# Properties

 Label 4600.2.a.bi.1.3 Level $4600$ Weight $2$ Character 4600.1 Self dual yes Analytic conductor $36.731$ Analytic rank $1$ Dimension $7$ CM no Inner twists $1$

# Learn more

## Newspace parameters

 Level: $$N$$ $$=$$ $$4600 = 2^{3} \cdot 5^{2} \cdot 23$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 4600.a (trivial)

## Newform invariants

 Self dual: yes Analytic conductor: $$36.7311849298$$ Analytic rank: $$1$$ Dimension: $$7$$ Coefficient field: $$\mathbb{Q}[x]/(x^{7} - \cdots)$$ Defining polynomial: $$x^{7} - 3 x^{6} - 7 x^{5} + 24 x^{4} + x^{3} - 35 x^{2} + 17 x - 2$$ Coefficient ring: $$\Z[a_1, \ldots, a_{7}]$$ Coefficient ring index: $$2$$ Twist minimal: no (minimal twist has level 920) Fricke sign: $$1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

 Embedding label 1.3 Root $$0.189375$$ of defining polynomial Character $$\chi$$ $$=$$ 4600.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+0.189375 q^{3} -1.65661 q^{7} -2.96414 q^{9} +O(q^{10})$$ $$q+0.189375 q^{3} -1.65661 q^{7} -2.96414 q^{9} +0.0759321 q^{11} -1.24146 q^{13} +5.17593 q^{17} +0.792262 q^{19} -0.313721 q^{21} -1.00000 q^{23} -1.12946 q^{27} -2.85401 q^{29} +8.90112 q^{31} +0.0143797 q^{33} +6.92065 q^{37} -0.235102 q^{39} +4.64279 q^{41} -1.75255 q^{43} +10.0033 q^{47} -4.25565 q^{49} +0.980193 q^{51} -11.1284 q^{53} +0.150035 q^{57} -12.4581 q^{59} -12.0098 q^{61} +4.91041 q^{63} -6.96067 q^{67} -0.189375 q^{69} -7.71650 q^{71} -7.49476 q^{73} -0.125790 q^{77} -15.6615 q^{79} +8.67852 q^{81} +6.68518 q^{83} -0.540478 q^{87} -3.03333 q^{89} +2.05661 q^{91} +1.68565 q^{93} -3.21747 q^{97} -0.225073 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$7q + 3q^{3} + 4q^{7} + 2q^{9} + O(q^{10})$$ $$7q + 3q^{3} + 4q^{7} + 2q^{9} - 7q^{11} - 7q^{13} - 7q^{19} - 6q^{21} - 7q^{23} - 11q^{29} - 10q^{31} - 19q^{33} - 19q^{37} - 24q^{39} - 16q^{41} + 6q^{43} + 6q^{47} - 17q^{49} - 7q^{51} - 15q^{53} - 8q^{57} - 11q^{59} + 5q^{61} + 13q^{63} + 9q^{67} - 3q^{69} - 14q^{71} - 10q^{73} - 6q^{77} - 32q^{79} - 5q^{81} + q^{83} + 10q^{87} - 24q^{89} - 7q^{91} - 26q^{93} + 7q^{97} - 61q^{99} + O(q^{100})$$

## 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
$$3$$ 0.189375 0.109336 0.0546680 0.998505i $$-0.482590\pi$$
0.0546680 + 0.998505i $$0.482590\pi$$
$$4$$ 0 0
$$5$$ 0 0
$$6$$ 0 0
$$7$$ −1.65661 −0.626139 −0.313070 0.949730i $$-0.601357\pi$$
−0.313070 + 0.949730i $$0.601357\pi$$
$$8$$ 0 0
$$9$$ −2.96414 −0.988046
$$10$$ 0 0
$$11$$ 0.0759321 0.0228944 0.0114472 0.999934i $$-0.496356\pi$$
0.0114472 + 0.999934i $$0.496356\pi$$
$$12$$ 0 0
$$13$$ −1.24146 −0.344319 −0.172159 0.985069i $$-0.555074\pi$$
−0.172159 + 0.985069i $$0.555074\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ 5.17593 1.25535 0.627673 0.778477i $$-0.284007\pi$$
0.627673 + 0.778477i $$0.284007\pi$$
$$18$$ 0 0
$$19$$ 0.792262 0.181757 0.0908787 0.995862i $$-0.471032\pi$$
0.0908787 + 0.995862i $$0.471032\pi$$
$$20$$ 0 0
$$21$$ −0.313721 −0.0684595
$$22$$ 0 0
$$23$$ −1.00000 −0.208514
$$24$$ 0 0
$$25$$ 0 0
$$26$$ 0 0
$$27$$ −1.12946 −0.217365
$$28$$ 0 0
$$29$$ −2.85401 −0.529976 −0.264988 0.964252i $$-0.585368\pi$$
−0.264988 + 0.964252i $$0.585368\pi$$
$$30$$ 0 0
$$31$$ 8.90112 1.59869 0.799345 0.600873i $$-0.205180\pi$$
0.799345 + 0.600873i $$0.205180\pi$$
$$32$$ 0 0
$$33$$ 0.0143797 0.00250318
$$34$$ 0 0
$$35$$ 0 0
$$36$$ 0 0
$$37$$ 6.92065 1.13775 0.568874 0.822425i $$-0.307379\pi$$
0.568874 + 0.822425i $$0.307379\pi$$
$$38$$ 0 0
$$39$$ −0.235102 −0.0376464
$$40$$ 0 0
$$41$$ 4.64279 0.725082 0.362541 0.931968i $$-0.381909\pi$$
0.362541 + 0.931968i $$0.381909\pi$$
$$42$$ 0 0
$$43$$ −1.75255 −0.267262 −0.133631 0.991031i $$-0.542664\pi$$
−0.133631 + 0.991031i $$0.542664\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ 10.0033 1.45913 0.729563 0.683914i $$-0.239724\pi$$
0.729563 + 0.683914i $$0.239724\pi$$
$$48$$ 0 0
$$49$$ −4.25565 −0.607950
$$50$$ 0 0
$$51$$ 0.980193 0.137254
$$52$$ 0 0
$$53$$ −11.1284 −1.52860 −0.764301 0.644859i $$-0.776916\pi$$
−0.764301 + 0.644859i $$0.776916\pi$$
$$54$$ 0 0
$$55$$ 0 0
$$56$$ 0 0
$$57$$ 0.150035 0.0198726
$$58$$ 0 0
$$59$$ −12.4581 −1.62191 −0.810955 0.585108i $$-0.801052\pi$$
−0.810955 + 0.585108i $$0.801052\pi$$
$$60$$ 0 0
$$61$$ −12.0098 −1.53770 −0.768849 0.639430i $$-0.779170\pi$$
−0.768849 + 0.639430i $$0.779170\pi$$
$$62$$ 0 0
$$63$$ 4.91041 0.618654
$$64$$ 0 0
$$65$$ 0 0
$$66$$ 0 0
$$67$$ −6.96067 −0.850381 −0.425191 0.905104i $$-0.639793\pi$$
−0.425191 + 0.905104i $$0.639793\pi$$
$$68$$ 0 0
$$69$$ −0.189375 −0.0227981
$$70$$ 0 0
$$71$$ −7.71650 −0.915779 −0.457890 0.889009i $$-0.651395\pi$$
−0.457890 + 0.889009i $$0.651395\pi$$
$$72$$ 0 0
$$73$$ −7.49476 −0.877196 −0.438598 0.898683i $$-0.644525\pi$$
−0.438598 + 0.898683i $$0.644525\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 0 0
$$77$$ −0.125790 −0.0143351
$$78$$ 0 0
$$79$$ −15.6615 −1.76206 −0.881029 0.473063i $$-0.843148\pi$$
−0.881029 + 0.473063i $$0.843148\pi$$
$$80$$ 0 0
$$81$$ 8.67852 0.964280
$$82$$ 0 0
$$83$$ 6.68518 0.733793 0.366897 0.930262i $$-0.380420\pi$$
0.366897 + 0.930262i $$0.380420\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ 0 0
$$87$$ −0.540478 −0.0579454
$$88$$ 0 0
$$89$$ −3.03333 −0.321532 −0.160766 0.986993i $$-0.551396\pi$$
−0.160766 + 0.986993i $$0.551396\pi$$
$$90$$ 0 0
$$91$$ 2.05661 0.215592
$$92$$ 0 0
$$93$$ 1.68565 0.174794
$$94$$ 0 0
$$95$$ 0 0
$$96$$ 0 0
$$97$$ −3.21747 −0.326684 −0.163342 0.986569i $$-0.552227\pi$$
−0.163342 + 0.986569i $$0.552227\pi$$
$$98$$ 0 0
$$99$$ −0.225073 −0.0226207
$$100$$ 0 0
$$101$$ −16.6059 −1.65235 −0.826173 0.563417i $$-0.809486\pi$$
−0.826173 + 0.563417i $$0.809486\pi$$
$$102$$ 0 0
$$103$$ 7.30241 0.719528 0.359764 0.933043i $$-0.382857\pi$$
0.359764 + 0.933043i $$0.382857\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ 0.356936 0.0345063 0.0172532 0.999851i $$-0.494508\pi$$
0.0172532 + 0.999851i $$0.494508\pi$$
$$108$$ 0 0
$$109$$ 14.0359 1.34440 0.672198 0.740371i $$-0.265350\pi$$
0.672198 + 0.740371i $$0.265350\pi$$
$$110$$ 0 0
$$111$$ 1.31060 0.124397
$$112$$ 0 0
$$113$$ 1.17924 0.110933 0.0554667 0.998461i $$-0.482335\pi$$
0.0554667 + 0.998461i $$0.482335\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ 0 0
$$117$$ 3.67986 0.340203
$$118$$ 0 0
$$119$$ −8.57448 −0.786022
$$120$$ 0 0
$$121$$ −10.9942 −0.999476
$$122$$ 0 0
$$123$$ 0.879230 0.0792775
$$124$$ 0 0
$$125$$ 0 0
$$126$$ 0 0
$$127$$ −19.0097 −1.68684 −0.843420 0.537255i $$-0.819461\pi$$
−0.843420 + 0.537255i $$0.819461\pi$$
$$128$$ 0 0
$$129$$ −0.331890 −0.0292213
$$130$$ 0 0
$$131$$ 4.29043 0.374857 0.187428 0.982278i $$-0.439985\pi$$
0.187428 + 0.982278i $$0.439985\pi$$
$$132$$ 0 0
$$133$$ −1.31247 −0.113805
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ −12.2499 −1.04658 −0.523290 0.852155i $$-0.675296\pi$$
−0.523290 + 0.852155i $$0.675296\pi$$
$$138$$ 0 0
$$139$$ 2.61437 0.221748 0.110874 0.993834i $$-0.464635\pi$$
0.110874 + 0.993834i $$0.464635\pi$$
$$140$$ 0 0
$$141$$ 1.89437 0.159535
$$142$$ 0 0
$$143$$ −0.0942666 −0.00788297
$$144$$ 0 0
$$145$$ 0 0
$$146$$ 0 0
$$147$$ −0.805915 −0.0664707
$$148$$ 0 0
$$149$$ −19.0404 −1.55985 −0.779927 0.625870i $$-0.784744\pi$$
−0.779927 + 0.625870i $$0.784744\pi$$
$$150$$ 0 0
$$151$$ −18.3252 −1.49128 −0.745640 0.666349i $$-0.767856\pi$$
−0.745640 + 0.666349i $$0.767856\pi$$
$$152$$ 0 0
$$153$$ −15.3422 −1.24034
$$154$$ 0 0
$$155$$ 0 0
$$156$$ 0 0
$$157$$ −4.37467 −0.349137 −0.174569 0.984645i $$-0.555853\pi$$
−0.174569 + 0.984645i $$0.555853\pi$$
$$158$$ 0 0
$$159$$ −2.10744 −0.167131
$$160$$ 0 0
$$161$$ 1.65661 0.130559
$$162$$ 0 0
$$163$$ 11.8050 0.924639 0.462319 0.886714i $$-0.347017\pi$$
0.462319 + 0.886714i $$0.347017\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ 5.19760 0.402202 0.201101 0.979570i $$-0.435548\pi$$
0.201101 + 0.979570i $$0.435548\pi$$
$$168$$ 0 0
$$169$$ −11.4588 −0.881444
$$170$$ 0 0
$$171$$ −2.34837 −0.179585
$$172$$ 0 0
$$173$$ −2.61834 −0.199069 −0.0995345 0.995034i $$-0.531735\pi$$
−0.0995345 + 0.995034i $$0.531735\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 0 0
$$177$$ −2.35926 −0.177333
$$178$$ 0 0
$$179$$ 0.627563 0.0469062 0.0234531 0.999725i $$-0.492534\pi$$
0.0234531 + 0.999725i $$0.492534\pi$$
$$180$$ 0 0
$$181$$ −6.15848 −0.457756 −0.228878 0.973455i $$-0.573506\pi$$
−0.228878 + 0.973455i $$0.573506\pi$$
$$182$$ 0 0
$$183$$ −2.27436 −0.168126
$$184$$ 0 0
$$185$$ 0 0
$$186$$ 0 0
$$187$$ 0.393019 0.0287404
$$188$$ 0 0
$$189$$ 1.87107 0.136101
$$190$$ 0 0
$$191$$ −19.1343 −1.38451 −0.692254 0.721654i $$-0.743382\pi$$
−0.692254 + 0.721654i $$0.743382\pi$$
$$192$$ 0 0
$$193$$ −0.810900 −0.0583698 −0.0291849 0.999574i $$-0.509291\pi$$
−0.0291849 + 0.999574i $$0.509291\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ −6.15110 −0.438248 −0.219124 0.975697i $$-0.570320\pi$$
−0.219124 + 0.975697i $$0.570320\pi$$
$$198$$ 0 0
$$199$$ 7.03061 0.498387 0.249193 0.968454i $$-0.419834\pi$$
0.249193 + 0.968454i $$0.419834\pi$$
$$200$$ 0 0
$$201$$ −1.31818 −0.0929772
$$202$$ 0 0
$$203$$ 4.72797 0.331838
$$204$$ 0 0
$$205$$ 0 0
$$206$$ 0 0
$$207$$ 2.96414 0.206022
$$208$$ 0 0
$$209$$ 0.0601581 0.00416122
$$210$$ 0 0
$$211$$ 8.12120 0.559086 0.279543 0.960133i $$-0.409817\pi$$
0.279543 + 0.960133i $$0.409817\pi$$
$$212$$ 0 0
$$213$$ −1.46131 −0.100128
$$214$$ 0 0
$$215$$ 0 0
$$216$$ 0 0
$$217$$ −14.7457 −1.00100
$$218$$ 0 0
$$219$$ −1.41932 −0.0959090
$$220$$ 0 0
$$221$$ −6.42570 −0.432240
$$222$$ 0 0
$$223$$ 2.86268 0.191699 0.0958495 0.995396i $$-0.469443\pi$$
0.0958495 + 0.995396i $$0.469443\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ 27.4500 1.82192 0.910960 0.412496i $$-0.135343\pi$$
0.910960 + 0.412496i $$0.135343\pi$$
$$228$$ 0 0
$$229$$ 1.11319 0.0735613 0.0367807 0.999323i $$-0.488290\pi$$
0.0367807 + 0.999323i $$0.488290\pi$$
$$230$$ 0 0
$$231$$ −0.0238215 −0.00156734
$$232$$ 0 0
$$233$$ 21.2957 1.39513 0.697564 0.716523i $$-0.254267\pi$$
0.697564 + 0.716523i $$0.254267\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ 0 0
$$237$$ −2.96590 −0.192656
$$238$$ 0 0
$$239$$ 7.68036 0.496801 0.248401 0.968657i $$-0.420095\pi$$
0.248401 + 0.968657i $$0.420095\pi$$
$$240$$ 0 0
$$241$$ 8.42476 0.542687 0.271343 0.962483i $$-0.412532\pi$$
0.271343 + 0.962483i $$0.412532\pi$$
$$242$$ 0 0
$$243$$ 5.03188 0.322795
$$244$$ 0 0
$$245$$ 0 0
$$246$$ 0 0
$$247$$ −0.983561 −0.0625825
$$248$$ 0 0
$$249$$ 1.26601 0.0802300
$$250$$ 0 0
$$251$$ −2.56210 −0.161718 −0.0808590 0.996726i $$-0.525766\pi$$
−0.0808590 + 0.996726i $$0.525766\pi$$
$$252$$ 0 0
$$253$$ −0.0759321 −0.00477381
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ 4.39999 0.274464 0.137232 0.990539i $$-0.456179\pi$$
0.137232 + 0.990539i $$0.456179\pi$$
$$258$$ 0 0
$$259$$ −11.4648 −0.712388
$$260$$ 0 0
$$261$$ 8.45966 0.523640
$$262$$ 0 0
$$263$$ 24.8510 1.53238 0.766191 0.642613i $$-0.222150\pi$$
0.766191 + 0.642613i $$0.222150\pi$$
$$264$$ 0 0
$$265$$ 0 0
$$266$$ 0 0
$$267$$ −0.574437 −0.0351550
$$268$$ 0 0
$$269$$ −10.8742 −0.663012 −0.331506 0.943453i $$-0.607557\pi$$
−0.331506 + 0.943453i $$0.607557\pi$$
$$270$$ 0 0
$$271$$ −2.60290 −0.158115 −0.0790575 0.996870i $$-0.525191\pi$$
−0.0790575 + 0.996870i $$0.525191\pi$$
$$272$$ 0 0
$$273$$ 0.389472 0.0235719
$$274$$ 0 0
$$275$$ 0 0
$$276$$ 0 0
$$277$$ −12.1918 −0.732537 −0.366269 0.930509i $$-0.619365\pi$$
−0.366269 + 0.930509i $$0.619365\pi$$
$$278$$ 0 0
$$279$$ −26.3842 −1.57958
$$280$$ 0 0
$$281$$ 5.85068 0.349022 0.174511 0.984655i $$-0.444165\pi$$
0.174511 + 0.984655i $$0.444165\pi$$
$$282$$ 0 0
$$283$$ 10.7223 0.637375 0.318688 0.947860i $$-0.396758\pi$$
0.318688 + 0.947860i $$0.396758\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ −7.69129 −0.454002
$$288$$ 0 0
$$289$$ 9.79021 0.575895
$$290$$ 0 0
$$291$$ −0.609309 −0.0357183
$$292$$ 0 0
$$293$$ −2.72596 −0.159252 −0.0796261 0.996825i $$-0.525373\pi$$
−0.0796261 + 0.996825i $$0.525373\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ 0 0
$$297$$ −0.0857623 −0.00497643
$$298$$ 0 0
$$299$$ 1.24146 0.0717955
$$300$$ 0 0
$$301$$ 2.90329 0.167343
$$302$$ 0 0
$$303$$ −3.14474 −0.180661
$$304$$ 0 0
$$305$$ 0 0
$$306$$ 0 0
$$307$$ 22.4979 1.28402 0.642012 0.766695i $$-0.278100\pi$$
0.642012 + 0.766695i $$0.278100\pi$$
$$308$$ 0 0
$$309$$ 1.38290 0.0786703
$$310$$ 0 0
$$311$$ 17.9597 1.01840 0.509200 0.860648i $$-0.329942\pi$$
0.509200 + 0.860648i $$0.329942\pi$$
$$312$$ 0 0
$$313$$ −14.4728 −0.818052 −0.409026 0.912523i $$-0.634131\pi$$
−0.409026 + 0.912523i $$0.634131\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ 7.47689 0.419944 0.209972 0.977707i $$-0.432663\pi$$
0.209972 + 0.977707i $$0.432663\pi$$
$$318$$ 0 0
$$319$$ −0.216711 −0.0121335
$$320$$ 0 0
$$321$$ 0.0675949 0.00377278
$$322$$ 0 0
$$323$$ 4.10069 0.228168
$$324$$ 0 0
$$325$$ 0 0
$$326$$ 0 0
$$327$$ 2.65806 0.146991
$$328$$ 0 0
$$329$$ −16.5715 −0.913616
$$330$$ 0 0
$$331$$ −27.3565 −1.50365 −0.751826 0.659362i $$-0.770827\pi$$
−0.751826 + 0.659362i $$0.770827\pi$$
$$332$$ 0 0
$$333$$ −20.5137 −1.12415
$$334$$ 0 0
$$335$$ 0 0
$$336$$ 0 0
$$337$$ −5.65271 −0.307923 −0.153961 0.988077i $$-0.549203\pi$$
−0.153961 + 0.988077i $$0.549203\pi$$
$$338$$ 0 0
$$339$$ 0.223319 0.0121290
$$340$$ 0 0
$$341$$ 0.675881 0.0366010
$$342$$ 0 0
$$343$$ 18.6462 1.00680
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ −15.5293 −0.833658 −0.416829 0.908985i $$-0.636859\pi$$
−0.416829 + 0.908985i $$0.636859\pi$$
$$348$$ 0 0
$$349$$ 11.0559 0.591810 0.295905 0.955217i $$-0.404379\pi$$
0.295905 + 0.955217i $$0.404379\pi$$
$$350$$ 0 0
$$351$$ 1.40218 0.0748428
$$352$$ 0 0
$$353$$ −6.85381 −0.364792 −0.182396 0.983225i $$-0.558385\pi$$
−0.182396 + 0.983225i $$0.558385\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ 0 0
$$357$$ −1.62380 −0.0859404
$$358$$ 0 0
$$359$$ 16.3104 0.860832 0.430416 0.902631i $$-0.358367\pi$$
0.430416 + 0.902631i $$0.358367\pi$$
$$360$$ 0 0
$$361$$ −18.3723 −0.966964
$$362$$ 0 0
$$363$$ −2.08204 −0.109279
$$364$$ 0 0
$$365$$ 0 0
$$366$$ 0 0
$$367$$ 31.6200 1.65055 0.825275 0.564731i $$-0.191020\pi$$
0.825275 + 0.564731i $$0.191020\pi$$
$$368$$ 0 0
$$369$$ −13.7619 −0.716414
$$370$$ 0 0
$$371$$ 18.4354 0.957118
$$372$$ 0 0
$$373$$ −28.2458 −1.46251 −0.731256 0.682104i $$-0.761065\pi$$
−0.731256 + 0.682104i $$0.761065\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ 3.54313 0.182481
$$378$$ 0 0
$$379$$ 2.98772 0.153469 0.0767345 0.997052i $$-0.475551\pi$$
0.0767345 + 0.997052i $$0.475551\pi$$
$$380$$ 0 0
$$381$$ −3.59997 −0.184432
$$382$$ 0 0
$$383$$ −12.5176 −0.639621 −0.319810 0.947482i $$-0.603619\pi$$
−0.319810 + 0.947482i $$0.603619\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 0 0
$$387$$ 5.19480 0.264067
$$388$$ 0 0
$$389$$ −19.4861 −0.987982 −0.493991 0.869467i $$-0.664462\pi$$
−0.493991 + 0.869467i $$0.664462\pi$$
$$390$$ 0 0
$$391$$ −5.17593 −0.261758
$$392$$ 0 0
$$393$$ 0.812503 0.0409853
$$394$$ 0 0
$$395$$ 0 0
$$396$$ 0 0
$$397$$ −17.3203 −0.869281 −0.434640 0.900604i $$-0.643124\pi$$
−0.434640 + 0.900604i $$0.643124\pi$$
$$398$$ 0 0
$$399$$ −0.248549 −0.0124430
$$400$$ 0 0
$$401$$ 17.3727 0.867553 0.433777 0.901020i $$-0.357181\pi$$
0.433777 + 0.901020i $$0.357181\pi$$
$$402$$ 0 0
$$403$$ −11.0504 −0.550459
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 0.525499 0.0260480
$$408$$ 0 0
$$409$$ −12.6874 −0.627350 −0.313675 0.949530i $$-0.601560\pi$$
−0.313675 + 0.949530i $$0.601560\pi$$
$$410$$ 0 0
$$411$$ −2.31983 −0.114429
$$412$$ 0 0
$$413$$ 20.6383 1.01554
$$414$$ 0 0
$$415$$ 0 0
$$416$$ 0 0
$$417$$ 0.495098 0.0242450
$$418$$ 0 0
$$419$$ −4.23468 −0.206878 −0.103439 0.994636i $$-0.532985\pi$$
−0.103439 + 0.994636i $$0.532985\pi$$
$$420$$ 0 0
$$421$$ 4.17837 0.203641 0.101821 0.994803i $$-0.467533\pi$$
0.101821 + 0.994803i $$0.467533\pi$$
$$422$$ 0 0
$$423$$ −29.6510 −1.44168
$$424$$ 0 0
$$425$$ 0 0
$$426$$ 0 0
$$427$$ 19.8956 0.962813
$$428$$ 0 0
$$429$$ −0.0178518 −0.000861892 0
$$430$$ 0 0
$$431$$ −21.9197 −1.05583 −0.527917 0.849296i $$-0.677027\pi$$
−0.527917 + 0.849296i $$0.677027\pi$$
$$432$$ 0 0
$$433$$ 20.2195 0.971688 0.485844 0.874046i $$-0.338512\pi$$
0.485844 + 0.874046i $$0.338512\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ −0.792262 −0.0378990
$$438$$ 0 0
$$439$$ −16.3149 −0.778666 −0.389333 0.921097i $$-0.627294\pi$$
−0.389333 + 0.921097i $$0.627294\pi$$
$$440$$ 0 0
$$441$$ 12.6143 0.600682
$$442$$ 0 0
$$443$$ −28.0868 −1.33444 −0.667222 0.744859i $$-0.732517\pi$$
−0.667222 + 0.744859i $$0.732517\pi$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ 0 0
$$447$$ −3.60579 −0.170548
$$448$$ 0 0
$$449$$ −24.5071 −1.15656 −0.578282 0.815837i $$-0.696277\pi$$
−0.578282 + 0.815837i $$0.696277\pi$$
$$450$$ 0 0
$$451$$ 0.352537 0.0166003
$$452$$ 0 0
$$453$$ −3.47033 −0.163050
$$454$$ 0 0
$$455$$ 0 0
$$456$$ 0 0
$$457$$ 2.87128 0.134313 0.0671564 0.997742i $$-0.478607\pi$$
0.0671564 + 0.997742i $$0.478607\pi$$
$$458$$ 0 0
$$459$$ −5.84601 −0.272868
$$460$$ 0 0
$$461$$ 15.2264 0.709162 0.354581 0.935025i $$-0.384623\pi$$
0.354581 + 0.935025i $$0.384623\pi$$
$$462$$ 0 0
$$463$$ 36.6480 1.70318 0.851588 0.524212i $$-0.175640\pi$$
0.851588 + 0.524212i $$0.175640\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ −14.9765 −0.693031 −0.346516 0.938044i $$-0.612635\pi$$
−0.346516 + 0.938044i $$0.612635\pi$$
$$468$$ 0 0
$$469$$ 11.5311 0.532457
$$470$$ 0 0
$$471$$ −0.828456 −0.0381732
$$472$$ 0 0
$$473$$ −0.133075 −0.00611879
$$474$$ 0 0
$$475$$ 0 0
$$476$$ 0 0
$$477$$ 32.9861 1.51033
$$478$$ 0 0
$$479$$ 4.03398 0.184317 0.0921587 0.995744i $$-0.470623\pi$$
0.0921587 + 0.995744i $$0.470623\pi$$
$$480$$ 0 0
$$481$$ −8.59171 −0.391748
$$482$$ 0 0
$$483$$ 0.313721 0.0142748
$$484$$ 0 0
$$485$$ 0 0
$$486$$ 0 0
$$487$$ −4.28846 −0.194329 −0.0971643 0.995268i $$-0.530977\pi$$
−0.0971643 + 0.995268i $$0.530977\pi$$
$$488$$ 0 0
$$489$$ 2.23558 0.101096
$$490$$ 0 0
$$491$$ −36.8754 −1.66416 −0.832081 0.554654i $$-0.812851\pi$$
−0.832081 + 0.554654i $$0.812851\pi$$
$$492$$ 0 0
$$493$$ −14.7721 −0.665303
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ 12.7832 0.573405
$$498$$ 0 0
$$499$$ −5.74707 −0.257274 −0.128637 0.991692i $$-0.541060\pi$$
−0.128637 + 0.991692i $$0.541060\pi$$
$$500$$ 0 0
$$501$$ 0.984298 0.0439752
$$502$$ 0 0
$$503$$ −18.7850 −0.837583 −0.418792 0.908082i $$-0.637546\pi$$
−0.418792 + 0.908082i $$0.637546\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ 0 0
$$507$$ −2.17001 −0.0963735
$$508$$ 0 0
$$509$$ −20.2669 −0.898313 −0.449157 0.893453i $$-0.648275\pi$$
−0.449157 + 0.893453i $$0.648275\pi$$
$$510$$ 0 0
$$511$$ 12.4159 0.549247
$$512$$ 0 0
$$513$$ −0.894829 −0.0395077
$$514$$ 0 0
$$515$$ 0 0
$$516$$ 0 0
$$517$$ 0.759568 0.0334058
$$518$$ 0 0
$$519$$ −0.495850 −0.0217654
$$520$$ 0 0
$$521$$ 6.47593 0.283716 0.141858 0.989887i $$-0.454692\pi$$
0.141858 + 0.989887i $$0.454692\pi$$
$$522$$ 0 0
$$523$$ −0.414671 −0.0181323 −0.00906615 0.999959i $$-0.502886\pi$$
−0.00906615 + 0.999959i $$0.502886\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ 46.0716 2.00691
$$528$$ 0 0
$$529$$ 1.00000 0.0434783
$$530$$ 0 0
$$531$$ 36.9276 1.60252
$$532$$ 0 0
$$533$$ −5.76384 −0.249659
$$534$$ 0 0
$$535$$ 0 0
$$536$$ 0 0
$$537$$ 0.118845 0.00512854
$$538$$ 0 0
$$539$$ −0.323140 −0.0139186
$$540$$ 0 0
$$541$$ 28.5708 1.22835 0.614177 0.789169i $$-0.289488\pi$$
0.614177 + 0.789169i $$0.289488\pi$$
$$542$$ 0 0
$$543$$ −1.16626 −0.0500492
$$544$$ 0 0
$$545$$ 0 0
$$546$$ 0 0
$$547$$ −39.0974 −1.67168 −0.835841 0.548971i $$-0.815020\pi$$
−0.835841 + 0.548971i $$0.815020\pi$$
$$548$$ 0 0
$$549$$ 35.5987 1.51932
$$550$$ 0 0
$$551$$ −2.26112 −0.0963270
$$552$$ 0 0
$$553$$ 25.9450 1.10329
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ −33.9136 −1.43696 −0.718482 0.695546i $$-0.755163\pi$$
−0.718482 + 0.695546i $$0.755163\pi$$
$$558$$ 0 0
$$559$$ 2.17572 0.0920232
$$560$$ 0 0
$$561$$ 0.0744281 0.00314236
$$562$$ 0 0
$$563$$ 25.6390 1.08056 0.540278 0.841486i $$-0.318319\pi$$
0.540278 + 0.841486i $$0.318319\pi$$
$$564$$ 0 0
$$565$$ 0 0
$$566$$ 0 0
$$567$$ −14.3769 −0.603773
$$568$$ 0 0
$$569$$ −13.6257 −0.571218 −0.285609 0.958346i $$-0.592196\pi$$
−0.285609 + 0.958346i $$0.592196\pi$$
$$570$$ 0 0
$$571$$ 0.354294 0.0148267 0.00741337 0.999973i $$-0.497640\pi$$
0.00741337 + 0.999973i $$0.497640\pi$$
$$572$$ 0 0
$$573$$ −3.62356 −0.151376
$$574$$ 0 0
$$575$$ 0 0
$$576$$ 0 0
$$577$$ −18.5870 −0.773788 −0.386894 0.922124i $$-0.626452\pi$$
−0.386894 + 0.922124i $$0.626452\pi$$
$$578$$ 0 0
$$579$$ −0.153564 −0.00638192
$$580$$ 0 0
$$581$$ −11.0747 −0.459457
$$582$$ 0 0
$$583$$ −0.845002 −0.0349964
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ 7.75193 0.319956 0.159978 0.987121i $$-0.448858\pi$$
0.159978 + 0.987121i $$0.448858\pi$$
$$588$$ 0 0
$$589$$ 7.05202 0.290573
$$590$$ 0 0
$$591$$ −1.16487 −0.0479162
$$592$$ 0 0
$$593$$ −23.3828 −0.960215 −0.480107 0.877210i $$-0.659402\pi$$
−0.480107 + 0.877210i $$0.659402\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 0 0
$$597$$ 1.33142 0.0544916
$$598$$ 0 0
$$599$$ −25.6075 −1.04629 −0.523146 0.852243i $$-0.675242\pi$$
−0.523146 + 0.852243i $$0.675242\pi$$
$$600$$ 0 0
$$601$$ 4.03750 0.164693 0.0823466 0.996604i $$-0.473759\pi$$
0.0823466 + 0.996604i $$0.473759\pi$$
$$602$$ 0 0
$$603$$ 20.6324 0.840215
$$604$$ 0 0
$$605$$ 0 0
$$606$$ 0 0
$$607$$ 45.8176 1.85968 0.929839 0.367967i $$-0.119946\pi$$
0.929839 + 0.367967i $$0.119946\pi$$
$$608$$ 0 0
$$609$$ 0.895361 0.0362819
$$610$$ 0 0
$$611$$ −12.4186 −0.502405
$$612$$ 0 0
$$613$$ −29.1714 −1.17822 −0.589112 0.808052i $$-0.700522\pi$$
−0.589112 + 0.808052i $$0.700522\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 17.0562 0.686659 0.343329 0.939215i $$-0.388445\pi$$
0.343329 + 0.939215i $$0.388445\pi$$
$$618$$ 0 0
$$619$$ 36.0620 1.44946 0.724728 0.689035i $$-0.241966\pi$$
0.724728 + 0.689035i $$0.241966\pi$$
$$620$$ 0 0
$$621$$ 1.12946 0.0453237
$$622$$ 0 0
$$623$$ 5.02503 0.201324
$$624$$ 0 0
$$625$$ 0 0
$$626$$ 0 0
$$627$$ 0.0113925 0.000454971 0
$$628$$ 0 0
$$629$$ 35.8208 1.42827
$$630$$ 0 0
$$631$$ 17.4958 0.696496 0.348248 0.937402i $$-0.386777\pi$$
0.348248 + 0.937402i $$0.386777\pi$$
$$632$$ 0 0
$$633$$ 1.53795 0.0611282
$$634$$ 0 0
$$635$$ 0 0
$$636$$ 0 0
$$637$$ 5.28322 0.209329
$$638$$ 0 0
$$639$$ 22.8727 0.904832
$$640$$ 0 0
$$641$$ −39.9200 −1.57675 −0.788373 0.615197i $$-0.789076\pi$$
−0.788373 + 0.615197i $$0.789076\pi$$
$$642$$ 0 0
$$643$$ 41.8187 1.64917 0.824584 0.565740i $$-0.191409\pi$$
0.824584 + 0.565740i $$0.191409\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ −38.8026 −1.52549 −0.762743 0.646702i $$-0.776148\pi$$
−0.762743 + 0.646702i $$0.776148\pi$$
$$648$$ 0 0
$$649$$ −0.945972 −0.0371327
$$650$$ 0 0
$$651$$ −2.79247 −0.109445
$$652$$ 0 0
$$653$$ −39.8995 −1.56139 −0.780694 0.624914i $$-0.785134\pi$$
−0.780694 + 0.624914i $$0.785134\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ 0 0
$$657$$ 22.2155 0.866709
$$658$$ 0 0
$$659$$ 22.9449 0.893808 0.446904 0.894582i $$-0.352527\pi$$
0.446904 + 0.894582i $$0.352527\pi$$
$$660$$ 0 0
$$661$$ 19.2759 0.749745 0.374873 0.927076i $$-0.377686\pi$$
0.374873 + 0.927076i $$0.377686\pi$$
$$662$$ 0 0
$$663$$ −1.21687 −0.0472593
$$664$$ 0 0
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 2.85401 0.110508
$$668$$ 0 0
$$669$$ 0.542121 0.0209596
$$670$$ 0 0
$$671$$ −0.911930 −0.0352047
$$672$$ 0 0
$$673$$ 38.0041 1.46495 0.732476 0.680793i $$-0.238365\pi$$
0.732476 + 0.680793i $$0.238365\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ −41.0387 −1.57725 −0.788623 0.614878i $$-0.789205\pi$$
−0.788623 + 0.614878i $$0.789205\pi$$
$$678$$ 0 0
$$679$$ 5.33008 0.204550
$$680$$ 0 0
$$681$$ 5.19835 0.199201
$$682$$ 0 0
$$683$$ −27.6705 −1.05878 −0.529390 0.848378i $$-0.677579\pi$$
−0.529390 + 0.848378i $$0.677579\pi$$
$$684$$ 0 0
$$685$$ 0 0
$$686$$ 0 0
$$687$$ 0.210810 0.00804290
$$688$$ 0 0
$$689$$ 13.8155 0.526327
$$690$$ 0 0
$$691$$ 33.8078 1.28611 0.643056 0.765820i $$-0.277666\pi$$
0.643056 + 0.765820i $$0.277666\pi$$
$$692$$ 0 0
$$693$$ 0.372858 0.0141637
$$694$$ 0 0
$$695$$ 0 0
$$696$$ 0 0
$$697$$ 24.0307 0.910229
$$698$$ 0 0
$$699$$ 4.03288 0.152538
$$700$$ 0 0
$$701$$ −46.4878 −1.75582 −0.877909 0.478827i $$-0.841062\pi$$
−0.877909 + 0.478827i $$0.841062\pi$$
$$702$$ 0 0
$$703$$ 5.48297 0.206794
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ 27.5094 1.03460
$$708$$ 0 0
$$709$$ −13.5298 −0.508122 −0.254061 0.967188i $$-0.581766\pi$$
−0.254061 + 0.967188i $$0.581766\pi$$
$$710$$ 0 0
$$711$$ 46.4229 1.74099
$$712$$ 0 0
$$713$$ −8.90112 −0.333350
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 0 0
$$717$$ 1.45447 0.0543182
$$718$$ 0 0
$$719$$ −2.64955 −0.0988115 −0.0494057 0.998779i $$-0.515733\pi$$
−0.0494057 + 0.998779i $$0.515733\pi$$
$$720$$ 0 0
$$721$$ −12.0972 −0.450525
$$722$$ 0 0
$$723$$ 1.59544 0.0593351
$$724$$ 0 0
$$725$$ 0 0
$$726$$ 0 0
$$727$$ −46.8796 −1.73867 −0.869334 0.494226i $$-0.835452\pi$$
−0.869334 + 0.494226i $$0.835452\pi$$
$$728$$ 0 0
$$729$$ −25.0826 −0.928987
$$730$$ 0 0
$$731$$ −9.07108 −0.335506
$$732$$ 0 0
$$733$$ −36.1389 −1.33482 −0.667410 0.744691i $$-0.732597\pi$$
−0.667410 + 0.744691i $$0.732597\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ −0.528538 −0.0194690
$$738$$ 0 0
$$739$$ 22.6473 0.833095 0.416547 0.909114i $$-0.363240\pi$$
0.416547 + 0.909114i $$0.363240\pi$$
$$740$$ 0 0
$$741$$ −0.186262 −0.00684252
$$742$$ 0 0
$$743$$ −7.04015 −0.258278 −0.129139 0.991627i $$-0.541221\pi$$
−0.129139 + 0.991627i $$0.541221\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ 0 0
$$747$$ −19.8158 −0.725021
$$748$$ 0 0
$$749$$ −0.591304 −0.0216058
$$750$$ 0 0
$$751$$ −5.94539 −0.216950 −0.108475 0.994099i $$-0.534597\pi$$
−0.108475 + 0.994099i $$0.534597\pi$$
$$752$$ 0 0
$$753$$ −0.485198 −0.0176816
$$754$$ 0 0
$$755$$ 0 0
$$756$$ 0 0
$$757$$ −43.9519 −1.59746 −0.798729 0.601691i $$-0.794494\pi$$
−0.798729 + 0.601691i $$0.794494\pi$$
$$758$$ 0 0
$$759$$ −0.0143797 −0.000521949 0
$$760$$ 0 0
$$761$$ 22.0290 0.798549 0.399274 0.916831i $$-0.369262\pi$$
0.399274 + 0.916831i $$0.369262\pi$$
$$762$$ 0 0
$$763$$ −23.2520 −0.841779
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ 15.4663 0.558455
$$768$$ 0 0
$$769$$ −17.6958 −0.638128 −0.319064 0.947733i $$-0.603368\pi$$
−0.319064 + 0.947733i $$0.603368\pi$$
$$770$$ 0 0
$$771$$ 0.833250 0.0300088
$$772$$ 0 0
$$773$$ −1.63758 −0.0588997 −0.0294498 0.999566i $$-0.509376\pi$$
−0.0294498 + 0.999566i $$0.509376\pi$$
$$774$$ 0 0
$$775$$ 0 0
$$776$$ 0 0
$$777$$ −2.17115 −0.0778896
$$778$$ 0 0
$$779$$ 3.67831 0.131789
$$780$$ 0 0
$$781$$ −0.585930 −0.0209662
$$782$$ 0 0
$$783$$ 3.22349 0.115198
$$784$$ 0 0
$$785$$ 0 0
$$786$$ 0 0
$$787$$ −27.6760 −0.986543 −0.493272 0.869875i $$-0.664199\pi$$
−0.493272 + 0.869875i $$0.664199\pi$$
$$788$$ 0 0
$$789$$ 4.70618 0.167544
$$790$$ 0 0
$$791$$ −1.95354 −0.0694598
$$792$$ 0 0
$$793$$ 14.9097 0.529459
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ 9.29831 0.329363 0.164681 0.986347i $$-0.447340\pi$$
0.164681 + 0.986347i $$0.447340\pi$$
$$798$$ 0 0
$$799$$ 51.7761 1.83171
$$800$$ 0 0
$$801$$ 8.99119 0.317688
$$802$$ 0 0
$$803$$ −0.569093 −0.0200829
$$804$$ 0 0
$$805$$ 0 0
$$806$$ 0 0
$$807$$ −2.05931 −0.0724911
$$808$$ 0 0
$$809$$ 48.8800 1.71853 0.859264 0.511532i $$-0.170922\pi$$
0.859264 + 0.511532i $$0.170922\pi$$
$$810$$ 0 0
$$811$$ 44.0615 1.54721 0.773604 0.633669i $$-0.218452\pi$$
0.773604 + 0.633669i $$0.218452\pi$$
$$812$$ 0 0
$$813$$ −0.492926 −0.0172877
$$814$$ 0 0
$$815$$ 0 0
$$816$$ 0 0
$$817$$ −1.38848 −0.0485768
$$818$$ 0 0
$$819$$ −6.09608 −0.213014
$$820$$ 0 0
$$821$$ 30.1832 1.05340 0.526700 0.850051i $$-0.323429\pi$$
0.526700 + 0.850051i $$0.323429\pi$$
$$822$$ 0 0
$$823$$ 32.0171 1.11605 0.558023 0.829826i $$-0.311560\pi$$
0.558023 + 0.829826i $$0.311560\pi$$
$$824$$ 0 0
$$825$$ 0 0
$$826$$ 0 0
$$827$$ 20.5192 0.713523 0.356761 0.934196i $$-0.383881\pi$$
0.356761 + 0.934196i $$0.383881\pi$$
$$828$$ 0 0
$$829$$ 38.0551 1.32171 0.660854 0.750515i $$-0.270194\pi$$
0.660854 + 0.750515i $$0.270194\pi$$
$$830$$ 0 0
$$831$$ −2.30884 −0.0800926
$$832$$ 0 0
$$833$$ −22.0269 −0.763188
$$834$$ 0 0
$$835$$ 0 0
$$836$$ 0 0
$$837$$ −10.0535 −0.347499
$$838$$ 0 0
$$839$$ 24.6946 0.852553 0.426277 0.904593i $$-0.359825\pi$$
0.426277 + 0.904593i $$0.359825\pi$$
$$840$$ 0 0
$$841$$ −20.8547 −0.719126
$$842$$ 0 0
$$843$$ 1.10797 0.0381607
$$844$$ 0 0
$$845$$ 0 0
$$846$$ 0 0
$$847$$ 18.2131 0.625811
$$848$$ 0 0
$$849$$ 2.03054 0.0696880
$$850$$ 0 0
$$851$$ −6.92065 −0.237237
$$852$$ 0 0
$$853$$ 23.4770 0.803837 0.401919 0.915675i $$-0.368343\pi$$
0.401919 + 0.915675i $$0.368343\pi$$
$$854$$ 0 0
$$855$$ 0 0
$$856$$ 0 0
$$857$$ 20.9632 0.716090 0.358045 0.933704i $$-0.383443\pi$$
0.358045 + 0.933704i $$0.383443\pi$$
$$858$$ 0 0
$$859$$ 35.7273 1.21900 0.609500 0.792786i $$-0.291370\pi$$
0.609500 + 0.792786i $$0.291370\pi$$
$$860$$ 0 0
$$861$$ −1.45654 −0.0496388
$$862$$ 0 0
$$863$$ 19.5880 0.666784 0.333392 0.942788i $$-0.391807\pi$$
0.333392 + 0.942788i $$0.391807\pi$$
$$864$$ 0 0
$$865$$ 0 0
$$866$$ 0 0
$$867$$ 1.85403 0.0629660
$$868$$ 0 0
$$869$$ −1.18921 −0.0403412
$$870$$ 0 0
$$871$$ 8.64139 0.292802
$$872$$ 0 0
$$873$$ 9.53702 0.322779
$$874$$ 0 0
$$875$$ 0 0
$$876$$ 0 0
$$877$$ −49.5791 −1.67417 −0.837084 0.547074i $$-0.815741\pi$$
−0.837084 + 0.547074i $$0.815741\pi$$
$$878$$ 0 0
$$879$$ −0.516230 −0.0174120
$$880$$ 0 0
$$881$$ 21.4406 0.722353 0.361177 0.932497i $$-0.382375\pi$$
0.361177 + 0.932497i $$0.382375\pi$$
$$882$$ 0 0
$$883$$ 52.7646 1.77567 0.887836 0.460161i $$-0.152208\pi$$
0.887836 + 0.460161i $$0.152208\pi$$
$$884$$ 0 0
$$885$$ 0 0
$$886$$ 0 0
$$887$$ −30.1462 −1.01221 −0.506105 0.862472i $$-0.668915\pi$$
−0.506105 + 0.862472i $$0.668915\pi$$
$$888$$ 0 0
$$889$$ 31.4917 1.05620
$$890$$ 0 0
$$891$$ 0.658978 0.0220766
$$892$$ 0 0
$$893$$ 7.92520 0.265207
$$894$$ 0 0
$$895$$ 0 0
$$896$$ 0 0
$$897$$ 0.235102 0.00784982
$$898$$ 0 0
$$899$$ −25.4039 −0.847266
$$900$$ 0 0
$$901$$ −57.5998 −1.91893
$$902$$ 0 0
$$903$$ 0.549812 0.0182966
$$904$$ 0 0
$$905$$ 0 0
$$906$$ 0 0
$$907$$ −20.3987 −0.677329 −0.338665 0.940907i $$-0.609975\pi$$
−0.338665 + 0.940907i $$0.609975\pi$$
$$908$$ 0 0
$$909$$ 49.2221 1.63259
$$910$$ 0 0
$$911$$ −57.7921 −1.91474 −0.957369 0.288869i $$-0.906721\pi$$
−0.957369 + 0.288869i $$0.906721\pi$$
$$912$$ 0 0
$$913$$ 0.507619 0.0167998
$$914$$ 0 0
$$915$$ 0 0
$$916$$ 0 0
$$917$$ −7.10757 −0.234713
$$918$$ 0 0
$$919$$ −26.0255 −0.858502 −0.429251 0.903185i $$-0.641222\pi$$
−0.429251 + 0.903185i $$0.641222\pi$$
$$920$$ 0 0
$$921$$ 4.26055 0.140390
$$922$$ 0 0
$$923$$ 9.57972 0.315320
$$924$$ 0 0
$$925$$ 0 0
$$926$$ 0 0
$$927$$ −21.6454 −0.710927
$$928$$ 0 0
$$929$$ 26.9839 0.885313 0.442656 0.896691i $$-0.354036\pi$$
0.442656 + 0.896691i $$0.354036\pi$$
$$930$$ 0 0
$$931$$ −3.37159 −0.110499
$$932$$ 0 0
$$933$$ 3.40112 0.111348
$$934$$ 0 0
$$935$$ 0 0
$$936$$ 0 0
$$937$$ 35.8201 1.17019 0.585096 0.810964i $$-0.301057\pi$$
0.585096 + 0.810964i $$0.301057\pi$$
$$938$$ 0 0
$$939$$ −2.74079 −0.0894424
$$940$$ 0 0
$$941$$ −32.0416 −1.04453 −0.522263 0.852785i $$-0.674912\pi$$
−0.522263 + 0.852785i $$0.674912\pi$$
$$942$$ 0 0
$$943$$ −4.64279 −0.151190
$$944$$ 0 0
$$945$$ 0 0
$$946$$ 0 0
$$947$$ −8.53256 −0.277271 −0.138635 0.990343i $$-0.544272\pi$$
−0.138635 + 0.990343i $$0.544272\pi$$
$$948$$ 0 0
$$949$$ 9.30445 0.302035
$$950$$ 0 0
$$951$$ 1.41594 0.0459150
$$952$$ 0 0
$$953$$ 42.4054 1.37365 0.686823 0.726825i $$-0.259005\pi$$
0.686823 + 0.726825i $$0.259005\pi$$
$$954$$ 0 0
$$955$$ 0 0
$$956$$ 0 0
$$957$$ −0.0410397 −0.00132662
$$958$$ 0 0
$$959$$ 20.2933 0.655305
$$960$$ 0 0
$$961$$ 48.2300 1.55581
$$962$$ 0 0
$$963$$ −1.05801 −0.0340938
$$964$$ 0 0
$$965$$ 0 0
$$966$$ 0 0
$$967$$ 10.0988 0.324755 0.162377 0.986729i $$-0.448084\pi$$
0.162377 + 0.986729i $$0.448084\pi$$
$$968$$ 0 0
$$969$$ 0.776570 0.0249470
$$970$$ 0 0
$$971$$ −15.7943 −0.506863 −0.253431 0.967353i $$-0.581559\pi$$
−0.253431 + 0.967353i $$0.581559\pi$$
$$972$$ 0 0
$$973$$ −4.33099 −0.138845
$$974$$ 0 0
$$975$$ 0 0
$$976$$ 0 0
$$977$$ 27.0055 0.863984 0.431992 0.901877i $$-0.357811\pi$$
0.431992 + 0.901877i $$0.357811\pi$$
$$978$$ 0 0
$$979$$ −0.230327 −0.00736128
$$980$$ 0 0
$$981$$ −41.6043 −1.32832
$$982$$ 0 0
$$983$$ 16.0647 0.512384 0.256192 0.966626i $$-0.417532\pi$$
0.256192 + 0.966626i $$0.417532\pi$$
$$984$$ 0 0
$$985$$ 0 0
$$986$$ 0 0
$$987$$ −3.13823 −0.0998910
$$988$$ 0 0
$$989$$ 1.75255 0.0557279
$$990$$ 0 0
$$991$$ 51.4433 1.63415 0.817075 0.576532i $$-0.195594\pi$$
0.817075 + 0.576532i $$0.195594\pi$$
$$992$$ 0 0
$$993$$ −5.18066 −0.164403
$$994$$ 0 0
$$995$$ 0 0
$$996$$ 0 0
$$997$$ 39.2639 1.24350 0.621751 0.783215i $$-0.286422\pi$$
0.621751 + 0.783215i $$0.286422\pi$$
$$998$$ 0 0
$$999$$ −7.81660 −0.247306
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 4600.2.a.bi.1.3 7
4.3 odd 2 9200.2.a.cz.1.5 7
5.2 odd 4 920.2.e.b.369.7 14
5.3 odd 4 920.2.e.b.369.8 yes 14
5.4 even 2 4600.2.a.bh.1.5 7
20.3 even 4 1840.2.e.g.369.7 14
20.7 even 4 1840.2.e.g.369.8 14
20.19 odd 2 9200.2.a.dc.1.3 7

By twisted newform
Twist Min Dim Char Parity Ord Type
920.2.e.b.369.7 14 5.2 odd 4
920.2.e.b.369.8 yes 14 5.3 odd 4
1840.2.e.g.369.7 14 20.3 even 4
1840.2.e.g.369.8 14 20.7 even 4
4600.2.a.bh.1.5 7 5.4 even 2
4600.2.a.bi.1.3 7 1.1 even 1 trivial
9200.2.a.cz.1.5 7 4.3 odd 2
9200.2.a.dc.1.3 7 20.19 odd 2