# Properties

 Label 1400.2.g.h.449.1 Level $1400$ Weight $2$ Character 1400.449 Analytic conductor $11.179$ Analytic rank $0$ Dimension $2$ CM no Inner twists $2$

# Learn more about

## Newspace parameters

 Level: $$N$$ $$=$$ $$1400 = 2^{3} \cdot 5^{2} \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1400.g (of order $$2$$, degree $$1$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$11.1790562830$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(i)$$ Defining polynomial: $$x^{2} + 1$$ Coefficient ring: $$\Z[a_1, \ldots, a_{7}]$$ Coefficient ring index: $$1$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

## Embedding invariants

 Embedding label 449.1 Root $$1.00000i$$ of defining polynomial Character $$\chi$$ $$=$$ 1400.449 Dual form 1400.2.g.h.449.2

## $q$-expansion

 $$f(q)$$ $$=$$ $$q-1.00000i q^{7} +3.00000 q^{9} +O(q^{10})$$ $$q-1.00000i q^{7} +3.00000 q^{9} +1.00000 q^{11} -2.00000i q^{13} +4.00000i q^{17} +2.00000 q^{19} -5.00000i q^{23} -1.00000 q^{29} -2.00000 q^{31} +3.00000i q^{37} +12.0000 q^{41} -11.0000i q^{43} +2.00000i q^{47} -1.00000 q^{49} -6.00000i q^{53} +10.0000 q^{59} +4.00000 q^{61} -3.00000i q^{63} +1.00000i q^{67} -3.00000 q^{71} -1.00000i q^{77} +9.00000 q^{79} +9.00000 q^{81} +2.00000i q^{83} +6.00000 q^{89} -2.00000 q^{91} +14.0000i q^{97} +3.00000 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2q + 6q^{9} + O(q^{10})$$ $$2q + 6q^{9} + 2q^{11} + 4q^{19} - 2q^{29} - 4q^{31} + 24q^{41} - 2q^{49} + 20q^{59} + 8q^{61} - 6q^{71} + 18q^{79} + 18q^{81} + 12q^{89} - 4q^{91} + 6q^{99} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1400\mathbb{Z}\right)^\times$$.

 $$n$$ $$351$$ $$701$$ $$801$$ $$1177$$ $$\chi(n)$$ $$1$$ $$1$$ $$1$$ $$-1$$

## 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
$$3$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$4$$ 0 0
$$5$$ 0 0
$$6$$ 0 0
$$7$$ − 1.00000i − 0.377964i
$$8$$ 0 0
$$9$$ 3.00000 1.00000
$$10$$ 0 0
$$11$$ 1.00000 0.301511 0.150756 0.988571i $$-0.451829\pi$$
0.150756 + 0.988571i $$0.451829\pi$$
$$12$$ 0 0
$$13$$ − 2.00000i − 0.554700i −0.960769 0.277350i $$-0.910544\pi$$
0.960769 0.277350i $$-0.0894562\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ 4.00000i 0.970143i 0.874475 + 0.485071i $$0.161206\pi$$
−0.874475 + 0.485071i $$0.838794\pi$$
$$18$$ 0 0
$$19$$ 2.00000 0.458831 0.229416 0.973329i $$-0.426318\pi$$
0.229416 + 0.973329i $$0.426318\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 0 0
$$23$$ − 5.00000i − 1.04257i −0.853382 0.521286i $$-0.825452\pi$$
0.853382 0.521286i $$-0.174548\pi$$
$$24$$ 0 0
$$25$$ 0 0
$$26$$ 0 0
$$27$$ 0 0
$$28$$ 0 0
$$29$$ −1.00000 −0.185695 −0.0928477 0.995680i $$-0.529597\pi$$
−0.0928477 + 0.995680i $$0.529597\pi$$
$$30$$ 0 0
$$31$$ −2.00000 −0.359211 −0.179605 0.983739i $$-0.557482\pi$$
−0.179605 + 0.983739i $$0.557482\pi$$
$$32$$ 0 0
$$33$$ 0 0
$$34$$ 0 0
$$35$$ 0 0
$$36$$ 0 0
$$37$$ 3.00000i 0.493197i 0.969118 + 0.246598i $$0.0793129\pi$$
−0.969118 + 0.246598i $$0.920687\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 0 0
$$41$$ 12.0000 1.87409 0.937043 0.349215i $$-0.113552\pi$$
0.937043 + 0.349215i $$0.113552\pi$$
$$42$$ 0 0
$$43$$ − 11.0000i − 1.67748i −0.544529 0.838742i $$-0.683292\pi$$
0.544529 0.838742i $$-0.316708\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ 2.00000i 0.291730i 0.989305 + 0.145865i $$0.0465965\pi$$
−0.989305 + 0.145865i $$0.953403\pi$$
$$48$$ 0 0
$$49$$ −1.00000 −0.142857
$$50$$ 0 0
$$51$$ 0 0
$$52$$ 0 0
$$53$$ − 6.00000i − 0.824163i −0.911147 0.412082i $$-0.864802\pi$$
0.911147 0.412082i $$-0.135198\pi$$
$$54$$ 0 0
$$55$$ 0 0
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 0 0
$$59$$ 10.0000 1.30189 0.650945 0.759125i $$-0.274373\pi$$
0.650945 + 0.759125i $$0.274373\pi$$
$$60$$ 0 0
$$61$$ 4.00000 0.512148 0.256074 0.966657i $$-0.417571\pi$$
0.256074 + 0.966657i $$0.417571\pi$$
$$62$$ 0 0
$$63$$ − 3.00000i − 0.377964i
$$64$$ 0 0
$$65$$ 0 0
$$66$$ 0 0
$$67$$ 1.00000i 0.122169i 0.998133 + 0.0610847i $$0.0194560\pi$$
−0.998133 + 0.0610847i $$0.980544\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ 0 0
$$71$$ −3.00000 −0.356034 −0.178017 0.984027i $$-0.556968\pi$$
−0.178017 + 0.984027i $$0.556968\pi$$
$$72$$ 0 0
$$73$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 0 0
$$77$$ − 1.00000i − 0.113961i
$$78$$ 0 0
$$79$$ 9.00000 1.01258 0.506290 0.862364i $$-0.331017\pi$$
0.506290 + 0.862364i $$0.331017\pi$$
$$80$$ 0 0
$$81$$ 9.00000 1.00000
$$82$$ 0 0
$$83$$ 2.00000i 0.219529i 0.993958 + 0.109764i $$0.0350096\pi$$
−0.993958 + 0.109764i $$0.964990\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ 0 0
$$87$$ 0 0
$$88$$ 0 0
$$89$$ 6.00000 0.635999 0.317999 0.948091i $$-0.396989\pi$$
0.317999 + 0.948091i $$0.396989\pi$$
$$90$$ 0 0
$$91$$ −2.00000 −0.209657
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 0 0
$$95$$ 0 0
$$96$$ 0 0
$$97$$ 14.0000i 1.42148i 0.703452 + 0.710742i $$0.251641\pi$$
−0.703452 + 0.710742i $$0.748359\pi$$
$$98$$ 0 0
$$99$$ 3.00000 0.301511
$$100$$ 0 0
$$101$$ 12.0000 1.19404 0.597022 0.802225i $$-0.296350\pi$$
0.597022 + 0.802225i $$0.296350\pi$$
$$102$$ 0 0
$$103$$ − 14.0000i − 1.37946i −0.724066 0.689730i $$-0.757729\pi$$
0.724066 0.689730i $$-0.242271\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ − 12.0000i − 1.16008i −0.814587 0.580042i $$-0.803036\pi$$
0.814587 0.580042i $$-0.196964\pi$$
$$108$$ 0 0
$$109$$ −5.00000 −0.478913 −0.239457 0.970907i $$-0.576969\pi$$
−0.239457 + 0.970907i $$0.576969\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 0 0
$$113$$ 3.00000i 0.282216i 0.989994 + 0.141108i $$0.0450665\pi$$
−0.989994 + 0.141108i $$0.954933\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ 0 0
$$117$$ − 6.00000i − 0.554700i
$$118$$ 0 0
$$119$$ 4.00000 0.366679
$$120$$ 0 0
$$121$$ −10.0000 −0.909091
$$122$$ 0 0
$$123$$ 0 0
$$124$$ 0 0
$$125$$ 0 0
$$126$$ 0 0
$$127$$ − 3.00000i − 0.266207i −0.991102 0.133103i $$-0.957506\pi$$
0.991102 0.133103i $$-0.0424943\pi$$
$$128$$ 0 0
$$129$$ 0 0
$$130$$ 0 0
$$131$$ −12.0000 −1.04844 −0.524222 0.851581i $$-0.675644\pi$$
−0.524222 + 0.851581i $$0.675644\pi$$
$$132$$ 0 0
$$133$$ − 2.00000i − 0.173422i
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ 14.0000i 1.19610i 0.801459 + 0.598050i $$0.204058\pi$$
−0.801459 + 0.598050i $$0.795942\pi$$
$$138$$ 0 0
$$139$$ −12.0000 −1.01783 −0.508913 0.860818i $$-0.669953\pi$$
−0.508913 + 0.860818i $$0.669953\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ − 2.00000i − 0.167248i
$$144$$ 0 0
$$145$$ 0 0
$$146$$ 0 0
$$147$$ 0 0
$$148$$ 0 0
$$149$$ −11.0000 −0.901155 −0.450578 0.892737i $$-0.648782\pi$$
−0.450578 + 0.892737i $$0.648782\pi$$
$$150$$ 0 0
$$151$$ 5.00000 0.406894 0.203447 0.979086i $$-0.434786\pi$$
0.203447 + 0.979086i $$0.434786\pi$$
$$152$$ 0 0
$$153$$ 12.0000i 0.970143i
$$154$$ 0 0
$$155$$ 0 0
$$156$$ 0 0
$$157$$ 8.00000i 0.638470i 0.947676 + 0.319235i $$0.103426\pi$$
−0.947676 + 0.319235i $$0.896574\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 0 0
$$161$$ −5.00000 −0.394055
$$162$$ 0 0
$$163$$ − 8.00000i − 0.626608i −0.949653 0.313304i $$-0.898564\pi$$
0.949653 0.313304i $$-0.101436\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ 6.00000i 0.464294i 0.972681 + 0.232147i $$0.0745750\pi$$
−0.972681 + 0.232147i $$0.925425\pi$$
$$168$$ 0 0
$$169$$ 9.00000 0.692308
$$170$$ 0 0
$$171$$ 6.00000 0.458831
$$172$$ 0 0
$$173$$ 2.00000i 0.152057i 0.997106 + 0.0760286i $$0.0242240\pi$$
−0.997106 + 0.0760286i $$0.975776\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 0 0
$$177$$ 0 0
$$178$$ 0 0
$$179$$ 4.00000 0.298974 0.149487 0.988764i $$-0.452238\pi$$
0.149487 + 0.988764i $$0.452238\pi$$
$$180$$ 0 0
$$181$$ 20.0000 1.48659 0.743294 0.668965i $$-0.233262\pi$$
0.743294 + 0.668965i $$0.233262\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 0 0
$$185$$ 0 0
$$186$$ 0 0
$$187$$ 4.00000i 0.292509i
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ −16.0000 −1.15772 −0.578860 0.815427i $$-0.696502\pi$$
−0.578860 + 0.815427i $$0.696502\pi$$
$$192$$ 0 0
$$193$$ 19.0000i 1.36765i 0.729646 + 0.683825i $$0.239685\pi$$
−0.729646 + 0.683825i $$0.760315\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ − 19.0000i − 1.35369i −0.736124 0.676847i $$-0.763346\pi$$
0.736124 0.676847i $$-0.236654\pi$$
$$198$$ 0 0
$$199$$ −20.0000 −1.41776 −0.708881 0.705328i $$-0.750800\pi$$
−0.708881 + 0.705328i $$0.750800\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ 0 0
$$203$$ 1.00000i 0.0701862i
$$204$$ 0 0
$$205$$ 0 0
$$206$$ 0 0
$$207$$ − 15.0000i − 1.04257i
$$208$$ 0 0
$$209$$ 2.00000 0.138343
$$210$$ 0 0
$$211$$ −28.0000 −1.92760 −0.963800 0.266627i $$-0.914091\pi$$
−0.963800 + 0.266627i $$0.914091\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 0 0
$$215$$ 0 0
$$216$$ 0 0
$$217$$ 2.00000i 0.135769i
$$218$$ 0 0
$$219$$ 0 0
$$220$$ 0 0
$$221$$ 8.00000 0.538138
$$222$$ 0 0
$$223$$ 20.0000i 1.33930i 0.742677 + 0.669650i $$0.233556\pi$$
−0.742677 + 0.669650i $$0.766444\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ − 18.0000i − 1.19470i −0.801980 0.597351i $$-0.796220\pi$$
0.801980 0.597351i $$-0.203780\pi$$
$$228$$ 0 0
$$229$$ −10.0000 −0.660819 −0.330409 0.943838i $$-0.607187\pi$$
−0.330409 + 0.943838i $$0.607187\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ − 3.00000i − 0.196537i −0.995160 0.0982683i $$-0.968670\pi$$
0.995160 0.0982683i $$-0.0313303\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 0 0
$$239$$ 12.0000 0.776215 0.388108 0.921614i $$-0.373129\pi$$
0.388108 + 0.921614i $$0.373129\pi$$
$$240$$ 0 0
$$241$$ −10.0000 −0.644157 −0.322078 0.946713i $$-0.604381\pi$$
−0.322078 + 0.946713i $$0.604381\pi$$
$$242$$ 0 0
$$243$$ 0 0
$$244$$ 0 0
$$245$$ 0 0
$$246$$ 0 0
$$247$$ − 4.00000i − 0.254514i
$$248$$ 0 0
$$249$$ 0 0
$$250$$ 0 0
$$251$$ 24.0000 1.51487 0.757433 0.652913i $$-0.226453\pi$$
0.757433 + 0.652913i $$0.226453\pi$$
$$252$$ 0 0
$$253$$ − 5.00000i − 0.314347i
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ − 18.0000i − 1.12281i −0.827541 0.561405i $$-0.810261\pi$$
0.827541 0.561405i $$-0.189739\pi$$
$$258$$ 0 0
$$259$$ 3.00000 0.186411
$$260$$ 0 0
$$261$$ −3.00000 −0.185695
$$262$$ 0 0
$$263$$ 21.0000i 1.29492i 0.762101 + 0.647458i $$0.224168\pi$$
−0.762101 + 0.647458i $$0.775832\pi$$
$$264$$ 0 0
$$265$$ 0 0
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 0 0
$$269$$ −26.0000 −1.58525 −0.792624 0.609711i $$-0.791286\pi$$
−0.792624 + 0.609711i $$0.791286\pi$$
$$270$$ 0 0
$$271$$ −30.0000 −1.82237 −0.911185 0.411997i $$-0.864831\pi$$
−0.911185 + 0.411997i $$0.864831\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ 0 0
$$276$$ 0 0
$$277$$ 22.0000i 1.32185i 0.750451 + 0.660926i $$0.229836\pi$$
−0.750451 + 0.660926i $$0.770164\pi$$
$$278$$ 0 0
$$279$$ −6.00000 −0.359211
$$280$$ 0 0
$$281$$ −11.0000 −0.656205 −0.328102 0.944642i $$-0.606409\pi$$
−0.328102 + 0.944642i $$0.606409\pi$$
$$282$$ 0 0
$$283$$ 14.0000i 0.832214i 0.909316 + 0.416107i $$0.136606\pi$$
−0.909316 + 0.416107i $$0.863394\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ − 12.0000i − 0.708338i
$$288$$ 0 0
$$289$$ 1.00000 0.0588235
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 0 0
$$293$$ 22.0000i 1.28525i 0.766179 + 0.642627i $$0.222155\pi$$
−0.766179 + 0.642627i $$0.777845\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ 0 0
$$297$$ 0 0
$$298$$ 0 0
$$299$$ −10.0000 −0.578315
$$300$$ 0 0
$$301$$ −11.0000 −0.634029
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 0 0
$$305$$ 0 0
$$306$$ 0 0
$$307$$ 32.0000i 1.82634i 0.407583 + 0.913168i $$0.366372\pi$$
−0.407583 + 0.913168i $$0.633628\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 0 0
$$311$$ 8.00000 0.453638 0.226819 0.973937i $$-0.427167\pi$$
0.226819 + 0.973937i $$0.427167\pi$$
$$312$$ 0 0
$$313$$ 14.0000i 0.791327i 0.918396 + 0.395663i $$0.129485\pi$$
−0.918396 + 0.395663i $$0.870515\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ − 15.0000i − 0.842484i −0.906948 0.421242i $$-0.861594\pi$$
0.906948 0.421242i $$-0.138406\pi$$
$$318$$ 0 0
$$319$$ −1.00000 −0.0559893
$$320$$ 0 0
$$321$$ 0 0
$$322$$ 0 0
$$323$$ 8.00000i 0.445132i
$$324$$ 0 0
$$325$$ 0 0
$$326$$ 0 0
$$327$$ 0 0
$$328$$ 0 0
$$329$$ 2.00000 0.110264
$$330$$ 0 0
$$331$$ −9.00000 −0.494685 −0.247342 0.968928i $$-0.579557\pi$$
−0.247342 + 0.968928i $$0.579557\pi$$
$$332$$ 0 0
$$333$$ 9.00000i 0.493197i
$$334$$ 0 0
$$335$$ 0 0
$$336$$ 0 0
$$337$$ 2.00000i 0.108947i 0.998515 + 0.0544735i $$0.0173480\pi$$
−0.998515 + 0.0544735i $$0.982652\pi$$
$$338$$ 0 0
$$339$$ 0 0
$$340$$ 0 0
$$341$$ −2.00000 −0.108306
$$342$$ 0 0
$$343$$ 1.00000i 0.0539949i
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ 7.00000i 0.375780i 0.982190 + 0.187890i $$0.0601648\pi$$
−0.982190 + 0.187890i $$0.939835\pi$$
$$348$$ 0 0
$$349$$ −30.0000 −1.60586 −0.802932 0.596071i $$-0.796728\pi$$
−0.802932 + 0.596071i $$0.796728\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0 0
$$353$$ 14.0000i 0.745145i 0.928003 + 0.372572i $$0.121524\pi$$
−0.928003 + 0.372572i $$0.878476\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ 15.0000 0.791670 0.395835 0.918322i $$-0.370455\pi$$
0.395835 + 0.918322i $$0.370455\pi$$
$$360$$ 0 0
$$361$$ −15.0000 −0.789474
$$362$$ 0 0
$$363$$ 0 0
$$364$$ 0 0
$$365$$ 0 0
$$366$$ 0 0
$$367$$ 16.0000i 0.835193i 0.908633 + 0.417597i $$0.137127\pi$$
−0.908633 + 0.417597i $$0.862873\pi$$
$$368$$ 0 0
$$369$$ 36.0000 1.87409
$$370$$ 0 0
$$371$$ −6.00000 −0.311504
$$372$$ 0 0
$$373$$ − 29.0000i − 1.50156i −0.660551 0.750782i $$-0.729677\pi$$
0.660551 0.750782i $$-0.270323\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ 2.00000i 0.103005i
$$378$$ 0 0
$$379$$ −31.0000 −1.59236 −0.796182 0.605058i $$-0.793150\pi$$
−0.796182 + 0.605058i $$0.793150\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 0 0
$$383$$ − 6.00000i − 0.306586i −0.988181 0.153293i $$-0.951012\pi$$
0.988181 0.153293i $$-0.0489878\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 0 0
$$387$$ − 33.0000i − 1.67748i
$$388$$ 0 0
$$389$$ −33.0000 −1.67317 −0.836583 0.547840i $$-0.815450\pi$$
−0.836583 + 0.547840i $$0.815450\pi$$
$$390$$ 0 0
$$391$$ 20.0000 1.01144
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 0 0
$$395$$ 0 0
$$396$$ 0 0
$$397$$ − 34.0000i − 1.70641i −0.521575 0.853206i $$-0.674655\pi$$
0.521575 0.853206i $$-0.325345\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0 0
$$401$$ −27.0000 −1.34832 −0.674158 0.738587i $$-0.735493\pi$$
−0.674158 + 0.738587i $$0.735493\pi$$
$$402$$ 0 0
$$403$$ 4.00000i 0.199254i
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 3.00000i 0.148704i
$$408$$ 0 0
$$409$$ 14.0000 0.692255 0.346128 0.938187i $$-0.387496\pi$$
0.346128 + 0.938187i $$0.387496\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 0 0
$$413$$ − 10.0000i − 0.492068i
$$414$$ 0 0
$$415$$ 0 0
$$416$$ 0 0
$$417$$ 0 0
$$418$$ 0 0
$$419$$ 6.00000 0.293119 0.146560 0.989202i $$-0.453180\pi$$
0.146560 + 0.989202i $$0.453180\pi$$
$$420$$ 0 0
$$421$$ −21.0000 −1.02348 −0.511739 0.859141i $$-0.670998\pi$$
−0.511739 + 0.859141i $$0.670998\pi$$
$$422$$ 0 0
$$423$$ 6.00000i 0.291730i
$$424$$ 0 0
$$425$$ 0 0
$$426$$ 0 0
$$427$$ − 4.00000i − 0.193574i
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 32.0000 1.54139 0.770693 0.637207i $$-0.219910\pi$$
0.770693 + 0.637207i $$0.219910\pi$$
$$432$$ 0 0
$$433$$ 20.0000i 0.961139i 0.876957 + 0.480569i $$0.159570\pi$$
−0.876957 + 0.480569i $$0.840430\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ − 10.0000i − 0.478365i
$$438$$ 0 0
$$439$$ −34.0000 −1.62273 −0.811366 0.584539i $$-0.801275\pi$$
−0.811366 + 0.584539i $$0.801275\pi$$
$$440$$ 0 0
$$441$$ −3.00000 −0.142857
$$442$$ 0 0
$$443$$ 24.0000i 1.14027i 0.821549 + 0.570137i $$0.193110\pi$$
−0.821549 + 0.570137i $$0.806890\pi$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 0 0
$$449$$ 21.0000 0.991051 0.495526 0.868593i $$-0.334975\pi$$
0.495526 + 0.868593i $$0.334975\pi$$
$$450$$ 0 0
$$451$$ 12.0000 0.565058
$$452$$ 0 0
$$453$$ 0 0
$$454$$ 0 0
$$455$$ 0 0
$$456$$ 0 0
$$457$$ 17.0000i 0.795226i 0.917553 + 0.397613i $$0.130161\pi$$
−0.917553 + 0.397613i $$0.869839\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 0 0
$$461$$ 30.0000 1.39724 0.698620 0.715493i $$-0.253798\pi$$
0.698620 + 0.715493i $$0.253798\pi$$
$$462$$ 0 0
$$463$$ − 24.0000i − 1.11537i −0.830051 0.557687i $$-0.811689\pi$$
0.830051 0.557687i $$-0.188311\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ 22.0000i 1.01804i 0.860755 + 0.509019i $$0.169992\pi$$
−0.860755 + 0.509019i $$0.830008\pi$$
$$468$$ 0 0
$$469$$ 1.00000 0.0461757
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0 0
$$473$$ − 11.0000i − 0.505781i
$$474$$ 0 0
$$475$$ 0 0
$$476$$ 0 0
$$477$$ − 18.0000i − 0.824163i
$$478$$ 0 0
$$479$$ 14.0000 0.639676 0.319838 0.947472i $$-0.396371\pi$$
0.319838 + 0.947472i $$0.396371\pi$$
$$480$$ 0 0
$$481$$ 6.00000 0.273576
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 0 0
$$485$$ 0 0
$$486$$ 0 0
$$487$$ − 1.00000i − 0.0453143i −0.999743 0.0226572i $$-0.992787\pi$$
0.999743 0.0226572i $$-0.00721262\pi$$
$$488$$ 0 0
$$489$$ 0 0
$$490$$ 0 0
$$491$$ −27.0000 −1.21849 −0.609246 0.792981i $$-0.708528\pi$$
−0.609246 + 0.792981i $$0.708528\pi$$
$$492$$ 0 0
$$493$$ − 4.00000i − 0.180151i
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ 3.00000i 0.134568i
$$498$$ 0 0
$$499$$ 4.00000 0.179065 0.0895323 0.995984i $$-0.471463\pi$$
0.0895323 + 0.995984i $$0.471463\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 0 0
$$503$$ 30.0000i 1.33763i 0.743427 + 0.668817i $$0.233199\pi$$
−0.743427 + 0.668817i $$0.766801\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ 0 0
$$507$$ 0 0
$$508$$ 0 0
$$509$$ 26.0000 1.15243 0.576215 0.817298i $$-0.304529\pi$$
0.576215 + 0.817298i $$0.304529\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ 0 0
$$513$$ 0 0
$$514$$ 0 0
$$515$$ 0 0
$$516$$ 0 0
$$517$$ 2.00000i 0.0879599i
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ −2.00000 −0.0876216 −0.0438108 0.999040i $$-0.513950\pi$$
−0.0438108 + 0.999040i $$0.513950\pi$$
$$522$$ 0 0
$$523$$ − 8.00000i − 0.349816i −0.984585 0.174908i $$-0.944037\pi$$
0.984585 0.174908i $$-0.0559627\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ − 8.00000i − 0.348485i
$$528$$ 0 0
$$529$$ −2.00000 −0.0869565
$$530$$ 0 0
$$531$$ 30.0000 1.30189
$$532$$ 0 0
$$533$$ − 24.0000i − 1.03956i
$$534$$ 0 0
$$535$$ 0 0
$$536$$ 0 0
$$537$$ 0 0
$$538$$ 0 0
$$539$$ −1.00000 −0.0430730
$$540$$ 0 0
$$541$$ −41.0000 −1.76273 −0.881364 0.472438i $$-0.843374\pi$$
−0.881364 + 0.472438i $$0.843374\pi$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ 0 0
$$545$$ 0 0
$$546$$ 0 0
$$547$$ 1.00000i 0.0427569i 0.999771 + 0.0213785i $$0.00680549\pi$$
−0.999771 + 0.0213785i $$0.993195\pi$$
$$548$$ 0 0
$$549$$ 12.0000 0.512148
$$550$$ 0 0
$$551$$ −2.00000 −0.0852029
$$552$$ 0 0
$$553$$ − 9.00000i − 0.382719i
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ − 11.0000i − 0.466085i −0.972467 0.233042i $$-0.925132\pi$$
0.972467 0.233042i $$-0.0748681\pi$$
$$558$$ 0 0
$$559$$ −22.0000 −0.930501
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ − 2.00000i − 0.0842900i −0.999112 0.0421450i $$-0.986581\pi$$
0.999112 0.0421450i $$-0.0134191\pi$$
$$564$$ 0 0
$$565$$ 0 0
$$566$$ 0 0
$$567$$ − 9.00000i − 0.377964i
$$568$$ 0 0
$$569$$ 19.0000 0.796521 0.398261 0.917272i $$-0.369614\pi$$
0.398261 + 0.917272i $$0.369614\pi$$
$$570$$ 0 0
$$571$$ 43.0000 1.79949 0.899747 0.436412i $$-0.143751\pi$$
0.899747 + 0.436412i $$0.143751\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ 0 0
$$576$$ 0 0
$$577$$ 46.0000i 1.91501i 0.288425 + 0.957503i $$0.406868\pi$$
−0.288425 + 0.957503i $$0.593132\pi$$
$$578$$ 0 0
$$579$$ 0 0
$$580$$ 0 0
$$581$$ 2.00000 0.0829740
$$582$$ 0 0
$$583$$ − 6.00000i − 0.248495i
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ 36.0000i 1.48588i 0.669359 + 0.742940i $$0.266569\pi$$
−0.669359 + 0.742940i $$0.733431\pi$$
$$588$$ 0 0
$$589$$ −4.00000 −0.164817
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 0 0
$$593$$ − 24.0000i − 0.985562i −0.870153 0.492781i $$-0.835980\pi$$
0.870153 0.492781i $$-0.164020\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 0 0
$$597$$ 0 0
$$598$$ 0 0
$$599$$ 9.00000 0.367730 0.183865 0.982952i $$-0.441139\pi$$
0.183865 + 0.982952i $$0.441139\pi$$
$$600$$ 0 0
$$601$$ 16.0000 0.652654 0.326327 0.945257i $$-0.394189\pi$$
0.326327 + 0.945257i $$0.394189\pi$$
$$602$$ 0 0
$$603$$ 3.00000i 0.122169i
$$604$$ 0 0
$$605$$ 0 0
$$606$$ 0 0
$$607$$ 42.0000i 1.70473i 0.522949 + 0.852364i $$0.324832\pi$$
−0.522949 + 0.852364i $$0.675168\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 4.00000 0.161823
$$612$$ 0 0
$$613$$ − 27.0000i − 1.09052i −0.838267 0.545260i $$-0.816431\pi$$
0.838267 0.545260i $$-0.183569\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ − 33.0000i − 1.32853i −0.747497 0.664265i $$-0.768745\pi$$
0.747497 0.664265i $$-0.231255\pi$$
$$618$$ 0 0
$$619$$ 22.0000 0.884255 0.442127 0.896952i $$-0.354224\pi$$
0.442127 + 0.896952i $$0.354224\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ − 6.00000i − 0.240385i
$$624$$ 0 0
$$625$$ 0 0
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 0 0
$$629$$ −12.0000 −0.478471
$$630$$ 0 0
$$631$$ 19.0000 0.756378 0.378189 0.925728i $$-0.376547\pi$$
0.378189 + 0.925728i $$0.376547\pi$$
$$632$$ 0 0
$$633$$ 0 0
$$634$$ 0 0
$$635$$ 0 0
$$636$$ 0 0
$$637$$ 2.00000i 0.0792429i
$$638$$ 0 0
$$639$$ −9.00000 −0.356034
$$640$$ 0 0
$$641$$ −15.0000 −0.592464 −0.296232 0.955116i $$-0.595730\pi$$
−0.296232 + 0.955116i $$0.595730\pi$$
$$642$$ 0 0
$$643$$ − 36.0000i − 1.41970i −0.704352 0.709851i $$-0.748762\pi$$
0.704352 0.709851i $$-0.251238\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 18.0000i 0.707653i 0.935311 + 0.353827i $$0.115120\pi$$
−0.935311 + 0.353827i $$0.884880\pi$$
$$648$$ 0 0
$$649$$ 10.0000 0.392534
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ − 34.0000i − 1.33052i −0.746611 0.665261i $$-0.768320\pi$$
0.746611 0.665261i $$-0.231680\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ 0 0
$$657$$ 0 0
$$658$$ 0 0
$$659$$ 12.0000 0.467454 0.233727 0.972302i $$-0.424908\pi$$
0.233727 + 0.972302i $$0.424908\pi$$
$$660$$ 0 0
$$661$$ −18.0000 −0.700119 −0.350059 0.936727i $$-0.613839\pi$$
−0.350059 + 0.936727i $$0.613839\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 5.00000i 0.193601i
$$668$$ 0 0
$$669$$ 0 0
$$670$$ 0 0
$$671$$ 4.00000 0.154418
$$672$$ 0 0
$$673$$ − 6.00000i − 0.231283i −0.993291 0.115642i $$-0.963108\pi$$
0.993291 0.115642i $$-0.0368924\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ − 46.0000i − 1.76792i −0.467559 0.883962i $$-0.654866\pi$$
0.467559 0.883962i $$-0.345134\pi$$
$$678$$ 0 0
$$679$$ 14.0000 0.537271
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 0 0
$$683$$ 9.00000i 0.344375i 0.985064 + 0.172188i $$0.0550836\pi$$
−0.985064 + 0.172188i $$0.944916\pi$$
$$684$$ 0 0
$$685$$ 0 0
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 0 0
$$689$$ −12.0000 −0.457164
$$690$$ 0 0
$$691$$ −28.0000 −1.06517 −0.532585 0.846376i $$-0.678779\pi$$
−0.532585 + 0.846376i $$0.678779\pi$$
$$692$$ 0 0
$$693$$ − 3.00000i − 0.113961i
$$694$$ 0 0
$$695$$ 0 0
$$696$$ 0 0
$$697$$ 48.0000i 1.81813i
$$698$$ 0 0
$$699$$ 0 0
$$700$$ 0 0
$$701$$ 38.0000 1.43524 0.717620 0.696435i $$-0.245231\pi$$
0.717620 + 0.696435i $$0.245231\pi$$
$$702$$ 0 0
$$703$$ 6.00000i 0.226294i
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ − 12.0000i − 0.451306i
$$708$$ 0 0
$$709$$ 10.0000 0.375558 0.187779 0.982211i $$-0.439871\pi$$
0.187779 + 0.982211i $$0.439871\pi$$
$$710$$ 0 0
$$711$$ 27.0000 1.01258
$$712$$ 0 0
$$713$$ 10.0000i 0.374503i
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 0 0
$$717$$ 0 0
$$718$$ 0 0
$$719$$ 32.0000 1.19340 0.596699 0.802465i $$-0.296479\pi$$
0.596699 + 0.802465i $$0.296479\pi$$
$$720$$ 0 0
$$721$$ −14.0000 −0.521387
$$722$$ 0 0
$$723$$ 0 0
$$724$$ 0 0
$$725$$ 0 0
$$726$$ 0 0
$$727$$ 16.0000i 0.593407i 0.954970 + 0.296704i $$0.0958873\pi$$
−0.954970 + 0.296704i $$0.904113\pi$$
$$728$$ 0 0
$$729$$ 27.0000 1.00000
$$730$$ 0 0
$$731$$ 44.0000 1.62740
$$732$$ 0 0
$$733$$ − 36.0000i − 1.32969i −0.746981 0.664845i $$-0.768498\pi$$
0.746981 0.664845i $$-0.231502\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 1.00000i 0.0368355i
$$738$$ 0 0
$$739$$ 3.00000 0.110357 0.0551784 0.998477i $$-0.482427\pi$$
0.0551784 + 0.998477i $$0.482427\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ − 12.0000i − 0.440237i −0.975473 0.220119i $$-0.929356\pi$$
0.975473 0.220119i $$-0.0706445\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ 0 0
$$747$$ 6.00000i 0.219529i
$$748$$ 0 0
$$749$$ −12.0000 −0.438470
$$750$$ 0 0
$$751$$ 12.0000 0.437886 0.218943 0.975738i $$-0.429739\pi$$
0.218943 + 0.975738i $$0.429739\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 0 0
$$755$$ 0 0
$$756$$ 0 0
$$757$$ − 17.0000i − 0.617876i −0.951082 0.308938i $$-0.900027\pi$$
0.951082 0.308938i $$-0.0999735\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$762$$ 0 0
$$763$$ 5.00000i 0.181012i
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ − 20.0000i − 0.722158i
$$768$$ 0 0
$$769$$ 32.0000 1.15395 0.576975 0.816762i $$-0.304233\pi$$
0.576975 + 0.816762i $$0.304233\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 0 0
$$773$$ − 30.0000i − 1.07903i −0.841978 0.539513i $$-0.818609\pi$$
0.841978 0.539513i $$-0.181391\pi$$
$$774$$ 0 0
$$775$$ 0 0
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ 24.0000 0.859889
$$780$$ 0 0
$$781$$ −3.00000 −0.107348
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 0 0
$$785$$ 0 0
$$786$$ 0 0
$$787$$ − 20.0000i − 0.712923i −0.934310 0.356462i $$-0.883983\pi$$
0.934310 0.356462i $$-0.116017\pi$$
$$788$$ 0 0
$$789$$ 0 0
$$790$$ 0 0
$$791$$ 3.00000 0.106668
$$792$$ 0 0
$$793$$ − 8.00000i − 0.284088i
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$798$$ 0 0
$$799$$ −8.00000 −0.283020
$$800$$ 0 0
$$801$$ 18.0000 0.635999
$$802$$ 0 0
$$803$$ 0 0
$$804$$ 0 0
$$805$$ 0 0
$$806$$ 0 0
$$807$$ 0 0
$$808$$ 0 0
$$809$$ 9.00000 0.316423 0.158212 0.987405i $$-0.449427\pi$$
0.158212 + 0.987405i $$0.449427\pi$$
$$810$$ 0 0
$$811$$ 26.0000 0.912983 0.456492 0.889728i $$-0.349106\pi$$
0.456492 + 0.889728i $$0.349106\pi$$
$$812$$ 0 0
$$813$$ 0 0
$$814$$ 0 0
$$815$$ 0 0
$$816$$ 0 0
$$817$$ − 22.0000i − 0.769683i
$$818$$ 0 0
$$819$$ −6.00000 −0.209657
$$820$$ 0 0
$$821$$ 10.0000 0.349002 0.174501 0.984657i $$-0.444169\pi$$
0.174501 + 0.984657i $$0.444169\pi$$
$$822$$ 0 0
$$823$$ 31.0000i 1.08059i 0.841475 + 0.540296i $$0.181688\pi$$
−0.841475 + 0.540296i $$0.818312\pi$$
$$824$$ 0 0
$$825$$ 0 0
$$826$$ 0 0
$$827$$ 27.0000i 0.938882i 0.882964 + 0.469441i $$0.155545\pi$$
−0.882964 + 0.469441i $$0.844455\pi$$
$$828$$ 0 0
$$829$$ −16.0000 −0.555703 −0.277851 0.960624i $$-0.589622\pi$$
−0.277851 + 0.960624i $$0.589622\pi$$
$$830$$ 0 0
$$831$$ 0 0
$$832$$ 0 0
$$833$$ − 4.00000i − 0.138592i
$$834$$ 0 0
$$835$$ 0 0
$$836$$ 0 0
$$837$$ 0 0
$$838$$ 0 0
$$839$$ −32.0000 −1.10476 −0.552381 0.833592i $$-0.686281\pi$$
−0.552381 + 0.833592i $$0.686281\pi$$
$$840$$ 0 0
$$841$$ −28.0000 −0.965517
$$842$$ 0 0
$$843$$ 0 0
$$844$$ 0 0
$$845$$ 0 0
$$846$$ 0 0
$$847$$ 10.0000i 0.343604i
$$848$$ 0 0
$$849$$ 0 0
$$850$$ 0 0
$$851$$ 15.0000 0.514193
$$852$$ 0 0
$$853$$ − 16.0000i − 0.547830i −0.961754 0.273915i $$-0.911681\pi$$
0.961754 0.273915i $$-0.0883186\pi$$
$$854$$ 0 0
$$855$$ 0 0
$$856$$ 0 0
$$857$$ − 12.0000i − 0.409912i −0.978771 0.204956i $$-0.934295\pi$$
0.978771 0.204956i $$-0.0657052\pi$$
$$858$$ 0 0
$$859$$ −50.0000 −1.70598 −0.852989 0.521929i $$-0.825213\pi$$
−0.852989 + 0.521929i $$0.825213\pi$$
$$860$$ 0 0
$$861$$ 0 0
$$862$$ 0 0
$$863$$ − 51.0000i − 1.73606i −0.496512 0.868030i $$-0.665386\pi$$
0.496512 0.868030i $$-0.334614\pi$$
$$864$$ 0 0
$$865$$ 0 0
$$866$$ 0 0
$$867$$ 0 0
$$868$$ 0 0
$$869$$ 9.00000 0.305304
$$870$$ 0 0
$$871$$ 2.00000 0.0677674
$$872$$ 0 0
$$873$$ 42.0000i 1.42148i
$$874$$ 0 0
$$875$$ 0 0
$$876$$ 0 0
$$877$$ 26.0000i 0.877958i 0.898497 + 0.438979i $$0.144660\pi$$
−0.898497 + 0.438979i $$0.855340\pi$$
$$878$$ 0 0
$$879$$ 0 0
$$880$$ 0 0
$$881$$ 18.0000 0.606435 0.303218 0.952921i $$-0.401939\pi$$
0.303218 + 0.952921i $$0.401939\pi$$
$$882$$ 0 0
$$883$$ − 25.0000i − 0.841317i −0.907219 0.420658i $$-0.861799\pi$$
0.907219 0.420658i $$-0.138201\pi$$
$$884$$ 0 0
$$885$$ 0 0
$$886$$ 0 0
$$887$$ 44.0000i 1.47738i 0.674048 + 0.738688i $$0.264554\pi$$
−0.674048 + 0.738688i $$0.735446\pi$$
$$888$$ 0 0
$$889$$ −3.00000 −0.100617
$$890$$ 0 0
$$891$$ 9.00000 0.301511
$$892$$ 0 0
$$893$$ 4.00000i 0.133855i
$$894$$ 0 0
$$895$$ 0 0
$$896$$ 0 0
$$897$$ 0 0
$$898$$ 0 0
$$899$$ 2.00000 0.0667037
$$900$$ 0 0
$$901$$ 24.0000 0.799556
$$902$$ 0 0
$$903$$ 0 0
$$904$$ 0 0
$$905$$ 0 0
$$906$$ 0 0
$$907$$ 12.0000i 0.398453i 0.979953 + 0.199227i $$0.0638430\pi$$
−0.979953 + 0.199227i $$0.936157\pi$$
$$908$$ 0 0
$$909$$ 36.0000 1.19404
$$910$$ 0 0
$$911$$ −41.0000 −1.35839 −0.679195 0.733958i $$-0.737671\pi$$
−0.679195 + 0.733958i $$0.737671\pi$$
$$912$$ 0 0
$$913$$ 2.00000i 0.0661903i
$$914$$ 0 0
$$915$$ 0 0
$$916$$ 0 0
$$917$$ 12.0000i 0.396275i
$$918$$ 0 0
$$919$$ 25.0000 0.824674 0.412337 0.911031i $$-0.364713\pi$$
0.412337 + 0.911031i $$0.364713\pi$$
$$920$$ 0 0
$$921$$ 0 0
$$922$$ 0 0
$$923$$ 6.00000i 0.197492i
$$924$$ 0 0
$$925$$ 0 0
$$926$$ 0 0
$$927$$ − 42.0000i − 1.37946i
$$928$$ 0 0
$$929$$ 20.0000 0.656179 0.328089 0.944647i $$-0.393595\pi$$
0.328089 + 0.944647i $$0.393595\pi$$
$$930$$ 0 0
$$931$$ −2.00000 −0.0655474
$$932$$ 0 0
$$933$$ 0 0
$$934$$ 0 0
$$935$$ 0 0
$$936$$ 0 0
$$937$$ 20.0000i 0.653372i 0.945133 + 0.326686i $$0.105932\pi$$
−0.945133 + 0.326686i $$0.894068\pi$$
$$938$$ 0 0
$$939$$ 0 0
$$940$$ 0 0
$$941$$ −14.0000 −0.456387 −0.228193 0.973616i $$-0.573282\pi$$
−0.228193 + 0.973616i $$0.573282\pi$$
$$942$$ 0 0
$$943$$ − 60.0000i − 1.95387i
$$944$$ 0 0
$$945$$ 0 0
$$946$$ 0 0
$$947$$ − 28.0000i − 0.909878i −0.890523 0.454939i $$-0.849661\pi$$
0.890523 0.454939i $$-0.150339\pi$$
$$948$$ 0 0
$$949$$ 0 0
$$950$$ 0 0
$$951$$ 0 0
$$952$$ 0 0
$$953$$ − 9.00000i − 0.291539i −0.989319 0.145769i $$-0.953434\pi$$
0.989319 0.145769i $$-0.0465657\pi$$
$$954$$ 0 0
$$955$$ 0 0
$$956$$ 0 0
$$957$$ 0 0
$$958$$ 0 0
$$959$$ 14.0000 0.452084
$$960$$ 0 0
$$961$$ −27.0000 −0.870968
$$962$$ 0 0
$$963$$ − 36.0000i − 1.16008i
$$964$$ 0 0
$$965$$ 0 0
$$966$$ 0 0
$$967$$ 24.0000i 0.771788i 0.922543 + 0.385894i $$0.126107\pi$$
−0.922543 + 0.385894i $$0.873893\pi$$
$$968$$ 0 0
$$969$$ 0 0
$$970$$ 0 0
$$971$$ −22.0000 −0.706014 −0.353007 0.935621i $$-0.614841\pi$$
−0.353007 + 0.935621i $$0.614841\pi$$
$$972$$ 0 0
$$973$$ 12.0000i 0.384702i
$$974$$ 0 0
$$975$$ 0 0
$$976$$ 0 0
$$977$$ 7.00000i 0.223950i 0.993711 + 0.111975i $$0.0357176\pi$$
−0.993711 + 0.111975i $$0.964282\pi$$
$$978$$ 0 0
$$979$$ 6.00000 0.191761
$$980$$ 0 0
$$981$$ −15.0000 −0.478913
$$982$$ 0 0
$$983$$ 30.0000i 0.956851i 0.878128 + 0.478426i $$0.158792\pi$$
−0.878128 + 0.478426i $$0.841208\pi$$
$$984$$ 0 0
$$985$$ 0 0
$$986$$ 0 0
$$987$$ 0 0
$$988$$ 0 0
$$989$$ −55.0000 −1.74890
$$990$$ 0 0
$$991$$ −61.0000 −1.93773 −0.968864 0.247592i $$-0.920361\pi$$
−0.968864 + 0.247592i $$0.920361\pi$$
$$992$$ 0 0
$$993$$ 0 0
$$994$$ 0 0
$$995$$ 0 0
$$996$$ 0 0
$$997$$ 6.00000i 0.190022i 0.995476 + 0.0950110i $$0.0302886\pi$$
−0.995476 + 0.0950110i $$0.969711\pi$$
$$998$$ 0 0
$$999$$ 0 0
Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000

## Twists

By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 1400.2.g.h.449.1 2
4.3 odd 2 2800.2.g.o.449.2 2
5.2 odd 4 1400.2.a.h.1.1 yes 1
5.3 odd 4 1400.2.a.f.1.1 1
5.4 even 2 inner 1400.2.g.h.449.2 2
20.3 even 4 2800.2.a.r.1.1 1
20.7 even 4 2800.2.a.n.1.1 1
20.19 odd 2 2800.2.g.o.449.1 2
35.13 even 4 9800.2.a.v.1.1 1
35.27 even 4 9800.2.a.w.1.1 1

By twisted newform
Twist Min Dim Char Parity Ord Type
1400.2.a.f.1.1 1 5.3 odd 4
1400.2.a.h.1.1 yes 1 5.2 odd 4
1400.2.g.h.449.1 2 1.1 even 1 trivial
1400.2.g.h.449.2 2 5.4 even 2 inner
2800.2.a.n.1.1 1 20.7 even 4
2800.2.a.r.1.1 1 20.3 even 4
2800.2.g.o.449.1 2 20.19 odd 2
2800.2.g.o.449.2 2 4.3 odd 2
9800.2.a.v.1.1 1 35.13 even 4
9800.2.a.w.1.1 1 35.27 even 4