# Properties

 Label 7350.2.a.bv.1.1 Level 7350 Weight 2 Character 7350.1 Self dual yes Analytic conductor 58.690 Analytic rank 0 Dimension 1 CM no Inner twists 1

# Learn more about

## Newspace parameters

 Level: $$N$$ $$=$$ $$7350 = 2 \cdot 3 \cdot 5^{2} \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 7350.a (trivial)

## Newform invariants

 Self dual: yes Analytic conductor: $$58.6900454856$$ Analytic rank: $$0$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 1050) Fricke sign: $$-1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

 Embedding label 1.1 Character $$\chi$$ $$=$$ 7350.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$$ $$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{12} -5.00000 q^{13} +1.00000 q^{16} +6.00000 q^{17} +1.00000 q^{18} -7.00000 q^{19} +6.00000 q^{23} -1.00000 q^{24} -5.00000 q^{26} -1.00000 q^{27} +8.00000 q^{31} +1.00000 q^{32} +6.00000 q^{34} +1.00000 q^{36} +1.00000 q^{37} -7.00000 q^{38} +5.00000 q^{39} -8.00000 q^{43} +6.00000 q^{46} -6.00000 q^{47} -1.00000 q^{48} -6.00000 q^{51} -5.00000 q^{52} +6.00000 q^{53} -1.00000 q^{54} +7.00000 q^{57} -6.00000 q^{59} -1.00000 q^{61} +8.00000 q^{62} +1.00000 q^{64} +13.0000 q^{67} +6.00000 q^{68} -6.00000 q^{69} +12.0000 q^{71} +1.00000 q^{72} -5.00000 q^{73} +1.00000 q^{74} -7.00000 q^{76} +5.00000 q^{78} -7.00000 q^{79} +1.00000 q^{81} +18.0000 q^{83} -8.00000 q^{86} -6.00000 q^{89} +6.00000 q^{92} -8.00000 q^{93} -6.00000 q^{94} -1.00000 q^{96} +7.00000 q^{97} +O(q^{100})$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 1.00000 0.707107
$$3$$ −1.00000 −0.577350
$$4$$ 1.00000 0.500000
$$5$$ 0 0
$$6$$ −1.00000 −0.408248
$$7$$ 0 0
$$8$$ 1.00000 0.353553
$$9$$ 1.00000 0.333333
$$10$$ 0 0
$$11$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$12$$ −1.00000 −0.288675
$$13$$ −5.00000 −1.38675 −0.693375 0.720577i $$-0.743877\pi$$
−0.693375 + 0.720577i $$0.743877\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 1.00000 0.250000
$$17$$ 6.00000 1.45521 0.727607 0.685994i $$-0.240633\pi$$
0.727607 + 0.685994i $$0.240633\pi$$
$$18$$ 1.00000 0.235702
$$19$$ −7.00000 −1.60591 −0.802955 0.596040i $$-0.796740\pi$$
−0.802955 + 0.596040i $$0.796740\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 0 0
$$23$$ 6.00000 1.25109 0.625543 0.780189i $$-0.284877\pi$$
0.625543 + 0.780189i $$0.284877\pi$$
$$24$$ −1.00000 −0.204124
$$25$$ 0 0
$$26$$ −5.00000 −0.980581
$$27$$ −1.00000 −0.192450
$$28$$ 0 0
$$29$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$30$$ 0 0
$$31$$ 8.00000 1.43684 0.718421 0.695608i $$-0.244865\pi$$
0.718421 + 0.695608i $$0.244865\pi$$
$$32$$ 1.00000 0.176777
$$33$$ 0 0
$$34$$ 6.00000 1.02899
$$35$$ 0 0
$$36$$ 1.00000 0.166667
$$37$$ 1.00000 0.164399 0.0821995 0.996616i $$-0.473806\pi$$
0.0821995 + 0.996616i $$0.473806\pi$$
$$38$$ −7.00000 −1.13555
$$39$$ 5.00000 0.800641
$$40$$ 0 0
$$41$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$42$$ 0 0
$$43$$ −8.00000 −1.21999 −0.609994 0.792406i $$-0.708828\pi$$
−0.609994 + 0.792406i $$0.708828\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 6.00000 0.884652
$$47$$ −6.00000 −0.875190 −0.437595 0.899172i $$-0.644170\pi$$
−0.437595 + 0.899172i $$0.644170\pi$$
$$48$$ −1.00000 −0.144338
$$49$$ 0 0
$$50$$ 0 0
$$51$$ −6.00000 −0.840168
$$52$$ −5.00000 −0.693375
$$53$$ 6.00000 0.824163 0.412082 0.911147i $$-0.364802\pi$$
0.412082 + 0.911147i $$0.364802\pi$$
$$54$$ −1.00000 −0.136083
$$55$$ 0 0
$$56$$ 0 0
$$57$$ 7.00000 0.927173
$$58$$ 0 0
$$59$$ −6.00000 −0.781133 −0.390567 0.920575i $$-0.627721\pi$$
−0.390567 + 0.920575i $$0.627721\pi$$
$$60$$ 0 0
$$61$$ −1.00000 −0.128037 −0.0640184 0.997949i $$-0.520392\pi$$
−0.0640184 + 0.997949i $$0.520392\pi$$
$$62$$ 8.00000 1.01600
$$63$$ 0 0
$$64$$ 1.00000 0.125000
$$65$$ 0 0
$$66$$ 0 0
$$67$$ 13.0000 1.58820 0.794101 0.607785i $$-0.207942\pi$$
0.794101 + 0.607785i $$0.207942\pi$$
$$68$$ 6.00000 0.727607
$$69$$ −6.00000 −0.722315
$$70$$ 0 0
$$71$$ 12.0000 1.42414 0.712069 0.702109i $$-0.247758\pi$$
0.712069 + 0.702109i $$0.247758\pi$$
$$72$$ 1.00000 0.117851
$$73$$ −5.00000 −0.585206 −0.292603 0.956234i $$-0.594521\pi$$
−0.292603 + 0.956234i $$0.594521\pi$$
$$74$$ 1.00000 0.116248
$$75$$ 0 0
$$76$$ −7.00000 −0.802955
$$77$$ 0 0
$$78$$ 5.00000 0.566139
$$79$$ −7.00000 −0.787562 −0.393781 0.919204i $$-0.628833\pi$$
−0.393781 + 0.919204i $$0.628833\pi$$
$$80$$ 0 0
$$81$$ 1.00000 0.111111
$$82$$ 0 0
$$83$$ 18.0000 1.97576 0.987878 0.155230i $$-0.0496119\pi$$
0.987878 + 0.155230i $$0.0496119\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ −8.00000 −0.862662
$$87$$ 0 0
$$88$$ 0 0
$$89$$ −6.00000 −0.635999 −0.317999 0.948091i $$-0.603011\pi$$
−0.317999 + 0.948091i $$0.603011\pi$$
$$90$$ 0 0
$$91$$ 0 0
$$92$$ 6.00000 0.625543
$$93$$ −8.00000 −0.829561
$$94$$ −6.00000 −0.618853
$$95$$ 0 0
$$96$$ −1.00000 −0.102062
$$97$$ 7.00000 0.710742 0.355371 0.934725i $$-0.384354\pi$$
0.355371 + 0.934725i $$0.384354\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ 0 0
$$101$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$102$$ −6.00000 −0.594089
$$103$$ 13.0000 1.28093 0.640464 0.767988i $$-0.278742\pi$$
0.640464 + 0.767988i $$0.278742\pi$$
$$104$$ −5.00000 −0.490290
$$105$$ 0 0
$$106$$ 6.00000 0.582772
$$107$$ 18.0000 1.74013 0.870063 0.492941i $$-0.164078\pi$$
0.870063 + 0.492941i $$0.164078\pi$$
$$108$$ −1.00000 −0.0962250
$$109$$ −7.00000 −0.670478 −0.335239 0.942133i $$-0.608817\pi$$
−0.335239 + 0.942133i $$0.608817\pi$$
$$110$$ 0 0
$$111$$ −1.00000 −0.0949158
$$112$$ 0 0
$$113$$ 6.00000 0.564433 0.282216 0.959351i $$-0.408930\pi$$
0.282216 + 0.959351i $$0.408930\pi$$
$$114$$ 7.00000 0.655610
$$115$$ 0 0
$$116$$ 0 0
$$117$$ −5.00000 −0.462250
$$118$$ −6.00000 −0.552345
$$119$$ 0 0
$$120$$ 0 0
$$121$$ −11.0000 −1.00000
$$122$$ −1.00000 −0.0905357
$$123$$ 0 0
$$124$$ 8.00000 0.718421
$$125$$ 0 0
$$126$$ 0 0
$$127$$ −11.0000 −0.976092 −0.488046 0.872818i $$-0.662290\pi$$
−0.488046 + 0.872818i $$0.662290\pi$$
$$128$$ 1.00000 0.0883883
$$129$$ 8.00000 0.704361
$$130$$ 0 0
$$131$$ 6.00000 0.524222 0.262111 0.965038i $$-0.415581\pi$$
0.262111 + 0.965038i $$0.415581\pi$$
$$132$$ 0 0
$$133$$ 0 0
$$134$$ 13.0000 1.12303
$$135$$ 0 0
$$136$$ 6.00000 0.514496
$$137$$ 18.0000 1.53784 0.768922 0.639343i $$-0.220793\pi$$
0.768922 + 0.639343i $$0.220793\pi$$
$$138$$ −6.00000 −0.510754
$$139$$ 11.0000 0.933008 0.466504 0.884519i $$-0.345513\pi$$
0.466504 + 0.884519i $$0.345513\pi$$
$$140$$ 0 0
$$141$$ 6.00000 0.505291
$$142$$ 12.0000 1.00702
$$143$$ 0 0
$$144$$ 1.00000 0.0833333
$$145$$ 0 0
$$146$$ −5.00000 −0.413803
$$147$$ 0 0
$$148$$ 1.00000 0.0821995
$$149$$ 12.0000 0.983078 0.491539 0.870855i $$-0.336434\pi$$
0.491539 + 0.870855i $$0.336434\pi$$
$$150$$ 0 0
$$151$$ −1.00000 −0.0813788 −0.0406894 0.999172i $$-0.512955\pi$$
−0.0406894 + 0.999172i $$0.512955\pi$$
$$152$$ −7.00000 −0.567775
$$153$$ 6.00000 0.485071
$$154$$ 0 0
$$155$$ 0 0
$$156$$ 5.00000 0.400320
$$157$$ 1.00000 0.0798087 0.0399043 0.999204i $$-0.487295\pi$$
0.0399043 + 0.999204i $$0.487295\pi$$
$$158$$ −7.00000 −0.556890
$$159$$ −6.00000 −0.475831
$$160$$ 0 0
$$161$$ 0 0
$$162$$ 1.00000 0.0785674
$$163$$ 1.00000 0.0783260 0.0391630 0.999233i $$-0.487531\pi$$
0.0391630 + 0.999233i $$0.487531\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 18.0000 1.39707
$$167$$ 6.00000 0.464294 0.232147 0.972681i $$-0.425425\pi$$
0.232147 + 0.972681i $$0.425425\pi$$
$$168$$ 0 0
$$169$$ 12.0000 0.923077
$$170$$ 0 0
$$171$$ −7.00000 −0.535303
$$172$$ −8.00000 −0.609994
$$173$$ −18.0000 −1.36851 −0.684257 0.729241i $$-0.739873\pi$$
−0.684257 + 0.729241i $$0.739873\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 0 0
$$177$$ 6.00000 0.450988
$$178$$ −6.00000 −0.449719
$$179$$ 12.0000 0.896922 0.448461 0.893802i $$-0.351972\pi$$
0.448461 + 0.893802i $$0.351972\pi$$
$$180$$ 0 0
$$181$$ −10.0000 −0.743294 −0.371647 0.928374i $$-0.621207\pi$$
−0.371647 + 0.928374i $$0.621207\pi$$
$$182$$ 0 0
$$183$$ 1.00000 0.0739221
$$184$$ 6.00000 0.442326
$$185$$ 0 0
$$186$$ −8.00000 −0.586588
$$187$$ 0 0
$$188$$ −6.00000 −0.437595
$$189$$ 0 0
$$190$$ 0 0
$$191$$ 24.0000 1.73658 0.868290 0.496058i $$-0.165220\pi$$
0.868290 + 0.496058i $$0.165220\pi$$
$$192$$ −1.00000 −0.0721688
$$193$$ 10.0000 0.719816 0.359908 0.932988i $$-0.382808\pi$$
0.359908 + 0.932988i $$0.382808\pi$$
$$194$$ 7.00000 0.502571
$$195$$ 0 0
$$196$$ 0 0
$$197$$ 12.0000 0.854965 0.427482 0.904024i $$-0.359401\pi$$
0.427482 + 0.904024i $$0.359401\pi$$
$$198$$ 0 0
$$199$$ 11.0000 0.779769 0.389885 0.920864i $$-0.372515\pi$$
0.389885 + 0.920864i $$0.372515\pi$$
$$200$$ 0 0
$$201$$ −13.0000 −0.916949
$$202$$ 0 0
$$203$$ 0 0
$$204$$ −6.00000 −0.420084
$$205$$ 0 0
$$206$$ 13.0000 0.905753
$$207$$ 6.00000 0.417029
$$208$$ −5.00000 −0.346688
$$209$$ 0 0
$$210$$ 0 0
$$211$$ −13.0000 −0.894957 −0.447478 0.894295i $$-0.647678\pi$$
−0.447478 + 0.894295i $$0.647678\pi$$
$$212$$ 6.00000 0.412082
$$213$$ −12.0000 −0.822226
$$214$$ 18.0000 1.23045
$$215$$ 0 0
$$216$$ −1.00000 −0.0680414
$$217$$ 0 0
$$218$$ −7.00000 −0.474100
$$219$$ 5.00000 0.337869
$$220$$ 0 0
$$221$$ −30.0000 −2.01802
$$222$$ −1.00000 −0.0671156
$$223$$ −17.0000 −1.13840 −0.569202 0.822198i $$-0.692748\pi$$
−0.569202 + 0.822198i $$0.692748\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 6.00000 0.399114
$$227$$ −12.0000 −0.796468 −0.398234 0.917284i $$-0.630377\pi$$
−0.398234 + 0.917284i $$0.630377\pi$$
$$228$$ 7.00000 0.463586
$$229$$ 5.00000 0.330409 0.165205 0.986259i $$-0.447172\pi$$
0.165205 + 0.986259i $$0.447172\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ −24.0000 −1.57229 −0.786146 0.618041i $$-0.787927\pi$$
−0.786146 + 0.618041i $$0.787927\pi$$
$$234$$ −5.00000 −0.326860
$$235$$ 0 0
$$236$$ −6.00000 −0.390567
$$237$$ 7.00000 0.454699
$$238$$ 0 0
$$239$$ −12.0000 −0.776215 −0.388108 0.921614i $$-0.626871\pi$$
−0.388108 + 0.921614i $$0.626871\pi$$
$$240$$ 0 0
$$241$$ 5.00000 0.322078 0.161039 0.986948i $$-0.448515\pi$$
0.161039 + 0.986948i $$0.448515\pi$$
$$242$$ −11.0000 −0.707107
$$243$$ −1.00000 −0.0641500
$$244$$ −1.00000 −0.0640184
$$245$$ 0 0
$$246$$ 0 0
$$247$$ 35.0000 2.22700
$$248$$ 8.00000 0.508001
$$249$$ −18.0000 −1.14070
$$250$$ 0 0
$$251$$ −24.0000 −1.51487 −0.757433 0.652913i $$-0.773547\pi$$
−0.757433 + 0.652913i $$0.773547\pi$$
$$252$$ 0 0
$$253$$ 0 0
$$254$$ −11.0000 −0.690201
$$255$$ 0 0
$$256$$ 1.00000 0.0625000
$$257$$ 24.0000 1.49708 0.748539 0.663090i $$-0.230755\pi$$
0.748539 + 0.663090i $$0.230755\pi$$
$$258$$ 8.00000 0.498058
$$259$$ 0 0
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 6.00000 0.370681
$$263$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$264$$ 0 0
$$265$$ 0 0
$$266$$ 0 0
$$267$$ 6.00000 0.367194
$$268$$ 13.0000 0.794101
$$269$$ −24.0000 −1.46331 −0.731653 0.681677i $$-0.761251\pi$$
−0.731653 + 0.681677i $$0.761251\pi$$
$$270$$ 0 0
$$271$$ 20.0000 1.21491 0.607457 0.794353i $$-0.292190\pi$$
0.607457 + 0.794353i $$0.292190\pi$$
$$272$$ 6.00000 0.363803
$$273$$ 0 0
$$274$$ 18.0000 1.08742
$$275$$ 0 0
$$276$$ −6.00000 −0.361158
$$277$$ 19.0000 1.14160 0.570800 0.821089i $$-0.306633\pi$$
0.570800 + 0.821089i $$0.306633\pi$$
$$278$$ 11.0000 0.659736
$$279$$ 8.00000 0.478947
$$280$$ 0 0
$$281$$ −18.0000 −1.07379 −0.536895 0.843649i $$-0.680403\pi$$
−0.536895 + 0.843649i $$0.680403\pi$$
$$282$$ 6.00000 0.357295
$$283$$ −5.00000 −0.297219 −0.148610 0.988896i $$-0.547480\pi$$
−0.148610 + 0.988896i $$0.547480\pi$$
$$284$$ 12.0000 0.712069
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 0 0
$$288$$ 1.00000 0.0589256
$$289$$ 19.0000 1.11765
$$290$$ 0 0
$$291$$ −7.00000 −0.410347
$$292$$ −5.00000 −0.292603
$$293$$ 24.0000 1.40209 0.701047 0.713115i $$-0.252716\pi$$
0.701047 + 0.713115i $$0.252716\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ 1.00000 0.0581238
$$297$$ 0 0
$$298$$ 12.0000 0.695141
$$299$$ −30.0000 −1.73494
$$300$$ 0 0
$$301$$ 0 0
$$302$$ −1.00000 −0.0575435
$$303$$ 0 0
$$304$$ −7.00000 −0.401478
$$305$$ 0 0
$$306$$ 6.00000 0.342997
$$307$$ 28.0000 1.59804 0.799022 0.601302i $$-0.205351\pi$$
0.799022 + 0.601302i $$0.205351\pi$$
$$308$$ 0 0
$$309$$ −13.0000 −0.739544
$$310$$ 0 0
$$311$$ 18.0000 1.02069 0.510343 0.859971i $$-0.329518\pi$$
0.510343 + 0.859971i $$0.329518\pi$$
$$312$$ 5.00000 0.283069
$$313$$ −14.0000 −0.791327 −0.395663 0.918396i $$-0.629485\pi$$
−0.395663 + 0.918396i $$0.629485\pi$$
$$314$$ 1.00000 0.0564333
$$315$$ 0 0
$$316$$ −7.00000 −0.393781
$$317$$ 18.0000 1.01098 0.505490 0.862832i $$-0.331312\pi$$
0.505490 + 0.862832i $$0.331312\pi$$
$$318$$ −6.00000 −0.336463
$$319$$ 0 0
$$320$$ 0 0
$$321$$ −18.0000 −1.00466
$$322$$ 0 0
$$323$$ −42.0000 −2.33694
$$324$$ 1.00000 0.0555556
$$325$$ 0 0
$$326$$ 1.00000 0.0553849
$$327$$ 7.00000 0.387101
$$328$$ 0 0
$$329$$ 0 0
$$330$$ 0 0
$$331$$ −19.0000 −1.04433 −0.522167 0.852843i $$-0.674876\pi$$
−0.522167 + 0.852843i $$0.674876\pi$$
$$332$$ 18.0000 0.987878
$$333$$ 1.00000 0.0547997
$$334$$ 6.00000 0.328305
$$335$$ 0 0
$$336$$ 0 0
$$337$$ 34.0000 1.85210 0.926049 0.377403i $$-0.123183\pi$$
0.926049 + 0.377403i $$0.123183\pi$$
$$338$$ 12.0000 0.652714
$$339$$ −6.00000 −0.325875
$$340$$ 0 0
$$341$$ 0 0
$$342$$ −7.00000 −0.378517
$$343$$ 0 0
$$344$$ −8.00000 −0.431331
$$345$$ 0 0
$$346$$ −18.0000 −0.967686
$$347$$ −18.0000 −0.966291 −0.483145 0.875540i $$-0.660506\pi$$
−0.483145 + 0.875540i $$0.660506\pi$$
$$348$$ 0 0
$$349$$ 26.0000 1.39175 0.695874 0.718164i $$-0.255017\pi$$
0.695874 + 0.718164i $$0.255017\pi$$
$$350$$ 0 0
$$351$$ 5.00000 0.266880
$$352$$ 0 0
$$353$$ 24.0000 1.27739 0.638696 0.769460i $$-0.279474\pi$$
0.638696 + 0.769460i $$0.279474\pi$$
$$354$$ 6.00000 0.318896
$$355$$ 0 0
$$356$$ −6.00000 −0.317999
$$357$$ 0 0
$$358$$ 12.0000 0.634220
$$359$$ 30.0000 1.58334 0.791670 0.610949i $$-0.209212\pi$$
0.791670 + 0.610949i $$0.209212\pi$$
$$360$$ 0 0
$$361$$ 30.0000 1.57895
$$362$$ −10.0000 −0.525588
$$363$$ 11.0000 0.577350
$$364$$ 0 0
$$365$$ 0 0
$$366$$ 1.00000 0.0522708
$$367$$ −8.00000 −0.417597 −0.208798 0.977959i $$-0.566955\pi$$
−0.208798 + 0.977959i $$0.566955\pi$$
$$368$$ 6.00000 0.312772
$$369$$ 0 0
$$370$$ 0 0
$$371$$ 0 0
$$372$$ −8.00000 −0.414781
$$373$$ 13.0000 0.673114 0.336557 0.941663i $$-0.390737\pi$$
0.336557 + 0.941663i $$0.390737\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ −6.00000 −0.309426
$$377$$ 0 0
$$378$$ 0 0
$$379$$ 11.0000 0.565032 0.282516 0.959263i $$-0.408831\pi$$
0.282516 + 0.959263i $$0.408831\pi$$
$$380$$ 0 0
$$381$$ 11.0000 0.563547
$$382$$ 24.0000 1.22795
$$383$$ 6.00000 0.306586 0.153293 0.988181i $$-0.451012\pi$$
0.153293 + 0.988181i $$0.451012\pi$$
$$384$$ −1.00000 −0.0510310
$$385$$ 0 0
$$386$$ 10.0000 0.508987
$$387$$ −8.00000 −0.406663
$$388$$ 7.00000 0.355371
$$389$$ −12.0000 −0.608424 −0.304212 0.952604i $$-0.598393\pi$$
−0.304212 + 0.952604i $$0.598393\pi$$
$$390$$ 0 0
$$391$$ 36.0000 1.82060
$$392$$ 0 0
$$393$$ −6.00000 −0.302660
$$394$$ 12.0000 0.604551
$$395$$ 0 0
$$396$$ 0 0
$$397$$ −14.0000 −0.702640 −0.351320 0.936255i $$-0.614267\pi$$
−0.351320 + 0.936255i $$0.614267\pi$$
$$398$$ 11.0000 0.551380
$$399$$ 0 0
$$400$$ 0 0
$$401$$ −36.0000 −1.79775 −0.898877 0.438201i $$-0.855616\pi$$
−0.898877 + 0.438201i $$0.855616\pi$$
$$402$$ −13.0000 −0.648381
$$403$$ −40.0000 −1.99254
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 0 0
$$408$$ −6.00000 −0.297044
$$409$$ 5.00000 0.247234 0.123617 0.992330i $$-0.460551\pi$$
0.123617 + 0.992330i $$0.460551\pi$$
$$410$$ 0 0
$$411$$ −18.0000 −0.887875
$$412$$ 13.0000 0.640464
$$413$$ 0 0
$$414$$ 6.00000 0.294884
$$415$$ 0 0
$$416$$ −5.00000 −0.245145
$$417$$ −11.0000 −0.538672
$$418$$ 0 0
$$419$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$420$$ 0 0
$$421$$ 5.00000 0.243685 0.121843 0.992549i $$-0.461120\pi$$
0.121843 + 0.992549i $$0.461120\pi$$
$$422$$ −13.0000 −0.632830
$$423$$ −6.00000 −0.291730
$$424$$ 6.00000 0.291386
$$425$$ 0 0
$$426$$ −12.0000 −0.581402
$$427$$ 0 0
$$428$$ 18.0000 0.870063
$$429$$ 0 0
$$430$$ 0 0
$$431$$ −18.0000 −0.867029 −0.433515 0.901146i $$-0.642727\pi$$
−0.433515 + 0.901146i $$0.642727\pi$$
$$432$$ −1.00000 −0.0481125
$$433$$ 34.0000 1.63394 0.816968 0.576683i $$-0.195653\pi$$
0.816968 + 0.576683i $$0.195653\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ −7.00000 −0.335239
$$437$$ −42.0000 −2.00913
$$438$$ 5.00000 0.238909
$$439$$ 5.00000 0.238637 0.119318 0.992856i $$-0.461929\pi$$
0.119318 + 0.992856i $$0.461929\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ −30.0000 −1.42695
$$443$$ 42.0000 1.99548 0.997740 0.0671913i $$-0.0214038\pi$$
0.997740 + 0.0671913i $$0.0214038\pi$$
$$444$$ −1.00000 −0.0474579
$$445$$ 0 0
$$446$$ −17.0000 −0.804973
$$447$$ −12.0000 −0.567581
$$448$$ 0 0
$$449$$ 6.00000 0.283158 0.141579 0.989927i $$-0.454782\pi$$
0.141579 + 0.989927i $$0.454782\pi$$
$$450$$ 0 0
$$451$$ 0 0
$$452$$ 6.00000 0.282216
$$453$$ 1.00000 0.0469841
$$454$$ −12.0000 −0.563188
$$455$$ 0 0
$$456$$ 7.00000 0.327805
$$457$$ −29.0000 −1.35656 −0.678281 0.734802i $$-0.737275\pi$$
−0.678281 + 0.734802i $$0.737275\pi$$
$$458$$ 5.00000 0.233635
$$459$$ −6.00000 −0.280056
$$460$$ 0 0
$$461$$ 6.00000 0.279448 0.139724 0.990190i $$-0.455378\pi$$
0.139724 + 0.990190i $$0.455378\pi$$
$$462$$ 0 0
$$463$$ 31.0000 1.44069 0.720346 0.693615i $$-0.243983\pi$$
0.720346 + 0.693615i $$0.243983\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ −24.0000 −1.11178
$$467$$ −30.0000 −1.38823 −0.694117 0.719862i $$-0.744205\pi$$
−0.694117 + 0.719862i $$0.744205\pi$$
$$468$$ −5.00000 −0.231125
$$469$$ 0 0
$$470$$ 0 0
$$471$$ −1.00000 −0.0460776
$$472$$ −6.00000 −0.276172
$$473$$ 0 0
$$474$$ 7.00000 0.321521
$$475$$ 0 0
$$476$$ 0 0
$$477$$ 6.00000 0.274721
$$478$$ −12.0000 −0.548867
$$479$$ 18.0000 0.822441 0.411220 0.911536i $$-0.365103\pi$$
0.411220 + 0.911536i $$0.365103\pi$$
$$480$$ 0 0
$$481$$ −5.00000 −0.227980
$$482$$ 5.00000 0.227744
$$483$$ 0 0
$$484$$ −11.0000 −0.500000
$$485$$ 0 0
$$486$$ −1.00000 −0.0453609
$$487$$ 40.0000 1.81257 0.906287 0.422664i $$-0.138905\pi$$
0.906287 + 0.422664i $$0.138905\pi$$
$$488$$ −1.00000 −0.0452679
$$489$$ −1.00000 −0.0452216
$$490$$ 0 0
$$491$$ −6.00000 −0.270776 −0.135388 0.990793i $$-0.543228\pi$$
−0.135388 + 0.990793i $$0.543228\pi$$
$$492$$ 0 0
$$493$$ 0 0
$$494$$ 35.0000 1.57472
$$495$$ 0 0
$$496$$ 8.00000 0.359211
$$497$$ 0 0
$$498$$ −18.0000 −0.806599
$$499$$ 5.00000 0.223831 0.111915 0.993718i $$-0.464301\pi$$
0.111915 + 0.993718i $$0.464301\pi$$
$$500$$ 0 0
$$501$$ −6.00000 −0.268060
$$502$$ −24.0000 −1.07117
$$503$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ 0 0
$$507$$ −12.0000 −0.532939
$$508$$ −11.0000 −0.488046
$$509$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ 1.00000 0.0441942
$$513$$ 7.00000 0.309058
$$514$$ 24.0000 1.05859
$$515$$ 0 0
$$516$$ 8.00000 0.352180
$$517$$ 0 0
$$518$$ 0 0
$$519$$ 18.0000 0.790112
$$520$$ 0 0
$$521$$ 42.0000 1.84005 0.920027 0.391856i $$-0.128167\pi$$
0.920027 + 0.391856i $$0.128167\pi$$
$$522$$ 0 0
$$523$$ −32.0000 −1.39926 −0.699631 0.714504i $$-0.746652\pi$$
−0.699631 + 0.714504i $$0.746652\pi$$
$$524$$ 6.00000 0.262111
$$525$$ 0 0
$$526$$ 0 0
$$527$$ 48.0000 2.09091
$$528$$ 0 0
$$529$$ 13.0000 0.565217
$$530$$ 0 0
$$531$$ −6.00000 −0.260378
$$532$$ 0 0
$$533$$ 0 0
$$534$$ 6.00000 0.259645
$$535$$ 0 0
$$536$$ 13.0000 0.561514
$$537$$ −12.0000 −0.517838
$$538$$ −24.0000 −1.03471
$$539$$ 0 0
$$540$$ 0 0
$$541$$ −43.0000 −1.84871 −0.924357 0.381528i $$-0.875398\pi$$
−0.924357 + 0.381528i $$0.875398\pi$$
$$542$$ 20.0000 0.859074
$$543$$ 10.0000 0.429141
$$544$$ 6.00000 0.257248
$$545$$ 0 0
$$546$$ 0 0
$$547$$ 28.0000 1.19719 0.598597 0.801050i $$-0.295725\pi$$
0.598597 + 0.801050i $$0.295725\pi$$
$$548$$ 18.0000 0.768922
$$549$$ −1.00000 −0.0426790
$$550$$ 0 0
$$551$$ 0 0
$$552$$ −6.00000 −0.255377
$$553$$ 0 0
$$554$$ 19.0000 0.807233
$$555$$ 0 0
$$556$$ 11.0000 0.466504
$$557$$ 12.0000 0.508456 0.254228 0.967144i $$-0.418179\pi$$
0.254228 + 0.967144i $$0.418179\pi$$
$$558$$ 8.00000 0.338667
$$559$$ 40.0000 1.69182
$$560$$ 0 0
$$561$$ 0 0
$$562$$ −18.0000 −0.759284
$$563$$ 12.0000 0.505740 0.252870 0.967500i $$-0.418626\pi$$
0.252870 + 0.967500i $$0.418626\pi$$
$$564$$ 6.00000 0.252646
$$565$$ 0 0
$$566$$ −5.00000 −0.210166
$$567$$ 0 0
$$568$$ 12.0000 0.503509
$$569$$ −36.0000 −1.50920 −0.754599 0.656186i $$-0.772169\pi$$
−0.754599 + 0.656186i $$0.772169\pi$$
$$570$$ 0 0
$$571$$ 5.00000 0.209243 0.104622 0.994512i $$-0.466637\pi$$
0.104622 + 0.994512i $$0.466637\pi$$
$$572$$ 0 0
$$573$$ −24.0000 −1.00261
$$574$$ 0 0
$$575$$ 0 0
$$576$$ 1.00000 0.0416667
$$577$$ −14.0000 −0.582828 −0.291414 0.956597i $$-0.594126\pi$$
−0.291414 + 0.956597i $$0.594126\pi$$
$$578$$ 19.0000 0.790296
$$579$$ −10.0000 −0.415586
$$580$$ 0 0
$$581$$ 0 0
$$582$$ −7.00000 −0.290159
$$583$$ 0 0
$$584$$ −5.00000 −0.206901
$$585$$ 0 0
$$586$$ 24.0000 0.991431
$$587$$ 30.0000 1.23823 0.619116 0.785299i $$-0.287491\pi$$
0.619116 + 0.785299i $$0.287491\pi$$
$$588$$ 0 0
$$589$$ −56.0000 −2.30744
$$590$$ 0 0
$$591$$ −12.0000 −0.493614
$$592$$ 1.00000 0.0410997
$$593$$ 6.00000 0.246390 0.123195 0.992382i $$-0.460686\pi$$
0.123195 + 0.992382i $$0.460686\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 12.0000 0.491539
$$597$$ −11.0000 −0.450200
$$598$$ −30.0000 −1.22679
$$599$$ −30.0000 −1.22577 −0.612883 0.790173i $$-0.709990\pi$$
−0.612883 + 0.790173i $$0.709990\pi$$
$$600$$ 0 0
$$601$$ 35.0000 1.42768 0.713840 0.700309i $$-0.246954\pi$$
0.713840 + 0.700309i $$0.246954\pi$$
$$602$$ 0 0
$$603$$ 13.0000 0.529401
$$604$$ −1.00000 −0.0406894
$$605$$ 0 0
$$606$$ 0 0
$$607$$ 43.0000 1.74532 0.872658 0.488332i $$-0.162394\pi$$
0.872658 + 0.488332i $$0.162394\pi$$
$$608$$ −7.00000 −0.283887
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 30.0000 1.21367
$$612$$ 6.00000 0.242536
$$613$$ −38.0000 −1.53481 −0.767403 0.641165i $$-0.778451\pi$$
−0.767403 + 0.641165i $$0.778451\pi$$
$$614$$ 28.0000 1.12999
$$615$$ 0 0
$$616$$ 0 0
$$617$$ −48.0000 −1.93241 −0.966204 0.257780i $$-0.917009\pi$$
−0.966204 + 0.257780i $$0.917009\pi$$
$$618$$ −13.0000 −0.522937
$$619$$ 20.0000 0.803868 0.401934 0.915669i $$-0.368338\pi$$
0.401934 + 0.915669i $$0.368338\pi$$
$$620$$ 0 0
$$621$$ −6.00000 −0.240772
$$622$$ 18.0000 0.721734
$$623$$ 0 0
$$624$$ 5.00000 0.200160
$$625$$ 0 0
$$626$$ −14.0000 −0.559553
$$627$$ 0 0
$$628$$ 1.00000 0.0399043
$$629$$ 6.00000 0.239236
$$630$$ 0 0
$$631$$ −19.0000 −0.756378 −0.378189 0.925728i $$-0.623453\pi$$
−0.378189 + 0.925728i $$0.623453\pi$$
$$632$$ −7.00000 −0.278445
$$633$$ 13.0000 0.516704
$$634$$ 18.0000 0.714871
$$635$$ 0 0
$$636$$ −6.00000 −0.237915
$$637$$ 0 0
$$638$$ 0 0
$$639$$ 12.0000 0.474713
$$640$$ 0 0
$$641$$ −24.0000 −0.947943 −0.473972 0.880540i $$-0.657180\pi$$
−0.473972 + 0.880540i $$0.657180\pi$$
$$642$$ −18.0000 −0.710403
$$643$$ −11.0000 −0.433798 −0.216899 0.976194i $$-0.569594\pi$$
−0.216899 + 0.976194i $$0.569594\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ −42.0000 −1.65247
$$647$$ 12.0000 0.471769 0.235884 0.971781i $$-0.424201\pi$$
0.235884 + 0.971781i $$0.424201\pi$$
$$648$$ 1.00000 0.0392837
$$649$$ 0 0
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 1.00000 0.0391630
$$653$$ 36.0000 1.40879 0.704394 0.709809i $$-0.251219\pi$$
0.704394 + 0.709809i $$0.251219\pi$$
$$654$$ 7.00000 0.273722
$$655$$ 0 0
$$656$$ 0 0
$$657$$ −5.00000 −0.195069
$$658$$ 0 0
$$659$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$660$$ 0 0
$$661$$ 35.0000 1.36134 0.680671 0.732589i $$-0.261688\pi$$
0.680671 + 0.732589i $$0.261688\pi$$
$$662$$ −19.0000 −0.738456
$$663$$ 30.0000 1.16510
$$664$$ 18.0000 0.698535
$$665$$ 0 0
$$666$$ 1.00000 0.0387492
$$667$$ 0 0
$$668$$ 6.00000 0.232147
$$669$$ 17.0000 0.657258
$$670$$ 0 0
$$671$$ 0 0
$$672$$ 0 0
$$673$$ 1.00000 0.0385472 0.0192736 0.999814i $$-0.493865\pi$$
0.0192736 + 0.999814i $$0.493865\pi$$
$$674$$ 34.0000 1.30963
$$675$$ 0 0
$$676$$ 12.0000 0.461538
$$677$$ −42.0000 −1.61419 −0.807096 0.590421i $$-0.798962\pi$$
−0.807096 + 0.590421i $$0.798962\pi$$
$$678$$ −6.00000 −0.230429
$$679$$ 0 0
$$680$$ 0 0
$$681$$ 12.0000 0.459841
$$682$$ 0 0
$$683$$ −24.0000 −0.918334 −0.459167 0.888350i $$-0.651852\pi$$
−0.459167 + 0.888350i $$0.651852\pi$$
$$684$$ −7.00000 −0.267652
$$685$$ 0 0
$$686$$ 0 0
$$687$$ −5.00000 −0.190762
$$688$$ −8.00000 −0.304997
$$689$$ −30.0000 −1.14291
$$690$$ 0 0
$$691$$ −7.00000 −0.266293 −0.133146 0.991096i $$-0.542508\pi$$
−0.133146 + 0.991096i $$0.542508\pi$$
$$692$$ −18.0000 −0.684257
$$693$$ 0 0
$$694$$ −18.0000 −0.683271
$$695$$ 0 0
$$696$$ 0 0
$$697$$ 0 0
$$698$$ 26.0000 0.984115
$$699$$ 24.0000 0.907763
$$700$$ 0 0
$$701$$ −30.0000 −1.13308 −0.566542 0.824033i $$-0.691719\pi$$
−0.566542 + 0.824033i $$0.691719\pi$$
$$702$$ 5.00000 0.188713
$$703$$ −7.00000 −0.264010
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 24.0000 0.903252
$$707$$ 0 0
$$708$$ 6.00000 0.225494
$$709$$ −7.00000 −0.262891 −0.131445 0.991323i $$-0.541962\pi$$
−0.131445 + 0.991323i $$0.541962\pi$$
$$710$$ 0 0
$$711$$ −7.00000 −0.262521
$$712$$ −6.00000 −0.224860
$$713$$ 48.0000 1.79761
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 12.0000 0.448461
$$717$$ 12.0000 0.448148
$$718$$ 30.0000 1.11959
$$719$$ −36.0000 −1.34257 −0.671287 0.741198i $$-0.734258\pi$$
−0.671287 + 0.741198i $$0.734258\pi$$
$$720$$ 0 0
$$721$$ 0 0
$$722$$ 30.0000 1.11648
$$723$$ −5.00000 −0.185952
$$724$$ −10.0000 −0.371647
$$725$$ 0 0
$$726$$ 11.0000 0.408248
$$727$$ 37.0000 1.37225 0.686127 0.727482i $$-0.259309\pi$$
0.686127 + 0.727482i $$0.259309\pi$$
$$728$$ 0 0
$$729$$ 1.00000 0.0370370
$$730$$ 0 0
$$731$$ −48.0000 −1.77534
$$732$$ 1.00000 0.0369611
$$733$$ −41.0000 −1.51437 −0.757185 0.653201i $$-0.773426\pi$$
−0.757185 + 0.653201i $$0.773426\pi$$
$$734$$ −8.00000 −0.295285
$$735$$ 0 0
$$736$$ 6.00000 0.221163
$$737$$ 0 0
$$738$$ 0 0
$$739$$ −25.0000 −0.919640 −0.459820 0.888012i $$-0.652086\pi$$
−0.459820 + 0.888012i $$0.652086\pi$$
$$740$$ 0 0
$$741$$ −35.0000 −1.28576
$$742$$ 0 0
$$743$$ −30.0000 −1.10059 −0.550297 0.834969i $$-0.685485\pi$$
−0.550297 + 0.834969i $$0.685485\pi$$
$$744$$ −8.00000 −0.293294
$$745$$ 0 0
$$746$$ 13.0000 0.475964
$$747$$ 18.0000 0.658586
$$748$$ 0 0
$$749$$ 0 0
$$750$$ 0 0
$$751$$ −25.0000 −0.912263 −0.456131 0.889912i $$-0.650765\pi$$
−0.456131 + 0.889912i $$0.650765\pi$$
$$752$$ −6.00000 −0.218797
$$753$$ 24.0000 0.874609
$$754$$ 0 0
$$755$$ 0 0
$$756$$ 0 0
$$757$$ −29.0000 −1.05402 −0.527011 0.849858i $$-0.676688\pi$$
−0.527011 + 0.849858i $$0.676688\pi$$
$$758$$ 11.0000 0.399538
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 18.0000 0.652499 0.326250 0.945284i $$-0.394215\pi$$
0.326250 + 0.945284i $$0.394215\pi$$
$$762$$ 11.0000 0.398488
$$763$$ 0 0
$$764$$ 24.0000 0.868290
$$765$$ 0 0
$$766$$ 6.00000 0.216789
$$767$$ 30.0000 1.08324
$$768$$ −1.00000 −0.0360844
$$769$$ −10.0000 −0.360609 −0.180305 0.983611i $$-0.557708\pi$$
−0.180305 + 0.983611i $$0.557708\pi$$
$$770$$ 0 0
$$771$$ −24.0000 −0.864339
$$772$$ 10.0000 0.359908
$$773$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$774$$ −8.00000 −0.287554
$$775$$ 0 0
$$776$$ 7.00000 0.251285
$$777$$ 0 0
$$778$$ −12.0000 −0.430221
$$779$$ 0 0
$$780$$ 0 0
$$781$$ 0 0
$$782$$ 36.0000 1.28736
$$783$$ 0 0
$$784$$ 0 0
$$785$$ 0 0
$$786$$ −6.00000 −0.214013
$$787$$ −23.0000 −0.819861 −0.409931 0.912117i $$-0.634447\pi$$
−0.409931 + 0.912117i $$0.634447\pi$$
$$788$$ 12.0000 0.427482
$$789$$ 0 0
$$790$$ 0 0
$$791$$ 0 0
$$792$$ 0 0
$$793$$ 5.00000 0.177555
$$794$$ −14.0000 −0.496841
$$795$$ 0 0
$$796$$ 11.0000 0.389885
$$797$$ −54.0000 −1.91278 −0.956389 0.292096i $$-0.905647\pi$$
−0.956389 + 0.292096i $$0.905647\pi$$
$$798$$ 0 0
$$799$$ −36.0000 −1.27359
$$800$$ 0 0
$$801$$ −6.00000 −0.212000
$$802$$ −36.0000 −1.27120
$$803$$ 0 0
$$804$$ −13.0000 −0.458475
$$805$$ 0 0
$$806$$ −40.0000 −1.40894
$$807$$ 24.0000 0.844840
$$808$$ 0 0
$$809$$ −30.0000 −1.05474 −0.527372 0.849635i $$-0.676823\pi$$
−0.527372 + 0.849635i $$0.676823\pi$$
$$810$$ 0 0
$$811$$ 11.0000 0.386262 0.193131 0.981173i $$-0.438136\pi$$
0.193131 + 0.981173i $$0.438136\pi$$
$$812$$ 0 0
$$813$$ −20.0000 −0.701431
$$814$$ 0 0
$$815$$ 0 0
$$816$$ −6.00000 −0.210042
$$817$$ 56.0000 1.95919
$$818$$ 5.00000 0.174821
$$819$$ 0 0
$$820$$ 0 0
$$821$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$822$$ −18.0000 −0.627822
$$823$$ −5.00000 −0.174289 −0.0871445 0.996196i $$-0.527774\pi$$
−0.0871445 + 0.996196i $$0.527774\pi$$
$$824$$ 13.0000 0.452876
$$825$$ 0 0
$$826$$ 0 0
$$827$$ 24.0000 0.834562 0.417281 0.908778i $$-0.362983\pi$$
0.417281 + 0.908778i $$0.362983\pi$$
$$828$$ 6.00000 0.208514
$$829$$ −7.00000 −0.243120 −0.121560 0.992584i $$-0.538790\pi$$
−0.121560 + 0.992584i $$0.538790\pi$$
$$830$$ 0 0
$$831$$ −19.0000 −0.659103
$$832$$ −5.00000 −0.173344
$$833$$ 0 0
$$834$$ −11.0000 −0.380899
$$835$$ 0 0
$$836$$ 0 0
$$837$$ −8.00000 −0.276520
$$838$$ 0 0
$$839$$ −18.0000 −0.621429 −0.310715 0.950503i $$-0.600568\pi$$
−0.310715 + 0.950503i $$0.600568\pi$$
$$840$$ 0 0
$$841$$ −29.0000 −1.00000
$$842$$ 5.00000 0.172311
$$843$$ 18.0000 0.619953
$$844$$ −13.0000 −0.447478
$$845$$ 0 0
$$846$$ −6.00000 −0.206284
$$847$$ 0 0
$$848$$ 6.00000 0.206041
$$849$$ 5.00000 0.171600
$$850$$ 0 0
$$851$$ 6.00000 0.205677
$$852$$ −12.0000 −0.411113
$$853$$ −26.0000 −0.890223 −0.445112 0.895475i $$-0.646836\pi$$
−0.445112 + 0.895475i $$0.646836\pi$$
$$854$$ 0 0
$$855$$ 0 0
$$856$$ 18.0000 0.615227
$$857$$ −18.0000 −0.614868 −0.307434 0.951569i $$-0.599470\pi$$
−0.307434 + 0.951569i $$0.599470\pi$$
$$858$$ 0 0
$$859$$ −4.00000 −0.136478 −0.0682391 0.997669i $$-0.521738\pi$$
−0.0682391 + 0.997669i $$0.521738\pi$$
$$860$$ 0 0
$$861$$ 0 0
$$862$$ −18.0000 −0.613082
$$863$$ −30.0000 −1.02121 −0.510606 0.859815i $$-0.670579\pi$$
−0.510606 + 0.859815i $$0.670579\pi$$
$$864$$ −1.00000 −0.0340207
$$865$$ 0 0
$$866$$ 34.0000 1.15537
$$867$$ −19.0000 −0.645274
$$868$$ 0 0
$$869$$ 0 0
$$870$$ 0 0
$$871$$ −65.0000 −2.20244
$$872$$ −7.00000 −0.237050
$$873$$ 7.00000 0.236914
$$874$$ −42.0000 −1.42067
$$875$$ 0 0
$$876$$ 5.00000 0.168934
$$877$$ −47.0000 −1.58708 −0.793539 0.608520i $$-0.791764\pi$$
−0.793539 + 0.608520i $$0.791764\pi$$
$$878$$ 5.00000 0.168742
$$879$$ −24.0000 −0.809500
$$880$$ 0 0
$$881$$ −12.0000 −0.404290 −0.202145 0.979356i $$-0.564791\pi$$
−0.202145 + 0.979356i $$0.564791\pi$$
$$882$$ 0 0
$$883$$ 25.0000 0.841317 0.420658 0.907219i $$-0.361799\pi$$
0.420658 + 0.907219i $$0.361799\pi$$
$$884$$ −30.0000 −1.00901
$$885$$ 0 0
$$886$$ 42.0000 1.41102
$$887$$ 6.00000 0.201460 0.100730 0.994914i $$-0.467882\pi$$
0.100730 + 0.994914i $$0.467882\pi$$
$$888$$ −1.00000 −0.0335578
$$889$$ 0 0
$$890$$ 0 0
$$891$$ 0 0
$$892$$ −17.0000 −0.569202
$$893$$ 42.0000 1.40548
$$894$$ −12.0000 −0.401340
$$895$$ 0 0
$$896$$ 0 0
$$897$$ 30.0000 1.00167
$$898$$ 6.00000 0.200223
$$899$$ 0 0
$$900$$ 0 0
$$901$$ 36.0000 1.19933
$$902$$ 0 0
$$903$$ 0 0
$$904$$ 6.00000 0.199557
$$905$$ 0 0
$$906$$ 1.00000 0.0332228
$$907$$ 7.00000 0.232431 0.116216 0.993224i $$-0.462924\pi$$
0.116216 + 0.993224i $$0.462924\pi$$
$$908$$ −12.0000 −0.398234
$$909$$ 0 0
$$910$$ 0 0
$$911$$ 30.0000 0.993944 0.496972 0.867766i $$-0.334445\pi$$
0.496972 + 0.867766i $$0.334445\pi$$
$$912$$ 7.00000 0.231793
$$913$$ 0 0
$$914$$ −29.0000 −0.959235
$$915$$ 0 0
$$916$$ 5.00000 0.165205
$$917$$ 0 0
$$918$$ −6.00000 −0.198030
$$919$$ 8.00000 0.263896 0.131948 0.991257i $$-0.457877\pi$$
0.131948 + 0.991257i $$0.457877\pi$$
$$920$$ 0 0
$$921$$ −28.0000 −0.922631
$$922$$ 6.00000 0.197599
$$923$$ −60.0000 −1.97492
$$924$$ 0 0
$$925$$ 0 0
$$926$$ 31.0000 1.01872
$$927$$ 13.0000 0.426976
$$928$$ 0 0
$$929$$ −36.0000 −1.18112 −0.590561 0.806993i $$-0.701093\pi$$
−0.590561 + 0.806993i $$0.701093\pi$$
$$930$$ 0 0
$$931$$ 0 0
$$932$$ −24.0000 −0.786146
$$933$$ −18.0000 −0.589294
$$934$$ −30.0000 −0.981630
$$935$$ 0 0
$$936$$ −5.00000 −0.163430
$$937$$ 10.0000 0.326686 0.163343 0.986569i $$-0.447772\pi$$
0.163343 + 0.986569i $$0.447772\pi$$
$$938$$ 0 0
$$939$$ 14.0000 0.456873
$$940$$ 0 0
$$941$$ −6.00000 −0.195594 −0.0977972 0.995206i $$-0.531180\pi$$
−0.0977972 + 0.995206i $$0.531180\pi$$
$$942$$ −1.00000 −0.0325818
$$943$$ 0 0
$$944$$ −6.00000 −0.195283
$$945$$ 0 0
$$946$$ 0 0
$$947$$ −42.0000 −1.36482 −0.682408 0.730971i $$-0.739067\pi$$
−0.682408 + 0.730971i $$0.739067\pi$$
$$948$$ 7.00000 0.227349
$$949$$ 25.0000 0.811534
$$950$$ 0 0
$$951$$ −18.0000 −0.583690
$$952$$ 0 0
$$953$$ 12.0000 0.388718 0.194359 0.980930i $$-0.437737\pi$$
0.194359 + 0.980930i $$0.437737\pi$$
$$954$$ 6.00000 0.194257
$$955$$ 0 0
$$956$$ −12.0000 −0.388108
$$957$$ 0 0
$$958$$ 18.0000 0.581554
$$959$$ 0 0
$$960$$ 0 0
$$961$$ 33.0000 1.06452
$$962$$ −5.00000 −0.161206
$$963$$ 18.0000 0.580042
$$964$$ 5.00000 0.161039
$$965$$ 0 0
$$966$$ 0 0
$$967$$ −41.0000 −1.31847 −0.659236 0.751936i $$-0.729120\pi$$
−0.659236 + 0.751936i $$0.729120\pi$$
$$968$$ −11.0000 −0.353553
$$969$$ 42.0000 1.34923
$$970$$ 0 0
$$971$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$972$$ −1.00000 −0.0320750
$$973$$ 0 0
$$974$$ 40.0000 1.28168
$$975$$ 0 0
$$976$$ −1.00000 −0.0320092
$$977$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$978$$ −1.00000 −0.0319765
$$979$$ 0 0
$$980$$ 0 0
$$981$$ −7.00000 −0.223493
$$982$$ −6.00000 −0.191468
$$983$$ 30.0000 0.956851 0.478426 0.878128i $$-0.341208\pi$$
0.478426 + 0.878128i $$0.341208\pi$$
$$984$$ 0 0
$$985$$ 0 0
$$986$$ 0 0
$$987$$ 0 0
$$988$$ 35.0000 1.11350
$$989$$ −48.0000 −1.52631
$$990$$ 0 0
$$991$$ 32.0000 1.01651 0.508257 0.861206i $$-0.330290\pi$$
0.508257 + 0.861206i $$0.330290\pi$$
$$992$$ 8.00000 0.254000
$$993$$ 19.0000 0.602947
$$994$$ 0 0
$$995$$ 0 0
$$996$$ −18.0000 −0.570352
$$997$$ 13.0000 0.411714 0.205857 0.978582i $$-0.434002\pi$$
0.205857 + 0.978582i $$0.434002\pi$$
$$998$$ 5.00000 0.158272
$$999$$ −1.00000 −0.0316386
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 7350.2.a.bv.1.1 1
5.4 even 2 7350.2.a.bf.1.1 1
7.2 even 3 1050.2.i.g.151.1 2
7.4 even 3 1050.2.i.g.751.1 yes 2
7.6 odd 2 7350.2.a.cv.1.1 1
35.2 odd 12 1050.2.o.d.949.2 4
35.4 even 6 1050.2.i.n.751.1 yes 2
35.9 even 6 1050.2.i.n.151.1 yes 2
35.18 odd 12 1050.2.o.d.499.2 4
35.23 odd 12 1050.2.o.d.949.1 4
35.32 odd 12 1050.2.o.d.499.1 4
35.34 odd 2 7350.2.a.k.1.1 1

By twisted newform
Twist Min Dim Char Parity Ord Type
1050.2.i.g.151.1 2 7.2 even 3
1050.2.i.g.751.1 yes 2 7.4 even 3
1050.2.i.n.151.1 yes 2 35.9 even 6
1050.2.i.n.751.1 yes 2 35.4 even 6
1050.2.o.d.499.1 4 35.32 odd 12
1050.2.o.d.499.2 4 35.18 odd 12
1050.2.o.d.949.1 4 35.23 odd 12
1050.2.o.d.949.2 4 35.2 odd 12
7350.2.a.k.1.1 1 35.34 odd 2
7350.2.a.bf.1.1 1 5.4 even 2
7350.2.a.bv.1.1 1 1.1 even 1 trivial
7350.2.a.cv.1.1 1 7.6 odd 2