# Properties

 Label 1710.2.a.a.1.1 Level $1710$ Weight $2$ Character 1710.1 Self dual yes Analytic conductor $13.654$ Analytic rank $1$ Dimension $1$ CM no Inner twists $1$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$1710 = 2 \cdot 3^{2} \cdot 5 \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1710.a (trivial)

## Newform invariants

 Self dual: yes Analytic conductor: $$13.6544187456$$ Analytic rank: $$1$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: yes Fricke sign: $$1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

 Embedding label 1.1 Character $$\chi$$ $$=$$ 1710.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q-1.00000 q^{2} +1.00000 q^{4} -1.00000 q^{5} -4.00000 q^{7} -1.00000 q^{8} +O(q^{10})$$ $$q-1.00000 q^{2} +1.00000 q^{4} -1.00000 q^{5} -4.00000 q^{7} -1.00000 q^{8} +1.00000 q^{10} +6.00000 q^{11} +4.00000 q^{14} +1.00000 q^{16} -4.00000 q^{17} -1.00000 q^{19} -1.00000 q^{20} -6.00000 q^{22} +4.00000 q^{23} +1.00000 q^{25} -4.00000 q^{28} +10.0000 q^{29} -2.00000 q^{31} -1.00000 q^{32} +4.00000 q^{34} +4.00000 q^{35} -4.00000 q^{37} +1.00000 q^{38} +1.00000 q^{40} -10.0000 q^{41} -12.0000 q^{43} +6.00000 q^{44} -4.00000 q^{46} +9.00000 q^{49} -1.00000 q^{50} +6.00000 q^{53} -6.00000 q^{55} +4.00000 q^{56} -10.0000 q^{58} -4.00000 q^{59} -10.0000 q^{61} +2.00000 q^{62} +1.00000 q^{64} -8.00000 q^{67} -4.00000 q^{68} -4.00000 q^{70} +6.00000 q^{73} +4.00000 q^{74} -1.00000 q^{76} -24.0000 q^{77} -10.0000 q^{79} -1.00000 q^{80} +10.0000 q^{82} -14.0000 q^{83} +4.00000 q^{85} +12.0000 q^{86} -6.00000 q^{88} -10.0000 q^{89} +4.00000 q^{92} +1.00000 q^{95} -6.00000 q^{97} -9.00000 q^{98} +O(q^{100})$$

## 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
$$3$$ 0 0
$$4$$ 1.00000 0.500000
$$5$$ −1.00000 −0.447214
$$6$$ 0 0
$$7$$ −4.00000 −1.51186 −0.755929 0.654654i $$-0.772814\pi$$
−0.755929 + 0.654654i $$0.772814\pi$$
$$8$$ −1.00000 −0.353553
$$9$$ 0 0
$$10$$ 1.00000 0.316228
$$11$$ 6.00000 1.80907 0.904534 0.426401i $$-0.140219\pi$$
0.904534 + 0.426401i $$0.140219\pi$$
$$12$$ 0 0
$$13$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$14$$ 4.00000 1.06904
$$15$$ 0 0
$$16$$ 1.00000 0.250000
$$17$$ −4.00000 −0.970143 −0.485071 0.874475i $$-0.661206\pi$$
−0.485071 + 0.874475i $$0.661206\pi$$
$$18$$ 0 0
$$19$$ −1.00000 −0.229416
$$20$$ −1.00000 −0.223607
$$21$$ 0 0
$$22$$ −6.00000 −1.27920
$$23$$ 4.00000 0.834058 0.417029 0.908893i $$-0.363071\pi$$
0.417029 + 0.908893i $$0.363071\pi$$
$$24$$ 0 0
$$25$$ 1.00000 0.200000
$$26$$ 0 0
$$27$$ 0 0
$$28$$ −4.00000 −0.755929
$$29$$ 10.0000 1.85695 0.928477 0.371391i $$-0.121119\pi$$
0.928477 + 0.371391i $$0.121119\pi$$
$$30$$ 0 0
$$31$$ −2.00000 −0.359211 −0.179605 0.983739i $$-0.557482\pi$$
−0.179605 + 0.983739i $$0.557482\pi$$
$$32$$ −1.00000 −0.176777
$$33$$ 0 0
$$34$$ 4.00000 0.685994
$$35$$ 4.00000 0.676123
$$36$$ 0 0
$$37$$ −4.00000 −0.657596 −0.328798 0.944400i $$-0.606644\pi$$
−0.328798 + 0.944400i $$0.606644\pi$$
$$38$$ 1.00000 0.162221
$$39$$ 0 0
$$40$$ 1.00000 0.158114
$$41$$ −10.0000 −1.56174 −0.780869 0.624695i $$-0.785223\pi$$
−0.780869 + 0.624695i $$0.785223\pi$$
$$42$$ 0 0
$$43$$ −12.0000 −1.82998 −0.914991 0.403473i $$-0.867803\pi$$
−0.914991 + 0.403473i $$0.867803\pi$$
$$44$$ 6.00000 0.904534
$$45$$ 0 0
$$46$$ −4.00000 −0.589768
$$47$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$48$$ 0 0
$$49$$ 9.00000 1.28571
$$50$$ −1.00000 −0.141421
$$51$$ 0 0
$$52$$ 0 0
$$53$$ 6.00000 0.824163 0.412082 0.911147i $$-0.364802\pi$$
0.412082 + 0.911147i $$0.364802\pi$$
$$54$$ 0 0
$$55$$ −6.00000 −0.809040
$$56$$ 4.00000 0.534522
$$57$$ 0 0
$$58$$ −10.0000 −1.31306
$$59$$ −4.00000 −0.520756 −0.260378 0.965507i $$-0.583847\pi$$
−0.260378 + 0.965507i $$0.583847\pi$$
$$60$$ 0 0
$$61$$ −10.0000 −1.28037 −0.640184 0.768221i $$-0.721142\pi$$
−0.640184 + 0.768221i $$0.721142\pi$$
$$62$$ 2.00000 0.254000
$$63$$ 0 0
$$64$$ 1.00000 0.125000
$$65$$ 0 0
$$66$$ 0 0
$$67$$ −8.00000 −0.977356 −0.488678 0.872464i $$-0.662521\pi$$
−0.488678 + 0.872464i $$0.662521\pi$$
$$68$$ −4.00000 −0.485071
$$69$$ 0 0
$$70$$ −4.00000 −0.478091
$$71$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$72$$ 0 0
$$73$$ 6.00000 0.702247 0.351123 0.936329i $$-0.385800\pi$$
0.351123 + 0.936329i $$0.385800\pi$$
$$74$$ 4.00000 0.464991
$$75$$ 0 0
$$76$$ −1.00000 −0.114708
$$77$$ −24.0000 −2.73505
$$78$$ 0 0
$$79$$ −10.0000 −1.12509 −0.562544 0.826767i $$-0.690177\pi$$
−0.562544 + 0.826767i $$0.690177\pi$$
$$80$$ −1.00000 −0.111803
$$81$$ 0 0
$$82$$ 10.0000 1.10432
$$83$$ −14.0000 −1.53670 −0.768350 0.640030i $$-0.778922\pi$$
−0.768350 + 0.640030i $$0.778922\pi$$
$$84$$ 0 0
$$85$$ 4.00000 0.433861
$$86$$ 12.0000 1.29399
$$87$$ 0 0
$$88$$ −6.00000 −0.639602
$$89$$ −10.0000 −1.06000 −0.529999 0.847998i $$-0.677808\pi$$
−0.529999 + 0.847998i $$0.677808\pi$$
$$90$$ 0 0
$$91$$ 0 0
$$92$$ 4.00000 0.417029
$$93$$ 0 0
$$94$$ 0 0
$$95$$ 1.00000 0.102598
$$96$$ 0 0
$$97$$ −6.00000 −0.609208 −0.304604 0.952479i $$-0.598524\pi$$
−0.304604 + 0.952479i $$0.598524\pi$$
$$98$$ −9.00000 −0.909137
$$99$$ 0 0
$$100$$ 1.00000 0.100000
$$101$$ −10.0000 −0.995037 −0.497519 0.867453i $$-0.665755\pi$$
−0.497519 + 0.867453i $$0.665755\pi$$
$$102$$ 0 0
$$103$$ 18.0000 1.77359 0.886796 0.462160i $$-0.152926\pi$$
0.886796 + 0.462160i $$0.152926\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ −6.00000 −0.582772
$$107$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$108$$ 0 0
$$109$$ −8.00000 −0.766261 −0.383131 0.923694i $$-0.625154\pi$$
−0.383131 + 0.923694i $$0.625154\pi$$
$$110$$ 6.00000 0.572078
$$111$$ 0 0
$$112$$ −4.00000 −0.377964
$$113$$ 2.00000 0.188144 0.0940721 0.995565i $$-0.470012\pi$$
0.0940721 + 0.995565i $$0.470012\pi$$
$$114$$ 0 0
$$115$$ −4.00000 −0.373002
$$116$$ 10.0000 0.928477
$$117$$ 0 0
$$118$$ 4.00000 0.368230
$$119$$ 16.0000 1.46672
$$120$$ 0 0
$$121$$ 25.0000 2.27273
$$122$$ 10.0000 0.905357
$$123$$ 0 0
$$124$$ −2.00000 −0.179605
$$125$$ −1.00000 −0.0894427
$$126$$ 0 0
$$127$$ 18.0000 1.59724 0.798621 0.601834i $$-0.205563\pi$$
0.798621 + 0.601834i $$0.205563\pi$$
$$128$$ −1.00000 −0.0883883
$$129$$ 0 0
$$130$$ 0 0
$$131$$ 10.0000 0.873704 0.436852 0.899533i $$-0.356093\pi$$
0.436852 + 0.899533i $$0.356093\pi$$
$$132$$ 0 0
$$133$$ 4.00000 0.346844
$$134$$ 8.00000 0.691095
$$135$$ 0 0
$$136$$ 4.00000 0.342997
$$137$$ −12.0000 −1.02523 −0.512615 0.858619i $$-0.671323\pi$$
−0.512615 + 0.858619i $$0.671323\pi$$
$$138$$ 0 0
$$139$$ −12.0000 −1.01783 −0.508913 0.860818i $$-0.669953\pi$$
−0.508913 + 0.860818i $$0.669953\pi$$
$$140$$ 4.00000 0.338062
$$141$$ 0 0
$$142$$ 0 0
$$143$$ 0 0
$$144$$ 0 0
$$145$$ −10.0000 −0.830455
$$146$$ −6.00000 −0.496564
$$147$$ 0 0
$$148$$ −4.00000 −0.328798
$$149$$ 10.0000 0.819232 0.409616 0.912258i $$-0.365663\pi$$
0.409616 + 0.912258i $$0.365663\pi$$
$$150$$ 0 0
$$151$$ −18.0000 −1.46482 −0.732410 0.680864i $$-0.761604\pi$$
−0.732410 + 0.680864i $$0.761604\pi$$
$$152$$ 1.00000 0.0811107
$$153$$ 0 0
$$154$$ 24.0000 1.93398
$$155$$ 2.00000 0.160644
$$156$$ 0 0
$$157$$ −18.0000 −1.43656 −0.718278 0.695756i $$-0.755069\pi$$
−0.718278 + 0.695756i $$0.755069\pi$$
$$158$$ 10.0000 0.795557
$$159$$ 0 0
$$160$$ 1.00000 0.0790569
$$161$$ −16.0000 −1.26098
$$162$$ 0 0
$$163$$ 12.0000 0.939913 0.469956 0.882690i $$-0.344270\pi$$
0.469956 + 0.882690i $$0.344270\pi$$
$$164$$ −10.0000 −0.780869
$$165$$ 0 0
$$166$$ 14.0000 1.08661
$$167$$ 8.00000 0.619059 0.309529 0.950890i $$-0.399829\pi$$
0.309529 + 0.950890i $$0.399829\pi$$
$$168$$ 0 0
$$169$$ −13.0000 −1.00000
$$170$$ −4.00000 −0.306786
$$171$$ 0 0
$$172$$ −12.0000 −0.914991
$$173$$ −18.0000 −1.36851 −0.684257 0.729241i $$-0.739873\pi$$
−0.684257 + 0.729241i $$0.739873\pi$$
$$174$$ 0 0
$$175$$ −4.00000 −0.302372
$$176$$ 6.00000 0.452267
$$177$$ 0 0
$$178$$ 10.0000 0.749532
$$179$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$180$$ 0 0
$$181$$ −16.0000 −1.18927 −0.594635 0.803996i $$-0.702704\pi$$
−0.594635 + 0.803996i $$0.702704\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ −4.00000 −0.294884
$$185$$ 4.00000 0.294086
$$186$$ 0 0
$$187$$ −24.0000 −1.75505
$$188$$ 0 0
$$189$$ 0 0
$$190$$ −1.00000 −0.0725476
$$191$$ −16.0000 −1.15772 −0.578860 0.815427i $$-0.696502\pi$$
−0.578860 + 0.815427i $$0.696502\pi$$
$$192$$ 0 0
$$193$$ −2.00000 −0.143963 −0.0719816 0.997406i $$-0.522932\pi$$
−0.0719816 + 0.997406i $$0.522932\pi$$
$$194$$ 6.00000 0.430775
$$195$$ 0 0
$$196$$ 9.00000 0.642857
$$197$$ −10.0000 −0.712470 −0.356235 0.934396i $$-0.615940\pi$$
−0.356235 + 0.934396i $$0.615940\pi$$
$$198$$ 0 0
$$199$$ 20.0000 1.41776 0.708881 0.705328i $$-0.249200\pi$$
0.708881 + 0.705328i $$0.249200\pi$$
$$200$$ −1.00000 −0.0707107
$$201$$ 0 0
$$202$$ 10.0000 0.703598
$$203$$ −40.0000 −2.80745
$$204$$ 0 0
$$205$$ 10.0000 0.698430
$$206$$ −18.0000 −1.25412
$$207$$ 0 0
$$208$$ 0 0
$$209$$ −6.00000 −0.415029
$$210$$ 0 0
$$211$$ −4.00000 −0.275371 −0.137686 0.990476i $$-0.543966\pi$$
−0.137686 + 0.990476i $$0.543966\pi$$
$$212$$ 6.00000 0.412082
$$213$$ 0 0
$$214$$ 0 0
$$215$$ 12.0000 0.818393
$$216$$ 0 0
$$217$$ 8.00000 0.543075
$$218$$ 8.00000 0.541828
$$219$$ 0 0
$$220$$ −6.00000 −0.404520
$$221$$ 0 0
$$222$$ 0 0
$$223$$ 14.0000 0.937509 0.468755 0.883328i $$-0.344703\pi$$
0.468755 + 0.883328i $$0.344703\pi$$
$$224$$ 4.00000 0.267261
$$225$$ 0 0
$$226$$ −2.00000 −0.133038
$$227$$ 8.00000 0.530979 0.265489 0.964114i $$-0.414466\pi$$
0.265489 + 0.964114i $$0.414466\pi$$
$$228$$ 0 0
$$229$$ −18.0000 −1.18947 −0.594737 0.803921i $$-0.702744\pi$$
−0.594737 + 0.803921i $$0.702744\pi$$
$$230$$ 4.00000 0.263752
$$231$$ 0 0
$$232$$ −10.0000 −0.656532
$$233$$ −4.00000 −0.262049 −0.131024 0.991379i $$-0.541827\pi$$
−0.131024 + 0.991379i $$0.541827\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ −4.00000 −0.260378
$$237$$ 0 0
$$238$$ −16.0000 −1.03713
$$239$$ 12.0000 0.776215 0.388108 0.921614i $$-0.373129\pi$$
0.388108 + 0.921614i $$0.373129\pi$$
$$240$$ 0 0
$$241$$ −22.0000 −1.41714 −0.708572 0.705638i $$-0.750660\pi$$
−0.708572 + 0.705638i $$0.750660\pi$$
$$242$$ −25.0000 −1.60706
$$243$$ 0 0
$$244$$ −10.0000 −0.640184
$$245$$ −9.00000 −0.574989
$$246$$ 0 0
$$247$$ 0 0
$$248$$ 2.00000 0.127000
$$249$$ 0 0
$$250$$ 1.00000 0.0632456
$$251$$ −2.00000 −0.126239 −0.0631194 0.998006i $$-0.520105\pi$$
−0.0631194 + 0.998006i $$0.520105\pi$$
$$252$$ 0 0
$$253$$ 24.0000 1.50887
$$254$$ −18.0000 −1.12942
$$255$$ 0 0
$$256$$ 1.00000 0.0625000
$$257$$ 6.00000 0.374270 0.187135 0.982334i $$-0.440080\pi$$
0.187135 + 0.982334i $$0.440080\pi$$
$$258$$ 0 0
$$259$$ 16.0000 0.994192
$$260$$ 0 0
$$261$$ 0 0
$$262$$ −10.0000 −0.617802
$$263$$ −20.0000 −1.23325 −0.616626 0.787256i $$-0.711501\pi$$
−0.616626 + 0.787256i $$0.711501\pi$$
$$264$$ 0 0
$$265$$ −6.00000 −0.368577
$$266$$ −4.00000 −0.245256
$$267$$ 0 0
$$268$$ −8.00000 −0.488678
$$269$$ 14.0000 0.853595 0.426798 0.904347i $$-0.359642\pi$$
0.426798 + 0.904347i $$0.359642\pi$$
$$270$$ 0 0
$$271$$ −4.00000 −0.242983 −0.121491 0.992592i $$-0.538768\pi$$
−0.121491 + 0.992592i $$0.538768\pi$$
$$272$$ −4.00000 −0.242536
$$273$$ 0 0
$$274$$ 12.0000 0.724947
$$275$$ 6.00000 0.361814
$$276$$ 0 0
$$277$$ 10.0000 0.600842 0.300421 0.953807i $$-0.402873\pi$$
0.300421 + 0.953807i $$0.402873\pi$$
$$278$$ 12.0000 0.719712
$$279$$ 0 0
$$280$$ −4.00000 −0.239046
$$281$$ 10.0000 0.596550 0.298275 0.954480i $$-0.403589\pi$$
0.298275 + 0.954480i $$0.403589\pi$$
$$282$$ 0 0
$$283$$ 28.0000 1.66443 0.832214 0.554455i $$-0.187073\pi$$
0.832214 + 0.554455i $$0.187073\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 40.0000 2.36113
$$288$$ 0 0
$$289$$ −1.00000 −0.0588235
$$290$$ 10.0000 0.587220
$$291$$ 0 0
$$292$$ 6.00000 0.351123
$$293$$ −26.0000 −1.51894 −0.759468 0.650545i $$-0.774541\pi$$
−0.759468 + 0.650545i $$0.774541\pi$$
$$294$$ 0 0
$$295$$ 4.00000 0.232889
$$296$$ 4.00000 0.232495
$$297$$ 0 0
$$298$$ −10.0000 −0.579284
$$299$$ 0 0
$$300$$ 0 0
$$301$$ 48.0000 2.76667
$$302$$ 18.0000 1.03578
$$303$$ 0 0
$$304$$ −1.00000 −0.0573539
$$305$$ 10.0000 0.572598
$$306$$ 0 0
$$307$$ −20.0000 −1.14146 −0.570730 0.821138i $$-0.693340\pi$$
−0.570730 + 0.821138i $$0.693340\pi$$
$$308$$ −24.0000 −1.36753
$$309$$ 0 0
$$310$$ −2.00000 −0.113592
$$311$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$312$$ 0 0
$$313$$ −14.0000 −0.791327 −0.395663 0.918396i $$-0.629485\pi$$
−0.395663 + 0.918396i $$0.629485\pi$$
$$314$$ 18.0000 1.01580
$$315$$ 0 0
$$316$$ −10.0000 −0.562544
$$317$$ 30.0000 1.68497 0.842484 0.538721i $$-0.181092\pi$$
0.842484 + 0.538721i $$0.181092\pi$$
$$318$$ 0 0
$$319$$ 60.0000 3.35936
$$320$$ −1.00000 −0.0559017
$$321$$ 0 0
$$322$$ 16.0000 0.891645
$$323$$ 4.00000 0.222566
$$324$$ 0 0
$$325$$ 0 0
$$326$$ −12.0000 −0.664619
$$327$$ 0 0
$$328$$ 10.0000 0.552158
$$329$$ 0 0
$$330$$ 0 0
$$331$$ 28.0000 1.53902 0.769510 0.638635i $$-0.220501\pi$$
0.769510 + 0.638635i $$0.220501\pi$$
$$332$$ −14.0000 −0.768350
$$333$$ 0 0
$$334$$ −8.00000 −0.437741
$$335$$ 8.00000 0.437087
$$336$$ 0 0
$$337$$ −26.0000 −1.41631 −0.708155 0.706057i $$-0.750472\pi$$
−0.708155 + 0.706057i $$0.750472\pi$$
$$338$$ 13.0000 0.707107
$$339$$ 0 0
$$340$$ 4.00000 0.216930
$$341$$ −12.0000 −0.649836
$$342$$ 0 0
$$343$$ −8.00000 −0.431959
$$344$$ 12.0000 0.646997
$$345$$ 0 0
$$346$$ 18.0000 0.967686
$$347$$ −6.00000 −0.322097 −0.161048 0.986947i $$-0.551488\pi$$
−0.161048 + 0.986947i $$0.551488\pi$$
$$348$$ 0 0
$$349$$ 10.0000 0.535288 0.267644 0.963518i $$-0.413755\pi$$
0.267644 + 0.963518i $$0.413755\pi$$
$$350$$ 4.00000 0.213809
$$351$$ 0 0
$$352$$ −6.00000 −0.319801
$$353$$ −24.0000 −1.27739 −0.638696 0.769460i $$-0.720526\pi$$
−0.638696 + 0.769460i $$0.720526\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ −10.0000 −0.529999
$$357$$ 0 0
$$358$$ 0 0
$$359$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$360$$ 0 0
$$361$$ 1.00000 0.0526316
$$362$$ 16.0000 0.840941
$$363$$ 0 0
$$364$$ 0 0
$$365$$ −6.00000 −0.314054
$$366$$ 0 0
$$367$$ 8.00000 0.417597 0.208798 0.977959i $$-0.433045\pi$$
0.208798 + 0.977959i $$0.433045\pi$$
$$368$$ 4.00000 0.208514
$$369$$ 0 0
$$370$$ −4.00000 −0.207950
$$371$$ −24.0000 −1.24602
$$372$$ 0 0
$$373$$ 12.0000 0.621336 0.310668 0.950518i $$-0.399447\pi$$
0.310668 + 0.950518i $$0.399447\pi$$
$$374$$ 24.0000 1.24101
$$375$$ 0 0
$$376$$ 0 0
$$377$$ 0 0
$$378$$ 0 0
$$379$$ 20.0000 1.02733 0.513665 0.857991i $$-0.328287\pi$$
0.513665 + 0.857991i $$0.328287\pi$$
$$380$$ 1.00000 0.0512989
$$381$$ 0 0
$$382$$ 16.0000 0.818631
$$383$$ 24.0000 1.22634 0.613171 0.789950i $$-0.289894\pi$$
0.613171 + 0.789950i $$0.289894\pi$$
$$384$$ 0 0
$$385$$ 24.0000 1.22315
$$386$$ 2.00000 0.101797
$$387$$ 0 0
$$388$$ −6.00000 −0.304604
$$389$$ 18.0000 0.912636 0.456318 0.889817i $$-0.349168\pi$$
0.456318 + 0.889817i $$0.349168\pi$$
$$390$$ 0 0
$$391$$ −16.0000 −0.809155
$$392$$ −9.00000 −0.454569
$$393$$ 0 0
$$394$$ 10.0000 0.503793
$$395$$ 10.0000 0.503155
$$396$$ 0 0
$$397$$ 22.0000 1.10415 0.552074 0.833795i $$-0.313837\pi$$
0.552074 + 0.833795i $$0.313837\pi$$
$$398$$ −20.0000 −1.00251
$$399$$ 0 0
$$400$$ 1.00000 0.0500000
$$401$$ 6.00000 0.299626 0.149813 0.988714i $$-0.452133\pi$$
0.149813 + 0.988714i $$0.452133\pi$$
$$402$$ 0 0
$$403$$ 0 0
$$404$$ −10.0000 −0.497519
$$405$$ 0 0
$$406$$ 40.0000 1.98517
$$407$$ −24.0000 −1.18964
$$408$$ 0 0
$$409$$ 2.00000 0.0988936 0.0494468 0.998777i $$-0.484254\pi$$
0.0494468 + 0.998777i $$0.484254\pi$$
$$410$$ −10.0000 −0.493865
$$411$$ 0 0
$$412$$ 18.0000 0.886796
$$413$$ 16.0000 0.787309
$$414$$ 0 0
$$415$$ 14.0000 0.687233
$$416$$ 0 0
$$417$$ 0 0
$$418$$ 6.00000 0.293470
$$419$$ −26.0000 −1.27018 −0.635092 0.772437i $$-0.719038\pi$$
−0.635092 + 0.772437i $$0.719038\pi$$
$$420$$ 0 0
$$421$$ 28.0000 1.36464 0.682318 0.731055i $$-0.260972\pi$$
0.682318 + 0.731055i $$0.260972\pi$$
$$422$$ 4.00000 0.194717
$$423$$ 0 0
$$424$$ −6.00000 −0.291386
$$425$$ −4.00000 −0.194029
$$426$$ 0 0
$$427$$ 40.0000 1.93574
$$428$$ 0 0
$$429$$ 0 0
$$430$$ −12.0000 −0.578691
$$431$$ 24.0000 1.15604 0.578020 0.816023i $$-0.303826\pi$$
0.578020 + 0.816023i $$0.303826\pi$$
$$432$$ 0 0
$$433$$ 6.00000 0.288342 0.144171 0.989553i $$-0.453949\pi$$
0.144171 + 0.989553i $$0.453949\pi$$
$$434$$ −8.00000 −0.384012
$$435$$ 0 0
$$436$$ −8.00000 −0.383131
$$437$$ −4.00000 −0.191346
$$438$$ 0 0
$$439$$ 10.0000 0.477274 0.238637 0.971109i $$-0.423299\pi$$
0.238637 + 0.971109i $$0.423299\pi$$
$$440$$ 6.00000 0.286039
$$441$$ 0 0
$$442$$ 0 0
$$443$$ −6.00000 −0.285069 −0.142534 0.989790i $$-0.545525\pi$$
−0.142534 + 0.989790i $$0.545525\pi$$
$$444$$ 0 0
$$445$$ 10.0000 0.474045
$$446$$ −14.0000 −0.662919
$$447$$ 0 0
$$448$$ −4.00000 −0.188982
$$449$$ 26.0000 1.22702 0.613508 0.789689i $$-0.289758\pi$$
0.613508 + 0.789689i $$0.289758\pi$$
$$450$$ 0 0
$$451$$ −60.0000 −2.82529
$$452$$ 2.00000 0.0940721
$$453$$ 0 0
$$454$$ −8.00000 −0.375459
$$455$$ 0 0
$$456$$ 0 0
$$457$$ −38.0000 −1.77757 −0.888783 0.458329i $$-0.848448\pi$$
−0.888783 + 0.458329i $$0.848448\pi$$
$$458$$ 18.0000 0.841085
$$459$$ 0 0
$$460$$ −4.00000 −0.186501
$$461$$ 2.00000 0.0931493 0.0465746 0.998915i $$-0.485169\pi$$
0.0465746 + 0.998915i $$0.485169\pi$$
$$462$$ 0 0
$$463$$ −32.0000 −1.48717 −0.743583 0.668644i $$-0.766875\pi$$
−0.743583 + 0.668644i $$0.766875\pi$$
$$464$$ 10.0000 0.464238
$$465$$ 0 0
$$466$$ 4.00000 0.185296
$$467$$ 10.0000 0.462745 0.231372 0.972865i $$-0.425678\pi$$
0.231372 + 0.972865i $$0.425678\pi$$
$$468$$ 0 0
$$469$$ 32.0000 1.47762
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 4.00000 0.184115
$$473$$ −72.0000 −3.31056
$$474$$ 0 0
$$475$$ −1.00000 −0.0458831
$$476$$ 16.0000 0.733359
$$477$$ 0 0
$$478$$ −12.0000 −0.548867
$$479$$ 24.0000 1.09659 0.548294 0.836286i $$-0.315277\pi$$
0.548294 + 0.836286i $$0.315277\pi$$
$$480$$ 0 0
$$481$$ 0 0
$$482$$ 22.0000 1.00207
$$483$$ 0 0
$$484$$ 25.0000 1.13636
$$485$$ 6.00000 0.272446
$$486$$ 0 0
$$487$$ −2.00000 −0.0906287 −0.0453143 0.998973i $$-0.514429\pi$$
−0.0453143 + 0.998973i $$0.514429\pi$$
$$488$$ 10.0000 0.452679
$$489$$ 0 0
$$490$$ 9.00000 0.406579
$$491$$ 26.0000 1.17336 0.586682 0.809818i $$-0.300434\pi$$
0.586682 + 0.809818i $$0.300434\pi$$
$$492$$ 0 0
$$493$$ −40.0000 −1.80151
$$494$$ 0 0
$$495$$ 0 0
$$496$$ −2.00000 −0.0898027
$$497$$ 0 0
$$498$$ 0 0
$$499$$ −36.0000 −1.61158 −0.805791 0.592200i $$-0.798259\pi$$
−0.805791 + 0.592200i $$0.798259\pi$$
$$500$$ −1.00000 −0.0447214
$$501$$ 0 0
$$502$$ 2.00000 0.0892644
$$503$$ 28.0000 1.24846 0.624229 0.781241i $$-0.285413\pi$$
0.624229 + 0.781241i $$0.285413\pi$$
$$504$$ 0 0
$$505$$ 10.0000 0.444994
$$506$$ −24.0000 −1.06693
$$507$$ 0 0
$$508$$ 18.0000 0.798621
$$509$$ 18.0000 0.797836 0.398918 0.916987i $$-0.369386\pi$$
0.398918 + 0.916987i $$0.369386\pi$$
$$510$$ 0 0
$$511$$ −24.0000 −1.06170
$$512$$ −1.00000 −0.0441942
$$513$$ 0 0
$$514$$ −6.00000 −0.264649
$$515$$ −18.0000 −0.793175
$$516$$ 0 0
$$517$$ 0 0
$$518$$ −16.0000 −0.703000
$$519$$ 0 0
$$520$$ 0 0
$$521$$ −42.0000 −1.84005 −0.920027 0.391856i $$-0.871833\pi$$
−0.920027 + 0.391856i $$0.871833\pi$$
$$522$$ 0 0
$$523$$ −16.0000 −0.699631 −0.349816 0.936819i $$-0.613756\pi$$
−0.349816 + 0.936819i $$0.613756\pi$$
$$524$$ 10.0000 0.436852
$$525$$ 0 0
$$526$$ 20.0000 0.872041
$$527$$ 8.00000 0.348485
$$528$$ 0 0
$$529$$ −7.00000 −0.304348
$$530$$ 6.00000 0.260623
$$531$$ 0 0
$$532$$ 4.00000 0.173422
$$533$$ 0 0
$$534$$ 0 0
$$535$$ 0 0
$$536$$ 8.00000 0.345547
$$537$$ 0 0
$$538$$ −14.0000 −0.603583
$$539$$ 54.0000 2.32594
$$540$$ 0 0
$$541$$ −22.0000 −0.945854 −0.472927 0.881102i $$-0.656803\pi$$
−0.472927 + 0.881102i $$0.656803\pi$$
$$542$$ 4.00000 0.171815
$$543$$ 0 0
$$544$$ 4.00000 0.171499
$$545$$ 8.00000 0.342682
$$546$$ 0 0
$$547$$ 4.00000 0.171028 0.0855138 0.996337i $$-0.472747\pi$$
0.0855138 + 0.996337i $$0.472747\pi$$
$$548$$ −12.0000 −0.512615
$$549$$ 0 0
$$550$$ −6.00000 −0.255841
$$551$$ −10.0000 −0.426014
$$552$$ 0 0
$$553$$ 40.0000 1.70097
$$554$$ −10.0000 −0.424859
$$555$$ 0 0
$$556$$ −12.0000 −0.508913
$$557$$ −22.0000 −0.932170 −0.466085 0.884740i $$-0.654336\pi$$
−0.466085 + 0.884740i $$0.654336\pi$$
$$558$$ 0 0
$$559$$ 0 0
$$560$$ 4.00000 0.169031
$$561$$ 0 0
$$562$$ −10.0000 −0.421825
$$563$$ 4.00000 0.168580 0.0842900 0.996441i $$-0.473138\pi$$
0.0842900 + 0.996441i $$0.473138\pi$$
$$564$$ 0 0
$$565$$ −2.00000 −0.0841406
$$566$$ −28.0000 −1.17693
$$567$$ 0 0
$$568$$ 0 0
$$569$$ 34.0000 1.42535 0.712677 0.701492i $$-0.247483\pi$$
0.712677 + 0.701492i $$0.247483\pi$$
$$570$$ 0 0
$$571$$ −20.0000 −0.836974 −0.418487 0.908223i $$-0.637439\pi$$
−0.418487 + 0.908223i $$0.637439\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ −40.0000 −1.66957
$$575$$ 4.00000 0.166812
$$576$$ 0 0
$$577$$ −2.00000 −0.0832611 −0.0416305 0.999133i $$-0.513255\pi$$
−0.0416305 + 0.999133i $$0.513255\pi$$
$$578$$ 1.00000 0.0415945
$$579$$ 0 0
$$580$$ −10.0000 −0.415227
$$581$$ 56.0000 2.32327
$$582$$ 0 0
$$583$$ 36.0000 1.49097
$$584$$ −6.00000 −0.248282
$$585$$ 0 0
$$586$$ 26.0000 1.07405
$$587$$ −42.0000 −1.73353 −0.866763 0.498721i $$-0.833803\pi$$
−0.866763 + 0.498721i $$0.833803\pi$$
$$588$$ 0 0
$$589$$ 2.00000 0.0824086
$$590$$ −4.00000 −0.164677
$$591$$ 0 0
$$592$$ −4.00000 −0.164399
$$593$$ 44.0000 1.80686 0.903432 0.428732i $$-0.141040\pi$$
0.903432 + 0.428732i $$0.141040\pi$$
$$594$$ 0 0
$$595$$ −16.0000 −0.655936
$$596$$ 10.0000 0.409616
$$597$$ 0 0
$$598$$ 0 0
$$599$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$600$$ 0 0
$$601$$ 26.0000 1.06056 0.530281 0.847822i $$-0.322086\pi$$
0.530281 + 0.847822i $$0.322086\pi$$
$$602$$ −48.0000 −1.95633
$$603$$ 0 0
$$604$$ −18.0000 −0.732410
$$605$$ −25.0000 −1.01639
$$606$$ 0 0
$$607$$ 22.0000 0.892952 0.446476 0.894795i $$-0.352679\pi$$
0.446476 + 0.894795i $$0.352679\pi$$
$$608$$ 1.00000 0.0405554
$$609$$ 0 0
$$610$$ −10.0000 −0.404888
$$611$$ 0 0
$$612$$ 0 0
$$613$$ 14.0000 0.565455 0.282727 0.959200i $$-0.408761\pi$$
0.282727 + 0.959200i $$0.408761\pi$$
$$614$$ 20.0000 0.807134
$$615$$ 0 0
$$616$$ 24.0000 0.966988
$$617$$ −8.00000 −0.322068 −0.161034 0.986949i $$-0.551483\pi$$
−0.161034 + 0.986949i $$0.551483\pi$$
$$618$$ 0 0
$$619$$ −20.0000 −0.803868 −0.401934 0.915669i $$-0.631662\pi$$
−0.401934 + 0.915669i $$0.631662\pi$$
$$620$$ 2.00000 0.0803219
$$621$$ 0 0
$$622$$ 0 0
$$623$$ 40.0000 1.60257
$$624$$ 0 0
$$625$$ 1.00000 0.0400000
$$626$$ 14.0000 0.559553
$$627$$ 0 0
$$628$$ −18.0000 −0.718278
$$629$$ 16.0000 0.637962
$$630$$ 0 0
$$631$$ −36.0000 −1.43314 −0.716569 0.697517i $$-0.754288\pi$$
−0.716569 + 0.697517i $$0.754288\pi$$
$$632$$ 10.0000 0.397779
$$633$$ 0 0
$$634$$ −30.0000 −1.19145
$$635$$ −18.0000 −0.714308
$$636$$ 0 0
$$637$$ 0 0
$$638$$ −60.0000 −2.37542
$$639$$ 0 0
$$640$$ 1.00000 0.0395285
$$641$$ −42.0000 −1.65890 −0.829450 0.558581i $$-0.811346\pi$$
−0.829450 + 0.558581i $$0.811346\pi$$
$$642$$ 0 0
$$643$$ 28.0000 1.10421 0.552106 0.833774i $$-0.313824\pi$$
0.552106 + 0.833774i $$0.313824\pi$$
$$644$$ −16.0000 −0.630488
$$645$$ 0 0
$$646$$ −4.00000 −0.157378
$$647$$ 12.0000 0.471769 0.235884 0.971781i $$-0.424201\pi$$
0.235884 + 0.971781i $$0.424201\pi$$
$$648$$ 0 0
$$649$$ −24.0000 −0.942082
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 12.0000 0.469956
$$653$$ 42.0000 1.64359 0.821794 0.569785i $$-0.192974\pi$$
0.821794 + 0.569785i $$0.192974\pi$$
$$654$$ 0 0
$$655$$ −10.0000 −0.390732
$$656$$ −10.0000 −0.390434
$$657$$ 0 0
$$658$$ 0 0
$$659$$ 36.0000 1.40236 0.701180 0.712984i $$-0.252657\pi$$
0.701180 + 0.712984i $$0.252657\pi$$
$$660$$ 0 0
$$661$$ −40.0000 −1.55582 −0.777910 0.628376i $$-0.783720\pi$$
−0.777910 + 0.628376i $$0.783720\pi$$
$$662$$ −28.0000 −1.08825
$$663$$ 0 0
$$664$$ 14.0000 0.543305
$$665$$ −4.00000 −0.155113
$$666$$ 0 0
$$667$$ 40.0000 1.54881
$$668$$ 8.00000 0.309529
$$669$$ 0 0
$$670$$ −8.00000 −0.309067
$$671$$ −60.0000 −2.31627
$$672$$ 0 0
$$673$$ −10.0000 −0.385472 −0.192736 0.981251i $$-0.561736\pi$$
−0.192736 + 0.981251i $$0.561736\pi$$
$$674$$ 26.0000 1.00148
$$675$$ 0 0
$$676$$ −13.0000 −0.500000
$$677$$ −2.00000 −0.0768662 −0.0384331 0.999261i $$-0.512237\pi$$
−0.0384331 + 0.999261i $$0.512237\pi$$
$$678$$ 0 0
$$679$$ 24.0000 0.921035
$$680$$ −4.00000 −0.153393
$$681$$ 0 0
$$682$$ 12.0000 0.459504
$$683$$ −36.0000 −1.37750 −0.688751 0.724998i $$-0.741841\pi$$
−0.688751 + 0.724998i $$0.741841\pi$$
$$684$$ 0 0
$$685$$ 12.0000 0.458496
$$686$$ 8.00000 0.305441
$$687$$ 0 0
$$688$$ −12.0000 −0.457496
$$689$$ 0 0
$$690$$ 0 0
$$691$$ 28.0000 1.06517 0.532585 0.846376i $$-0.321221\pi$$
0.532585 + 0.846376i $$0.321221\pi$$
$$692$$ −18.0000 −0.684257
$$693$$ 0 0
$$694$$ 6.00000 0.227757
$$695$$ 12.0000 0.455186
$$696$$ 0 0
$$697$$ 40.0000 1.51511
$$698$$ −10.0000 −0.378506
$$699$$ 0 0
$$700$$ −4.00000 −0.151186
$$701$$ 30.0000 1.13308 0.566542 0.824033i $$-0.308281\pi$$
0.566542 + 0.824033i $$0.308281\pi$$
$$702$$ 0 0
$$703$$ 4.00000 0.150863
$$704$$ 6.00000 0.226134
$$705$$ 0 0
$$706$$ 24.0000 0.903252
$$707$$ 40.0000 1.50435
$$708$$ 0 0
$$709$$ −34.0000 −1.27690 −0.638448 0.769665i $$-0.720423\pi$$
−0.638448 + 0.769665i $$0.720423\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 10.0000 0.374766
$$713$$ −8.00000 −0.299602
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 0 0
$$717$$ 0 0
$$718$$ 0 0
$$719$$ −16.0000 −0.596699 −0.298350 0.954457i $$-0.596436\pi$$
−0.298350 + 0.954457i $$0.596436\pi$$
$$720$$ 0 0
$$721$$ −72.0000 −2.68142
$$722$$ −1.00000 −0.0372161
$$723$$ 0 0
$$724$$ −16.0000 −0.594635
$$725$$ 10.0000 0.371391
$$726$$ 0 0
$$727$$ −28.0000 −1.03846 −0.519231 0.854634i $$-0.673782\pi$$
−0.519231 + 0.854634i $$0.673782\pi$$
$$728$$ 0 0
$$729$$ 0 0
$$730$$ 6.00000 0.222070
$$731$$ 48.0000 1.77534
$$732$$ 0 0
$$733$$ −18.0000 −0.664845 −0.332423 0.943131i $$-0.607866\pi$$
−0.332423 + 0.943131i $$0.607866\pi$$
$$734$$ −8.00000 −0.295285
$$735$$ 0 0
$$736$$ −4.00000 −0.147442
$$737$$ −48.0000 −1.76810
$$738$$ 0 0
$$739$$ −4.00000 −0.147142 −0.0735712 0.997290i $$-0.523440\pi$$
−0.0735712 + 0.997290i $$0.523440\pi$$
$$740$$ 4.00000 0.147043
$$741$$ 0 0
$$742$$ 24.0000 0.881068
$$743$$ −8.00000 −0.293492 −0.146746 0.989174i $$-0.546880\pi$$
−0.146746 + 0.989174i $$0.546880\pi$$
$$744$$ 0 0
$$745$$ −10.0000 −0.366372
$$746$$ −12.0000 −0.439351
$$747$$ 0 0
$$748$$ −24.0000 −0.877527
$$749$$ 0 0
$$750$$ 0 0
$$751$$ 46.0000 1.67856 0.839282 0.543696i $$-0.182976\pi$$
0.839282 + 0.543696i $$0.182976\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 0 0
$$755$$ 18.0000 0.655087
$$756$$ 0 0
$$757$$ −26.0000 −0.944986 −0.472493 0.881334i $$-0.656646\pi$$
−0.472493 + 0.881334i $$0.656646\pi$$
$$758$$ −20.0000 −0.726433
$$759$$ 0 0
$$760$$ −1.00000 −0.0362738
$$761$$ −24.0000 −0.869999 −0.435000 0.900431i $$-0.643252\pi$$
−0.435000 + 0.900431i $$0.643252\pi$$
$$762$$ 0 0
$$763$$ 32.0000 1.15848
$$764$$ −16.0000 −0.578860
$$765$$ 0 0
$$766$$ −24.0000 −0.867155
$$767$$ 0 0
$$768$$ 0 0
$$769$$ −14.0000 −0.504853 −0.252426 0.967616i $$-0.581229\pi$$
−0.252426 + 0.967616i $$0.581229\pi$$
$$770$$ −24.0000 −0.864900
$$771$$ 0 0
$$772$$ −2.00000 −0.0719816
$$773$$ −30.0000 −1.07903 −0.539513 0.841978i $$-0.681391\pi$$
−0.539513 + 0.841978i $$0.681391\pi$$
$$774$$ 0 0
$$775$$ −2.00000 −0.0718421
$$776$$ 6.00000 0.215387
$$777$$ 0 0
$$778$$ −18.0000 −0.645331
$$779$$ 10.0000 0.358287
$$780$$ 0 0
$$781$$ 0 0
$$782$$ 16.0000 0.572159
$$783$$ 0 0
$$784$$ 9.00000 0.321429
$$785$$ 18.0000 0.642448
$$786$$ 0 0
$$787$$ −52.0000 −1.85360 −0.926800 0.375555i $$-0.877452\pi$$
−0.926800 + 0.375555i $$0.877452\pi$$
$$788$$ −10.0000 −0.356235
$$789$$ 0 0
$$790$$ −10.0000 −0.355784
$$791$$ −8.00000 −0.284447
$$792$$ 0 0
$$793$$ 0 0
$$794$$ −22.0000 −0.780751
$$795$$ 0 0
$$796$$ 20.0000 0.708881
$$797$$ 2.00000 0.0708436 0.0354218 0.999372i $$-0.488723\pi$$
0.0354218 + 0.999372i $$0.488723\pi$$
$$798$$ 0 0
$$799$$ 0 0
$$800$$ −1.00000 −0.0353553
$$801$$ 0 0
$$802$$ −6.00000 −0.211867
$$803$$ 36.0000 1.27041
$$804$$ 0 0
$$805$$ 16.0000 0.563926
$$806$$ 0 0
$$807$$ 0 0
$$808$$ 10.0000 0.351799
$$809$$ −36.0000 −1.26569 −0.632846 0.774277i $$-0.718114\pi$$
−0.632846 + 0.774277i $$0.718114\pi$$
$$810$$ 0 0
$$811$$ 20.0000 0.702295 0.351147 0.936320i $$-0.385792\pi$$
0.351147 + 0.936320i $$0.385792\pi$$
$$812$$ −40.0000 −1.40372
$$813$$ 0 0
$$814$$ 24.0000 0.841200
$$815$$ −12.0000 −0.420342
$$816$$ 0 0
$$817$$ 12.0000 0.419827
$$818$$ −2.00000 −0.0699284
$$819$$ 0 0
$$820$$ 10.0000 0.349215
$$821$$ −50.0000 −1.74501 −0.872506 0.488603i $$-0.837507\pi$$
−0.872506 + 0.488603i $$0.837507\pi$$
$$822$$ 0 0
$$823$$ −16.0000 −0.557725 −0.278862 0.960331i $$-0.589957\pi$$
−0.278862 + 0.960331i $$0.589957\pi$$
$$824$$ −18.0000 −0.627060
$$825$$ 0 0
$$826$$ −16.0000 −0.556711
$$827$$ 36.0000 1.25184 0.625921 0.779886i $$-0.284723\pi$$
0.625921 + 0.779886i $$0.284723\pi$$
$$828$$ 0 0
$$829$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$830$$ −14.0000 −0.485947
$$831$$ 0 0
$$832$$ 0 0
$$833$$ −36.0000 −1.24733
$$834$$ 0 0
$$835$$ −8.00000 −0.276851
$$836$$ −6.00000 −0.207514
$$837$$ 0 0
$$838$$ 26.0000 0.898155
$$839$$ 24.0000 0.828572 0.414286 0.910147i $$-0.364031\pi$$
0.414286 + 0.910147i $$0.364031\pi$$
$$840$$ 0 0
$$841$$ 71.0000 2.44828
$$842$$ −28.0000 −0.964944
$$843$$ 0 0
$$844$$ −4.00000 −0.137686
$$845$$ 13.0000 0.447214
$$846$$ 0 0
$$847$$ −100.000 −3.43604
$$848$$ 6.00000 0.206041
$$849$$ 0 0
$$850$$ 4.00000 0.137199
$$851$$ −16.0000 −0.548473
$$852$$ 0 0
$$853$$ 2.00000 0.0684787 0.0342393 0.999414i $$-0.489099\pi$$
0.0342393 + 0.999414i $$0.489099\pi$$
$$854$$ −40.0000 −1.36877
$$855$$ 0 0
$$856$$ 0 0
$$857$$ −30.0000 −1.02478 −0.512390 0.858753i $$-0.671240\pi$$
−0.512390 + 0.858753i $$0.671240\pi$$
$$858$$ 0 0
$$859$$ −28.0000 −0.955348 −0.477674 0.878537i $$-0.658520\pi$$
−0.477674 + 0.878537i $$0.658520\pi$$
$$860$$ 12.0000 0.409197
$$861$$ 0 0
$$862$$ −24.0000 −0.817443
$$863$$ 48.0000 1.63394 0.816970 0.576681i $$-0.195652\pi$$
0.816970 + 0.576681i $$0.195652\pi$$
$$864$$ 0 0
$$865$$ 18.0000 0.612018
$$866$$ −6.00000 −0.203888
$$867$$ 0 0
$$868$$ 8.00000 0.271538
$$869$$ −60.0000 −2.03536
$$870$$ 0 0
$$871$$ 0 0
$$872$$ 8.00000 0.270914
$$873$$ 0 0
$$874$$ 4.00000 0.135302
$$875$$ 4.00000 0.135225
$$876$$ 0 0
$$877$$ 4.00000 0.135070 0.0675352 0.997717i $$-0.478487\pi$$
0.0675352 + 0.997717i $$0.478487\pi$$
$$878$$ −10.0000 −0.337484
$$879$$ 0 0
$$880$$ −6.00000 −0.202260
$$881$$ 20.0000 0.673817 0.336909 0.941537i $$-0.390619\pi$$
0.336909 + 0.941537i $$0.390619\pi$$
$$882$$ 0 0
$$883$$ 20.0000 0.673054 0.336527 0.941674i $$-0.390748\pi$$
0.336527 + 0.941674i $$0.390748\pi$$
$$884$$ 0 0
$$885$$ 0 0
$$886$$ 6.00000 0.201574
$$887$$ 16.0000 0.537227 0.268614 0.963248i $$-0.413434\pi$$
0.268614 + 0.963248i $$0.413434\pi$$
$$888$$ 0 0
$$889$$ −72.0000 −2.41480
$$890$$ −10.0000 −0.335201
$$891$$ 0 0
$$892$$ 14.0000 0.468755
$$893$$ 0 0
$$894$$ 0 0
$$895$$ 0 0
$$896$$ 4.00000 0.133631
$$897$$ 0 0
$$898$$ −26.0000 −0.867631
$$899$$ −20.0000 −0.667037
$$900$$ 0 0
$$901$$ −24.0000 −0.799556
$$902$$ 60.0000 1.99778
$$903$$ 0 0
$$904$$ −2.00000 −0.0665190
$$905$$ 16.0000 0.531858
$$906$$ 0 0
$$907$$ 32.0000 1.06254 0.531271 0.847202i $$-0.321714\pi$$
0.531271 + 0.847202i $$0.321714\pi$$
$$908$$ 8.00000 0.265489
$$909$$ 0 0
$$910$$ 0 0
$$911$$ −32.0000 −1.06021 −0.530104 0.847933i $$-0.677847\pi$$
−0.530104 + 0.847933i $$0.677847\pi$$
$$912$$ 0 0
$$913$$ −84.0000 −2.77999
$$914$$ 38.0000 1.25693
$$915$$ 0 0
$$916$$ −18.0000 −0.594737
$$917$$ −40.0000 −1.32092
$$918$$ 0 0
$$919$$ −52.0000 −1.71532 −0.857661 0.514216i $$-0.828083\pi$$
−0.857661 + 0.514216i $$0.828083\pi$$
$$920$$ 4.00000 0.131876
$$921$$ 0 0
$$922$$ −2.00000 −0.0658665
$$923$$ 0 0
$$924$$ 0 0
$$925$$ −4.00000 −0.131519
$$926$$ 32.0000 1.05159
$$927$$ 0 0
$$928$$ −10.0000 −0.328266
$$929$$ 36.0000 1.18112 0.590561 0.806993i $$-0.298907\pi$$
0.590561 + 0.806993i $$0.298907\pi$$
$$930$$ 0 0
$$931$$ −9.00000 −0.294963
$$932$$ −4.00000 −0.131024
$$933$$ 0 0
$$934$$ −10.0000 −0.327210
$$935$$ 24.0000 0.784884
$$936$$ 0 0
$$937$$ 14.0000 0.457360 0.228680 0.973502i $$-0.426559\pi$$
0.228680 + 0.973502i $$0.426559\pi$$
$$938$$ −32.0000 −1.04484
$$939$$ 0 0
$$940$$ 0 0
$$941$$ 50.0000 1.62995 0.814977 0.579494i $$-0.196750\pi$$
0.814977 + 0.579494i $$0.196750\pi$$
$$942$$ 0 0
$$943$$ −40.0000 −1.30258
$$944$$ −4.00000 −0.130189
$$945$$ 0 0
$$946$$ 72.0000 2.34092
$$947$$ 38.0000 1.23483 0.617417 0.786636i $$-0.288179\pi$$
0.617417 + 0.786636i $$0.288179\pi$$
$$948$$ 0 0
$$949$$ 0 0
$$950$$ 1.00000 0.0324443
$$951$$ 0 0
$$952$$ −16.0000 −0.518563
$$953$$ −34.0000 −1.10137 −0.550684 0.834714i $$-0.685633\pi$$
−0.550684 + 0.834714i $$0.685633\pi$$
$$954$$ 0 0
$$955$$ 16.0000 0.517748
$$956$$ 12.0000 0.388108
$$957$$ 0 0
$$958$$ −24.0000 −0.775405
$$959$$ 48.0000 1.55000
$$960$$ 0 0
$$961$$ −27.0000 −0.870968
$$962$$ 0 0
$$963$$ 0 0
$$964$$ −22.0000 −0.708572
$$965$$ 2.00000 0.0643823
$$966$$ 0 0
$$967$$ 12.0000 0.385894 0.192947 0.981209i $$-0.438195\pi$$
0.192947 + 0.981209i $$0.438195\pi$$
$$968$$ −25.0000 −0.803530
$$969$$ 0 0
$$970$$ −6.00000 −0.192648
$$971$$ 60.0000 1.92549 0.962746 0.270408i $$-0.0871586\pi$$
0.962746 + 0.270408i $$0.0871586\pi$$
$$972$$ 0 0
$$973$$ 48.0000 1.53881
$$974$$ 2.00000 0.0640841
$$975$$ 0 0
$$976$$ −10.0000 −0.320092
$$977$$ 18.0000 0.575871 0.287936 0.957650i $$-0.407031\pi$$
0.287936 + 0.957650i $$0.407031\pi$$
$$978$$ 0 0
$$979$$ −60.0000 −1.91761
$$980$$ −9.00000 −0.287494
$$981$$ 0 0
$$982$$ −26.0000 −0.829693
$$983$$ 24.0000 0.765481 0.382741 0.923856i $$-0.374980\pi$$
0.382741 + 0.923856i $$0.374980\pi$$
$$984$$ 0 0
$$985$$ 10.0000 0.318626
$$986$$ 40.0000 1.27386
$$987$$ 0 0
$$988$$ 0 0
$$989$$ −48.0000 −1.52631
$$990$$ 0 0
$$991$$ −34.0000 −1.08005 −0.540023 0.841650i $$-0.681584\pi$$
−0.540023 + 0.841650i $$0.681584\pi$$
$$992$$ 2.00000 0.0635001
$$993$$ 0 0
$$994$$ 0 0
$$995$$ −20.0000 −0.634043
$$996$$ 0 0
$$997$$ −10.0000 −0.316703 −0.158352 0.987383i $$-0.550618\pi$$
−0.158352 + 0.987383i $$0.550618\pi$$
$$998$$ 36.0000 1.13956
$$999$$ 0 0
Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000

## Twists

By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 1710.2.a.a.1.1 1
3.2 odd 2 1710.2.a.p.1.1 yes 1
5.4 even 2 8550.2.a.bl.1.1 1
15.14 odd 2 8550.2.a.q.1.1 1

By twisted newform
Twist Min Dim Char Parity Ord Type
1710.2.a.a.1.1 1 1.1 even 1 trivial
1710.2.a.p.1.1 yes 1 3.2 odd 2
8550.2.a.q.1.1 1 15.14 odd 2
8550.2.a.bl.1.1 1 5.4 even 2