − 3.21110i − 0.122511i
$$688$$ 0 0
$$689$$ 0 0
$$690$$ 0 0
$$691$$ −42.0555 −1.59987 −0.799934 0.600089i $$-0.795132\pi$$
−0.799934 + 0.600089i $$0.795132\pi$$
$$692$$ 0 0
$$693$$ 12.0000i 0.455842i
$$694$$ 0 0
$$695$$ 0 0
$$696$$ 0 0
$$697$$ − 13.2111i − 0.500406i
$$698$$ 0 0
$$699$$ −16.4222 −0.621145
$$700$$ 0 0
$$701$$ 6.00000 0.226617 0.113308 0.993560i $$-0.463855\pi$$
0.113308 + 0.993560i $$0.463855\pi$$
$$702$$ 0 0
$$703$$ − 3.39445i − 0.128024i
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ − 18.7889i − 0.706629i
$$708$$ 0 0
$$709$$ 25.6333 0.962679 0.481340 0.876534i $$-0.340150\pi$$
0.481340 + 0.876534i $$0.340150\pi$$
$$710$$ 0 0
$$711$$ 8.00000 0.300023
$$712$$ 0 0
$$713$$ − 8.00000i − 0.299602i
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 0 0
$$717$$ 25.8167i 0.964141i
$$718$$ 0 0
$$719$$ −16.2389 −0.605607 −0.302804 0.953053i $$-0.597923\pi$$
−0.302804 + 0.953053i $$0.597923\pi$$
$$720$$ 0 0
$$721$$ −48.0000 −1.78761
$$722$$ 0 0
$$723$$ 10.0000i 0.371904i
$$724$$ 0 0
$$725$$ 0 0
$$726$$ 0 0
$$727$$ 17.3944i 0.645124i 0.946548 + 0.322562i $$0.104544\pi$$
−0.946548 + 0.322562i $$0.895456\pi$$
$$728$$ 0 0
$$729$$ −1.00000 −0.0370370
$$730$$ 0 0
$$731$$ 21.2111 0.784521
$$732$$ 0 0
$$733$$ − 24.4222i − 0.902055i −0.892510 0.451027i $$-0.851058\pi$$
0.892510 0.451027i $$-0.148942\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 18.4222i 0.678591i
$$738$$ 0 0
$$739$$ −38.4222 −1.41338 −0.706692 0.707521i $$-0.749813\pi$$
−0.706692 + 0.707521i $$0.749813\pi$$
$$740$$ 0 0
$$741$$ 4.60555 0.169189
$$742$$ 0 0
$$743$$ − 20.0000i − 0.733729i −0.930274 0.366864i $$-0.880431\pi$$
0.930274 0.366864i $$-0.119569\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ 0 0
$$747$$ 11.2111i 0.410193i
$$748$$ 0 0
$$749$$ 48.0000 1.75388
$$750$$ 0 0
$$751$$ 40.8444 1.49043 0.745217 0.666822i $$-0.232346\pi$$
0.745217 + 0.666822i $$0.232346\pi$$
$$752$$ 0 0
$$753$$ 6.18335i 0.225334i
$$754$$ 0 0
$$755$$ 0 0
$$756$$ 0 0
$$757$$ 36.0555i 1.31046i 0.755429 + 0.655230i $$0.227428\pi$$
−0.755429 + 0.655230i $$0.772572\pi$$
$$758$$ 0 0
$$759$$ 9.21110 0.334342
$$760$$ 0 0
$$761$$ 30.0000 1.08750 0.543750 0.839248i $$-0.317004\pi$$
0.543750 + 0.839248i $$0.317004\pi$$
$$762$$ 0 0
$$763$$ 29.2111i 1.05751i
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ − 24.0000i − 0.866590i
$$768$$ 0 0
$$769$$ 20.4222 0.736444 0.368222 0.929738i $$-0.379967\pi$$
0.368222 + 0.929738i $$0.379967\pi$$
$$770$$ 0 0
$$771$$ −2.78890 −0.100440
$$772$$ 0 0
$$773$$ − 43.2666i − 1.55619i −0.628145 0.778096i $$-0.716186\pi$$
0.628145 0.778096i $$-0.283814\pi$$
$$774$$ 0 0
$$775$$ 0 0
$$776$$ 0 0
$$777$$ − 8.84441i − 0.317291i
$$778$$ 0 0
$$779$$ 6.60555 0.236668
$$780$$ 0 0
$$781$$ 42.4222 1.51799
$$782$$ 0 0
$$783$$ − 2.60555i − 0.0931148i
$$784$$ 0 0
$$785$$ 0 0
$$786$$ 0 0
$$787$$ 19.6333i 0.699852i 0.936777 + 0.349926i $$0.113793\pi$$
−0.936777 + 0.349926i $$0.886207\pi$$
$$788$$ 0 0
$$789$$ 7.21110 0.256722
$$790$$ 0 0
$$791$$ 3.15559 0.112200
$$792$$ 0 0
$$793$$ − 33.2111i − 1.17936i
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ − 17.2111i − 0.609649i −0.952409 0.304824i $$-0.901402\pi$$
0.952409 0.304824i $$-0.0985977\pi$$
$$798$$ 0 0
$$799$$ −12.0000 −0.424529
$$800$$ 0 0
$$801$$ 6.60555 0.233396
$$802$$ 0 0
$$803$$ − 27.6333i − 0.975158i
$$804$$ 0 0
$$805$$ 0 0
$$806$$ 0 0
$$807$$ − 17.3944i − 0.612314i
$$808$$ 0 0
$$809$$ 48.4222 1.70243 0.851217 0.524814i $$-0.175865\pi$$
0.851217 + 0.524814i $$0.175865\pi$$
$$810$$ 0 0
$$811$$ −40.8444 −1.43424 −0.717121 0.696949i $$-0.754540\pi$$
−0.717121 + 0.696949i $$0.754540\pi$$
$$812$$ 0 0
$$813$$ − 11.6333i − 0.407998i
$$814$$ 0 0
$$815$$ 0 0
$$816$$ 0 0
$$817$$ 10.6056i 0.371041i
$$818$$ 0 0
$$819$$ 12.0000 0.419314
$$820$$ 0 0
$$821$$ 43.2111 1.50808 0.754039 0.656830i $$-0.228103\pi$$
0.754039 + 0.656830i $$0.228103\pi$$
$$822$$ 0 0
$$823$$ − 47.8167i − 1.66678i −0.552683 0.833392i $$-0.686396\pi$$
0.552683 0.833392i $$-0.313604\pi$$
$$824$$ 0 0
$$825$$ 0 0
$$826$$ 0 0
$$827$$ 27.6333i 0.960904i 0.877021 + 0.480452i $$0.159527\pi$$
−0.877021 + 0.480452i $$0.840473\pi$$
$$828$$ 0 0
$$829$$ −15.2111 −0.528303 −0.264152 0.964481i $$-0.585092\pi$$
−0.264152 + 0.964481i $$0.585092\pi$$
$$830$$ 0 0
$$831$$ 2.00000 0.0693792
$$832$$ 0 0
$$833$$ − 0.422205i − 0.0146285i
$$834$$ 0 0
$$835$$ 0 0
$$836$$ 0 0
$$837$$ 4.00000i 0.138260i
$$838$$ 0 0
$$839$$ −27.6333 −0.954008 −0.477004 0.878901i $$-0.658277\pi$$
−0.477004 + 0.878901i $$0.658277\pi$$
$$840$$ 0 0
$$841$$ −22.2111 −0.765900
$$842$$ 0 0
$$843$$ − 18.2389i − 0.628180i
$$844$$ 0 0
$$845$$ 0 0
$$846$$ 0 0
$$847$$ 26.6056i 0.914178i
$$848$$ 0 0
$$849$$ −18.6056 −0.638541
$$850$$ 0 0
$$851$$ −6.78890 −0.232720
$$852$$ 0 0
$$853$$ 29.6333i 1.01463i 0.861762 + 0.507313i $$0.169361\pi$$
−0.861762 + 0.507313i $$0.830639\pi$$
$$854$$ 0 0
$$855$$ 0 0
$$856$$ 0 0
$$857$$ − 6.42221i − 0.219378i −0.993966 0.109689i $$-0.965014\pi$$
0.993966 0.109689i $$-0.0349855\pi$$
$$858$$ 0 0
$$859$$ −8.84441 −0.301767 −0.150884 0.988552i $$-0.548212\pi$$
−0.150884 + 0.988552i $$0.548212\pi$$
$$860$$ 0 0
$$861$$ 17.2111 0.586553
$$862$$ 0 0
$$863$$ 6.42221i 0.218614i 0.994008 + 0.109307i $$0.0348632\pi$$
−0.994008 + 0.109307i $$0.965137\pi$$
$$864$$ 0 0
$$865$$ 0 0
$$866$$ 0 0
$$867$$ − 13.0000i − 0.441503i
$$868$$ 0 0
$$869$$ 36.8444 1.24986
$$870$$ 0 0
$$871$$ 18.4222 0.624213
$$872$$ 0 0
$$873$$ 16.6056i 0.562013i
$$874$$ 0 0
$$875$$ 0 0
$$876$$ 0 0
$$877$$ − 27.0278i − 0.912662i −0.889810 0.456331i $$-0.849163\pi$$
0.889810 0.456331i $$-0.150837\pi$$
$$878$$ 0 0
$$879$$ 19.6333 0.662215
$$880$$ 0 0
$$881$$ 59.2111 1.99487 0.997436 0.0715590i $$-0.0227974\pi$$
0.997436 + 0.0715590i $$0.0227974\pi$$
$$882$$ 0 0
$$883$$ 27.8167i 0.936105i 0.883701 + 0.468052i $$0.155044\pi$$
−0.883701 + 0.468052i $$0.844956\pi$$
$$884$$ 0 0
$$885$$ 0 0
$$886$$ 0 0
$$887$$ 20.8444i 0.699887i 0.936771 + 0.349943i $$0.113799\pi$$
−0.936771 + 0.349943i $$0.886201\pi$$
$$888$$ 0 0
$$889$$ 48.0000 1.60987
$$890$$ 0 0
$$891$$ −4.60555 −0.154292
$$892$$ 0 0
$$893$$ − 6.00000i − 0.200782i
$$894$$ 0 0
$$895$$ 0 0
$$896$$ 0 0
$$897$$ − 9.21110i − 0.307550i
$$898$$ 0 0
$$899$$ −10.4222 −0.347600
$$900$$ 0 0
$$901$$ 0 0
$$902$$ 0 0
$$903$$ 27.6333i 0.919579i
$$904$$ 0 0
$$905$$ 0 0
$$906$$ 0 0
$$907$$ − 30.0555i − 0.997977i −0.866609 0.498988i $$-0.833705\pi$$
0.866609 0.498988i $$-0.166295\pi$$
$$908$$ 0 0
$$909$$ 7.21110 0.239177
$$910$$ 0 0
$$911$$ 10.4222 0.345303 0.172652 0.984983i $$-0.444767\pi$$
0.172652 + 0.984983i $$0.444767\pi$$
$$912$$ 0 0
$$913$$ 51.6333i 1.70881i
$$914$$ 0 0
$$915$$ 0 0
$$916$$ 0 0
$$917$$ − 40.1110i − 1.32458i
$$918$$ 0 0
$$919$$ 16.0000 0.527791 0.263896 0.964551i $$-0.414993\pi$$
0.263896 + 0.964551i $$0.414993\pi$$
$$920$$ 0 0
$$921$$ 11.6333 0.383331
$$922$$ 0 0
$$923$$ − 42.4222i − 1.39634i
$$924$$ 0 0
$$925$$ 0 0
$$926$$ 0 0
$$927$$ − 18.4222i − 0.605065i
$$928$$ 0 0
$$929$$ 45.6333 1.49718 0.748590 0.663033i $$-0.230731\pi$$
0.748590 + 0.663033i $$0.230731\pi$$
$$930$$ 0 0
$$931$$ 0.211103 0.00691861
$$932$$ 0 0
$$933$$ − 16.6056i − 0.543641i
$$934$$ 0 0
$$935$$ 0 0
$$936$$ 0 0
$$937$$ 19.2111i 0.627599i 0.949489 + 0.313800i $$0.101602\pi$$
−0.949489 + 0.313800i $$0.898398\pi$$
$$938$$ 0 0
$$939$$ 0.788897 0.0257447
$$940$$ 0 0
$$941$$ −30.2389 −0.985759 −0.492879 0.870098i $$-0.664056\pi$$
−0.492879 + 0.870098i $$0.664056\pi$$
$$942$$ 0 0
$$943$$ − 13.2111i − 0.430213i
$$944$$ 0 0
$$945$$ 0 0
$$946$$ 0 0
$$947$$ 7.21110i 0.234329i 0.993113 + 0.117165i $$0.0373805\pi$$
−0.993113 + 0.117165i $$0.962619\pi$$
$$948$$ 0 0
$$949$$ −27.6333 −0.897015
$$950$$ 0 0
$$951$$ 6.42221 0.208254
$$952$$ 0 0
$$953$$ 5.21110i 0.168804i 0.996432 + 0.0844021i $$0.0268980\pi$$
−0.996432 + 0.0844021i $$0.973102\pi$$
$$954$$ 0 0
$$955$$ 0 0
$$956$$ 0 0
$$957$$ − 12.0000i − 0.387905i
$$958$$ 0 0
$$959$$ −32.3667 −1.04518
$$960$$ 0 0
$$961$$ −15.0000 −0.483871
$$962$$ 0 0
$$963$$ 18.4222i 0.593647i
$$964$$ 0 0
$$965$$ 0 0
$$966$$ 0 0
$$967$$ 26.2389i 0.843785i 0.906646 + 0.421892i $$0.138634\pi$$
−0.906646 + 0.421892i $$0.861366\pi$$
$$968$$ 0 0
$$969$$ −2.00000 −0.0642493
$$970$$ 0 0
$$971$$ −12.0000 −0.385098 −0.192549 0.981287i $$-0.561675\pi$$
−0.192549 + 0.981287i $$0.561675\pi$$
$$972$$ 0 0
$$973$$ − 24.0000i − 0.769405i
$$974$$ 0 0
$$975$$ 0 0
$$976$$ 0 0
$$977$$ − 6.42221i − 0.205465i −0.994709 0.102732i $$-0.967242\pi$$
0.994709 0.102732i $$-0.0327585\pi$$
$$978$$ 0 0
$$979$$ 30.4222 0.972298
$$980$$ 0 0
$$981$$ −11.2111 −0.357943
$$982$$ 0 0
$$983$$ − 9.21110i − 0.293789i −0.989152 0.146894i $$-0.953072\pi$$
0.989152 0.146894i $$-0.0469277\pi$$
$$984$$ 0 0
$$985$$ 0 0
$$986$$ 0 0
$$987$$ − 15.6333i − 0.497614i
$$988$$ 0 0
$$989$$ 21.2111 0.674474
$$990$$ 0 0
$$991$$ 50.4222 1.60171 0.800857 0.598856i $$-0.204378\pi$$
0.800857 + 0.598856i $$0.204378\pi$$
$$992$$ 0 0
$$993$$ 8.00000i 0.253872i
$$994$$ 0 0
$$995$$ 0 0
$$996$$ 0 0
$$997$$ 61.6333i 1.95195i 0.217891 + 0.975973i $$0.430082\pi$$
−0.217891 + 0.975973i $$0.569918\pi$$
$$998$$ 0 0
$$999$$ 3.39445 0.107396
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 5700.2.f.n.3649.2 4
5.2 odd 4 1140.2.a.e.1.1 2
5.3 odd 4 5700.2.a.u.1.2 2
5.4 even 2 inner 5700.2.f.n.3649.3 4
15.2 even 4 3420.2.a.i.1.1 2
20.7 even 4 4560.2.a.bl.1.2 2

By twisted newform
Twist Min Dim Char Parity Ord Type
1140.2.a.e.1.1 2 5.2 odd 4
3420.2.a.i.1.1 2 15.2 even 4
4560.2.a.bl.1.2 2 20.7 even 4
5700.2.a.u.1.2 2 5.3 odd 4
5700.2.f.n.3649.2 4 1.1 even 1 trivial
5700.2.f.n.3649.3 4 5.4 even 2 inner