# Properties

 Label 7350.2.a.bt.1.1 Level 7350 Weight 2 Character 7350.1 Self dual yes Analytic conductor 58.690 Analytic rank 1 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: $$1$$ 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

 $$f(q)$$ $$=$$ $$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$$ $$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} -2.00000 q^{11} -1.00000 q^{12} +4.00000 q^{13} +1.00000 q^{16} +5.00000 q^{17} +1.00000 q^{18} -4.00000 q^{19} -2.00000 q^{22} -5.00000 q^{23} -1.00000 q^{24} +4.00000 q^{26} -1.00000 q^{27} -6.00000 q^{29} -11.0000 q^{31} +1.00000 q^{32} +2.00000 q^{33} +5.00000 q^{34} +1.00000 q^{36} -8.00000 q^{37} -4.00000 q^{38} -4.00000 q^{39} +5.00000 q^{41} -2.00000 q^{44} -5.00000 q^{46} +1.00000 q^{47} -1.00000 q^{48} -5.00000 q^{51} +4.00000 q^{52} -12.0000 q^{53} -1.00000 q^{54} +4.00000 q^{57} -6.00000 q^{58} -2.00000 q^{59} +10.0000 q^{61} -11.0000 q^{62} +1.00000 q^{64} +2.00000 q^{66} +5.00000 q^{68} +5.00000 q^{69} -1.00000 q^{71} +1.00000 q^{72} -2.00000 q^{73} -8.00000 q^{74} -4.00000 q^{76} -4.00000 q^{78} +9.00000 q^{79} +1.00000 q^{81} +5.00000 q^{82} -6.00000 q^{83} +6.00000 q^{87} -2.00000 q^{88} +11.0000 q^{89} -5.00000 q^{92} +11.0000 q^{93} +1.00000 q^{94} -1.00000 q^{96} +1.00000 q^{97} -2.00000 q^{99} +O(q^{100})$$

## Coefficient data

For each $$n$$ we display the coefficients of the $$q$$-expansion $$a_n$$, the Satake parameters $$\alpha_p$$, and the Satake angles $$\theta_p = \textrm{Arg}(\alpha_p)$$.

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 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
$$11$$ −2.00000 −0.603023 −0.301511 0.953463i $$-0.597491\pi$$
−0.301511 + 0.953463i $$0.597491\pi$$
$$12$$ −1.00000 −0.288675
$$13$$ 4.00000 1.10940 0.554700 0.832050i $$-0.312833\pi$$
0.554700 + 0.832050i $$0.312833\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 1.00000 0.250000
$$17$$ 5.00000 1.21268 0.606339 0.795206i $$-0.292637\pi$$
0.606339 + 0.795206i $$0.292637\pi$$
$$18$$ 1.00000 0.235702
$$19$$ −4.00000 −0.917663 −0.458831 0.888523i $$-0.651732\pi$$
−0.458831 + 0.888523i $$0.651732\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ −2.00000 −0.426401
$$23$$ −5.00000 −1.04257 −0.521286 0.853382i $$-0.674548\pi$$
−0.521286 + 0.853382i $$0.674548\pi$$
$$24$$ −1.00000 −0.204124
$$25$$ 0 0
$$26$$ 4.00000 0.784465
$$27$$ −1.00000 −0.192450
$$28$$ 0 0
$$29$$ −6.00000 −1.11417 −0.557086 0.830455i $$-0.688081\pi$$
−0.557086 + 0.830455i $$0.688081\pi$$
$$30$$ 0 0
$$31$$ −11.0000 −1.97566 −0.987829 0.155543i $$-0.950287\pi$$
−0.987829 + 0.155543i $$0.950287\pi$$
$$32$$ 1.00000 0.176777
$$33$$ 2.00000 0.348155
$$34$$ 5.00000 0.857493
$$35$$ 0 0
$$36$$ 1.00000 0.166667
$$37$$ −8.00000 −1.31519 −0.657596 0.753371i $$-0.728427\pi$$
−0.657596 + 0.753371i $$0.728427\pi$$
$$38$$ −4.00000 −0.648886
$$39$$ −4.00000 −0.640513
$$40$$ 0 0
$$41$$ 5.00000 0.780869 0.390434 0.920631i $$-0.372325\pi$$
0.390434 + 0.920631i $$0.372325\pi$$
$$42$$ 0 0
$$43$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$44$$ −2.00000 −0.301511
$$45$$ 0 0
$$46$$ −5.00000 −0.737210
$$47$$ 1.00000 0.145865 0.0729325 0.997337i $$-0.476764\pi$$
0.0729325 + 0.997337i $$0.476764\pi$$
$$48$$ −1.00000 −0.144338
$$49$$ 0 0
$$50$$ 0 0
$$51$$ −5.00000 −0.700140
$$52$$ 4.00000 0.554700
$$53$$ −12.0000 −1.64833 −0.824163 0.566352i $$-0.808354\pi$$
−0.824163 + 0.566352i $$0.808354\pi$$
$$54$$ −1.00000 −0.136083
$$55$$ 0 0
$$56$$ 0 0
$$57$$ 4.00000 0.529813
$$58$$ −6.00000 −0.787839
$$59$$ −2.00000 −0.260378 −0.130189 0.991489i $$-0.541558\pi$$
−0.130189 + 0.991489i $$0.541558\pi$$
$$60$$ 0 0
$$61$$ 10.0000 1.28037 0.640184 0.768221i $$-0.278858\pi$$
0.640184 + 0.768221i $$0.278858\pi$$
$$62$$ −11.0000 −1.39700
$$63$$ 0 0
$$64$$ 1.00000 0.125000
$$65$$ 0 0
$$66$$ 2.00000 0.246183
$$67$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$68$$ 5.00000 0.606339
$$69$$ 5.00000 0.601929
$$70$$ 0 0
$$71$$ −1.00000 −0.118678 −0.0593391 0.998238i $$-0.518899\pi$$
−0.0593391 + 0.998238i $$0.518899\pi$$
$$72$$ 1.00000 0.117851
$$73$$ −2.00000 −0.234082 −0.117041 0.993127i $$-0.537341\pi$$
−0.117041 + 0.993127i $$0.537341\pi$$
$$74$$ −8.00000 −0.929981
$$75$$ 0 0
$$76$$ −4.00000 −0.458831
$$77$$ 0 0
$$78$$ −4.00000 −0.452911
$$79$$ 9.00000 1.01258 0.506290 0.862364i $$-0.331017\pi$$
0.506290 + 0.862364i $$0.331017\pi$$
$$80$$ 0 0
$$81$$ 1.00000 0.111111
$$82$$ 5.00000 0.552158
$$83$$ −6.00000 −0.658586 −0.329293 0.944228i $$-0.606810\pi$$
−0.329293 + 0.944228i $$0.606810\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ 0 0
$$87$$ 6.00000 0.643268
$$88$$ −2.00000 −0.213201
$$89$$ 11.0000 1.16600 0.582999 0.812473i $$-0.301879\pi$$
0.582999 + 0.812473i $$0.301879\pi$$
$$90$$ 0 0
$$91$$ 0 0
$$92$$ −5.00000 −0.521286
$$93$$ 11.0000 1.14065
$$94$$ 1.00000 0.103142
$$95$$ 0 0
$$96$$ −1.00000 −0.102062
$$97$$ 1.00000 0.101535 0.0507673 0.998711i $$-0.483833\pi$$
0.0507673 + 0.998711i $$0.483833\pi$$
$$98$$ 0 0
$$99$$ −2.00000 −0.201008
$$100$$ 0 0
$$101$$ 12.0000 1.19404 0.597022 0.802225i $$-0.296350\pi$$
0.597022 + 0.802225i $$0.296350\pi$$
$$102$$ −5.00000 −0.495074
$$103$$ −13.0000 −1.28093 −0.640464 0.767988i $$-0.721258\pi$$
−0.640464 + 0.767988i $$0.721258\pi$$
$$104$$ 4.00000 0.392232
$$105$$ 0 0
$$106$$ −12.0000 −1.16554
$$107$$ −2.00000 −0.193347 −0.0966736 0.995316i $$-0.530820\pi$$
−0.0966736 + 0.995316i $$0.530820\pi$$
$$108$$ −1.00000 −0.0962250
$$109$$ 4.00000 0.383131 0.191565 0.981480i $$-0.438644\pi$$
0.191565 + 0.981480i $$0.438644\pi$$
$$110$$ 0 0
$$111$$ 8.00000 0.759326
$$112$$ 0 0
$$113$$ −5.00000 −0.470360 −0.235180 0.971952i $$-0.575568\pi$$
−0.235180 + 0.971952i $$0.575568\pi$$
$$114$$ 4.00000 0.374634
$$115$$ 0 0
$$116$$ −6.00000 −0.557086
$$117$$ 4.00000 0.369800
$$118$$ −2.00000 −0.184115
$$119$$ 0 0
$$120$$ 0 0
$$121$$ −7.00000 −0.636364
$$122$$ 10.0000 0.905357
$$123$$ −5.00000 −0.450835
$$124$$ −11.0000 −0.987829
$$125$$ 0 0
$$126$$ 0 0
$$127$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$128$$ 1.00000 0.0883883
$$129$$ 0 0
$$130$$ 0 0
$$131$$ 6.00000 0.524222 0.262111 0.965038i $$-0.415581\pi$$
0.262111 + 0.965038i $$0.415581\pi$$
$$132$$ 2.00000 0.174078
$$133$$ 0 0
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 5.00000 0.428746
$$137$$ −23.0000 −1.96502 −0.982511 0.186203i $$-0.940382\pi$$
−0.982511 + 0.186203i $$0.940382\pi$$
$$138$$ 5.00000 0.425628
$$139$$ 2.00000 0.169638 0.0848189 0.996396i $$-0.472969\pi$$
0.0848189 + 0.996396i $$0.472969\pi$$
$$140$$ 0 0
$$141$$ −1.00000 −0.0842152
$$142$$ −1.00000 −0.0839181
$$143$$ −8.00000 −0.668994
$$144$$ 1.00000 0.0833333
$$145$$ 0 0
$$146$$ −2.00000 −0.165521
$$147$$ 0 0
$$148$$ −8.00000 −0.657596
$$149$$ 18.0000 1.47462 0.737309 0.675556i $$-0.236096\pi$$
0.737309 + 0.675556i $$0.236096\pi$$
$$150$$ 0 0
$$151$$ −16.0000 −1.30206 −0.651031 0.759051i $$-0.725663\pi$$
−0.651031 + 0.759051i $$0.725663\pi$$
$$152$$ −4.00000 −0.324443
$$153$$ 5.00000 0.404226
$$154$$ 0 0
$$155$$ 0 0
$$156$$ −4.00000 −0.320256
$$157$$ 14.0000 1.11732 0.558661 0.829396i $$-0.311315\pi$$
0.558661 + 0.829396i $$0.311315\pi$$
$$158$$ 9.00000 0.716002
$$159$$ 12.0000 0.951662
$$160$$ 0 0
$$161$$ 0 0
$$162$$ 1.00000 0.0785674
$$163$$ −24.0000 −1.87983 −0.939913 0.341415i $$-0.889094\pi$$
−0.939913 + 0.341415i $$0.889094\pi$$
$$164$$ 5.00000 0.390434
$$165$$ 0 0
$$166$$ −6.00000 −0.465690
$$167$$ −16.0000 −1.23812 −0.619059 0.785345i $$-0.712486\pi$$
−0.619059 + 0.785345i $$0.712486\pi$$
$$168$$ 0 0
$$169$$ 3.00000 0.230769
$$170$$ 0 0
$$171$$ −4.00000 −0.305888
$$172$$ 0 0
$$173$$ 2.00000 0.152057 0.0760286 0.997106i $$-0.475776\pi$$
0.0760286 + 0.997106i $$0.475776\pi$$
$$174$$ 6.00000 0.454859
$$175$$ 0 0
$$176$$ −2.00000 −0.150756
$$177$$ 2.00000 0.150329
$$178$$ 11.0000 0.824485
$$179$$ 22.0000 1.64436 0.822179 0.569230i $$-0.192758\pi$$
0.822179 + 0.569230i $$0.192758\pi$$
$$180$$ 0 0
$$181$$ −22.0000 −1.63525 −0.817624 0.575753i $$-0.804709\pi$$
−0.817624 + 0.575753i $$0.804709\pi$$
$$182$$ 0 0
$$183$$ −10.0000 −0.739221
$$184$$ −5.00000 −0.368605
$$185$$ 0 0
$$186$$ 11.0000 0.806559
$$187$$ −10.0000 −0.731272
$$188$$ 1.00000 0.0729325
$$189$$ 0 0
$$190$$ 0 0
$$191$$ −25.0000 −1.80894 −0.904468 0.426541i $$-0.859732\pi$$
−0.904468 + 0.426541i $$0.859732\pi$$
$$192$$ −1.00000 −0.0721688
$$193$$ −11.0000 −0.791797 −0.395899 0.918294i $$-0.629567\pi$$
−0.395899 + 0.918294i $$0.629567\pi$$
$$194$$ 1.00000 0.0717958
$$195$$ 0 0
$$196$$ 0 0
$$197$$ 24.0000 1.70993 0.854965 0.518686i $$-0.173579\pi$$
0.854965 + 0.518686i $$0.173579\pi$$
$$198$$ −2.00000 −0.142134
$$199$$ 5.00000 0.354441 0.177220 0.984171i $$-0.443289\pi$$
0.177220 + 0.984171i $$0.443289\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ 12.0000 0.844317
$$203$$ 0 0
$$204$$ −5.00000 −0.350070
$$205$$ 0 0
$$206$$ −13.0000 −0.905753
$$207$$ −5.00000 −0.347524
$$208$$ 4.00000 0.277350
$$209$$ 8.00000 0.553372
$$210$$ 0 0
$$211$$ −16.0000 −1.10149 −0.550743 0.834675i $$-0.685655\pi$$
−0.550743 + 0.834675i $$0.685655\pi$$
$$212$$ −12.0000 −0.824163
$$213$$ 1.00000 0.0685189
$$214$$ −2.00000 −0.136717
$$215$$ 0 0
$$216$$ −1.00000 −0.0680414
$$217$$ 0 0
$$218$$ 4.00000 0.270914
$$219$$ 2.00000 0.135147
$$220$$ 0 0
$$221$$ 20.0000 1.34535
$$222$$ 8.00000 0.536925
$$223$$ −21.0000 −1.40626 −0.703132 0.711059i $$-0.748216\pi$$
−0.703132 + 0.711059i $$0.748216\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ −5.00000 −0.332595
$$227$$ −18.0000 −1.19470 −0.597351 0.801980i $$-0.703780\pi$$
−0.597351 + 0.801980i $$0.703780\pi$$
$$228$$ 4.00000 0.264906
$$229$$ −14.0000 −0.925146 −0.462573 0.886581i $$-0.653074\pi$$
−0.462573 + 0.886581i $$0.653074\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ −6.00000 −0.393919
$$233$$ −26.0000 −1.70332 −0.851658 0.524097i $$-0.824403\pi$$
−0.851658 + 0.524097i $$0.824403\pi$$
$$234$$ 4.00000 0.261488
$$235$$ 0 0
$$236$$ −2.00000 −0.130189
$$237$$ −9.00000 −0.584613
$$238$$ 0 0
$$239$$ 11.0000 0.711531 0.355765 0.934575i $$-0.384220\pi$$
0.355765 + 0.934575i $$0.384220\pi$$
$$240$$ 0 0
$$241$$ −6.00000 −0.386494 −0.193247 0.981150i $$-0.561902\pi$$
−0.193247 + 0.981150i $$0.561902\pi$$
$$242$$ −7.00000 −0.449977
$$243$$ −1.00000 −0.0641500
$$244$$ 10.0000 0.640184
$$245$$ 0 0
$$246$$ −5.00000 −0.318788
$$247$$ −16.0000 −1.01806
$$248$$ −11.0000 −0.698501
$$249$$ 6.00000 0.380235
$$250$$ 0 0
$$251$$ −8.00000 −0.504956 −0.252478 0.967603i $$-0.581245\pi$$
−0.252478 + 0.967603i $$0.581245\pi$$
$$252$$ 0 0
$$253$$ 10.0000 0.628695
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 1.00000 0.0625000
$$257$$ 14.0000 0.873296 0.436648 0.899632i $$-0.356166\pi$$
0.436648 + 0.899632i $$0.356166\pi$$
$$258$$ 0 0
$$259$$ 0 0
$$260$$ 0 0
$$261$$ −6.00000 −0.371391
$$262$$ 6.00000 0.370681
$$263$$ 21.0000 1.29492 0.647458 0.762101i $$-0.275832\pi$$
0.647458 + 0.762101i $$0.275832\pi$$
$$264$$ 2.00000 0.123091
$$265$$ 0 0
$$266$$ 0 0
$$267$$ −11.0000 −0.673189
$$268$$ 0 0
$$269$$ −24.0000 −1.46331 −0.731653 0.681677i $$-0.761251\pi$$
−0.731653 + 0.681677i $$0.761251\pi$$
$$270$$ 0 0
$$271$$ −9.00000 −0.546711 −0.273356 0.961913i $$-0.588134\pi$$
−0.273356 + 0.961913i $$0.588134\pi$$
$$272$$ 5.00000 0.303170
$$273$$ 0 0
$$274$$ −23.0000 −1.38948
$$275$$ 0 0
$$276$$ 5.00000 0.300965
$$277$$ 2.00000 0.120168 0.0600842 0.998193i $$-0.480863\pi$$
0.0600842 + 0.998193i $$0.480863\pi$$
$$278$$ 2.00000 0.119952
$$279$$ −11.0000 −0.658553
$$280$$ 0 0
$$281$$ −29.0000 −1.72999 −0.864997 0.501776i $$-0.832680\pi$$
−0.864997 + 0.501776i $$0.832680\pi$$
$$282$$ −1.00000 −0.0595491
$$283$$ 26.0000 1.54554 0.772770 0.634686i $$-0.218871\pi$$
0.772770 + 0.634686i $$0.218871\pi$$
$$284$$ −1.00000 −0.0593391
$$285$$ 0 0
$$286$$ −8.00000 −0.473050
$$287$$ 0 0
$$288$$ 1.00000 0.0589256
$$289$$ 8.00000 0.470588
$$290$$ 0 0
$$291$$ −1.00000 −0.0586210
$$292$$ −2.00000 −0.117041
$$293$$ −18.0000 −1.05157 −0.525786 0.850617i $$-0.676229\pi$$
−0.525786 + 0.850617i $$0.676229\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ −8.00000 −0.464991
$$297$$ 2.00000 0.116052
$$298$$ 18.0000 1.04271
$$299$$ −20.0000 −1.15663
$$300$$ 0 0
$$301$$ 0 0
$$302$$ −16.0000 −0.920697
$$303$$ −12.0000 −0.689382
$$304$$ −4.00000 −0.229416
$$305$$ 0 0
$$306$$ 5.00000 0.285831
$$307$$ −28.0000 −1.59804 −0.799022 0.601302i $$-0.794649\pi$$
−0.799022 + 0.601302i $$0.794649\pi$$
$$308$$ 0 0
$$309$$ 13.0000 0.739544
$$310$$ 0 0
$$311$$ 29.0000 1.64444 0.822220 0.569170i $$-0.192736\pi$$
0.822220 + 0.569170i $$0.192736\pi$$
$$312$$ −4.00000 −0.226455
$$313$$ 1.00000 0.0565233 0.0282617 0.999601i $$-0.491003\pi$$
0.0282617 + 0.999601i $$0.491003\pi$$
$$314$$ 14.0000 0.790066
$$315$$ 0 0
$$316$$ 9.00000 0.506290
$$317$$ −4.00000 −0.224662 −0.112331 0.993671i $$-0.535832\pi$$
−0.112331 + 0.993671i $$0.535832\pi$$
$$318$$ 12.0000 0.672927
$$319$$ 12.0000 0.671871
$$320$$ 0 0
$$321$$ 2.00000 0.111629
$$322$$ 0 0
$$323$$ −20.0000 −1.11283
$$324$$ 1.00000 0.0555556
$$325$$ 0 0
$$326$$ −24.0000 −1.32924
$$327$$ −4.00000 −0.221201
$$328$$ 5.00000 0.276079
$$329$$ 0 0
$$330$$ 0 0
$$331$$ 10.0000 0.549650 0.274825 0.961494i $$-0.411380\pi$$
0.274825 + 0.961494i $$0.411380\pi$$
$$332$$ −6.00000 −0.329293
$$333$$ −8.00000 −0.438397
$$334$$ −16.0000 −0.875481
$$335$$ 0 0
$$336$$ 0 0
$$337$$ −13.0000 −0.708155 −0.354078 0.935216i $$-0.615205\pi$$
−0.354078 + 0.935216i $$0.615205\pi$$
$$338$$ 3.00000 0.163178
$$339$$ 5.00000 0.271563
$$340$$ 0 0
$$341$$ 22.0000 1.19137
$$342$$ −4.00000 −0.216295
$$343$$ 0 0
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 2.00000 0.107521
$$347$$ 18.0000 0.966291 0.483145 0.875540i $$-0.339494\pi$$
0.483145 + 0.875540i $$0.339494\pi$$
$$348$$ 6.00000 0.321634
$$349$$ −4.00000 −0.214115 −0.107058 0.994253i $$-0.534143\pi$$
−0.107058 + 0.994253i $$0.534143\pi$$
$$350$$ 0 0
$$351$$ −4.00000 −0.213504
$$352$$ −2.00000 −0.106600
$$353$$ −9.00000 −0.479022 −0.239511 0.970894i $$-0.576987\pi$$
−0.239511 + 0.970894i $$0.576987\pi$$
$$354$$ 2.00000 0.106299
$$355$$ 0 0
$$356$$ 11.0000 0.582999
$$357$$ 0 0
$$358$$ 22.0000 1.16274
$$359$$ −20.0000 −1.05556 −0.527780 0.849381i $$-0.676975\pi$$
−0.527780 + 0.849381i $$0.676975\pi$$
$$360$$ 0 0
$$361$$ −3.00000 −0.157895
$$362$$ −22.0000 −1.15629
$$363$$ 7.00000 0.367405
$$364$$ 0 0
$$365$$ 0 0
$$366$$ −10.0000 −0.522708
$$367$$ 4.00000 0.208798 0.104399 0.994535i $$-0.466708\pi$$
0.104399 + 0.994535i $$0.466708\pi$$
$$368$$ −5.00000 −0.260643
$$369$$ 5.00000 0.260290
$$370$$ 0 0
$$371$$ 0 0
$$372$$ 11.0000 0.570323
$$373$$ 32.0000 1.65690 0.828449 0.560065i $$-0.189224\pi$$
0.828449 + 0.560065i $$0.189224\pi$$
$$374$$ −10.0000 −0.517088
$$375$$ 0 0
$$376$$ 1.00000 0.0515711
$$377$$ −24.0000 −1.23606
$$378$$ 0 0
$$379$$ −2.00000 −0.102733 −0.0513665 0.998680i $$-0.516358\pi$$
−0.0513665 + 0.998680i $$0.516358\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ −25.0000 −1.27911
$$383$$ −3.00000 −0.153293 −0.0766464 0.997058i $$-0.524421\pi$$
−0.0766464 + 0.997058i $$0.524421\pi$$
$$384$$ −1.00000 −0.0510310
$$385$$ 0 0
$$386$$ −11.0000 −0.559885
$$387$$ 0 0
$$388$$ 1.00000 0.0507673
$$389$$ 24.0000 1.21685 0.608424 0.793612i $$-0.291802\pi$$
0.608424 + 0.793612i $$0.291802\pi$$
$$390$$ 0 0
$$391$$ −25.0000 −1.26430
$$392$$ 0 0
$$393$$ −6.00000 −0.302660
$$394$$ 24.0000 1.20910
$$395$$ 0 0
$$396$$ −2.00000 −0.100504
$$397$$ 34.0000 1.70641 0.853206 0.521575i $$-0.174655\pi$$
0.853206 + 0.521575i $$0.174655\pi$$
$$398$$ 5.00000 0.250627
$$399$$ 0 0
$$400$$ 0 0
$$401$$ −6.00000 −0.299626 −0.149813 0.988714i $$-0.547867\pi$$
−0.149813 + 0.988714i $$0.547867\pi$$
$$402$$ 0 0
$$403$$ −44.0000 −2.19180
$$404$$ 12.0000 0.597022
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 16.0000 0.793091
$$408$$ −5.00000 −0.247537
$$409$$ −35.0000 −1.73064 −0.865319 0.501221i $$-0.832884\pi$$
−0.865319 + 0.501221i $$0.832884\pi$$
$$410$$ 0 0
$$411$$ 23.0000 1.13451
$$412$$ −13.0000 −0.640464
$$413$$ 0 0
$$414$$ −5.00000 −0.245737
$$415$$ 0 0
$$416$$ 4.00000 0.196116
$$417$$ −2.00000 −0.0979404
$$418$$ 8.00000 0.391293
$$419$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$420$$ 0 0
$$421$$ 28.0000 1.36464 0.682318 0.731055i $$-0.260972\pi$$
0.682318 + 0.731055i $$0.260972\pi$$
$$422$$ −16.0000 −0.778868
$$423$$ 1.00000 0.0486217
$$424$$ −12.0000 −0.582772
$$425$$ 0 0
$$426$$ 1.00000 0.0484502
$$427$$ 0 0
$$428$$ −2.00000 −0.0966736
$$429$$ 8.00000 0.386244
$$430$$ 0 0
$$431$$ −3.00000 −0.144505 −0.0722525 0.997386i $$-0.523019\pi$$
−0.0722525 + 0.997386i $$0.523019\pi$$
$$432$$ −1.00000 −0.0481125
$$433$$ 9.00000 0.432512 0.216256 0.976337i $$-0.430615\pi$$
0.216256 + 0.976337i $$0.430615\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 4.00000 0.191565
$$437$$ 20.0000 0.956730
$$438$$ 2.00000 0.0955637
$$439$$ 35.0000 1.67046 0.835229 0.549902i $$-0.185335\pi$$
0.835229 + 0.549902i $$0.185335\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 20.0000 0.951303
$$443$$ 8.00000 0.380091 0.190046 0.981775i $$-0.439136\pi$$
0.190046 + 0.981775i $$0.439136\pi$$
$$444$$ 8.00000 0.379663
$$445$$ 0 0
$$446$$ −21.0000 −0.994379
$$447$$ −18.0000 −0.851371
$$448$$ 0 0
$$449$$ 37.0000 1.74614 0.873069 0.487597i $$-0.162126\pi$$
0.873069 + 0.487597i $$0.162126\pi$$
$$450$$ 0 0
$$451$$ −10.0000 −0.470882
$$452$$ −5.00000 −0.235180
$$453$$ 16.0000 0.751746
$$454$$ −18.0000 −0.844782
$$455$$ 0 0
$$456$$ 4.00000 0.187317
$$457$$ −14.0000 −0.654892 −0.327446 0.944870i $$-0.606188\pi$$
−0.327446 + 0.944870i $$0.606188\pi$$
$$458$$ −14.0000 −0.654177
$$459$$ −5.00000 −0.233380
$$460$$ 0 0
$$461$$ 20.0000 0.931493 0.465746 0.884918i $$-0.345786\pi$$
0.465746 + 0.884918i $$0.345786\pi$$
$$462$$ 0 0
$$463$$ −13.0000 −0.604161 −0.302081 0.953282i $$-0.597681\pi$$
−0.302081 + 0.953282i $$0.597681\pi$$
$$464$$ −6.00000 −0.278543
$$465$$ 0 0
$$466$$ −26.0000 −1.20443
$$467$$ 34.0000 1.57333 0.786666 0.617379i $$-0.211805\pi$$
0.786666 + 0.617379i $$0.211805\pi$$
$$468$$ 4.00000 0.184900
$$469$$ 0 0
$$470$$ 0 0
$$471$$ −14.0000 −0.645086
$$472$$ −2.00000 −0.0920575
$$473$$ 0 0
$$474$$ −9.00000 −0.413384
$$475$$ 0 0
$$476$$ 0 0
$$477$$ −12.0000 −0.549442
$$478$$ 11.0000 0.503128
$$479$$ −3.00000 −0.137073 −0.0685367 0.997649i $$-0.521833\pi$$
−0.0685367 + 0.997649i $$0.521833\pi$$
$$480$$ 0 0
$$481$$ −32.0000 −1.45907
$$482$$ −6.00000 −0.273293
$$483$$ 0 0
$$484$$ −7.00000 −0.318182
$$485$$ 0 0
$$486$$ −1.00000 −0.0453609
$$487$$ 39.0000 1.76726 0.883629 0.468187i $$-0.155093\pi$$
0.883629 + 0.468187i $$0.155093\pi$$
$$488$$ 10.0000 0.452679
$$489$$ 24.0000 1.08532
$$490$$ 0 0
$$491$$ 12.0000 0.541552 0.270776 0.962642i $$-0.412720\pi$$
0.270776 + 0.962642i $$0.412720\pi$$
$$492$$ −5.00000 −0.225417
$$493$$ −30.0000 −1.35113
$$494$$ −16.0000 −0.719874
$$495$$ 0 0
$$496$$ −11.0000 −0.493915
$$497$$ 0 0
$$498$$ 6.00000 0.268866
$$499$$ 22.0000 0.984855 0.492428 0.870353i $$-0.336110\pi$$
0.492428 + 0.870353i $$0.336110\pi$$
$$500$$ 0 0
$$501$$ 16.0000 0.714827
$$502$$ −8.00000 −0.357057
$$503$$ −8.00000 −0.356702 −0.178351 0.983967i $$-0.557076\pi$$
−0.178351 + 0.983967i $$0.557076\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ 10.0000 0.444554
$$507$$ −3.00000 −0.133235
$$508$$ 0 0
$$509$$ 2.00000 0.0886484 0.0443242 0.999017i $$-0.485887\pi$$
0.0443242 + 0.999017i $$0.485887\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ 1.00000 0.0441942
$$513$$ 4.00000 0.176604
$$514$$ 14.0000 0.617514
$$515$$ 0 0
$$516$$ 0 0
$$517$$ −2.00000 −0.0879599
$$518$$ 0 0
$$519$$ −2.00000 −0.0877903
$$520$$ 0 0
$$521$$ −3.00000 −0.131432 −0.0657162 0.997838i $$-0.520933\pi$$
−0.0657162 + 0.997838i $$0.520933\pi$$
$$522$$ −6.00000 −0.262613
$$523$$ 14.0000 0.612177 0.306089 0.952003i $$-0.400980\pi$$
0.306089 + 0.952003i $$0.400980\pi$$
$$524$$ 6.00000 0.262111
$$525$$ 0 0
$$526$$ 21.0000 0.915644
$$527$$ −55.0000 −2.39584
$$528$$ 2.00000 0.0870388
$$529$$ 2.00000 0.0869565
$$530$$ 0 0
$$531$$ −2.00000 −0.0867926
$$532$$ 0 0
$$533$$ 20.0000 0.866296
$$534$$ −11.0000 −0.476017
$$535$$ 0 0
$$536$$ 0 0
$$537$$ −22.0000 −0.949370
$$538$$ −24.0000 −1.03471
$$539$$ 0 0
$$540$$ 0 0
$$541$$ −4.00000 −0.171973 −0.0859867 0.996296i $$-0.527404\pi$$
−0.0859867 + 0.996296i $$0.527404\pi$$
$$542$$ −9.00000 −0.386583
$$543$$ 22.0000 0.944110
$$544$$ 5.00000 0.214373
$$545$$ 0 0
$$546$$ 0 0
$$547$$ −8.00000 −0.342055 −0.171028 0.985266i $$-0.554709\pi$$
−0.171028 + 0.985266i $$0.554709\pi$$
$$548$$ −23.0000 −0.982511
$$549$$ 10.0000 0.426790
$$550$$ 0 0
$$551$$ 24.0000 1.02243
$$552$$ 5.00000 0.212814
$$553$$ 0 0
$$554$$ 2.00000 0.0849719
$$555$$ 0 0
$$556$$ 2.00000 0.0848189
$$557$$ −38.0000 −1.61011 −0.805056 0.593199i $$-0.797865\pi$$
−0.805056 + 0.593199i $$0.797865\pi$$
$$558$$ −11.0000 −0.465667
$$559$$ 0 0
$$560$$ 0 0
$$561$$ 10.0000 0.422200
$$562$$ −29.0000 −1.22329
$$563$$ 36.0000 1.51722 0.758610 0.651546i $$-0.225879\pi$$
0.758610 + 0.651546i $$0.225879\pi$$
$$564$$ −1.00000 −0.0421076
$$565$$ 0 0
$$566$$ 26.0000 1.09286
$$567$$ 0 0
$$568$$ −1.00000 −0.0419591
$$569$$ 9.00000 0.377300 0.188650 0.982044i $$-0.439589\pi$$
0.188650 + 0.982044i $$0.439589\pi$$
$$570$$ 0 0
$$571$$ −44.0000 −1.84134 −0.920671 0.390339i $$-0.872358\pi$$
−0.920671 + 0.390339i $$0.872358\pi$$
$$572$$ −8.00000 −0.334497
$$573$$ 25.0000 1.04439
$$574$$ 0 0
$$575$$ 0 0
$$576$$ 1.00000 0.0416667
$$577$$ 2.00000 0.0832611 0.0416305 0.999133i $$-0.486745\pi$$
0.0416305 + 0.999133i $$0.486745\pi$$
$$578$$ 8.00000 0.332756
$$579$$ 11.0000 0.457144
$$580$$ 0 0
$$581$$ 0 0
$$582$$ −1.00000 −0.0414513
$$583$$ 24.0000 0.993978
$$584$$ −2.00000 −0.0827606
$$585$$ 0 0
$$586$$ −18.0000 −0.743573
$$587$$ −6.00000 −0.247647 −0.123823 0.992304i $$-0.539516\pi$$
−0.123823 + 0.992304i $$0.539516\pi$$
$$588$$ 0 0
$$589$$ 44.0000 1.81299
$$590$$ 0 0
$$591$$ −24.0000 −0.987228
$$592$$ −8.00000 −0.328798
$$593$$ −9.00000 −0.369586 −0.184793 0.982777i $$-0.559161\pi$$
−0.184793 + 0.982777i $$0.559161\pi$$
$$594$$ 2.00000 0.0820610
$$595$$ 0 0
$$596$$ 18.0000 0.737309
$$597$$ −5.00000 −0.204636
$$598$$ −20.0000 −0.817861
$$599$$ 17.0000 0.694601 0.347301 0.937754i $$-0.387098\pi$$
0.347301 + 0.937754i $$0.387098\pi$$
$$600$$ 0 0
$$601$$ −34.0000 −1.38689 −0.693444 0.720510i $$-0.743908\pi$$
−0.693444 + 0.720510i $$0.743908\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ −16.0000 −0.651031
$$605$$ 0 0
$$606$$ −12.0000 −0.487467
$$607$$ 27.0000 1.09590 0.547948 0.836512i $$-0.315409\pi$$
0.547948 + 0.836512i $$0.315409\pi$$
$$608$$ −4.00000 −0.162221
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 4.00000 0.161823
$$612$$ 5.00000 0.202113
$$613$$ −34.0000 −1.37325 −0.686624 0.727013i $$-0.740908\pi$$
−0.686624 + 0.727013i $$0.740908\pi$$
$$614$$ −28.0000 −1.12999
$$615$$ 0 0
$$616$$ 0 0
$$617$$ −29.0000 −1.16750 −0.583748 0.811935i $$-0.698414\pi$$
−0.583748 + 0.811935i $$0.698414\pi$$
$$618$$ 13.0000 0.522937
$$619$$ −14.0000 −0.562708 −0.281354 0.959604i $$-0.590783\pi$$
−0.281354 + 0.959604i $$0.590783\pi$$
$$620$$ 0 0
$$621$$ 5.00000 0.200643
$$622$$ 29.0000 1.16279
$$623$$ 0 0
$$624$$ −4.00000 −0.160128
$$625$$ 0 0
$$626$$ 1.00000 0.0399680
$$627$$ −8.00000 −0.319489
$$628$$ 14.0000 0.558661
$$629$$ −40.0000 −1.59490
$$630$$ 0 0
$$631$$ 33.0000 1.31371 0.656855 0.754017i $$-0.271887\pi$$
0.656855 + 0.754017i $$0.271887\pi$$
$$632$$ 9.00000 0.358001
$$633$$ 16.0000 0.635943
$$634$$ −4.00000 −0.158860
$$635$$ 0 0
$$636$$ 12.0000 0.475831
$$637$$ 0 0
$$638$$ 12.0000 0.475085
$$639$$ −1.00000 −0.0395594
$$640$$ 0 0
$$641$$ −15.0000 −0.592464 −0.296232 0.955116i $$-0.595730\pi$$
−0.296232 + 0.955116i $$0.595730\pi$$
$$642$$ 2.00000 0.0789337
$$643$$ −26.0000 −1.02534 −0.512670 0.858586i $$-0.671344\pi$$
−0.512670 + 0.858586i $$0.671344\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ −20.0000 −0.786889
$$647$$ 28.0000 1.10079 0.550397 0.834903i $$-0.314476\pi$$
0.550397 + 0.834903i $$0.314476\pi$$
$$648$$ 1.00000 0.0392837
$$649$$ 4.00000 0.157014
$$650$$ 0 0
$$651$$ 0 0
$$652$$ −24.0000 −0.939913
$$653$$ −28.0000 −1.09572 −0.547862 0.836569i $$-0.684558\pi$$
−0.547862 + 0.836569i $$0.684558\pi$$
$$654$$ −4.00000 −0.156412
$$655$$ 0 0
$$656$$ 5.00000 0.195217
$$657$$ −2.00000 −0.0780274
$$658$$ 0 0
$$659$$ −14.0000 −0.545363 −0.272681 0.962104i $$-0.587910\pi$$
−0.272681 + 0.962104i $$0.587910\pi$$
$$660$$ 0 0
$$661$$ 14.0000 0.544537 0.272268 0.962221i $$-0.412226\pi$$
0.272268 + 0.962221i $$0.412226\pi$$
$$662$$ 10.0000 0.388661
$$663$$ −20.0000 −0.776736
$$664$$ −6.00000 −0.232845
$$665$$ 0 0
$$666$$ −8.00000 −0.309994
$$667$$ 30.0000 1.16160
$$668$$ −16.0000 −0.619059
$$669$$ 21.0000 0.811907
$$670$$ 0 0
$$671$$ −20.0000 −0.772091
$$672$$ 0 0
$$673$$ −19.0000 −0.732396 −0.366198 0.930537i $$-0.619341\pi$$
−0.366198 + 0.930537i $$0.619341\pi$$
$$674$$ −13.0000 −0.500741
$$675$$ 0 0
$$676$$ 3.00000 0.115385
$$677$$ 18.0000 0.691796 0.345898 0.938272i $$-0.387574\pi$$
0.345898 + 0.938272i $$0.387574\pi$$
$$678$$ 5.00000 0.192024
$$679$$ 0 0
$$680$$ 0 0
$$681$$ 18.0000 0.689761
$$682$$ 22.0000 0.842424
$$683$$ 2.00000 0.0765279 0.0382639 0.999268i $$-0.487817\pi$$
0.0382639 + 0.999268i $$0.487817\pi$$
$$684$$ −4.00000 −0.152944
$$685$$ 0 0
$$686$$ 0 0
$$687$$ 14.0000 0.534133
$$688$$ 0 0
$$689$$ −48.0000 −1.82865
$$690$$ 0 0
$$691$$ −2.00000 −0.0760836 −0.0380418 0.999276i $$-0.512112\pi$$
−0.0380418 + 0.999276i $$0.512112\pi$$
$$692$$ 2.00000 0.0760286
$$693$$ 0 0
$$694$$ 18.0000 0.683271
$$695$$ 0 0
$$696$$ 6.00000 0.227429
$$697$$ 25.0000 0.946943
$$698$$ −4.00000 −0.151402
$$699$$ 26.0000 0.983410
$$700$$ 0 0
$$701$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$702$$ −4.00000 −0.150970
$$703$$ 32.0000 1.20690
$$704$$ −2.00000 −0.0753778
$$705$$ 0 0
$$706$$ −9.00000 −0.338719
$$707$$ 0 0
$$708$$ 2.00000 0.0751646
$$709$$ 10.0000 0.375558 0.187779 0.982211i $$-0.439871\pi$$
0.187779 + 0.982211i $$0.439871\pi$$
$$710$$ 0 0
$$711$$ 9.00000 0.337526
$$712$$ 11.0000 0.412242
$$713$$ 55.0000 2.05977
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 22.0000 0.822179
$$717$$ −11.0000 −0.410803
$$718$$ −20.0000 −0.746393
$$719$$ −3.00000 −0.111881 −0.0559406 0.998434i $$-0.517816\pi$$
−0.0559406 + 0.998434i $$0.517816\pi$$
$$720$$ 0 0
$$721$$ 0 0
$$722$$ −3.00000 −0.111648
$$723$$ 6.00000 0.223142
$$724$$ −22.0000 −0.817624
$$725$$ 0 0
$$726$$ 7.00000 0.259794
$$727$$ 33.0000 1.22390 0.611951 0.790896i $$-0.290385\pi$$
0.611951 + 0.790896i $$0.290385\pi$$
$$728$$ 0 0
$$729$$ 1.00000 0.0370370
$$730$$ 0 0
$$731$$ 0 0
$$732$$ −10.0000 −0.369611
$$733$$ −30.0000 −1.10808 −0.554038 0.832492i $$-0.686914\pi$$
−0.554038 + 0.832492i $$0.686914\pi$$
$$734$$ 4.00000 0.147643
$$735$$ 0 0
$$736$$ −5.00000 −0.184302
$$737$$ 0 0
$$738$$ 5.00000 0.184053
$$739$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$740$$ 0 0
$$741$$ 16.0000 0.587775
$$742$$ 0 0
$$743$$ 33.0000 1.21065 0.605326 0.795977i $$-0.293043\pi$$
0.605326 + 0.795977i $$0.293043\pi$$
$$744$$ 11.0000 0.403280
$$745$$ 0 0
$$746$$ 32.0000 1.17160
$$747$$ −6.00000 −0.219529
$$748$$ −10.0000 −0.365636
$$749$$ 0 0
$$750$$ 0 0
$$751$$ −32.0000 −1.16770 −0.583848 0.811863i $$-0.698454\pi$$
−0.583848 + 0.811863i $$0.698454\pi$$
$$752$$ 1.00000 0.0364662
$$753$$ 8.00000 0.291536
$$754$$ −24.0000 −0.874028
$$755$$ 0 0
$$756$$ 0 0
$$757$$ −28.0000 −1.01768 −0.508839 0.860862i $$-0.669925\pi$$
−0.508839 + 0.860862i $$0.669925\pi$$
$$758$$ −2.00000 −0.0726433
$$759$$ −10.0000 −0.362977
$$760$$ 0 0
$$761$$ 17.0000 0.616250 0.308125 0.951346i $$-0.400299\pi$$
0.308125 + 0.951346i $$0.400299\pi$$
$$762$$ 0 0
$$763$$ 0 0
$$764$$ −25.0000 −0.904468
$$765$$ 0 0
$$766$$ −3.00000 −0.108394
$$767$$ −8.00000 −0.288863
$$768$$ −1.00000 −0.0360844
$$769$$ −14.0000 −0.504853 −0.252426 0.967616i $$-0.581229\pi$$
−0.252426 + 0.967616i $$0.581229\pi$$
$$770$$ 0 0
$$771$$ −14.0000 −0.504198
$$772$$ −11.0000 −0.395899
$$773$$ 4.00000 0.143870 0.0719350 0.997409i $$-0.477083\pi$$
0.0719350 + 0.997409i $$0.477083\pi$$
$$774$$ 0 0
$$775$$ 0 0
$$776$$ 1.00000 0.0358979
$$777$$ 0 0
$$778$$ 24.0000 0.860442
$$779$$ −20.0000 −0.716574
$$780$$ 0 0
$$781$$ 2.00000 0.0715656
$$782$$ −25.0000 −0.893998
$$783$$ 6.00000 0.214423
$$784$$ 0 0
$$785$$ 0 0
$$786$$ −6.00000 −0.214013
$$787$$ −40.0000 −1.42585 −0.712923 0.701242i $$-0.752629\pi$$
−0.712923 + 0.701242i $$0.752629\pi$$
$$788$$ 24.0000 0.854965
$$789$$ −21.0000 −0.747620
$$790$$ 0 0
$$791$$ 0 0
$$792$$ −2.00000 −0.0710669
$$793$$ 40.0000 1.42044
$$794$$ 34.0000 1.20661
$$795$$ 0 0
$$796$$ 5.00000 0.177220
$$797$$ −42.0000 −1.48772 −0.743858 0.668338i $$-0.767006\pi$$
−0.743858 + 0.668338i $$0.767006\pi$$
$$798$$ 0 0
$$799$$ 5.00000 0.176887
$$800$$ 0 0
$$801$$ 11.0000 0.388666
$$802$$ −6.00000 −0.211867
$$803$$ 4.00000 0.141157
$$804$$ 0 0
$$805$$ 0 0
$$806$$ −44.0000 −1.54983
$$807$$ 24.0000 0.844840
$$808$$ 12.0000 0.422159
$$809$$ 10.0000 0.351581 0.175791 0.984428i $$-0.443752\pi$$
0.175791 + 0.984428i $$0.443752\pi$$
$$810$$ 0 0
$$811$$ −48.0000 −1.68551 −0.842754 0.538299i $$-0.819067\pi$$
−0.842754 + 0.538299i $$0.819067\pi$$
$$812$$ 0 0
$$813$$ 9.00000 0.315644
$$814$$ 16.0000 0.560800
$$815$$ 0 0
$$816$$ −5.00000 −0.175035
$$817$$ 0 0
$$818$$ −35.0000 −1.22375
$$819$$ 0 0
$$820$$ 0 0
$$821$$ 52.0000 1.81481 0.907406 0.420255i $$-0.138059\pi$$
0.907406 + 0.420255i $$0.138059\pi$$
$$822$$ 23.0000 0.802217
$$823$$ −20.0000 −0.697156 −0.348578 0.937280i $$-0.613335\pi$$
−0.348578 + 0.937280i $$0.613335\pi$$
$$824$$ −13.0000 −0.452876
$$825$$ 0 0
$$826$$ 0 0
$$827$$ 30.0000 1.04320 0.521601 0.853189i $$-0.325335\pi$$
0.521601 + 0.853189i $$0.325335\pi$$
$$828$$ −5.00000 −0.173762
$$829$$ 26.0000 0.903017 0.451509 0.892267i $$-0.350886\pi$$
0.451509 + 0.892267i $$0.350886\pi$$
$$830$$ 0 0
$$831$$ −2.00000 −0.0693792
$$832$$ 4.00000 0.138675
$$833$$ 0 0
$$834$$ −2.00000 −0.0692543
$$835$$ 0 0
$$836$$ 8.00000 0.276686
$$837$$ 11.0000 0.380216
$$838$$ 0 0
$$839$$ −9.00000 −0.310715 −0.155357 0.987858i $$-0.549653\pi$$
−0.155357 + 0.987858i $$0.549653\pi$$
$$840$$ 0 0
$$841$$ 7.00000 0.241379
$$842$$ 28.0000 0.964944
$$843$$ 29.0000 0.998813
$$844$$ −16.0000 −0.550743
$$845$$ 0 0
$$846$$ 1.00000 0.0343807
$$847$$ 0 0
$$848$$ −12.0000 −0.412082
$$849$$ −26.0000 −0.892318
$$850$$ 0 0
$$851$$ 40.0000 1.37118
$$852$$ 1.00000 0.0342594
$$853$$ −20.0000 −0.684787 −0.342393 0.939557i $$-0.611238\pi$$
−0.342393 + 0.939557i $$0.611238\pi$$
$$854$$ 0 0
$$855$$ 0 0
$$856$$ −2.00000 −0.0683586
$$857$$ −58.0000 −1.98124 −0.990621 0.136637i $$-0.956370\pi$$
−0.990621 + 0.136637i $$0.956370\pi$$
$$858$$ 8.00000 0.273115
$$859$$ −10.0000 −0.341196 −0.170598 0.985341i $$-0.554570\pi$$
−0.170598 + 0.985341i $$0.554570\pi$$
$$860$$ 0 0
$$861$$ 0 0
$$862$$ −3.00000 −0.102180
$$863$$ −51.0000 −1.73606 −0.868030 0.496512i $$-0.834614\pi$$
−0.868030 + 0.496512i $$0.834614\pi$$
$$864$$ −1.00000 −0.0340207
$$865$$ 0 0
$$866$$ 9.00000 0.305832
$$867$$ −8.00000 −0.271694
$$868$$ 0 0
$$869$$ −18.0000 −0.610608
$$870$$ 0 0
$$871$$ 0 0
$$872$$ 4.00000 0.135457
$$873$$ 1.00000 0.0338449
$$874$$ 20.0000 0.676510
$$875$$ 0 0
$$876$$ 2.00000 0.0675737
$$877$$ −22.0000 −0.742887 −0.371444 0.928456i $$-0.621137\pi$$
−0.371444 + 0.928456i $$0.621137\pi$$
$$878$$ 35.0000 1.18119
$$879$$ 18.0000 0.607125
$$880$$ 0 0
$$881$$ 39.0000 1.31394 0.656972 0.753915i $$-0.271837\pi$$
0.656972 + 0.753915i $$0.271837\pi$$
$$882$$ 0 0
$$883$$ −2.00000 −0.0673054 −0.0336527 0.999434i $$-0.510714\pi$$
−0.0336527 + 0.999434i $$0.510714\pi$$
$$884$$ 20.0000 0.672673
$$885$$ 0 0
$$886$$ 8.00000 0.268765
$$887$$ −56.0000 −1.88030 −0.940148 0.340766i $$-0.889313\pi$$
−0.940148 + 0.340766i $$0.889313\pi$$
$$888$$ 8.00000 0.268462
$$889$$ 0 0
$$890$$ 0 0
$$891$$ −2.00000 −0.0670025
$$892$$ −21.0000 −0.703132
$$893$$ −4.00000 −0.133855
$$894$$ −18.0000 −0.602010
$$895$$ 0 0
$$896$$ 0 0
$$897$$ 20.0000 0.667781
$$898$$ 37.0000 1.23471
$$899$$ 66.0000 2.20122
$$900$$ 0 0
$$901$$ −60.0000 −1.99889
$$902$$ −10.0000 −0.332964
$$903$$ 0 0
$$904$$ −5.00000 −0.166298
$$905$$ 0 0
$$906$$ 16.0000 0.531564
$$907$$ −18.0000 −0.597680 −0.298840 0.954303i $$-0.596600\pi$$
−0.298840 + 0.954303i $$0.596600\pi$$
$$908$$ −18.0000 −0.597351
$$909$$ 12.0000 0.398015
$$910$$ 0 0
$$911$$ 51.0000 1.68971 0.844853 0.534999i $$-0.179688\pi$$
0.844853 + 0.534999i $$0.179688\pi$$
$$912$$ 4.00000 0.132453
$$913$$ 12.0000 0.397142
$$914$$ −14.0000 −0.463079
$$915$$ 0 0
$$916$$ −14.0000 −0.462573
$$917$$ 0 0
$$918$$ −5.00000 −0.165025
$$919$$ 43.0000 1.41844 0.709220 0.704988i $$-0.249047\pi$$
0.709220 + 0.704988i $$0.249047\pi$$
$$920$$ 0 0
$$921$$ 28.0000 0.922631
$$922$$ 20.0000 0.658665
$$923$$ −4.00000 −0.131662
$$924$$ 0 0
$$925$$ 0 0
$$926$$ −13.0000 −0.427207
$$927$$ −13.0000 −0.426976
$$928$$ −6.00000 −0.196960
$$929$$ 34.0000 1.11550 0.557752 0.830008i $$-0.311664\pi$$
0.557752 + 0.830008i $$0.311664\pi$$
$$930$$ 0 0
$$931$$ 0 0
$$932$$ −26.0000 −0.851658
$$933$$ −29.0000 −0.949417
$$934$$ 34.0000 1.11251
$$935$$ 0 0
$$936$$ 4.00000 0.130744
$$937$$ 30.0000 0.980057 0.490029 0.871706i $$-0.336986\pi$$
0.490029 + 0.871706i $$0.336986\pi$$
$$938$$ 0 0
$$939$$ −1.00000 −0.0326338
$$940$$ 0 0
$$941$$ 36.0000 1.17357 0.586783 0.809744i $$-0.300394\pi$$
0.586783 + 0.809744i $$0.300394\pi$$
$$942$$ −14.0000 −0.456145
$$943$$ −25.0000 −0.814112
$$944$$ −2.00000 −0.0650945
$$945$$ 0 0
$$946$$ 0 0
$$947$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$948$$ −9.00000 −0.292306
$$949$$ −8.00000 −0.259691
$$950$$ 0 0
$$951$$ 4.00000 0.129709
$$952$$ 0 0
$$953$$ 6.00000 0.194359 0.0971795 0.995267i $$-0.469018\pi$$
0.0971795 + 0.995267i $$0.469018\pi$$
$$954$$ −12.0000 −0.388514
$$955$$ 0 0
$$956$$ 11.0000 0.355765
$$957$$ −12.0000 −0.387905
$$958$$ −3.00000 −0.0969256
$$959$$ 0 0
$$960$$ 0 0
$$961$$ 90.0000 2.90323
$$962$$ −32.0000 −1.03172
$$963$$ −2.00000 −0.0644491
$$964$$ −6.00000 −0.193247
$$965$$ 0 0
$$966$$ 0 0
$$967$$ 1.00000 0.0321578 0.0160789 0.999871i $$-0.494882\pi$$
0.0160789 + 0.999871i $$0.494882\pi$$
$$968$$ −7.00000 −0.224989
$$969$$ 20.0000 0.642493
$$970$$ 0 0
$$971$$ 6.00000 0.192549 0.0962746 0.995355i $$-0.469307\pi$$
0.0962746 + 0.995355i $$0.469307\pi$$
$$972$$ −1.00000 −0.0320750
$$973$$ 0 0
$$974$$ 39.0000 1.24964
$$975$$ 0 0
$$976$$ 10.0000 0.320092
$$977$$ 33.0000 1.05576 0.527882 0.849318i $$-0.322986\pi$$
0.527882 + 0.849318i $$0.322986\pi$$
$$978$$ 24.0000 0.767435
$$979$$ −22.0000 −0.703123
$$980$$ 0 0
$$981$$ 4.00000 0.127710
$$982$$ 12.0000 0.382935
$$983$$ −16.0000 −0.510321 −0.255160 0.966899i $$-0.582128\pi$$
−0.255160 + 0.966899i $$0.582128\pi$$
$$984$$ −5.00000 −0.159394
$$985$$ 0 0
$$986$$ −30.0000 −0.955395
$$987$$ 0 0
$$988$$ −16.0000 −0.509028
$$989$$ 0 0
$$990$$ 0 0
$$991$$ 37.0000 1.17534 0.587672 0.809099i $$-0.300045\pi$$
0.587672 + 0.809099i $$0.300045\pi$$
$$992$$ −11.0000 −0.349250
$$993$$ −10.0000 −0.317340
$$994$$ 0 0
$$995$$ 0 0
$$996$$ 6.00000 0.190117
$$997$$ −4.00000 −0.126681 −0.0633406 0.997992i $$-0.520175\pi$$
−0.0633406 + 0.997992i $$0.520175\pi$$
$$998$$ 22.0000 0.696398
$$999$$ 8.00000 0.253109
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.bt.1.1 1
5.4 even 2 7350.2.a.z.1.1 1
7.2 even 3 1050.2.i.j.151.1 2
7.4 even 3 1050.2.i.j.751.1 yes 2
7.6 odd 2 7350.2.a.cn.1.1 1
35.2 odd 12 1050.2.o.f.949.2 4
35.4 even 6 1050.2.i.k.751.1 yes 2
35.9 even 6 1050.2.i.k.151.1 yes 2
35.18 odd 12 1050.2.o.f.499.2 4
35.23 odd 12 1050.2.o.f.949.1 4
35.32 odd 12 1050.2.o.f.499.1 4
35.34 odd 2 7350.2.a.h.1.1 1

By twisted newform
Twist Min Dim Char Parity Ord Type
1050.2.i.j.151.1 2 7.2 even 3
1050.2.i.j.751.1 yes 2 7.4 even 3
1050.2.i.k.151.1 yes 2 35.9 even 6
1050.2.i.k.751.1 yes 2 35.4 even 6
1050.2.o.f.499.1 4 35.32 odd 12
1050.2.o.f.499.2 4 35.18 odd 12
1050.2.o.f.949.1 4 35.23 odd 12
1050.2.o.f.949.2 4 35.2 odd 12
7350.2.a.h.1.1 1 35.34 odd 2
7350.2.a.z.1.1 1 5.4 even 2
7350.2.a.bt.1.1 1 1.1 even 1 trivial
7350.2.a.cn.1.1 1 7.6 odd 2