# Properties

 Label 320.6.a.v.1.1 Level 320 Weight 6 Character 320.1 Self dual yes Analytic conductor 51.323 Analytic rank 1 Dimension 2 CM no Inner twists 1

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$320 = 2^{6} \cdot 5$$ Weight: $$k$$ $$=$$ $$6$$ Character orbit: $$[\chi]$$ $$=$$ 320.a (trivial)

## Newform invariants

 Self dual: yes Analytic conductor: $$51.3228223402$$ Analytic rank: $$1$$ Dimension: $$2$$ Coefficient field: $$\Q(\sqrt{70})$$ Defining polynomial: $$x^{2} - 70$$ Coefficient ring: $$\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$2$$ Twist minimal: no (minimal twist has level 160) Fricke sign: $$1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

 Embedding label 1.1 Root $$-8.36660$$ of defining polynomial Character $$\chi$$ $$=$$ 320.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q-12.7332 q^{3} -25.0000 q^{5} -68.7332 q^{7} -80.8656 q^{9} +O(q^{10})$$ $$q-12.7332 q^{3} -25.0000 q^{5} -68.7332 q^{7} -80.8656 q^{9} +327.332 q^{11} +719.328 q^{13} +318.330 q^{15} -379.328 q^{17} +1029.33 q^{19} +875.194 q^{21} +779.120 q^{23} +625.000 q^{25} +4123.85 q^{27} -1392.66 q^{29} -2744.68 q^{31} -4167.98 q^{33} +1718.33 q^{35} -12640.6 q^{37} -9159.35 q^{39} +8210.43 q^{41} +22524.5 q^{43} +2021.64 q^{45} -7739.18 q^{47} -12082.7 q^{49} +4830.06 q^{51} +2401.86 q^{53} -8183.30 q^{55} -13106.6 q^{57} +15734.7 q^{59} -32082.1 q^{61} +5558.15 q^{63} -17983.2 q^{65} +9009.07 q^{67} -9920.70 q^{69} -43832.3 q^{71} -65837.5 q^{73} -7958.25 q^{75} -22498.6 q^{77} -39601.3 q^{79} -32859.4 q^{81} -63101.4 q^{83} +9483.20 q^{85} +17733.0 q^{87} +34510.9 q^{89} -49441.7 q^{91} +34948.6 q^{93} -25733.2 q^{95} -14081.3 q^{97} -26469.9 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2q + 8q^{3} - 50q^{5} - 104q^{7} + 106q^{9} + O(q^{10})$$ $$2q + 8q^{3} - 50q^{5} - 104q^{7} + 106q^{9} + 320q^{11} + 100q^{13} - 200q^{15} + 580q^{17} + 720q^{19} + 144q^{21} - 1688q^{23} + 1250q^{25} + 2960q^{27} - 108q^{29} - 9840q^{31} - 4320q^{33} + 2600q^{35} - 6540q^{37} - 22000q^{39} - 10620q^{41} + 25672q^{43} - 2650q^{45} - 28296q^{47} - 27646q^{49} + 24720q^{51} - 31340q^{53} - 8000q^{55} - 19520q^{57} + 30800q^{59} - 24540q^{61} - 1032q^{63} - 2500q^{65} + 34584q^{67} - 61072q^{69} + 12400q^{71} - 7180q^{73} + 5000q^{75} - 22240q^{77} - 71840q^{79} - 102398q^{81} - 31928q^{83} - 14500q^{85} + 44368q^{87} - 40748q^{89} - 27600q^{91} - 112160q^{93} - 18000q^{95} - 190140q^{97} - 27840q^{99} + O(q^{100})$$

## 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
$$3$$ −12.7332 −0.816835 −0.408418 0.912795i $$-0.633919\pi$$
−0.408418 + 0.912795i $$0.633919\pi$$
$$4$$ 0 0
$$5$$ −25.0000 −0.447214
$$6$$ 0 0
$$7$$ −68.7332 −0.530178 −0.265089 0.964224i $$-0.585401\pi$$
−0.265089 + 0.964224i $$0.585401\pi$$
$$8$$ 0 0
$$9$$ −80.8656 −0.332780
$$10$$ 0 0
$$11$$ 327.332 0.815655 0.407828 0.913059i $$-0.366286\pi$$
0.407828 + 0.913059i $$0.366286\pi$$
$$12$$ 0 0
$$13$$ 719.328 1.18051 0.590254 0.807218i $$-0.299028\pi$$
0.590254 + 0.807218i $$0.299028\pi$$
$$14$$ 0 0
$$15$$ 318.330 0.365300
$$16$$ 0 0
$$17$$ −379.328 −0.318341 −0.159171 0.987251i $$-0.550882\pi$$
−0.159171 + 0.987251i $$0.550882\pi$$
$$18$$ 0 0
$$19$$ 1029.33 0.654139 0.327069 0.945000i $$-0.393939\pi$$
0.327069 + 0.945000i $$0.393939\pi$$
$$20$$ 0 0
$$21$$ 875.194 0.433068
$$22$$ 0 0
$$23$$ 779.120 0.307104 0.153552 0.988141i $$-0.450929\pi$$
0.153552 + 0.988141i $$0.450929\pi$$
$$24$$ 0 0
$$25$$ 625.000 0.200000
$$26$$ 0 0
$$27$$ 4123.85 1.08866
$$28$$ 0 0
$$29$$ −1392.66 −0.307503 −0.153751 0.988110i $$-0.549135\pi$$
−0.153751 + 0.988110i $$0.549135\pi$$
$$30$$ 0 0
$$31$$ −2744.68 −0.512965 −0.256483 0.966549i $$-0.582564\pi$$
−0.256483 + 0.966549i $$0.582564\pi$$
$$32$$ 0 0
$$33$$ −4167.98 −0.666256
$$34$$ 0 0
$$35$$ 1718.33 0.237103
$$36$$ 0 0
$$37$$ −12640.6 −1.51797 −0.758985 0.651108i $$-0.774304\pi$$
−0.758985 + 0.651108i $$0.774304\pi$$
$$38$$ 0 0
$$39$$ −9159.35 −0.964280
$$40$$ 0 0
$$41$$ 8210.43 0.762792 0.381396 0.924412i $$-0.375443\pi$$
0.381396 + 0.924412i $$0.375443\pi$$
$$42$$ 0 0
$$43$$ 22524.5 1.85774 0.928869 0.370408i $$-0.120782\pi$$
0.928869 + 0.370408i $$0.120782\pi$$
$$44$$ 0 0
$$45$$ 2021.64 0.148824
$$46$$ 0 0
$$47$$ −7739.18 −0.511035 −0.255517 0.966804i $$-0.582246\pi$$
−0.255517 + 0.966804i $$0.582246\pi$$
$$48$$ 0 0
$$49$$ −12082.7 −0.718912
$$50$$ 0 0
$$51$$ 4830.06 0.260032
$$52$$ 0 0
$$53$$ 2401.86 0.117451 0.0587256 0.998274i $$-0.481296\pi$$
0.0587256 + 0.998274i $$0.481296\pi$$
$$54$$ 0 0
$$55$$ −8183.30 −0.364772
$$56$$ 0 0
$$57$$ −13106.6 −0.534323
$$58$$ 0 0
$$59$$ 15734.7 0.588474 0.294237 0.955732i $$-0.404934\pi$$
0.294237 + 0.955732i $$0.404934\pi$$
$$60$$ 0 0
$$61$$ −32082.1 −1.10392 −0.551961 0.833870i $$-0.686120\pi$$
−0.551961 + 0.833870i $$0.686120\pi$$
$$62$$ 0 0
$$63$$ 5558.15 0.176433
$$64$$ 0 0
$$65$$ −17983.2 −0.527939
$$66$$ 0 0
$$67$$ 9009.07 0.245184 0.122592 0.992457i $$-0.460879\pi$$
0.122592 + 0.992457i $$0.460879\pi$$
$$68$$ 0 0
$$69$$ −9920.70 −0.250853
$$70$$ 0 0
$$71$$ −43832.3 −1.03192 −0.515962 0.856611i $$-0.672566\pi$$
−0.515962 + 0.856611i $$0.672566\pi$$
$$72$$ 0 0
$$73$$ −65837.5 −1.44599 −0.722997 0.690852i $$-0.757236\pi$$
−0.722997 + 0.690852i $$0.757236\pi$$
$$74$$ 0 0
$$75$$ −7958.25 −0.163367
$$76$$ 0 0
$$77$$ −22498.6 −0.432442
$$78$$ 0 0
$$79$$ −39601.3 −0.713907 −0.356954 0.934122i $$-0.616185\pi$$
−0.356954 + 0.934122i $$0.616185\pi$$
$$80$$ 0 0
$$81$$ −32859.4 −0.556477
$$82$$ 0 0
$$83$$ −63101.4 −1.00541 −0.502706 0.864458i $$-0.667662\pi$$
−0.502706 + 0.864458i $$0.667662\pi$$
$$84$$ 0 0
$$85$$ 9483.20 0.142366
$$86$$ 0 0
$$87$$ 17733.0 0.251179
$$88$$ 0 0
$$89$$ 34510.9 0.461829 0.230915 0.972974i $$-0.425828\pi$$
0.230915 + 0.972974i $$0.425828\pi$$
$$90$$ 0 0
$$91$$ −49441.7 −0.625879
$$92$$ 0 0
$$93$$ 34948.6 0.419008
$$94$$ 0 0
$$95$$ −25733.2 −0.292540
$$96$$ 0 0
$$97$$ −14081.3 −0.151955 −0.0759773 0.997110i $$-0.524208\pi$$
−0.0759773 + 0.997110i $$0.524208\pi$$
$$98$$ 0 0
$$99$$ −26469.9 −0.271434
$$100$$ 0 0
$$101$$ −184018. −1.79497 −0.897485 0.441044i $$-0.854608\pi$$
−0.897485 + 0.441044i $$0.854608\pi$$
$$102$$ 0 0
$$103$$ 70168.0 0.651697 0.325849 0.945422i $$-0.394350\pi$$
0.325849 + 0.945422i $$0.394350\pi$$
$$104$$ 0 0
$$105$$ −21879.8 −0.193674
$$106$$ 0 0
$$107$$ 7952.89 0.0671530 0.0335765 0.999436i $$-0.489310\pi$$
0.0335765 + 0.999436i $$0.489310\pi$$
$$108$$ 0 0
$$109$$ −168681. −1.35988 −0.679939 0.733269i $$-0.737994\pi$$
−0.679939 + 0.733269i $$0.737994\pi$$
$$110$$ 0 0
$$111$$ 160955. 1.23993
$$112$$ 0 0
$$113$$ −61891.3 −0.455967 −0.227984 0.973665i $$-0.573213\pi$$
−0.227984 + 0.973665i $$0.573213\pi$$
$$114$$ 0 0
$$115$$ −19478.0 −0.137341
$$116$$ 0 0
$$117$$ −58168.9 −0.392849
$$118$$ 0 0
$$119$$ 26072.4 0.168777
$$120$$ 0 0
$$121$$ −53904.8 −0.334706
$$122$$ 0 0
$$123$$ −104545. −0.623075
$$124$$ 0 0
$$125$$ −15625.0 −0.0894427
$$126$$ 0 0
$$127$$ 358695. 1.97340 0.986702 0.162538i $$-0.0519681\pi$$
0.986702 + 0.162538i $$0.0519681\pi$$
$$128$$ 0 0
$$129$$ −286809. −1.51747
$$130$$ 0 0
$$131$$ −312592. −1.59148 −0.795738 0.605641i $$-0.792917\pi$$
−0.795738 + 0.605641i $$0.792917\pi$$
$$132$$ 0 0
$$133$$ −70749.0 −0.346810
$$134$$ 0 0
$$135$$ −103096. −0.486864
$$136$$ 0 0
$$137$$ −33573.9 −0.152827 −0.0764135 0.997076i $$-0.524347\pi$$
−0.0764135 + 0.997076i $$0.524347\pi$$
$$138$$ 0 0
$$139$$ 342175. 1.50214 0.751072 0.660220i $$-0.229537\pi$$
0.751072 + 0.660220i $$0.229537\pi$$
$$140$$ 0 0
$$141$$ 98544.6 0.417431
$$142$$ 0 0
$$143$$ 235459. 0.962887
$$144$$ 0 0
$$145$$ 34816.4 0.137519
$$146$$ 0 0
$$147$$ 153852. 0.587232
$$148$$ 0 0
$$149$$ 239318. 0.883099 0.441549 0.897237i $$-0.354429\pi$$
0.441549 + 0.897237i $$0.354429\pi$$
$$150$$ 0 0
$$151$$ −169513. −0.605007 −0.302503 0.953148i $$-0.597822\pi$$
−0.302503 + 0.953148i $$0.597822\pi$$
$$152$$ 0 0
$$153$$ 30674.6 0.105938
$$154$$ 0 0
$$155$$ 68617.1 0.229405
$$156$$ 0 0
$$157$$ −186382. −0.603469 −0.301735 0.953392i $$-0.597566\pi$$
−0.301735 + 0.953392i $$0.597566\pi$$
$$158$$ 0 0
$$159$$ −30583.3 −0.0959383
$$160$$ 0 0
$$161$$ −53551.4 −0.162820
$$162$$ 0 0
$$163$$ −403058. −1.18822 −0.594112 0.804382i $$-0.702496\pi$$
−0.594112 + 0.804382i $$0.702496\pi$$
$$164$$ 0 0
$$165$$ 104200. 0.297959
$$166$$ 0 0
$$167$$ −167631. −0.465119 −0.232560 0.972582i $$-0.574710\pi$$
−0.232560 + 0.972582i $$0.574710\pi$$
$$168$$ 0 0
$$169$$ 146140. 0.393597
$$170$$ 0 0
$$171$$ −83237.2 −0.217684
$$172$$ 0 0
$$173$$ −84080.4 −0.213589 −0.106795 0.994281i $$-0.534059\pi$$
−0.106795 + 0.994281i $$0.534059\pi$$
$$174$$ 0 0
$$175$$ −42958.3 −0.106036
$$176$$ 0 0
$$177$$ −200353. −0.480686
$$178$$ 0 0
$$179$$ 741698. 1.73019 0.865096 0.501607i $$-0.167257\pi$$
0.865096 + 0.501607i $$0.167257\pi$$
$$180$$ 0 0
$$181$$ 343670. 0.779732 0.389866 0.920872i $$-0.372521\pi$$
0.389866 + 0.920872i $$0.372521\pi$$
$$182$$ 0 0
$$183$$ 408508. 0.901722
$$184$$ 0 0
$$185$$ 316015. 0.678857
$$186$$ 0 0
$$187$$ −124166. −0.259657
$$188$$ 0 0
$$189$$ −283445. −0.577184
$$190$$ 0 0
$$191$$ −631035. −1.25161 −0.625806 0.779978i $$-0.715230\pi$$
−0.625806 + 0.779978i $$0.715230\pi$$
$$192$$ 0 0
$$193$$ 847791. 1.63831 0.819154 0.573574i $$-0.194444\pi$$
0.819154 + 0.573574i $$0.194444\pi$$
$$194$$ 0 0
$$195$$ 228984. 0.431239
$$196$$ 0 0
$$197$$ 397282. 0.729346 0.364673 0.931136i $$-0.381181\pi$$
0.364673 + 0.931136i $$0.381181\pi$$
$$198$$ 0 0
$$199$$ −896038. −1.60396 −0.801980 0.597350i $$-0.796220\pi$$
−0.801980 + 0.597350i $$0.796220\pi$$
$$200$$ 0 0
$$201$$ −114714. −0.200275
$$202$$ 0 0
$$203$$ 95721.7 0.163031
$$204$$ 0 0
$$205$$ −205261. −0.341131
$$206$$ 0 0
$$207$$ −63004.0 −0.102198
$$208$$ 0 0
$$209$$ 336932. 0.533552
$$210$$ 0 0
$$211$$ −876761. −1.35574 −0.677868 0.735184i $$-0.737096\pi$$
−0.677868 + 0.735184i $$0.737096\pi$$
$$212$$ 0 0
$$213$$ 558125. 0.842913
$$214$$ 0 0
$$215$$ −563113. −0.830806
$$216$$ 0 0
$$217$$ 188651. 0.271963
$$218$$ 0 0
$$219$$ 838322. 1.18114
$$220$$ 0 0
$$221$$ −272861. −0.375804
$$222$$ 0 0
$$223$$ −54891.1 −0.0739162 −0.0369581 0.999317i $$-0.511767\pi$$
−0.0369581 + 0.999317i $$0.511767\pi$$
$$224$$ 0 0
$$225$$ −50541.0 −0.0665561
$$226$$ 0 0
$$227$$ 803329. 1.03473 0.517367 0.855764i $$-0.326912\pi$$
0.517367 + 0.855764i $$0.326912\pi$$
$$228$$ 0 0
$$229$$ 589546. 0.742898 0.371449 0.928453i $$-0.378861\pi$$
0.371449 + 0.928453i $$0.378861\pi$$
$$230$$ 0 0
$$231$$ 286479. 0.353234
$$232$$ 0 0
$$233$$ 1.02048e6 1.23144 0.615720 0.787965i $$-0.288865\pi$$
0.615720 + 0.787965i $$0.288865\pi$$
$$234$$ 0 0
$$235$$ 193480. 0.228542
$$236$$ 0 0
$$237$$ 504251. 0.583145
$$238$$ 0 0
$$239$$ −1.65512e6 −1.87428 −0.937139 0.348956i $$-0.886536\pi$$
−0.937139 + 0.348956i $$0.886536\pi$$
$$240$$ 0 0
$$241$$ −1.19028e6 −1.32010 −0.660049 0.751223i $$-0.729464\pi$$
−0.660049 + 0.751223i $$0.729464\pi$$
$$242$$ 0 0
$$243$$ −583689. −0.634112
$$244$$ 0 0
$$245$$ 302069. 0.321507
$$246$$ 0 0
$$247$$ 740424. 0.772215
$$248$$ 0 0
$$249$$ 803483. 0.821256
$$250$$ 0 0
$$251$$ −23776.0 −0.0238207 −0.0119104 0.999929i $$-0.503791\pi$$
−0.0119104 + 0.999929i $$0.503791\pi$$
$$252$$ 0 0
$$253$$ 255031. 0.250491
$$254$$ 0 0
$$255$$ −120751. −0.116290
$$256$$ 0 0
$$257$$ −341681. −0.322692 −0.161346 0.986898i $$-0.551584\pi$$
−0.161346 + 0.986898i $$0.551584\pi$$
$$258$$ 0 0
$$259$$ 868828. 0.804794
$$260$$ 0 0
$$261$$ 112618. 0.102331
$$262$$ 0 0
$$263$$ 1.09120e6 0.972782 0.486391 0.873741i $$-0.338313\pi$$
0.486391 + 0.873741i $$0.338313\pi$$
$$264$$ 0 0
$$265$$ −60046.4 −0.0525258
$$266$$ 0 0
$$267$$ −439434. −0.377238
$$268$$ 0 0
$$269$$ 922907. 0.777638 0.388819 0.921314i $$-0.372883\pi$$
0.388819 + 0.921314i $$0.372883\pi$$
$$270$$ 0 0
$$271$$ 1.34302e6 1.11086 0.555430 0.831564i $$-0.312554\pi$$
0.555430 + 0.831564i $$0.312554\pi$$
$$272$$ 0 0
$$273$$ 629551. 0.511240
$$274$$ 0 0
$$275$$ 204583. 0.163131
$$276$$ 0 0
$$277$$ 247543. 0.193843 0.0969217 0.995292i $$-0.469100\pi$$
0.0969217 + 0.995292i $$0.469100\pi$$
$$278$$ 0 0
$$279$$ 221951. 0.170705
$$280$$ 0 0
$$281$$ 1.03588e6 0.782604 0.391302 0.920262i $$-0.372025\pi$$
0.391302 + 0.920262i $$0.372025\pi$$
$$282$$ 0 0
$$283$$ −2.39427e6 −1.77708 −0.888542 0.458795i $$-0.848281\pi$$
−0.888542 + 0.458795i $$0.848281\pi$$
$$284$$ 0 0
$$285$$ 327666. 0.238957
$$286$$ 0 0
$$287$$ −564329. −0.404415
$$288$$ 0 0
$$289$$ −1.27597e6 −0.898659
$$290$$ 0 0
$$291$$ 179300. 0.124122
$$292$$ 0 0
$$293$$ 2.44817e6 1.66599 0.832995 0.553280i $$-0.186624\pi$$
0.832995 + 0.553280i $$0.186624\pi$$
$$294$$ 0 0
$$295$$ −393367. −0.263174
$$296$$ 0 0
$$297$$ 1.34987e6 0.887973
$$298$$ 0 0
$$299$$ 560443. 0.362538
$$300$$ 0 0
$$301$$ −1.54818e6 −0.984931
$$302$$ 0 0
$$303$$ 2.34314e6 1.46620
$$304$$ 0 0
$$305$$ 802053. 0.493689
$$306$$ 0 0
$$307$$ −939476. −0.568905 −0.284453 0.958690i $$-0.591812\pi$$
−0.284453 + 0.958690i $$0.591812\pi$$
$$308$$ 0 0
$$309$$ −893463. −0.532329
$$310$$ 0 0
$$311$$ 1.13941e6 0.668004 0.334002 0.942572i $$-0.391601\pi$$
0.334002 + 0.942572i $$0.391601\pi$$
$$312$$ 0 0
$$313$$ 1.51692e6 0.875191 0.437595 0.899172i $$-0.355830\pi$$
0.437595 + 0.899172i $$0.355830\pi$$
$$314$$ 0 0
$$315$$ −138954. −0.0789031
$$316$$ 0 0
$$317$$ −2.73484e6 −1.52857 −0.764284 0.644880i $$-0.776907\pi$$
−0.764284 + 0.644880i $$0.776907\pi$$
$$318$$ 0 0
$$319$$ −455861. −0.250816
$$320$$ 0 0
$$321$$ −101266. −0.0548530
$$322$$ 0 0
$$323$$ −390453. −0.208239
$$324$$ 0 0
$$325$$ 449580. 0.236101
$$326$$ 0 0
$$327$$ 2.14785e6 1.11080
$$328$$ 0 0
$$329$$ 531939. 0.270939
$$330$$ 0 0
$$331$$ 122807. 0.0616104 0.0308052 0.999525i $$-0.490193\pi$$
0.0308052 + 0.999525i $$0.490193\pi$$
$$332$$ 0 0
$$333$$ 1.02219e6 0.505150
$$334$$ 0 0
$$335$$ −225227. −0.109650
$$336$$ 0 0
$$337$$ −1.65582e6 −0.794217 −0.397108 0.917772i $$-0.629986\pi$$
−0.397108 + 0.917772i $$0.629986\pi$$
$$338$$ 0 0
$$339$$ 788075. 0.372450
$$340$$ 0 0
$$341$$ −898423. −0.418403
$$342$$ 0 0
$$343$$ 1.98568e6 0.911329
$$344$$ 0 0
$$345$$ 248017. 0.112185
$$346$$ 0 0
$$347$$ −1.63896e6 −0.730711 −0.365355 0.930868i $$-0.619052\pi$$
−0.365355 + 0.930868i $$0.619052\pi$$
$$348$$ 0 0
$$349$$ −2.07756e6 −0.913040 −0.456520 0.889713i $$-0.650904\pi$$
−0.456520 + 0.889713i $$0.650904\pi$$
$$350$$ 0 0
$$351$$ 2.96640e6 1.28517
$$352$$ 0 0
$$353$$ −3.87344e6 −1.65447 −0.827236 0.561854i $$-0.810088\pi$$
−0.827236 + 0.561854i $$0.810088\pi$$
$$354$$ 0 0
$$355$$ 1.09581e6 0.461491
$$356$$ 0 0
$$357$$ −331985. −0.137863
$$358$$ 0 0
$$359$$ −3.16016e6 −1.29411 −0.647057 0.762441i $$-0.724001\pi$$
−0.647057 + 0.762441i $$0.724001\pi$$
$$360$$ 0 0
$$361$$ −1.41658e6 −0.572103
$$362$$ 0 0
$$363$$ 686380. 0.273400
$$364$$ 0 0
$$365$$ 1.64594e6 0.646668
$$366$$ 0 0
$$367$$ −1.76875e6 −0.685491 −0.342745 0.939428i $$-0.611357\pi$$
−0.342745 + 0.939428i $$0.611357\pi$$
$$368$$ 0 0
$$369$$ −663941. −0.253842
$$370$$ 0 0
$$371$$ −165087. −0.0622700
$$372$$ 0 0
$$373$$ 3.86744e6 1.43930 0.719651 0.694336i $$-0.244302\pi$$
0.719651 + 0.694336i $$0.244302\pi$$
$$374$$ 0 0
$$375$$ 198956. 0.0730600
$$376$$ 0 0
$$377$$ −1.00178e6 −0.363009
$$378$$ 0 0
$$379$$ −5.06193e6 −1.81016 −0.905082 0.425236i $$-0.860191\pi$$
−0.905082 + 0.425236i $$0.860191\pi$$
$$380$$ 0 0
$$381$$ −4.56734e6 −1.61195
$$382$$ 0 0
$$383$$ −4.23524e6 −1.47530 −0.737652 0.675181i $$-0.764065\pi$$
−0.737652 + 0.675181i $$0.764065\pi$$
$$384$$ 0 0
$$385$$ 562464. 0.193394
$$386$$ 0 0
$$387$$ −1.82146e6 −0.618219
$$388$$ 0 0
$$389$$ 390940. 0.130989 0.0654947 0.997853i $$-0.479137\pi$$
0.0654947 + 0.997853i $$0.479137\pi$$
$$390$$ 0 0
$$391$$ −295542. −0.0977637
$$392$$ 0 0
$$393$$ 3.98030e6 1.29997
$$394$$ 0 0
$$395$$ 990033. 0.319269
$$396$$ 0 0
$$397$$ −3.36908e6 −1.07284 −0.536421 0.843951i $$-0.680224\pi$$
−0.536421 + 0.843951i $$0.680224\pi$$
$$398$$ 0 0
$$399$$ 900861. 0.283286
$$400$$ 0 0
$$401$$ −5.51542e6 −1.71284 −0.856422 0.516277i $$-0.827318\pi$$
−0.856422 + 0.516277i $$0.827318\pi$$
$$402$$ 0 0
$$403$$ −1.97433e6 −0.605559
$$404$$ 0 0
$$405$$ 821485. 0.248864
$$406$$ 0 0
$$407$$ −4.13767e6 −1.23814
$$408$$ 0 0
$$409$$ −3.29662e6 −0.974453 −0.487227 0.873276i $$-0.661991\pi$$
−0.487227 + 0.873276i $$0.661991\pi$$
$$410$$ 0 0
$$411$$ 427503. 0.124834
$$412$$ 0 0
$$413$$ −1.08149e6 −0.311996
$$414$$ 0 0
$$415$$ 1.57754e6 0.449634
$$416$$ 0 0
$$417$$ −4.35699e6 −1.22700
$$418$$ 0 0
$$419$$ 6.88088e6 1.91474 0.957368 0.288870i $$-0.0932795\pi$$
0.957368 + 0.288870i $$0.0932795\pi$$
$$420$$ 0 0
$$421$$ −3.04971e6 −0.838596 −0.419298 0.907849i $$-0.637724\pi$$
−0.419298 + 0.907849i $$0.637724\pi$$
$$422$$ 0 0
$$423$$ 625834. 0.170062
$$424$$ 0 0
$$425$$ −237080. −0.0636682
$$426$$ 0 0
$$427$$ 2.20511e6 0.585275
$$428$$ 0 0
$$429$$ −2.99815e6 −0.786520
$$430$$ 0 0
$$431$$ −6.20632e6 −1.60931 −0.804657 0.593740i $$-0.797651\pi$$
−0.804657 + 0.593740i $$0.797651\pi$$
$$432$$ 0 0
$$433$$ 1.87723e6 0.481169 0.240585 0.970628i $$-0.422661\pi$$
0.240585 + 0.970628i $$0.422661\pi$$
$$434$$ 0 0
$$435$$ −443324. −0.112331
$$436$$ 0 0
$$437$$ 801971. 0.200888
$$438$$ 0 0
$$439$$ −1.85883e6 −0.460341 −0.230170 0.973150i $$-0.573928\pi$$
−0.230170 + 0.973150i $$0.573928\pi$$
$$440$$ 0 0
$$441$$ 977079. 0.239240
$$442$$ 0 0
$$443$$ 4.39604e6 1.06427 0.532136 0.846659i $$-0.321390\pi$$
0.532136 + 0.846659i $$0.321390\pi$$
$$444$$ 0 0
$$445$$ −862772. −0.206536
$$446$$ 0 0
$$447$$ −3.04728e6 −0.721346
$$448$$ 0 0
$$449$$ −984885. −0.230552 −0.115276 0.993333i $$-0.536775\pi$$
−0.115276 + 0.993333i $$0.536775\pi$$
$$450$$ 0 0
$$451$$ 2.68754e6 0.622175
$$452$$ 0 0
$$453$$ 2.15844e6 0.494191
$$454$$ 0 0
$$455$$ 1.23604e6 0.279901
$$456$$ 0 0
$$457$$ −696014. −0.155893 −0.0779466 0.996958i $$-0.524836\pi$$
−0.0779466 + 0.996958i $$0.524836\pi$$
$$458$$ 0 0
$$459$$ −1.56429e6 −0.346566
$$460$$ 0 0
$$461$$ −6.03623e6 −1.32286 −0.661430 0.750007i $$-0.730050\pi$$
−0.661430 + 0.750007i $$0.730050\pi$$
$$462$$ 0 0
$$463$$ −2.07793e6 −0.450483 −0.225241 0.974303i $$-0.572317\pi$$
−0.225241 + 0.974303i $$0.572317\pi$$
$$464$$ 0 0
$$465$$ −873715. −0.187386
$$466$$ 0 0
$$467$$ 1.81361e6 0.384816 0.192408 0.981315i $$-0.438370\pi$$
0.192408 + 0.981315i $$0.438370\pi$$
$$468$$ 0 0
$$469$$ −619222. −0.129991
$$470$$ 0 0
$$471$$ 2.37324e6 0.492935
$$472$$ 0 0
$$473$$ 7.37300e6 1.51527
$$474$$ 0 0
$$475$$ 643330. 0.130828
$$476$$ 0 0
$$477$$ −194228. −0.0390854
$$478$$ 0 0
$$479$$ 6.10687e6 1.21613 0.608065 0.793887i $$-0.291946\pi$$
0.608065 + 0.793887i $$0.291946\pi$$
$$480$$ 0 0
$$481$$ −9.09273e6 −1.79197
$$482$$ 0 0
$$483$$ 681881. 0.132997
$$484$$ 0 0
$$485$$ 352033. 0.0679561
$$486$$ 0 0
$$487$$ 1.32848e6 0.253823 0.126912 0.991914i $$-0.459494\pi$$
0.126912 + 0.991914i $$0.459494\pi$$
$$488$$ 0 0
$$489$$ 5.13222e6 0.970583
$$490$$ 0 0
$$491$$ 8.72480e6 1.63325 0.816623 0.577171i $$-0.195843\pi$$
0.816623 + 0.577171i $$0.195843\pi$$
$$492$$ 0 0
$$493$$ 528273. 0.0978907
$$494$$ 0 0
$$495$$ 661748. 0.121389
$$496$$ 0 0
$$497$$ 3.01273e6 0.547104
$$498$$ 0 0
$$499$$ −5.20143e6 −0.935129 −0.467564 0.883959i $$-0.654868\pi$$
−0.467564 + 0.883959i $$0.654868\pi$$
$$500$$ 0 0
$$501$$ 2.13448e6 0.379926
$$502$$ 0 0
$$503$$ −6.44189e6 −1.13525 −0.567627 0.823286i $$-0.692139\pi$$
−0.567627 + 0.823286i $$0.692139\pi$$
$$504$$ 0 0
$$505$$ 4.60045e6 0.802735
$$506$$ 0 0
$$507$$ −1.86083e6 −0.321504
$$508$$ 0 0
$$509$$ 2.31511e6 0.396075 0.198038 0.980194i $$-0.436543\pi$$
0.198038 + 0.980194i $$0.436543\pi$$
$$510$$ 0 0
$$511$$ 4.52522e6 0.766633
$$512$$ 0 0
$$513$$ 4.24479e6 0.712136
$$514$$ 0 0
$$515$$ −1.75420e6 −0.291448
$$516$$ 0 0
$$517$$ −2.53328e6 −0.416828
$$518$$ 0 0
$$519$$ 1.07061e6 0.174467
$$520$$ 0 0
$$521$$ −9.65617e6 −1.55851 −0.779257 0.626705i $$-0.784403\pi$$
−0.779257 + 0.626705i $$0.784403\pi$$
$$522$$ 0 0
$$523$$ 6.40583e6 1.02405 0.512025 0.858970i $$-0.328895\pi$$
0.512025 + 0.858970i $$0.328895\pi$$
$$524$$ 0 0
$$525$$ 546996. 0.0866136
$$526$$ 0 0
$$527$$ 1.04114e6 0.163298
$$528$$ 0 0
$$529$$ −5.82931e6 −0.905687
$$530$$ 0 0
$$531$$ −1.27239e6 −0.195833
$$532$$ 0 0
$$533$$ 5.90599e6 0.900481
$$534$$ 0 0
$$535$$ −198822. −0.0300317
$$536$$ 0 0
$$537$$ −9.44418e6 −1.41328
$$538$$ 0 0
$$539$$ −3.95507e6 −0.586384
$$540$$ 0 0
$$541$$ −1.32300e6 −0.194342 −0.0971709 0.995268i $$-0.530979\pi$$
−0.0971709 + 0.995268i $$0.530979\pi$$
$$542$$ 0 0
$$543$$ −4.37602e6 −0.636912
$$544$$ 0 0
$$545$$ 4.21702e6 0.608156
$$546$$ 0 0
$$547$$ −4.68044e6 −0.668834 −0.334417 0.942425i $$-0.608539\pi$$
−0.334417 + 0.942425i $$0.608539\pi$$
$$548$$ 0 0
$$549$$ 2.59434e6 0.367363
$$550$$ 0 0
$$551$$ −1.43350e6 −0.201149
$$552$$ 0 0
$$553$$ 2.72192e6 0.378498
$$554$$ 0 0
$$555$$ −4.02388e6 −0.554514
$$556$$ 0 0
$$557$$ −7.58860e6 −1.03639 −0.518195 0.855262i $$-0.673396\pi$$
−0.518195 + 0.855262i $$0.673396\pi$$
$$558$$ 0 0
$$559$$ 1.62025e7 2.19307
$$560$$ 0 0
$$561$$ 1.58103e6 0.212097
$$562$$ 0 0
$$563$$ 399946. 0.0531777 0.0265889 0.999646i $$-0.491536\pi$$
0.0265889 + 0.999646i $$0.491536\pi$$
$$564$$ 0 0
$$565$$ 1.54728e6 0.203915
$$566$$ 0 0
$$567$$ 2.25853e6 0.295032
$$568$$ 0 0
$$569$$ 1.57419e6 0.203834 0.101917 0.994793i $$-0.467502\pi$$
0.101917 + 0.994793i $$0.467502\pi$$
$$570$$ 0 0
$$571$$ −3.11290e6 −0.399554 −0.199777 0.979841i $$-0.564022\pi$$
−0.199777 + 0.979841i $$0.564022\pi$$
$$572$$ 0 0
$$573$$ 8.03509e6 1.02236
$$574$$ 0 0
$$575$$ 486950. 0.0614207
$$576$$ 0 0
$$577$$ −5.57621e6 −0.697267 −0.348634 0.937259i $$-0.613354\pi$$
−0.348634 + 0.937259i $$0.613354\pi$$
$$578$$ 0 0
$$579$$ −1.07951e7 −1.33823
$$580$$ 0 0
$$581$$ 4.33716e6 0.533047
$$582$$ 0 0
$$583$$ 786205. 0.0957997
$$584$$ 0 0
$$585$$ 1.45422e6 0.175688
$$586$$ 0 0
$$587$$ 1.11890e7 1.34028 0.670138 0.742236i $$-0.266235\pi$$
0.670138 + 0.742236i $$0.266235\pi$$
$$588$$ 0 0
$$589$$ −2.82518e6 −0.335551
$$590$$ 0 0
$$591$$ −5.05868e6 −0.595756
$$592$$ 0 0
$$593$$ 1.44707e7 1.68987 0.844934 0.534871i $$-0.179640\pi$$
0.844934 + 0.534871i $$0.179640\pi$$
$$594$$ 0 0
$$595$$ −651811. −0.0754795
$$596$$ 0 0
$$597$$ 1.14094e7 1.31017
$$598$$ 0 0
$$599$$ 2.32734e6 0.265028 0.132514 0.991181i $$-0.457695\pi$$
0.132514 + 0.991181i $$0.457695\pi$$
$$600$$ 0 0
$$601$$ 4.28568e6 0.483987 0.241993 0.970278i $$-0.422199\pi$$
0.241993 + 0.970278i $$0.422199\pi$$
$$602$$ 0 0
$$603$$ −728524. −0.0815925
$$604$$ 0 0
$$605$$ 1.34762e6 0.149685
$$606$$ 0 0
$$607$$ 1.04310e7 1.14909 0.574547 0.818471i $$-0.305178\pi$$
0.574547 + 0.818471i $$0.305178\pi$$
$$608$$ 0 0
$$609$$ −1.21884e6 −0.133170
$$610$$ 0 0
$$611$$ −5.56701e6 −0.603280
$$612$$ 0 0
$$613$$ −3.52495e6 −0.378880 −0.189440 0.981892i $$-0.560667\pi$$
−0.189440 + 0.981892i $$0.560667\pi$$
$$614$$ 0 0
$$615$$ 2.61363e6 0.278648
$$616$$ 0 0
$$617$$ 1.16178e7 1.22861 0.614303 0.789070i $$-0.289437\pi$$
0.614303 + 0.789070i $$0.289437\pi$$
$$618$$ 0 0
$$619$$ −1.04132e7 −1.09234 −0.546171 0.837673i $$-0.683915\pi$$
−0.546171 + 0.837673i $$0.683915\pi$$
$$620$$ 0 0
$$621$$ 3.21297e6 0.334332
$$622$$ 0 0
$$623$$ −2.37204e6 −0.244851
$$624$$ 0 0
$$625$$ 390625. 0.0400000
$$626$$ 0 0
$$627$$ −4.29022e6 −0.435824
$$628$$ 0 0
$$629$$ 4.79493e6 0.483232
$$630$$ 0 0
$$631$$ −6.57325e6 −0.657214 −0.328607 0.944467i $$-0.606579\pi$$
−0.328607 + 0.944467i $$0.606579\pi$$
$$632$$ 0 0
$$633$$ 1.11640e7 1.10741
$$634$$ 0 0
$$635$$ −8.96738e6 −0.882533
$$636$$ 0 0
$$637$$ −8.69146e6 −0.848680
$$638$$ 0 0
$$639$$ 3.54452e6 0.343404
$$640$$ 0 0
$$641$$ 7.21768e6 0.693829 0.346914 0.937897i $$-0.387229\pi$$
0.346914 + 0.937897i $$0.387229\pi$$
$$642$$ 0 0
$$643$$ −989729. −0.0944036 −0.0472018 0.998885i $$-0.515030\pi$$
−0.0472018 + 0.998885i $$0.515030\pi$$
$$644$$ 0 0
$$645$$ 7.17023e6 0.678631
$$646$$ 0 0
$$647$$ −4.31383e6 −0.405138 −0.202569 0.979268i $$-0.564929\pi$$
−0.202569 + 0.979268i $$0.564929\pi$$
$$648$$ 0 0
$$649$$ 5.15046e6 0.479992
$$650$$ 0 0
$$651$$ −2.40213e6 −0.222149
$$652$$ 0 0
$$653$$ 1.49637e7 1.37327 0.686633 0.727004i $$-0.259088\pi$$
0.686633 + 0.727004i $$0.259088\pi$$
$$654$$ 0 0
$$655$$ 7.81481e6 0.711730
$$656$$ 0 0
$$657$$ 5.32399e6 0.481198
$$658$$ 0 0
$$659$$ −4.42210e6 −0.396657 −0.198328 0.980136i $$-0.563551\pi$$
−0.198328 + 0.980136i $$0.563551\pi$$
$$660$$ 0 0
$$661$$ −1.57925e7 −1.40587 −0.702937 0.711252i $$-0.748128\pi$$
−0.702937 + 0.711252i $$0.748128\pi$$
$$662$$ 0 0
$$663$$ 3.47440e6 0.306970
$$664$$ 0 0
$$665$$ 1.76873e6 0.155098
$$666$$ 0 0
$$667$$ −1.08505e6 −0.0944352
$$668$$ 0 0
$$669$$ 698939. 0.0603773
$$670$$ 0 0
$$671$$ −1.05015e7 −0.900420
$$672$$ 0 0
$$673$$ −5.60799e6 −0.477276 −0.238638 0.971109i $$-0.576701\pi$$
−0.238638 + 0.971109i $$0.576701\pi$$
$$674$$ 0 0
$$675$$ 2.57740e6 0.217732
$$676$$ 0 0
$$677$$ 7.01232e6 0.588017 0.294009 0.955803i $$-0.405011\pi$$
0.294009 + 0.955803i $$0.405011\pi$$
$$678$$ 0 0
$$679$$ 967853. 0.0805629
$$680$$ 0 0
$$681$$ −1.02289e7 −0.845207
$$682$$ 0 0
$$683$$ 2.16662e7 1.77718 0.888590 0.458703i $$-0.151686\pi$$
0.888590 + 0.458703i $$0.151686\pi$$
$$684$$ 0 0
$$685$$ 839347. 0.0683463
$$686$$ 0 0
$$687$$ −7.50681e6 −0.606825
$$688$$ 0 0
$$689$$ 1.72772e6 0.138652
$$690$$ 0 0
$$691$$ 4.20276e6 0.334842 0.167421 0.985885i $$-0.446456\pi$$
0.167421 + 0.985885i $$0.446456\pi$$
$$692$$ 0 0
$$693$$ 1.81936e6 0.143908
$$694$$ 0 0
$$695$$ −8.55439e6 −0.671780
$$696$$ 0 0
$$697$$ −3.11444e6 −0.242828
$$698$$ 0 0
$$699$$ −1.29939e7 −1.00588
$$700$$ 0 0
$$701$$ 1.50989e6 0.116051 0.0580256 0.998315i $$-0.481519\pi$$
0.0580256 + 0.998315i $$0.481519\pi$$
$$702$$ 0 0
$$703$$ −1.30113e7 −0.992963
$$704$$ 0 0
$$705$$ −2.46361e6 −0.186681
$$706$$ 0 0
$$707$$ 1.26482e7 0.951653
$$708$$ 0 0
$$709$$ −2.08359e6 −0.155667 −0.0778336 0.996966i $$-0.524800\pi$$
−0.0778336 + 0.996966i $$0.524800\pi$$
$$710$$ 0 0
$$711$$ 3.20238e6 0.237574
$$712$$ 0 0
$$713$$ −2.13844e6 −0.157534
$$714$$ 0 0
$$715$$ −5.88648e6 −0.430616
$$716$$ 0 0
$$717$$ 2.10749e7 1.53098
$$718$$ 0 0
$$719$$ 1.03357e7 0.745618 0.372809 0.927908i $$-0.378395\pi$$
0.372809 + 0.927908i $$0.378395\pi$$
$$720$$ 0 0
$$721$$ −4.82287e6 −0.345515
$$722$$ 0 0
$$723$$ 1.51561e7 1.07830
$$724$$ 0 0
$$725$$ −870410. −0.0615005
$$726$$ 0 0
$$727$$ 3.39227e6 0.238042 0.119021 0.992892i $$-0.462024\pi$$
0.119021 + 0.992892i $$0.462024\pi$$
$$728$$ 0 0
$$729$$ 1.54171e7 1.07444
$$730$$ 0 0
$$731$$ −8.54418e6 −0.591394
$$732$$ 0 0
$$733$$ 1.99922e7 1.37436 0.687180 0.726487i $$-0.258848\pi$$
0.687180 + 0.726487i $$0.258848\pi$$
$$734$$ 0 0
$$735$$ −3.84630e6 −0.262618
$$736$$ 0 0
$$737$$ 2.94896e6 0.199986
$$738$$ 0 0
$$739$$ 2.37515e7 1.59986 0.799928 0.600096i $$-0.204871\pi$$
0.799928 + 0.600096i $$0.204871\pi$$
$$740$$ 0 0
$$741$$ −9.42797e6 −0.630773
$$742$$ 0 0
$$743$$ 768079. 0.0510427 0.0255214 0.999674i $$-0.491875\pi$$
0.0255214 + 0.999674i $$0.491875\pi$$
$$744$$ 0 0
$$745$$ −5.98294e6 −0.394934
$$746$$ 0 0
$$747$$ 5.10273e6 0.334581
$$748$$ 0 0
$$749$$ −546628. −0.0356030
$$750$$ 0 0
$$751$$ −2.34656e7 −1.51821 −0.759105 0.650968i $$-0.774363\pi$$
−0.759105 + 0.650968i $$0.774363\pi$$
$$752$$ 0 0
$$753$$ 302745. 0.0194576
$$754$$ 0 0
$$755$$ 4.23782e6 0.270567
$$756$$ 0 0
$$757$$ −2.58118e7 −1.63711 −0.818557 0.574425i $$-0.805226\pi$$
−0.818557 + 0.574425i $$0.805226\pi$$
$$758$$ 0 0
$$759$$ −3.24736e6 −0.204610
$$760$$ 0 0
$$761$$ 1.19501e7 0.748013 0.374006 0.927426i $$-0.377984\pi$$
0.374006 + 0.927426i $$0.377984\pi$$
$$762$$ 0 0
$$763$$ 1.15940e7 0.720977
$$764$$ 0 0
$$765$$ −766865. −0.0473767
$$766$$ 0 0
$$767$$ 1.13184e7 0.694698
$$768$$ 0 0
$$769$$ −1.61907e7 −0.987302 −0.493651 0.869660i $$-0.664338\pi$$
−0.493651 + 0.869660i $$0.664338\pi$$
$$770$$ 0 0
$$771$$ 4.35070e6 0.263586
$$772$$ 0 0
$$773$$ 1.40818e7 0.847637 0.423818 0.905747i $$-0.360689\pi$$
0.423818 + 0.905747i $$0.360689\pi$$
$$774$$ 0 0
$$775$$ −1.71543e6 −0.102593
$$776$$ 0 0
$$777$$ −1.10630e7 −0.657384
$$778$$ 0 0
$$779$$ 8.45122e6 0.498972
$$780$$ 0 0
$$781$$ −1.43477e7 −0.841695
$$782$$ 0 0
$$783$$ −5.74310e6 −0.334766
$$784$$ 0 0
$$785$$ 4.65955e6 0.269880
$$786$$ 0 0
$$787$$ 4.41819e6 0.254277 0.127139 0.991885i $$-0.459421\pi$$
0.127139 + 0.991885i $$0.459421\pi$$
$$788$$ 0 0
$$789$$ −1.38945e7 −0.794602
$$790$$ 0 0
$$791$$ 4.25399e6 0.241744
$$792$$ 0 0
$$793$$ −2.30776e7 −1.30319
$$794$$ 0 0
$$795$$ 764583. 0.0429049
$$796$$ 0 0
$$797$$ −6.04472e6 −0.337078 −0.168539 0.985695i $$-0.553905\pi$$
−0.168539 + 0.985695i $$0.553905\pi$$
$$798$$ 0 0
$$799$$ 2.93569e6 0.162683
$$800$$ 0 0
$$801$$ −2.79074e6 −0.153688
$$802$$ 0 0
$$803$$ −2.15507e7 −1.17943
$$804$$ 0 0
$$805$$ 1.33879e6 0.0728151
$$806$$ 0 0
$$807$$ −1.17516e7 −0.635202
$$808$$ 0 0
$$809$$ −1.71556e7 −0.921583 −0.460791 0.887509i $$-0.652434\pi$$
−0.460791 + 0.887509i $$0.652434\pi$$
$$810$$ 0 0
$$811$$ 1.83020e7 0.977114 0.488557 0.872532i $$-0.337523\pi$$
0.488557 + 0.872532i $$0.337523\pi$$
$$812$$ 0 0
$$813$$ −1.71009e7 −0.907389
$$814$$ 0 0
$$815$$ 1.00764e7 0.531390
$$816$$ 0 0
$$817$$ 2.31851e7 1.21522
$$818$$ 0 0
$$819$$ 3.99813e6 0.208280
$$820$$ 0 0
$$821$$ 77887.9 0.00403285 0.00201643 0.999998i $$-0.499358\pi$$
0.00201643 + 0.999998i $$0.499358\pi$$
$$822$$ 0 0
$$823$$ 423648. 0.0218025 0.0109012 0.999941i $$-0.496530\pi$$
0.0109012 + 0.999941i $$0.496530\pi$$
$$824$$ 0 0
$$825$$ −2.60499e6 −0.133251
$$826$$ 0 0
$$827$$ 5.18956e6 0.263856 0.131928 0.991259i $$-0.457883\pi$$
0.131928 + 0.991259i $$0.457883\pi$$
$$828$$ 0 0
$$829$$ 2.08613e7 1.05428 0.527139 0.849779i $$-0.323265\pi$$
0.527139 + 0.849779i $$0.323265\pi$$
$$830$$ 0 0
$$831$$ −3.15201e6 −0.158338
$$832$$ 0 0
$$833$$ 4.58332e6 0.228859
$$834$$ 0 0
$$835$$ 4.19079e6 0.208008
$$836$$ 0 0
$$837$$ −1.13187e7 −0.558446
$$838$$ 0 0
$$839$$ 8.18798e6 0.401580 0.200790 0.979634i $$-0.435649\pi$$
0.200790 + 0.979634i $$0.435649\pi$$
$$840$$ 0 0
$$841$$ −1.85717e7 −0.905442
$$842$$ 0 0
$$843$$ −1.31900e7 −0.639258
$$844$$ 0 0
$$845$$ −3.65350e6 −0.176022
$$846$$ 0 0
$$847$$ 3.70505e6 0.177454
$$848$$ 0 0
$$849$$ 3.04868e7 1.45158
$$850$$ 0 0
$$851$$ −9.84854e6 −0.466174
$$852$$ 0 0
$$853$$ −3.11924e7 −1.46783 −0.733915 0.679241i $$-0.762309\pi$$
−0.733915 + 0.679241i $$0.762309\pi$$
$$854$$ 0 0
$$855$$ 2.08093e6 0.0973514
$$856$$ 0 0
$$857$$ −1.88654e7 −0.877433 −0.438716 0.898626i $$-0.644567\pi$$
−0.438716 + 0.898626i $$0.644567\pi$$
$$858$$ 0 0
$$859$$ 1.30703e7 0.604369 0.302184 0.953249i $$-0.402284\pi$$
0.302184 + 0.953249i $$0.402284\pi$$
$$860$$ 0 0
$$861$$ 7.18571e6 0.330341
$$862$$ 0 0
$$863$$ −5.58115e6 −0.255092 −0.127546 0.991833i $$-0.540710\pi$$
−0.127546 + 0.991833i $$0.540710\pi$$
$$864$$ 0 0
$$865$$ 2.10201e6 0.0955201
$$866$$ 0 0
$$867$$ 1.62471e7 0.734056
$$868$$ 0 0
$$869$$ −1.29628e7 −0.582302
$$870$$ 0 0
$$871$$ 6.48047e6 0.289442
$$872$$ 0 0
$$873$$ 1.13869e6 0.0505675
$$874$$ 0 0
$$875$$ 1.07396e6 0.0474205
$$876$$ 0 0
$$877$$ −2.17437e7 −0.954629 −0.477315 0.878732i $$-0.658390\pi$$
−0.477315 + 0.878732i $$0.658390\pi$$
$$878$$ 0 0
$$879$$ −3.11730e7 −1.36084
$$880$$ 0 0
$$881$$ 2.26789e7 0.984425 0.492212 0.870475i $$-0.336188\pi$$
0.492212 + 0.870475i $$0.336188\pi$$
$$882$$ 0 0
$$883$$ −2.34145e7 −1.01061 −0.505304 0.862942i $$-0.668619\pi$$
−0.505304 + 0.862942i $$0.668619\pi$$
$$884$$ 0 0
$$885$$ 5.00882e6 0.214970
$$886$$ 0 0
$$887$$ 1.56731e7 0.668875 0.334437 0.942418i $$-0.391454\pi$$
0.334437 + 0.942418i $$0.391454\pi$$
$$888$$ 0 0
$$889$$ −2.46543e7 −1.04626
$$890$$ 0 0
$$891$$ −1.07559e7 −0.453894
$$892$$ 0 0
$$893$$ −7.96616e6 −0.334288
$$894$$ 0 0
$$895$$ −1.85424e7 −0.773765
$$896$$ 0 0
$$897$$ −7.13624e6 −0.296134
$$898$$ 0 0
$$899$$ 3.82240e6 0.157738
$$900$$ 0 0
$$901$$ −911092. −0.0373895
$$902$$ 0 0
$$903$$ 1.97133e7 0.804527
$$904$$ 0 0
$$905$$ −8.59175e6 −0.348707
$$906$$ 0 0
$$907$$ −3.67553e7 −1.48355 −0.741775 0.670649i $$-0.766016\pi$$
−0.741775 + 0.670649i $$0.766016\pi$$
$$908$$ 0 0
$$909$$ 1.48807e7 0.597331
$$910$$ 0 0
$$911$$ 2.11183e7 0.843067 0.421534 0.906813i $$-0.361492\pi$$
0.421534 + 0.906813i $$0.361492\pi$$
$$912$$ 0 0
$$913$$ −2.06551e7 −0.820070
$$914$$ 0 0
$$915$$ −1.02127e7 −0.403262
$$916$$ 0 0
$$917$$ 2.14855e7 0.843765
$$918$$ 0 0
$$919$$ −7.27922e6 −0.284312 −0.142156 0.989844i $$-0.545404\pi$$
−0.142156 + 0.989844i $$0.545404\pi$$
$$920$$ 0 0
$$921$$ 1.19625e7 0.464702
$$922$$ 0 0
$$923$$ −3.15298e7 −1.21819
$$924$$ 0 0
$$925$$ −7.90037e6 −0.303594
$$926$$ 0 0
$$927$$ −5.67418e6 −0.216872
$$928$$ 0 0
$$929$$ −3.41165e7 −1.29696 −0.648478 0.761234i $$-0.724594\pi$$
−0.648478 + 0.761234i $$0.724594\pi$$
$$930$$ 0 0
$$931$$ −1.24371e7 −0.470268
$$932$$ 0 0
$$933$$ −1.45083e7 −0.545649
$$934$$ 0 0
$$935$$ 3.10416e6 0.116122
$$936$$ 0 0
$$937$$ −4.73880e7 −1.76327 −0.881637 0.471929i $$-0.843558\pi$$
−0.881637 + 0.471929i $$0.843558\pi$$
$$938$$ 0 0
$$939$$ −1.93153e7 −0.714887
$$940$$ 0 0
$$941$$ 3.97476e7 1.46331 0.731656 0.681674i $$-0.238748\pi$$
0.731656 + 0.681674i $$0.238748\pi$$
$$942$$ 0 0
$$943$$ 6.39691e6 0.234256
$$944$$ 0 0
$$945$$ 7.08613e6 0.258125
$$946$$ 0 0
$$947$$ −2.76410e7 −1.00156 −0.500782 0.865573i $$-0.666954\pi$$
−0.500782 + 0.865573i $$0.666954\pi$$
$$948$$ 0 0
$$949$$ −4.73588e7 −1.70701
$$950$$ 0 0
$$951$$ 3.48233e7 1.24859
$$952$$ 0 0
$$953$$ −5.22977e6 −0.186531 −0.0932654 0.995641i $$-0.529731\pi$$
−0.0932654 + 0.995641i $$0.529731\pi$$
$$954$$ 0 0
$$955$$ 1.57759e7 0.559738
$$956$$ 0 0
$$957$$ 5.80457e6 0.204876
$$958$$ 0 0
$$959$$ 2.30764e6 0.0810255
$$960$$ 0 0
$$961$$ −2.10959e7 −0.736866
$$962$$ 0 0
$$963$$ −643115. −0.0223472
$$964$$ 0 0
$$965$$ −2.11948e7 −0.732673
$$966$$ 0 0
$$967$$ −1.76477e7 −0.606905 −0.303453 0.952847i $$-0.598139\pi$$
−0.303453 + 0.952847i $$0.598139\pi$$
$$968$$ 0 0
$$969$$ 4.97172e6 0.170097
$$970$$ 0 0
$$971$$ −3.66934e7 −1.24893 −0.624467 0.781051i $$-0.714684\pi$$
−0.624467 + 0.781051i $$0.714684\pi$$
$$972$$ 0 0
$$973$$ −2.35188e7 −0.796404
$$974$$ 0 0
$$975$$ −5.72459e6 −0.192856
$$976$$ 0 0
$$977$$ 3.16023e7 1.05921 0.529605 0.848244i $$-0.322340\pi$$
0.529605 + 0.848244i $$0.322340\pi$$
$$978$$ 0 0
$$979$$ 1.12965e7 0.376693
$$980$$ 0 0
$$981$$ 1.36405e7 0.452540
$$982$$ 0 0
$$983$$ 3.73829e7 1.23393 0.616963 0.786992i $$-0.288363\pi$$
0.616963 + 0.786992i $$0.288363\pi$$
$$984$$ 0 0
$$985$$ −9.93206e6 −0.326174
$$986$$ 0 0
$$987$$ −6.77328e6 −0.221313
$$988$$ 0 0
$$989$$ 1.75493e7 0.570518
$$990$$ 0 0
$$991$$ 2.84243e7 0.919401 0.459701 0.888074i $$-0.347957\pi$$
0.459701 + 0.888074i $$0.347957\pi$$
$$992$$ 0 0
$$993$$ −1.56373e6 −0.0503256
$$994$$ 0 0
$$995$$ 2.24010e7 0.717313
$$996$$ 0 0
$$997$$ 1.70600e7 0.543553 0.271776 0.962360i $$-0.412389\pi$$
0.271776 + 0.962360i $$0.412389\pi$$
$$998$$ 0 0
$$999$$ −5.21279e7 −1.65256
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 320.6.a.v.1.1 2
4.3 odd 2 320.6.a.r.1.2 2
8.3 odd 2 160.6.a.e.1.1 yes 2
8.5 even 2 160.6.a.a.1.2 2
40.3 even 4 800.6.c.g.449.2 4
40.13 odd 4 800.6.c.f.449.3 4
40.19 odd 2 800.6.a.g.1.2 2
40.27 even 4 800.6.c.g.449.3 4
40.29 even 2 800.6.a.l.1.1 2
40.37 odd 4 800.6.c.f.449.2 4

By twisted newform
Twist Min Dim Char Parity Ord Type
160.6.a.a.1.2 2 8.5 even 2
160.6.a.e.1.1 yes 2 8.3 odd 2
320.6.a.r.1.2 2 4.3 odd 2
320.6.a.v.1.1 2 1.1 even 1 trivial
800.6.a.g.1.2 2 40.19 odd 2
800.6.a.l.1.1 2 40.29 even 2
800.6.c.f.449.2 4 40.37 odd 4
800.6.c.f.449.3 4 40.13 odd 4
800.6.c.g.449.2 4 40.3 even 4
800.6.c.g.449.3 4 40.27 even 4