# Properties

 Label 320.6.a.s.1.1 Level 320 Weight 6 Character 320.1 Self dual yes Analytic conductor 51.323 Analytic rank 0 Dimension 2 CM no Inner twists 2

# 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: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(\sqrt{10})$$ Defining polynomial: $$x^{2} - 10$$ 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 $$-3.16228$$ of defining polynomial Character $$\chi$$ $$=$$ 320.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q-6.32456 q^{3} -25.0000 q^{5} +44.2719 q^{7} -203.000 q^{9} +O(q^{10})$$ $$q-6.32456 q^{3} -25.0000 q^{5} +44.2719 q^{7} -203.000 q^{9} +720.999 q^{11} +146.000 q^{13} +158.114 q^{15} -702.000 q^{17} -2732.21 q^{19} -280.000 q^{21} -4091.99 q^{23} +625.000 q^{25} +2820.75 q^{27} +4010.00 q^{29} +4566.33 q^{31} -4560.00 q^{33} -1106.80 q^{35} +14778.0 q^{37} -923.385 q^{39} -4350.00 q^{41} -12427.8 q^{43} +5075.00 q^{45} +6014.65 q^{47} -14847.0 q^{49} +4439.84 q^{51} +18154.0 q^{53} -18025.0 q^{55} +17280.0 q^{57} +19707.3 q^{59} +42130.0 q^{61} -8987.19 q^{63} -3650.00 q^{65} -16184.5 q^{67} +25880.0 q^{69} +45448.3 q^{71} +26266.0 q^{73} -3952.85 q^{75} +31920.0 q^{77} -8677.29 q^{79} +31489.0 q^{81} +98757.9 q^{83} +17550.0 q^{85} -25361.5 q^{87} +30570.0 q^{89} +6463.70 q^{91} -28880.0 q^{93} +68305.2 q^{95} +66882.0 q^{97} -146363. q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2q - 50q^{5} - 406q^{9} + O(q^{10})$$ $$2q - 50q^{5} - 406q^{9} + 292q^{13} - 1404q^{17} - 560q^{21} + 1250q^{25} + 8020q^{29} - 9120q^{33} + 29556q^{37} - 8700q^{41} + 10150q^{45} - 29694q^{49} + 36308q^{53} + 34560q^{57} + 84260q^{61} - 7300q^{65} + 51760q^{69} + 52532q^{73} + 63840q^{77} + 62978q^{81} + 35100q^{85} + 61140q^{89} - 57760q^{93} + 133764q^{97} + O(q^{100})$$

## 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
$$3$$ −6.32456 −0.405720 −0.202860 0.979208i $$-0.565024\pi$$
−0.202860 + 0.979208i $$0.565024\pi$$
$$4$$ 0 0
$$5$$ −25.0000 −0.447214
$$6$$ 0 0
$$7$$ 44.2719 0.341494 0.170747 0.985315i $$-0.445382\pi$$
0.170747 + 0.985315i $$0.445382\pi$$
$$8$$ 0 0
$$9$$ −203.000 −0.835391
$$10$$ 0 0
$$11$$ 720.999 1.79661 0.898304 0.439375i $$-0.144800\pi$$
0.898304 + 0.439375i $$0.144800\pi$$
$$12$$ 0 0
$$13$$ 146.000 0.239604 0.119802 0.992798i $$-0.461774\pi$$
0.119802 + 0.992798i $$0.461774\pi$$
$$14$$ 0 0
$$15$$ 158.114 0.181444
$$16$$ 0 0
$$17$$ −702.000 −0.589135 −0.294567 0.955631i $$-0.595176\pi$$
−0.294567 + 0.955631i $$0.595176\pi$$
$$18$$ 0 0
$$19$$ −2732.21 −1.73632 −0.868160 0.496285i $$-0.834697\pi$$
−0.868160 + 0.496285i $$0.834697\pi$$
$$20$$ 0 0
$$21$$ −280.000 −0.138551
$$22$$ 0 0
$$23$$ −4091.99 −1.61293 −0.806463 0.591284i $$-0.798621\pi$$
−0.806463 + 0.591284i $$0.798621\pi$$
$$24$$ 0 0
$$25$$ 625.000 0.200000
$$26$$ 0 0
$$27$$ 2820.75 0.744656
$$28$$ 0 0
$$29$$ 4010.00 0.885420 0.442710 0.896665i $$-0.354017\pi$$
0.442710 + 0.896665i $$0.354017\pi$$
$$30$$ 0 0
$$31$$ 4566.33 0.853420 0.426710 0.904388i $$-0.359672\pi$$
0.426710 + 0.904388i $$0.359672\pi$$
$$32$$ 0 0
$$33$$ −4560.00 −0.728920
$$34$$ 0 0
$$35$$ −1106.80 −0.152721
$$36$$ 0 0
$$37$$ 14778.0 1.77464 0.887322 0.461150i $$-0.152563\pi$$
0.887322 + 0.461150i $$0.152563\pi$$
$$38$$ 0 0
$$39$$ −923.385 −0.0972123
$$40$$ 0 0
$$41$$ −4350.00 −0.404138 −0.202069 0.979371i $$-0.564767\pi$$
−0.202069 + 0.979371i $$0.564767\pi$$
$$42$$ 0 0
$$43$$ −12427.8 −1.02499 −0.512497 0.858689i $$-0.671279\pi$$
−0.512497 + 0.858689i $$0.671279\pi$$
$$44$$ 0 0
$$45$$ 5075.00 0.373598
$$46$$ 0 0
$$47$$ 6014.65 0.397160 0.198580 0.980085i $$-0.436367\pi$$
0.198580 + 0.980085i $$0.436367\pi$$
$$48$$ 0 0
$$49$$ −14847.0 −0.883382
$$50$$ 0 0
$$51$$ 4439.84 0.239024
$$52$$ 0 0
$$53$$ 18154.0 0.887734 0.443867 0.896093i $$-0.353606\pi$$
0.443867 + 0.896093i $$0.353606\pi$$
$$54$$ 0 0
$$55$$ −18025.0 −0.803467
$$56$$ 0 0
$$57$$ 17280.0 0.704460
$$58$$ 0 0
$$59$$ 19707.3 0.737051 0.368525 0.929618i $$-0.379863\pi$$
0.368525 + 0.929618i $$0.379863\pi$$
$$60$$ 0 0
$$61$$ 42130.0 1.44966 0.724831 0.688927i $$-0.241918\pi$$
0.724831 + 0.688927i $$0.241918\pi$$
$$62$$ 0 0
$$63$$ −8987.19 −0.285281
$$64$$ 0 0
$$65$$ −3650.00 −0.107154
$$66$$ 0 0
$$67$$ −16184.5 −0.440467 −0.220233 0.975447i $$-0.570682\pi$$
−0.220233 + 0.975447i $$0.570682\pi$$
$$68$$ 0 0
$$69$$ 25880.0 0.654397
$$70$$ 0 0
$$71$$ 45448.3 1.06997 0.534985 0.844862i $$-0.320317\pi$$
0.534985 + 0.844862i $$0.320317\pi$$
$$72$$ 0 0
$$73$$ 26266.0 0.576882 0.288441 0.957498i $$-0.406863\pi$$
0.288441 + 0.957498i $$0.406863\pi$$
$$74$$ 0 0
$$75$$ −3952.85 −0.0811441
$$76$$ 0 0
$$77$$ 31920.0 0.613530
$$78$$ 0 0
$$79$$ −8677.29 −0.156429 −0.0782143 0.996937i $$-0.524922\pi$$
−0.0782143 + 0.996937i $$0.524922\pi$$
$$80$$ 0 0
$$81$$ 31489.0 0.533269
$$82$$ 0 0
$$83$$ 98757.9 1.57354 0.786768 0.617249i $$-0.211753\pi$$
0.786768 + 0.617249i $$0.211753\pi$$
$$84$$ 0 0
$$85$$ 17550.0 0.263469
$$86$$ 0 0
$$87$$ −25361.5 −0.359233
$$88$$ 0 0
$$89$$ 30570.0 0.409091 0.204546 0.978857i $$-0.434428\pi$$
0.204546 + 0.978857i $$0.434428\pi$$
$$90$$ 0 0
$$91$$ 6463.70 0.0818234
$$92$$ 0 0
$$93$$ −28880.0 −0.346250
$$94$$ 0 0
$$95$$ 68305.2 0.776506
$$96$$ 0 0
$$97$$ 66882.0 0.721739 0.360869 0.932616i $$-0.382480\pi$$
0.360869 + 0.932616i $$0.382480\pi$$
$$98$$ 0 0
$$99$$ −146363. −1.50087
$$100$$ 0 0
$$101$$ −42798.0 −0.417465 −0.208732 0.977973i $$-0.566934\pi$$
−0.208732 + 0.977973i $$0.566934\pi$$
$$102$$ 0 0
$$103$$ 10505.1 0.0975678 0.0487839 0.998809i $$-0.484465\pi$$
0.0487839 + 0.998809i $$0.484465\pi$$
$$104$$ 0 0
$$105$$ 7000.00 0.0619619
$$106$$ 0 0
$$107$$ −66856.9 −0.564529 −0.282265 0.959337i $$-0.591086\pi$$
−0.282265 + 0.959337i $$0.591086\pi$$
$$108$$ 0 0
$$109$$ 111714. 0.900620 0.450310 0.892872i $$-0.351314\pi$$
0.450310 + 0.892872i $$0.351314\pi$$
$$110$$ 0 0
$$111$$ −93464.3 −0.720009
$$112$$ 0 0
$$113$$ 216834. 1.59746 0.798732 0.601686i $$-0.205504\pi$$
0.798732 + 0.601686i $$0.205504\pi$$
$$114$$ 0 0
$$115$$ 102300. 0.721323
$$116$$ 0 0
$$117$$ −29638.0 −0.200163
$$118$$ 0 0
$$119$$ −31078.9 −0.201186
$$120$$ 0 0
$$121$$ 358789. 2.22780
$$122$$ 0 0
$$123$$ 27511.8 0.163967
$$124$$ 0 0
$$125$$ −15625.0 −0.0894427
$$126$$ 0 0
$$127$$ 62277.9 0.342629 0.171315 0.985216i $$-0.445199\pi$$
0.171315 + 0.985216i $$0.445199\pi$$
$$128$$ 0 0
$$129$$ 78600.0 0.415861
$$130$$ 0 0
$$131$$ −176189. −0.897019 −0.448510 0.893778i $$-0.648045\pi$$
−0.448510 + 0.893778i $$0.648045\pi$$
$$132$$ 0 0
$$133$$ −120960. −0.592943
$$134$$ 0 0
$$135$$ −70518.8 −0.333020
$$136$$ 0 0
$$137$$ 99802.0 0.454295 0.227147 0.973860i $$-0.427060\pi$$
0.227147 + 0.973860i $$0.427060\pi$$
$$138$$ 0 0
$$139$$ 271475. 1.19177 0.595886 0.803069i $$-0.296801\pi$$
0.595886 + 0.803069i $$0.296801\pi$$
$$140$$ 0 0
$$141$$ −38040.0 −0.161136
$$142$$ 0 0
$$143$$ 105266. 0.430475
$$144$$ 0 0
$$145$$ −100250. −0.395972
$$146$$ 0 0
$$147$$ 93900.7 0.358406
$$148$$ 0 0
$$149$$ 413626. 1.52631 0.763154 0.646217i $$-0.223650\pi$$
0.763154 + 0.646217i $$0.223650\pi$$
$$150$$ 0 0
$$151$$ 172496. 0.615654 0.307827 0.951442i $$-0.400398\pi$$
0.307827 + 0.951442i $$0.400398\pi$$
$$152$$ 0 0
$$153$$ 142506. 0.492158
$$154$$ 0 0
$$155$$ −114158. −0.381661
$$156$$ 0 0
$$157$$ −179358. −0.580726 −0.290363 0.956917i $$-0.593776\pi$$
−0.290363 + 0.956917i $$0.593776\pi$$
$$158$$ 0 0
$$159$$ −114816. −0.360172
$$160$$ 0 0
$$161$$ −181160. −0.550805
$$162$$ 0 0
$$163$$ −465924. −1.37355 −0.686777 0.726868i $$-0.740975\pi$$
−0.686777 + 0.726868i $$0.740975\pi$$
$$164$$ 0 0
$$165$$ 114000. 0.325983
$$166$$ 0 0
$$167$$ −609567. −1.69134 −0.845669 0.533708i $$-0.820798\pi$$
−0.845669 + 0.533708i $$0.820798\pi$$
$$168$$ 0 0
$$169$$ −349977. −0.942590
$$170$$ 0 0
$$171$$ 554638. 1.45051
$$172$$ 0 0
$$173$$ −591086. −1.50153 −0.750767 0.660567i $$-0.770316\pi$$
−0.750767 + 0.660567i $$0.770316\pi$$
$$174$$ 0 0
$$175$$ 27669.9 0.0682988
$$176$$ 0 0
$$177$$ −124640. −0.299037
$$178$$ 0 0
$$179$$ −211215. −0.492711 −0.246355 0.969180i $$-0.579233\pi$$
−0.246355 + 0.969180i $$0.579233\pi$$
$$180$$ 0 0
$$181$$ 97538.0 0.221298 0.110649 0.993860i $$-0.464707\pi$$
0.110649 + 0.993860i $$0.464707\pi$$
$$182$$ 0 0
$$183$$ −266454. −0.588158
$$184$$ 0 0
$$185$$ −369450. −0.793645
$$186$$ 0 0
$$187$$ −506142. −1.05844
$$188$$ 0 0
$$189$$ 124880. 0.254295
$$190$$ 0 0
$$191$$ 307158. 0.609227 0.304613 0.952476i $$-0.401473\pi$$
0.304613 + 0.952476i $$0.401473\pi$$
$$192$$ 0 0
$$193$$ 12434.0 0.0240280 0.0120140 0.999928i $$-0.496176\pi$$
0.0120140 + 0.999928i $$0.496176\pi$$
$$194$$ 0 0
$$195$$ 23084.6 0.0434747
$$196$$ 0 0
$$197$$ 378858. 0.695522 0.347761 0.937583i $$-0.386942\pi$$
0.347761 + 0.937583i $$0.386942\pi$$
$$198$$ 0 0
$$199$$ 767194. 1.37332 0.686661 0.726978i $$-0.259076\pi$$
0.686661 + 0.726978i $$0.259076\pi$$
$$200$$ 0 0
$$201$$ 102360. 0.178706
$$202$$ 0 0
$$203$$ 177530. 0.302366
$$204$$ 0 0
$$205$$ 108750. 0.180736
$$206$$ 0 0
$$207$$ 830673. 1.34742
$$208$$ 0 0
$$209$$ −1.96992e6 −3.11948
$$210$$ 0 0
$$211$$ 864529. 1.33682 0.668411 0.743793i $$-0.266975\pi$$
0.668411 + 0.743793i $$0.266975\pi$$
$$212$$ 0 0
$$213$$ −287440. −0.434108
$$214$$ 0 0
$$215$$ 310694. 0.458391
$$216$$ 0 0
$$217$$ 202160. 0.291438
$$218$$ 0 0
$$219$$ −166121. −0.234053
$$220$$ 0 0
$$221$$ −102492. −0.141159
$$222$$ 0 0
$$223$$ −639710. −0.861432 −0.430716 0.902488i $$-0.641739\pi$$
−0.430716 + 0.902488i $$0.641739\pi$$
$$224$$ 0 0
$$225$$ −126875. −0.167078
$$226$$ 0 0
$$227$$ 980515. 1.26296 0.631480 0.775392i $$-0.282448\pi$$
0.631480 + 0.775392i $$0.282448\pi$$
$$228$$ 0 0
$$229$$ 1.01261e6 1.27601 0.638004 0.770033i $$-0.279760\pi$$
0.638004 + 0.770033i $$0.279760\pi$$
$$230$$ 0 0
$$231$$ −201880. −0.248922
$$232$$ 0 0
$$233$$ −706326. −0.852345 −0.426172 0.904642i $$-0.640138\pi$$
−0.426172 + 0.904642i $$0.640138\pi$$
$$234$$ 0 0
$$235$$ −150366. −0.177616
$$236$$ 0 0
$$237$$ 54880.0 0.0634663
$$238$$ 0 0
$$239$$ −1.19390e6 −1.35199 −0.675994 0.736907i $$-0.736285\pi$$
−0.675994 + 0.736907i $$0.736285\pi$$
$$240$$ 0 0
$$241$$ 404410. 0.448517 0.224259 0.974530i $$-0.428004\pi$$
0.224259 + 0.974530i $$0.428004\pi$$
$$242$$ 0 0
$$243$$ −884597. −0.961014
$$244$$ 0 0
$$245$$ 371175. 0.395060
$$246$$ 0 0
$$247$$ −398902. −0.416030
$$248$$ 0 0
$$249$$ −624600. −0.638416
$$250$$ 0 0
$$251$$ −1.43258e6 −1.43527 −0.717634 0.696420i $$-0.754775\pi$$
−0.717634 + 0.696420i $$0.754775\pi$$
$$252$$ 0 0
$$253$$ −2.95032e6 −2.89780
$$254$$ 0 0
$$255$$ −110996. −0.106895
$$256$$ 0 0
$$257$$ −987982. −0.933074 −0.466537 0.884502i $$-0.654499\pi$$
−0.466537 + 0.884502i $$0.654499\pi$$
$$258$$ 0 0
$$259$$ 654250. 0.606030
$$260$$ 0 0
$$261$$ −814030. −0.739672
$$262$$ 0 0
$$263$$ 2.06222e6 1.83842 0.919210 0.393767i $$-0.128828\pi$$
0.919210 + 0.393767i $$0.128828\pi$$
$$264$$ 0 0
$$265$$ −453850. −0.397007
$$266$$ 0 0
$$267$$ −193342. −0.165977
$$268$$ 0 0
$$269$$ 780386. 0.657550 0.328775 0.944408i $$-0.393364\pi$$
0.328775 + 0.944408i $$0.393364\pi$$
$$270$$ 0 0
$$271$$ −562291. −0.465091 −0.232545 0.972586i $$-0.574705\pi$$
−0.232545 + 0.972586i $$0.574705\pi$$
$$272$$ 0 0
$$273$$ −40880.0 −0.0331974
$$274$$ 0 0
$$275$$ 450625. 0.359321
$$276$$ 0 0
$$277$$ −386758. −0.302859 −0.151429 0.988468i $$-0.548388\pi$$
−0.151429 + 0.988468i $$0.548388\pi$$
$$278$$ 0 0
$$279$$ −926965. −0.712940
$$280$$ 0 0
$$281$$ 1.55485e6 1.17469 0.587344 0.809337i $$-0.300173\pi$$
0.587344 + 0.809337i $$0.300173\pi$$
$$282$$ 0 0
$$283$$ 1.75157e6 1.30005 0.650026 0.759912i $$-0.274758\pi$$
0.650026 + 0.759912i $$0.274758\pi$$
$$284$$ 0 0
$$285$$ −432000. −0.315044
$$286$$ 0 0
$$287$$ −192583. −0.138011
$$288$$ 0 0
$$289$$ −927053. −0.652920
$$290$$ 0 0
$$291$$ −422999. −0.292824
$$292$$ 0 0
$$293$$ −1.55309e6 −1.05689 −0.528444 0.848968i $$-0.677224\pi$$
−0.528444 + 0.848968i $$0.677224\pi$$
$$294$$ 0 0
$$295$$ −492683. −0.329619
$$296$$ 0 0
$$297$$ 2.03376e6 1.33785
$$298$$ 0 0
$$299$$ −597430. −0.386464
$$300$$ 0 0
$$301$$ −550200. −0.350029
$$302$$ 0 0
$$303$$ 270678. 0.169374
$$304$$ 0 0
$$305$$ −1.05325e6 −0.648309
$$306$$ 0 0
$$307$$ −2.60409e6 −1.57692 −0.788461 0.615085i $$-0.789122\pi$$
−0.788461 + 0.615085i $$0.789122\pi$$
$$308$$ 0 0
$$309$$ −66440.0 −0.0395853
$$310$$ 0 0
$$311$$ −302124. −0.177127 −0.0885634 0.996071i $$-0.528228\pi$$
−0.0885634 + 0.996071i $$0.528228\pi$$
$$312$$ 0 0
$$313$$ 2.09455e6 1.20846 0.604228 0.796812i $$-0.293482\pi$$
0.604228 + 0.796812i $$0.293482\pi$$
$$314$$ 0 0
$$315$$ 224680. 0.127581
$$316$$ 0 0
$$317$$ −1.07624e6 −0.601534 −0.300767 0.953698i $$-0.597243\pi$$
−0.300767 + 0.953698i $$0.597243\pi$$
$$318$$ 0 0
$$319$$ 2.89121e6 1.59075
$$320$$ 0 0
$$321$$ 422840. 0.229041
$$322$$ 0 0
$$323$$ 1.91801e6 1.02293
$$324$$ 0 0
$$325$$ 91250.0 0.0479208
$$326$$ 0 0
$$327$$ −706541. −0.365400
$$328$$ 0 0
$$329$$ 266280. 0.135628
$$330$$ 0 0
$$331$$ −313002. −0.157028 −0.0785141 0.996913i $$-0.525018\pi$$
−0.0785141 + 0.996913i $$0.525018\pi$$
$$332$$ 0 0
$$333$$ −2.99993e6 −1.48252
$$334$$ 0 0
$$335$$ 404613. 0.196983
$$336$$ 0 0
$$337$$ 1.55400e6 0.745378 0.372689 0.927956i $$-0.378436\pi$$
0.372689 + 0.927956i $$0.378436\pi$$
$$338$$ 0 0
$$339$$ −1.37138e6 −0.648124
$$340$$ 0 0
$$341$$ 3.29232e6 1.53326
$$342$$ 0 0
$$343$$ −1.40138e6 −0.643163
$$344$$ 0 0
$$345$$ −647000. −0.292655
$$346$$ 0 0
$$347$$ 2.22208e6 0.990684 0.495342 0.868698i $$-0.335043\pi$$
0.495342 + 0.868698i $$0.335043\pi$$
$$348$$ 0 0
$$349$$ 774570. 0.340406 0.170203 0.985409i $$-0.445558\pi$$
0.170203 + 0.985409i $$0.445558\pi$$
$$350$$ 0 0
$$351$$ 411830. 0.178423
$$352$$ 0 0
$$353$$ −2.26217e6 −0.966249 −0.483125 0.875552i $$-0.660498\pi$$
−0.483125 + 0.875552i $$0.660498\pi$$
$$354$$ 0 0
$$355$$ −1.13621e6 −0.478505
$$356$$ 0 0
$$357$$ 196560. 0.0816253
$$358$$ 0 0
$$359$$ −869601. −0.356110 −0.178055 0.984021i $$-0.556980\pi$$
−0.178055 + 0.984021i $$0.556980\pi$$
$$360$$ 0 0
$$361$$ 4.98886e6 2.01481
$$362$$ 0 0
$$363$$ −2.26918e6 −0.903863
$$364$$ 0 0
$$365$$ −656650. −0.257989
$$366$$ 0 0
$$367$$ −1.25361e6 −0.485844 −0.242922 0.970046i $$-0.578106\pi$$
−0.242922 + 0.970046i $$0.578106\pi$$
$$368$$ 0 0
$$369$$ 883050. 0.337613
$$370$$ 0 0
$$371$$ 803712. 0.303156
$$372$$ 0 0
$$373$$ −175206. −0.0652044 −0.0326022 0.999468i $$-0.510379\pi$$
−0.0326022 + 0.999468i $$0.510379\pi$$
$$374$$ 0 0
$$375$$ 98821.2 0.0362887
$$376$$ 0 0
$$377$$ 585460. 0.212150
$$378$$ 0 0
$$379$$ 796945. 0.284990 0.142495 0.989795i $$-0.454487\pi$$
0.142495 + 0.989795i $$0.454487\pi$$
$$380$$ 0 0
$$381$$ −393880. −0.139012
$$382$$ 0 0
$$383$$ −3.36129e6 −1.17087 −0.585436 0.810719i $$-0.699077\pi$$
−0.585436 + 0.810719i $$0.699077\pi$$
$$384$$ 0 0
$$385$$ −798000. −0.274379
$$386$$ 0 0
$$387$$ 2.52283e6 0.856271
$$388$$ 0 0
$$389$$ 5.51959e6 1.84941 0.924705 0.380685i $$-0.124312\pi$$
0.924705 + 0.380685i $$0.124312\pi$$
$$390$$ 0 0
$$391$$ 2.87258e6 0.950232
$$392$$ 0 0
$$393$$ 1.11432e6 0.363939
$$394$$ 0 0
$$395$$ 216932. 0.0699570
$$396$$ 0 0
$$397$$ 1.74738e6 0.556430 0.278215 0.960519i $$-0.410257\pi$$
0.278215 + 0.960519i $$0.410257\pi$$
$$398$$ 0 0
$$399$$ 765018. 0.240569
$$400$$ 0 0
$$401$$ 541122. 0.168048 0.0840242 0.996464i $$-0.473223\pi$$
0.0840242 + 0.996464i $$0.473223\pi$$
$$402$$ 0 0
$$403$$ 666684. 0.204483
$$404$$ 0 0
$$405$$ −787225. −0.238485
$$406$$ 0 0
$$407$$ 1.06549e7 3.18834
$$408$$ 0 0
$$409$$ 3.79699e6 1.12236 0.561179 0.827694i $$-0.310348\pi$$
0.561179 + 0.827694i $$0.310348\pi$$
$$410$$ 0 0
$$411$$ −631203. −0.184317
$$412$$ 0 0
$$413$$ 872480. 0.251698
$$414$$ 0 0
$$415$$ −2.46895e6 −0.703707
$$416$$ 0 0
$$417$$ −1.71696e6 −0.483526
$$418$$ 0 0
$$419$$ 3.88108e6 1.07998 0.539992 0.841670i $$-0.318427\pi$$
0.539992 + 0.841670i $$0.318427\pi$$
$$420$$ 0 0
$$421$$ 6.66081e6 1.83156 0.915781 0.401677i $$-0.131573\pi$$
0.915781 + 0.401677i $$0.131573\pi$$
$$422$$ 0 0
$$423$$ −1.22097e6 −0.331784
$$424$$ 0 0
$$425$$ −438750. −0.117827
$$426$$ 0 0
$$427$$ 1.86517e6 0.495051
$$428$$ 0 0
$$429$$ −665760. −0.174652
$$430$$ 0 0
$$431$$ −4.65337e6 −1.20663 −0.603315 0.797503i $$-0.706154\pi$$
−0.603315 + 0.797503i $$0.706154\pi$$
$$432$$ 0 0
$$433$$ −6.23873e6 −1.59910 −0.799552 0.600597i $$-0.794930\pi$$
−0.799552 + 0.600597i $$0.794930\pi$$
$$434$$ 0 0
$$435$$ 634037. 0.160654
$$436$$ 0 0
$$437$$ 1.11802e7 2.80056
$$438$$ 0 0
$$439$$ −4.75743e6 −1.17818 −0.589089 0.808068i $$-0.700513\pi$$
−0.589089 + 0.808068i $$0.700513\pi$$
$$440$$ 0 0
$$441$$ 3.01394e6 0.737969
$$442$$ 0 0
$$443$$ −5.77073e6 −1.39708 −0.698541 0.715570i $$-0.746167\pi$$
−0.698541 + 0.715570i $$0.746167\pi$$
$$444$$ 0 0
$$445$$ −764250. −0.182951
$$446$$ 0 0
$$447$$ −2.61600e6 −0.619254
$$448$$ 0 0
$$449$$ −4.22765e6 −0.989654 −0.494827 0.868991i $$-0.664769\pi$$
−0.494827 + 0.868991i $$0.664769\pi$$
$$450$$ 0 0
$$451$$ −3.13635e6 −0.726077
$$452$$ 0 0
$$453$$ −1.09096e6 −0.249783
$$454$$ 0 0
$$455$$ −161592. −0.0365925
$$456$$ 0 0
$$457$$ 4.31374e6 0.966192 0.483096 0.875567i $$-0.339512\pi$$
0.483096 + 0.875567i $$0.339512\pi$$
$$458$$ 0 0
$$459$$ −1.98017e6 −0.438703
$$460$$ 0 0
$$461$$ 5.94820e6 1.30357 0.651784 0.758405i $$-0.274021\pi$$
0.651784 + 0.758405i $$0.274021\pi$$
$$462$$ 0 0
$$463$$ 8.39722e6 1.82047 0.910234 0.414094i $$-0.135902\pi$$
0.910234 + 0.414094i $$0.135902\pi$$
$$464$$ 0 0
$$465$$ 722000. 0.154848
$$466$$ 0 0
$$467$$ −5.30976e6 −1.12663 −0.563317 0.826241i $$-0.690475\pi$$
−0.563317 + 0.826241i $$0.690475\pi$$
$$468$$ 0 0
$$469$$ −716520. −0.150417
$$470$$ 0 0
$$471$$ 1.13436e6 0.235613
$$472$$ 0 0
$$473$$ −8.96040e6 −1.84151
$$474$$ 0 0
$$475$$ −1.70763e6 −0.347264
$$476$$ 0 0
$$477$$ −3.68526e6 −0.741605
$$478$$ 0 0
$$479$$ 5.83653e6 1.16229 0.581147 0.813799i $$-0.302604\pi$$
0.581147 + 0.813799i $$0.302604\pi$$
$$480$$ 0 0
$$481$$ 2.15759e6 0.425212
$$482$$ 0 0
$$483$$ 1.14576e6 0.223473
$$484$$ 0 0
$$485$$ −1.67205e6 −0.322771
$$486$$ 0 0
$$487$$ −8.75327e6 −1.67243 −0.836215 0.548402i $$-0.815236\pi$$
−0.836215 + 0.548402i $$0.815236\pi$$
$$488$$ 0 0
$$489$$ 2.94676e6 0.557279
$$490$$ 0 0
$$491$$ 5.16834e6 0.967492 0.483746 0.875209i $$-0.339276\pi$$
0.483746 + 0.875209i $$0.339276\pi$$
$$492$$ 0 0
$$493$$ −2.81502e6 −0.521632
$$494$$ 0 0
$$495$$ 3.65907e6 0.671209
$$496$$ 0 0
$$497$$ 2.01208e6 0.365388
$$498$$ 0 0
$$499$$ 5.36171e6 0.963943 0.481972 0.876187i $$-0.339921\pi$$
0.481972 + 0.876187i $$0.339921\pi$$
$$500$$ 0 0
$$501$$ 3.85524e6 0.686210
$$502$$ 0 0
$$503$$ −5.26635e6 −0.928089 −0.464045 0.885812i $$-0.653602\pi$$
−0.464045 + 0.885812i $$0.653602\pi$$
$$504$$ 0 0
$$505$$ 1.06995e6 0.186696
$$506$$ 0 0
$$507$$ 2.21345e6 0.382428
$$508$$ 0 0
$$509$$ −5.46847e6 −0.935559 −0.467780 0.883845i $$-0.654946\pi$$
−0.467780 + 0.883845i $$0.654946\pi$$
$$510$$ 0 0
$$511$$ 1.16285e6 0.197002
$$512$$ 0 0
$$513$$ −7.70688e6 −1.29296
$$514$$ 0 0
$$515$$ −262627. −0.0436337
$$516$$ 0 0
$$517$$ 4.33656e6 0.713541
$$518$$ 0 0
$$519$$ 3.73836e6 0.609203
$$520$$ 0 0
$$521$$ −3.05762e6 −0.493503 −0.246751 0.969079i $$-0.579363\pi$$
−0.246751 + 0.969079i $$0.579363\pi$$
$$522$$ 0 0
$$523$$ 9.64117e6 1.54126 0.770629 0.637284i $$-0.219942\pi$$
0.770629 + 0.637284i $$0.219942\pi$$
$$524$$ 0 0
$$525$$ −175000. −0.0277102
$$526$$ 0 0
$$527$$ −3.20556e6 −0.502780
$$528$$ 0 0
$$529$$ 1.03080e7 1.60153
$$530$$ 0 0
$$531$$ −4.00058e6 −0.615726
$$532$$ 0 0
$$533$$ −635100. −0.0968332
$$534$$ 0 0
$$535$$ 1.67142e6 0.252465
$$536$$ 0 0
$$537$$ 1.33584e6 0.199903
$$538$$ 0 0
$$539$$ −1.07047e7 −1.58709
$$540$$ 0 0
$$541$$ 4.15820e6 0.610819 0.305409 0.952221i $$-0.401207\pi$$
0.305409 + 0.952221i $$0.401207\pi$$
$$542$$ 0 0
$$543$$ −616884. −0.0897851
$$544$$ 0 0
$$545$$ −2.79285e6 −0.402769
$$546$$ 0 0
$$547$$ −5.32628e6 −0.761125 −0.380562 0.924755i $$-0.624270\pi$$
−0.380562 + 0.924755i $$0.624270\pi$$
$$548$$ 0 0
$$549$$ −8.55239e6 −1.21103
$$550$$ 0 0
$$551$$ −1.09562e7 −1.53737
$$552$$ 0 0
$$553$$ −384160. −0.0534194
$$554$$ 0 0
$$555$$ 2.33661e6 0.321998
$$556$$ 0 0
$$557$$ −999102. −0.136449 −0.0682247 0.997670i $$-0.521733\pi$$
−0.0682247 + 0.997670i $$0.521733\pi$$
$$558$$ 0 0
$$559$$ −1.81445e6 −0.245593
$$560$$ 0 0
$$561$$ 3.20112e6 0.429432
$$562$$ 0 0
$$563$$ −5.31886e6 −0.707208 −0.353604 0.935395i $$-0.615044\pi$$
−0.353604 + 0.935395i $$0.615044\pi$$
$$564$$ 0 0
$$565$$ −5.42085e6 −0.714408
$$566$$ 0 0
$$567$$ 1.39408e6 0.182108
$$568$$ 0 0
$$569$$ 6.56759e6 0.850404 0.425202 0.905099i $$-0.360203\pi$$
0.425202 + 0.905099i $$0.360203\pi$$
$$570$$ 0 0
$$571$$ 164173. 0.0210723 0.0105361 0.999944i $$-0.496646\pi$$
0.0105361 + 0.999944i $$0.496646\pi$$
$$572$$ 0 0
$$573$$ −1.94264e6 −0.247176
$$574$$ 0 0
$$575$$ −2.55749e6 −0.322585
$$576$$ 0 0
$$577$$ 9.27762e6 1.16010 0.580052 0.814579i $$-0.303032\pi$$
0.580052 + 0.814579i $$0.303032\pi$$
$$578$$ 0 0
$$579$$ −78639.5 −0.00974865
$$580$$ 0 0
$$581$$ 4.37220e6 0.537353
$$582$$ 0 0
$$583$$ 1.30890e7 1.59491
$$584$$ 0 0
$$585$$ 740950. 0.0895157
$$586$$ 0 0
$$587$$ 5.44474e6 0.652202 0.326101 0.945335i $$-0.394265\pi$$
0.326101 + 0.945335i $$0.394265\pi$$
$$588$$ 0 0
$$589$$ −1.24762e7 −1.48181
$$590$$ 0 0
$$591$$ −2.39611e6 −0.282187
$$592$$ 0 0
$$593$$ −1.50978e7 −1.76310 −0.881548 0.472094i $$-0.843498\pi$$
−0.881548 + 0.472094i $$0.843498\pi$$
$$594$$ 0 0
$$595$$ 776972. 0.0899731
$$596$$ 0 0
$$597$$ −4.85216e6 −0.557185
$$598$$ 0 0
$$599$$ −6.98593e6 −0.795531 −0.397765 0.917487i $$-0.630214\pi$$
−0.397765 + 0.917487i $$0.630214\pi$$
$$600$$ 0 0
$$601$$ 6.16941e6 0.696719 0.348359 0.937361i $$-0.386739\pi$$
0.348359 + 0.937361i $$0.386739\pi$$
$$602$$ 0 0
$$603$$ 3.28546e6 0.367962
$$604$$ 0 0
$$605$$ −8.96972e6 −0.996301
$$606$$ 0 0
$$607$$ 1.00769e7 1.11009 0.555043 0.831822i $$-0.312702\pi$$
0.555043 + 0.831822i $$0.312702\pi$$
$$608$$ 0 0
$$609$$ −1.12280e6 −0.122676
$$610$$ 0 0
$$611$$ 878139. 0.0951613
$$612$$ 0 0
$$613$$ −5.26885e6 −0.566324 −0.283162 0.959072i $$-0.591383\pi$$
−0.283162 + 0.959072i $$0.591383\pi$$
$$614$$ 0 0
$$615$$ −687795. −0.0733283
$$616$$ 0 0
$$617$$ −1.38112e7 −1.46056 −0.730280 0.683148i $$-0.760610\pi$$
−0.730280 + 0.683148i $$0.760610\pi$$
$$618$$ 0 0
$$619$$ 3.20903e6 0.336625 0.168313 0.985734i $$-0.446168\pi$$
0.168313 + 0.985734i $$0.446168\pi$$
$$620$$ 0 0
$$621$$ −1.15425e7 −1.20108
$$622$$ 0 0
$$623$$ 1.35339e6 0.139702
$$624$$ 0 0
$$625$$ 390625. 0.0400000
$$626$$ 0 0
$$627$$ 1.24589e7 1.26564
$$628$$ 0 0
$$629$$ −1.03742e7 −1.04551
$$630$$ 0 0
$$631$$ 6.07204e6 0.607102 0.303551 0.952815i $$-0.401828\pi$$
0.303551 + 0.952815i $$0.401828\pi$$
$$632$$ 0 0
$$633$$ −5.46776e6 −0.542376
$$634$$ 0 0
$$635$$ −1.55695e6 −0.153229
$$636$$ 0 0
$$637$$ −2.16766e6 −0.211662
$$638$$ 0 0
$$639$$ −9.22600e6 −0.893843
$$640$$ 0 0
$$641$$ −2.02767e6 −0.194918 −0.0974591 0.995240i $$-0.531072\pi$$
−0.0974591 + 0.995240i $$0.531072\pi$$
$$642$$ 0 0
$$643$$ −1.19769e7 −1.14240 −0.571199 0.820811i $$-0.693522\pi$$
−0.571199 + 0.820811i $$0.693522\pi$$
$$644$$ 0 0
$$645$$ −1.96500e6 −0.185979
$$646$$ 0 0
$$647$$ 1.44768e6 0.135961 0.0679803 0.997687i $$-0.478344\pi$$
0.0679803 + 0.997687i $$0.478344\pi$$
$$648$$ 0 0
$$649$$ 1.42090e7 1.32419
$$650$$ 0 0
$$651$$ −1.27857e6 −0.118242
$$652$$ 0 0
$$653$$ −4.82477e6 −0.442785 −0.221393 0.975185i $$-0.571060\pi$$
−0.221393 + 0.975185i $$0.571060\pi$$
$$654$$ 0 0
$$655$$ 4.40474e6 0.401159
$$656$$ 0 0
$$657$$ −5.33200e6 −0.481922
$$658$$ 0 0
$$659$$ 4.37616e6 0.392536 0.196268 0.980550i $$-0.437118\pi$$
0.196268 + 0.980550i $$0.437118\pi$$
$$660$$ 0 0
$$661$$ 7.34953e6 0.654268 0.327134 0.944978i $$-0.393917\pi$$
0.327134 + 0.944978i $$0.393917\pi$$
$$662$$ 0 0
$$663$$ 648216. 0.0572712
$$664$$ 0 0
$$665$$ 3.02400e6 0.265172
$$666$$ 0 0
$$667$$ −1.64089e7 −1.42812
$$668$$ 0 0
$$669$$ 4.04588e6 0.349500
$$670$$ 0 0
$$671$$ 3.03757e7 2.60447
$$672$$ 0 0
$$673$$ −1.75692e7 −1.49525 −0.747626 0.664119i $$-0.768807\pi$$
−0.747626 + 0.664119i $$0.768807\pi$$
$$674$$ 0 0
$$675$$ 1.76297e6 0.148931
$$676$$ 0 0
$$677$$ −5.60338e6 −0.469871 −0.234935 0.972011i $$-0.575488\pi$$
−0.234935 + 0.972011i $$0.575488\pi$$
$$678$$ 0 0
$$679$$ 2.96099e6 0.246469
$$680$$ 0 0
$$681$$ −6.20132e6 −0.512409
$$682$$ 0 0
$$683$$ 5.05809e6 0.414892 0.207446 0.978246i $$-0.433485\pi$$
0.207446 + 0.978246i $$0.433485\pi$$
$$684$$ 0 0
$$685$$ −2.49505e6 −0.203167
$$686$$ 0 0
$$687$$ −6.40431e6 −0.517703
$$688$$ 0 0
$$689$$ 2.65048e6 0.212705
$$690$$ 0 0
$$691$$ 1.47421e7 1.17453 0.587267 0.809393i $$-0.300204\pi$$
0.587267 + 0.809393i $$0.300204\pi$$
$$692$$ 0 0
$$693$$ −6.47976e6 −0.512538
$$694$$ 0 0
$$695$$ −6.78688e6 −0.532977
$$696$$ 0 0
$$697$$ 3.05370e6 0.238092
$$698$$ 0 0
$$699$$ 4.46720e6 0.345814
$$700$$ 0 0
$$701$$ 8.83317e6 0.678925 0.339462 0.940620i $$-0.389755\pi$$
0.339462 + 0.940620i $$0.389755\pi$$
$$702$$ 0 0
$$703$$ −4.03766e7 −3.08135
$$704$$ 0 0
$$705$$ 951000. 0.0720622
$$706$$ 0 0
$$707$$ −1.89475e6 −0.142562
$$708$$ 0 0
$$709$$ 1.93101e6 0.144268 0.0721338 0.997395i $$-0.477019\pi$$
0.0721338 + 0.997395i $$0.477019\pi$$
$$710$$ 0 0
$$711$$ 1.76149e6 0.130679
$$712$$ 0 0
$$713$$ −1.86854e7 −1.37650
$$714$$ 0 0
$$715$$ −2.63165e6 −0.192514
$$716$$ 0 0
$$717$$ 7.55088e6 0.548529
$$718$$ 0 0
$$719$$ 7.22373e6 0.521122 0.260561 0.965457i $$-0.416093\pi$$
0.260561 + 0.965457i $$0.416093\pi$$
$$720$$ 0 0
$$721$$ 465080. 0.0333188
$$722$$ 0 0
$$723$$ −2.55771e6 −0.181973
$$724$$ 0 0
$$725$$ 2.50625e6 0.177084
$$726$$ 0 0
$$727$$ −9.81106e6 −0.688462 −0.344231 0.938885i $$-0.611860\pi$$
−0.344231 + 0.938885i $$0.611860\pi$$
$$728$$ 0 0
$$729$$ −2.05715e6 −0.143366
$$730$$ 0 0
$$731$$ 8.72428e6 0.603860
$$732$$ 0 0
$$733$$ 2.40813e7 1.65547 0.827733 0.561122i $$-0.189630\pi$$
0.827733 + 0.561122i $$0.189630\pi$$
$$734$$ 0 0
$$735$$ −2.34752e6 −0.160284
$$736$$ 0 0
$$737$$ −1.16690e7 −0.791346
$$738$$ 0 0
$$739$$ −2.40518e7 −1.62008 −0.810040 0.586374i $$-0.800555\pi$$
−0.810040 + 0.586374i $$0.800555\pi$$
$$740$$ 0 0
$$741$$ 2.52288e6 0.168792
$$742$$ 0 0
$$743$$ 4.70160e6 0.312445 0.156223 0.987722i $$-0.450068\pi$$
0.156223 + 0.987722i $$0.450068\pi$$
$$744$$ 0 0
$$745$$ −1.03406e7 −0.682586
$$746$$ 0 0
$$747$$ −2.00479e7 −1.31452
$$748$$ 0 0
$$749$$ −2.95988e6 −0.192783
$$750$$ 0 0
$$751$$ −2.31282e7 −1.49638 −0.748189 0.663485i $$-0.769077\pi$$
−0.748189 + 0.663485i $$0.769077\pi$$
$$752$$ 0 0
$$753$$ 9.06040e6 0.582318
$$754$$ 0 0
$$755$$ −4.31240e6 −0.275329
$$756$$ 0 0
$$757$$ 1.26635e7 0.803181 0.401591 0.915819i $$-0.368458\pi$$
0.401591 + 0.915819i $$0.368458\pi$$
$$758$$ 0 0
$$759$$ 1.86595e7 1.17570
$$760$$ 0 0
$$761$$ −4.33524e6 −0.271363 −0.135682 0.990752i $$-0.543322\pi$$
−0.135682 + 0.990752i $$0.543322\pi$$
$$762$$ 0 0
$$763$$ 4.94579e6 0.307556
$$764$$ 0 0
$$765$$ −3.56265e6 −0.220100
$$766$$ 0 0
$$767$$ 2.87727e6 0.176600
$$768$$ 0 0
$$769$$ −364270. −0.0222130 −0.0111065 0.999938i $$-0.503535\pi$$
−0.0111065 + 0.999938i $$0.503535\pi$$
$$770$$ 0 0
$$771$$ 6.24855e6 0.378567
$$772$$ 0 0
$$773$$ 1.03051e6 0.0620300 0.0310150 0.999519i $$-0.490126\pi$$
0.0310150 + 0.999519i $$0.490126\pi$$
$$774$$ 0 0
$$775$$ 2.85396e6 0.170684
$$776$$ 0 0
$$777$$ −4.13784e6 −0.245879
$$778$$ 0 0
$$779$$ 1.18851e7 0.701713
$$780$$ 0 0
$$781$$ 3.27682e7 1.92231
$$782$$ 0 0
$$783$$ 1.13112e7 0.659333
$$784$$ 0 0
$$785$$ 4.48395e6 0.259709
$$786$$ 0 0
$$787$$ 1.95300e7 1.12400 0.561999 0.827138i $$-0.310032\pi$$
0.561999 + 0.827138i $$0.310032\pi$$
$$788$$ 0 0
$$789$$ −1.30426e7 −0.745885
$$790$$ 0 0
$$791$$ 9.59965e6 0.545524
$$792$$ 0 0
$$793$$ 6.15098e6 0.347345
$$794$$ 0 0
$$795$$ 2.87040e6 0.161074
$$796$$ 0 0
$$797$$ −7.86344e6 −0.438497 −0.219249 0.975669i $$-0.570361\pi$$
−0.219249 + 0.975669i $$0.570361\pi$$
$$798$$ 0 0
$$799$$ −4.22229e6 −0.233981
$$800$$ 0 0
$$801$$ −6.20571e6 −0.341751
$$802$$ 0 0
$$803$$ 1.89378e7 1.03643
$$804$$ 0 0
$$805$$ 4.52900e6 0.246327
$$806$$ 0 0
$$807$$ −4.93559e6 −0.266781
$$808$$ 0 0
$$809$$ −1.05014e7 −0.564127 −0.282064 0.959396i $$-0.591019\pi$$
−0.282064 + 0.959396i $$0.591019\pi$$
$$810$$ 0 0
$$811$$ −1.87803e7 −1.00265 −0.501325 0.865259i $$-0.667154\pi$$
−0.501325 + 0.865259i $$0.667154\pi$$
$$812$$ 0 0
$$813$$ 3.55624e6 0.188697
$$814$$ 0 0
$$815$$ 1.16481e7 0.614272
$$816$$ 0 0
$$817$$ 3.39552e7 1.77972
$$818$$ 0 0
$$819$$ −1.31213e6 −0.0683545
$$820$$ 0 0
$$821$$ −2.00557e7 −1.03844 −0.519220 0.854641i $$-0.673777\pi$$
−0.519220 + 0.854641i $$0.673777\pi$$
$$822$$ 0 0
$$823$$ 1.02444e7 0.527212 0.263606 0.964630i $$-0.415088\pi$$
0.263606 + 0.964630i $$0.415088\pi$$
$$824$$ 0 0
$$825$$ −2.85000e6 −0.145784
$$826$$ 0 0
$$827$$ −827524. −0.0420743 −0.0210371 0.999779i $$-0.506697\pi$$
−0.0210371 + 0.999779i $$0.506697\pi$$
$$828$$ 0 0
$$829$$ 3.80328e7 1.92208 0.961041 0.276407i $$-0.0891436\pi$$
0.961041 + 0.276407i $$0.0891436\pi$$
$$830$$ 0 0
$$831$$ 2.44607e6 0.122876
$$832$$ 0 0
$$833$$ 1.04226e7 0.520431
$$834$$ 0 0
$$835$$ 1.52392e7 0.756389
$$836$$ 0 0
$$837$$ 1.28805e7 0.635504
$$838$$ 0 0
$$839$$ −3.57628e7 −1.75399 −0.876993 0.480503i $$-0.840454\pi$$
−0.876993 + 0.480503i $$0.840454\pi$$
$$840$$ 0 0
$$841$$ −4.43105e6 −0.216031
$$842$$ 0 0
$$843$$ −9.83373e6 −0.476595
$$844$$ 0 0
$$845$$ 8.74943e6 0.421539
$$846$$ 0 0
$$847$$ 1.58843e7 0.760779
$$848$$ 0 0
$$849$$ −1.10779e7 −0.527457
$$850$$ 0 0
$$851$$ −6.04714e7 −2.86237
$$852$$ 0 0
$$853$$ −970214. −0.0456557 −0.0228278 0.999739i $$-0.507267\pi$$
−0.0228278 + 0.999739i $$0.507267\pi$$
$$854$$ 0 0
$$855$$ −1.38660e7 −0.648686
$$856$$ 0 0
$$857$$ 1.86468e6 0.0867267 0.0433633 0.999059i $$-0.486193\pi$$
0.0433633 + 0.999059i $$0.486193\pi$$
$$858$$ 0 0
$$859$$ −1.05785e6 −0.0489147 −0.0244573 0.999701i $$-0.507786\pi$$
−0.0244573 + 0.999701i $$0.507786\pi$$
$$860$$ 0 0
$$861$$ 1.21800e6 0.0559937
$$862$$ 0 0
$$863$$ 8.24333e6 0.376769 0.188385 0.982095i $$-0.439675\pi$$
0.188385 + 0.982095i $$0.439675\pi$$
$$864$$ 0 0
$$865$$ 1.47772e7 0.671507
$$866$$ 0 0
$$867$$ 5.86320e6 0.264903
$$868$$ 0 0
$$869$$ −6.25632e6 −0.281041
$$870$$ 0 0
$$871$$ −2.36294e6 −0.105538
$$872$$ 0 0
$$873$$ −1.35770e7 −0.602934
$$874$$ 0 0
$$875$$ −691748. −0.0305441
$$876$$ 0 0
$$877$$ 2.40362e7 1.05528 0.527640 0.849468i $$-0.323077\pi$$
0.527640 + 0.849468i $$0.323077\pi$$
$$878$$ 0 0
$$879$$ 9.82263e6 0.428801
$$880$$ 0 0
$$881$$ 3.68605e7 1.60000 0.800002 0.599997i $$-0.204831\pi$$
0.800002 + 0.599997i $$0.204831\pi$$
$$882$$ 0 0
$$883$$ −1.67403e7 −0.722541 −0.361271 0.932461i $$-0.617657\pi$$
−0.361271 + 0.932461i $$0.617657\pi$$
$$884$$ 0 0
$$885$$ 3.11600e6 0.133733
$$886$$ 0 0
$$887$$ −9.25364e6 −0.394915 −0.197457 0.980311i $$-0.563268\pi$$
−0.197457 + 0.980311i $$0.563268\pi$$
$$888$$ 0 0
$$889$$ 2.75716e6 0.117006
$$890$$ 0 0
$$891$$ 2.27035e7 0.958075
$$892$$ 0 0
$$893$$ −1.64333e7 −0.689597
$$894$$ 0 0
$$895$$ 5.28037e6 0.220347
$$896$$ 0 0
$$897$$ 3.77848e6 0.156796
$$898$$ 0 0
$$899$$ 1.83110e7 0.755635
$$900$$ 0 0
$$901$$ −1.27441e7 −0.522995
$$902$$ 0 0
$$903$$ 3.47977e6 0.142014
$$904$$ 0 0
$$905$$ −2.43845e6 −0.0989675
$$906$$ 0 0
$$907$$ 1.03030e7 0.415859 0.207929 0.978144i $$-0.433328\pi$$
0.207929 + 0.978144i $$0.433328\pi$$
$$908$$ 0 0
$$909$$ 8.68799e6 0.348746
$$910$$ 0 0
$$911$$ −3.82374e7 −1.52649 −0.763243 0.646111i $$-0.776394\pi$$
−0.763243 + 0.646111i $$0.776394\pi$$
$$912$$ 0 0
$$913$$ 7.12044e7 2.82703
$$914$$ 0 0
$$915$$ 6.66134e6 0.263032
$$916$$ 0 0
$$917$$ −7.80024e6 −0.306327
$$918$$ 0 0
$$919$$ 7.72150e6 0.301587 0.150794 0.988565i $$-0.451817\pi$$
0.150794 + 0.988565i $$0.451817\pi$$
$$920$$ 0 0
$$921$$ 1.64697e7 0.639790
$$922$$ 0 0
$$923$$ 6.63545e6 0.256369
$$924$$ 0 0
$$925$$ 9.23625e6 0.354929
$$926$$ 0 0
$$927$$ −2.13253e6 −0.0815073
$$928$$ 0 0
$$929$$ 3.39039e6 0.128888 0.0644438 0.997921i $$-0.479473\pi$$
0.0644438 + 0.997921i $$0.479473\pi$$
$$930$$ 0 0
$$931$$ 4.05651e7 1.53383
$$932$$ 0 0
$$933$$ 1.91080e6 0.0718640
$$934$$ 0 0
$$935$$ 1.26535e7 0.473351
$$936$$ 0 0
$$937$$ −7.67490e6 −0.285577 −0.142789 0.989753i $$-0.545607\pi$$
−0.142789 + 0.989753i $$0.545607\pi$$
$$938$$ 0 0
$$939$$ −1.32471e7 −0.490295
$$940$$ 0 0
$$941$$ −4.55115e7 −1.67551 −0.837756 0.546045i $$-0.816133\pi$$
−0.837756 + 0.546045i $$0.816133\pi$$
$$942$$ 0 0
$$943$$ 1.78001e7 0.651845
$$944$$ 0 0
$$945$$ −3.12200e6 −0.113724
$$946$$ 0 0
$$947$$ −2.28294e7 −0.827218 −0.413609 0.910455i $$-0.635732\pi$$
−0.413609 + 0.910455i $$0.635732\pi$$
$$948$$ 0 0
$$949$$ 3.83484e6 0.138223
$$950$$ 0 0
$$951$$ 6.80673e6 0.244055
$$952$$ 0 0
$$953$$ 4.64478e7 1.65666 0.828330 0.560241i $$-0.189291\pi$$
0.828330 + 0.560241i $$0.189291\pi$$
$$954$$ 0 0
$$955$$ −7.67896e6 −0.272454
$$956$$ 0 0
$$957$$ −1.82856e7 −0.645401
$$958$$ 0 0
$$959$$ 4.41842e6 0.155139
$$960$$ 0 0
$$961$$ −7.77779e6 −0.271674
$$962$$ 0 0
$$963$$ 1.35719e7 0.471603
$$964$$ 0 0
$$965$$ −310850. −0.0107456
$$966$$ 0 0
$$967$$ 2.63000e7 0.904460 0.452230 0.891901i $$-0.350629\pi$$
0.452230 + 0.891901i $$0.350629\pi$$
$$968$$ 0 0
$$969$$ −1.21306e7 −0.415022
$$970$$ 0 0
$$971$$ 2.19967e7 0.748704 0.374352 0.927287i $$-0.377865\pi$$
0.374352 + 0.927287i $$0.377865\pi$$
$$972$$ 0 0
$$973$$ 1.20187e7 0.406983
$$974$$ 0 0
$$975$$ −577116. −0.0194425
$$976$$ 0 0
$$977$$ 4.46750e7 1.49737 0.748683 0.662929i $$-0.230687\pi$$
0.748683 + 0.662929i $$0.230687\pi$$
$$978$$ 0 0
$$979$$ 2.20409e7 0.734977
$$980$$ 0 0
$$981$$ −2.26779e7 −0.752369
$$982$$ 0 0
$$983$$ −2.02740e7 −0.669201 −0.334600 0.942360i $$-0.608601\pi$$
−0.334600 + 0.942360i $$0.608601\pi$$
$$984$$ 0 0
$$985$$ −9.47145e6 −0.311047
$$986$$ 0 0
$$987$$ −1.68410e6 −0.0550270
$$988$$ 0 0
$$989$$ 5.08542e7 1.65324
$$990$$ 0 0
$$991$$ 1.49135e7 0.482386 0.241193 0.970477i $$-0.422461\pi$$
0.241193 + 0.970477i $$0.422461\pi$$
$$992$$ 0 0
$$993$$ 1.97960e6 0.0637095
$$994$$ 0 0
$$995$$ −1.91798e7 −0.614168
$$996$$ 0 0
$$997$$ −3.17032e7 −1.01010 −0.505052 0.863089i $$-0.668527\pi$$
−0.505052 + 0.863089i $$0.668527\pi$$
$$998$$ 0 0
$$999$$ 4.16851e7 1.32150
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.s.1.1 2
4.3 odd 2 inner 320.6.a.s.1.2 2
8.3 odd 2 160.6.a.d.1.1 2
8.5 even 2 160.6.a.d.1.2 yes 2
40.3 even 4 800.6.c.i.449.2 4
40.13 odd 4 800.6.c.i.449.3 4
40.19 odd 2 800.6.a.h.1.2 2
40.27 even 4 800.6.c.i.449.4 4
40.29 even 2 800.6.a.h.1.1 2
40.37 odd 4 800.6.c.i.449.1 4

By twisted newform
Twist Min Dim Char Parity Ord Type
160.6.a.d.1.1 2 8.3 odd 2
160.6.a.d.1.2 yes 2 8.5 even 2
320.6.a.s.1.1 2 1.1 even 1 trivial
320.6.a.s.1.2 2 4.3 odd 2 inner
800.6.a.h.1.1 2 40.29 even 2
800.6.a.h.1.2 2 40.19 odd 2
800.6.c.i.449.1 4 40.37 odd 4
800.6.c.i.449.2 4 40.3 even 4
800.6.c.i.449.3 4 40.13 odd 4
800.6.c.i.449.4 4 40.27 even 4