LMFDB - Embedded newform 2.72.a.a.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2,72,Mod(1,2)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2, base_ring=CyclotomicField(1))

chi = DirichletCharacter(H, H._module([]))

N = Newforms(chi, 72, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("2.1");

S:= CuspForms(chi, 72);

N := Newforms(S);

Level:	$ N $	$=$	$ 2 $
Weight:	$ k $	$=$	$ 72 $
Character orbit:	$[\chi]$	$=$	2.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$63.8492321122$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\mathbb{Q}[x]/(x^{2} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 63394039540968776880 $ x^2 - x - 63394039540968776880
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{7}\cdot 3^{6}\cdot 5^{2} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-7.96204e9$ of defining polynomial
Character	$\chi$	$=$	2.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+3.43597e10 q^{2} +1.90762e16 q^{3} +1.18059e21 q^{4} -4.48127e24 q^{5} +6.55455e26 q^{6} +7.01318e29 q^{7} +4.05648e31 q^{8} -7.14556e33 q^{9} +O(q^{10})$	\(q+3.43597e10 q^{2} +1.90762e16 q^{3} +1.18059e21 q^{4} -4.48127e24 q^{5} +6.55455e26 q^{6} +7.01318e29 q^{7} +4.05648e31 q^{8} -7.14556e33 q^{9} -1.53975e35 q^{10} +1.39666e36 q^{11} +2.25213e37 q^{12} +1.53777e39 q^{13} +2.40971e40 q^{14} -8.54858e40 q^{15} +1.39380e42 q^{16} -5.62631e43 q^{17} -2.45520e44 q^{18} +1.79942e45 q^{19} -5.29055e45 q^{20} +1.33785e46 q^{21} +4.79889e46 q^{22} -1.05979e48 q^{23} +7.73824e47 q^{24} -2.22699e49 q^{25} +5.28374e49 q^{26} -2.79563e50 q^{27} +8.27970e50 q^{28} +2.91198e51 q^{29} -2.93727e51 q^{30} -1.29140e53 q^{31} +4.78905e52 q^{32} +2.66431e52 q^{33} -1.93318e54 q^{34} -3.14279e54 q^{35} -8.43599e54 q^{36} -4.26561e55 q^{37} +6.18276e55 q^{38} +2.93349e55 q^{39} -1.81782e56 q^{40} -1.24989e56 q^{41} +4.59682e56 q^{42} +1.00872e58 q^{43} +1.64889e57 q^{44} +3.20212e58 q^{45} -3.64140e58 q^{46} -1.24115e59 q^{47} +2.65884e58 q^{48} -5.12678e59 q^{49} -7.65187e59 q^{50} -1.07329e60 q^{51} +1.81548e60 q^{52} +1.01729e61 q^{53} -9.60571e60 q^{54} -6.25882e60 q^{55} +2.84488e61 q^{56} +3.43262e61 q^{57} +1.00055e62 q^{58} -9.41671e62 q^{59} -1.00924e62 q^{60} -9.88843e62 q^{61} -4.43723e63 q^{62} -5.01131e63 q^{63} +1.64550e63 q^{64} -6.89116e63 q^{65} +9.15448e62 q^{66} -9.00666e64 q^{67} -6.64237e64 q^{68} -2.02168e64 q^{69} -1.07986e65 q^{70} -8.82699e65 q^{71} -2.89858e65 q^{72} -2.67264e66 q^{73} -1.46565e66 q^{74} -4.24825e65 q^{75} +2.12438e66 q^{76} +9.79503e65 q^{77} +1.00794e66 q^{78} -8.08409e66 q^{79} -6.24598e66 q^{80} +4.83264e67 q^{81} -4.29458e66 q^{82} +4.29941e67 q^{83} +1.57946e67 q^{84} +2.52130e68 q^{85} +3.46594e68 q^{86} +5.55497e67 q^{87} +5.66553e67 q^{88} +2.26737e69 q^{89} +1.10024e69 q^{90} +1.07847e69 q^{91} -1.25118e69 q^{92} -2.46351e69 q^{93} -4.26457e69 q^{94} -8.06368e69 q^{95} +9.13571e68 q^{96} -6.06899e70 q^{97} -1.76155e70 q^{98} -9.97993e69 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 68719476736 q^{2} - 73\!\cdots\!24 q^{3}+ \cdots - 61\!\cdots\!06 q^{9}+O(q^{10}) $ 2 * q + 68719476736 * q^2 - 73290552574846824 * q^3 + 2361183241434822606848 * q^4 + 4017561682270957567057500 * q^5 - 2518244211317885610315743232 * q^6 - 291238690173693964386145313552 * q^7 + 81129638414606681695789005144064 * q^8 - 6123404334975269213441745958191606 * q^9	$ 2 q + 68719476736 q^{2} - 73\!\cdots\!24 q^{3}+ \cdots - 25\!\cdots\!12 q^{99}+O(q^{100}) $ 2 * q + 68719476736 * q^2 - 73290552574846824 * q^3 + 2361183241434822606848 * q^4 + 4017561682270957567057500 * q^5 - 2518244211317885610315743232 * q^6 - 291238690173693964386145313552 * q^7 + 81129638414606681695789005144064 * q^8 - 6123404334975269213441745958191606 * q^9 + 138042368280132046088925515612160000 * q^10 + 8684021980716172090887525376850576904 * q^11 - 86526212247613054049400939322986725376 * q^12 - 1127526476847602121775517379388630880564 * q^13 - 10006885197007137092408662697676044763136 * q^14 - 870495707981432852912957098986798794190000 * q^15 + 2787593149816327892691964784081045188247552 * q^16 - 25310632831657129209270924115310927130954012 * q^17 - 210398570871227281924223539932585048573739008 * q^18 - 1515676621589311845828943656442220865774179720 * q^19 + 4743099657804439236107998378673316959354880000 * q^20 + 105057783932094120306762036640883833267054319424 * q^21 + 298380723239368814309358888863546426251303452672 * q^22 + 2203172021093641748810865503399372374910614063056 * q^23 - 2973018014802021769638859222271266932256426426368 * q^24 + 7608631123084092334620703396661508984732192968750 * q^25 - 38741514747476418312368452783630352849904496279552 * q^26 + 319648868947993055224983298099305125670447984140400 * q^27 - 343833957247777367123869889228909979682409491202048 * q^28 - 9698728689773075098486688545271532504346978353044820 * q^29 - 29910004776708962227849032598394684454226278481920000 * q^30 - 40152449056044233071756067933578167284289756136602176 * q^31 + 95780971304118053647396689196894323976171195136475136 * q^32 - 646467126733774659938188551326031765296979936890156448 * q^33 - 869666722024249947512519672631665319191092726559932416 * q^34 - 11578366136761156330569053956326057915336741584188620000 * q^35 - 7229239848136475225980096433630422626902243870395858944 * q^36 - 111302567218665505327715068364071188329715510661736133092 * q^37 - 52078252168302895367845656117167986656871260949011496960 * q^38 + 275519833227064980098009665274252977678408104840329524368 * q^39 + 162971663295510861461624602883383361666170966864035840000 * q^40 + 1293621751110559774763864122730511857252280974968281452724 * q^41 + 3609757969428628252091459480215598083336921089452940460032 * q^42 - 1570188515420028543133617556744083017145937257828102471224 * q^43 + 10252283584559329897127946035166644058616193652784990519296 * q^44 + 40708357615001912362112184537766135586032750500530146327500 * q^45 + 75700414224475307717463313812439049417335506592825614532608 * q^46 - 385166682154840572374711553898575384547395544426269119145312 * q^47 - 102152121151948219322231568723224690516220791896645696487424 * q^48 - 532035159715732504433438538355987707216238966761163005601134 * q^49 + 261430574727791417880321677225418373371479456953139200000000 * q^50 - 3932264303948319406691865647256788003255613422904957101311056 * q^51 - 1331148310703303321462704136062500237146241665952236108251136 * q^52 - 3099963518619652809000040240867303977580091183911870344857604 * q^53 + 10983051506680160776211401499861875800637953324417157378867200 * q^54 + 55675237030386993027088191557939523809594236008364091073990000 * q^55 - 11814044813067727683888054041578488163711785849542367105777664 * q^56 + 340530979210937295973262581310223186047069690231491850122484640 * q^57 - 333245780282818297674818451146232380367769998901979551377653760 * q^58 - 1634769282638530993938532031464170850734659495713497861208919640 * q^59 - 1027699938713350202229687163482744574649131800509079418306560000 * q^60 - 4880654092824262768274295733939273946937692231886071744774910356 * q^61 - 1379627644400128417380751464514180229965133097556173235859488768 * q^62 - 6025861853395026499121119084837033105792949783823904688557137744 * q^63 + 3291009114642412084309938365114701009965471731267159726697218048 * q^64 - 29543075418903360367582342730855024802992366467179006798718215000 * q^65 - 22212441338085195704544329675415390923261412452090927107868196864 * q^66 - 134179938663497929036082688157452363116312631094129088359318071272 * q^67 - 29881521036109411547967908356077030399545155480627042485522137088 * q^68 - 321605797179791219242936222377661308526135728863885795131895787072 * q^69 - 397829631188024238423499614496638648471785935450346828762972160000 * q^70 - 1460877510745740582710287713995347696234833946793802259869191016336 * q^71 - 248394789781489341122389789834951197865628377698933413906472763392 * q^72 - 3294544566820717164014310852275588208456751477490323839459061757324 * q^73 - 3824327089320080209166799848240719802335879866208768081693146873856 * q^74 - 3184606446584112229377097409458775389197568519591749999600534375000 * q^75 - 1789395119165616187416055863991190774635411515666290423769627361280 * q^76 - 6253614148334332819110227681464586033924531964755455804402474941504 * q^77 + 9466789384876945852702739096358587279675046525044436872190360551424 * q^78 + 32545937316211131695260490720524848524451973434380542886241294936160 * q^79 + 5599663712231541868723715427304950721493954977805868890975109120000 * q^80 - 14696790322123460114208775627144901209272992806663832631738624054318 * q^81 + 44448504915312847302911380237722229185910137671134107814183600914432 * q^82 + 29029289096582559444238889025865399025664140946681211932408984041976 * q^83 + 124030339401370609190995696547481222376098869028264558454981080907776 * q^84 + 515189414072415878332203587875687294826517223054383338648578942155000 * q^85 - 53951266578270514369163302115098086401206462253116960829150888722432 * q^86 + 1220360737986859838823441297151020036222068694550765089326808848685840 * q^87 + 352265781639999779838716580389548817134634070037714508800371015548928 * q^88 + 3892840256317115370330682179701204942142442453315338735392476328046420 * q^89 + 1398728517042446180581839536582579433906499662277636873109656043520000 * q^90 + 3723923831232087792375243174156474165096790899907919377283839137781664 * q^91 + 2601046427102197195248330727233686361926270850206227221189229484703744 * q^92 - 10683042981025141340950338658167930386609577245004285723682658026015488 * q^93 - 13234226426910936531546457451421780620973501002295527600190740093730816 * q^94 - 36238128778010894690559462260868212446184933626918861697256245230950000 * q^95 - 3509920156517179589395358987240212171415117269690520628101025242284032 * q^96 - 57797943272861961641603344152467986900234375803899254441558412075626172 * q^97 - 18280588890409662105806348248520070466174156498880209215855482804109312 * q^98 - 2531090145827533343099848313526915248178613009899410920700202513213912 * q^99

Display 100 coefficients 10 coefficients

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 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	3.43597e10	0.707107
$2$	3.43597e10	0.707107
$3$	1.90762e16	0.220135	0.110067	−	0.993924i	$-0.464893\pi$
$3$	1.90762e16	0.220135	0.110067	+	0.993924i	$0.464893\pi$
$4$	1.18059e21	0.500000
$5$	−4.48127e24	−0.688598	−0.344299	−	0.938860i	$-0.611883\pi$
$5$	−4.48127e24	−0.688598	−0.344299	+	0.938860i	$0.611883\pi$
$6$	6.55455e26	0.155659
$7$	7.01318e29	0.699736	0.349868	−	0.936799i	$-0.386226\pi$
$7$	7.01318e29	0.699736	0.349868	+	0.936799i	$0.386226\pi$
$8$	4.05648e31	0.353553
$9$	−7.14556e33	−0.951541
$10$	−1.53975e35	−0.486913
$11$	1.39666e36	0.149848	0.0749240	−	0.997189i	$-0.476129\pi$
$11$	1.39666e36	0.149848	0.0749240	+	0.997189i	$0.476129\pi$
$12$	2.25213e37	0.110067
$13$	1.53777e39	0.438432	0.219216	−	0.975676i	$-0.429650\pi$
$13$	1.53777e39	0.438432	0.219216	+	0.975676i	$0.429650\pi$
$14$	2.40971e40	0.494788
$15$	−8.54858e40	−0.151584
$16$	1.39380e42	0.250000
$17$	−5.62631e43	−1.17297	−0.586485	−	0.809960i	$-0.699489\pi$
$17$	−5.62631e43	−1.17297	−0.586485	+	0.809960i	$0.699489\pi$
$18$	−2.45520e44	−0.672841
$19$	1.79942e45	0.723402	0.361701	−	0.932294i	$-0.382196\pi$
$19$	1.79942e45	0.723402	0.361701	+	0.932294i	$0.382196\pi$
$20$	−5.29055e45	−0.344299
$21$	1.33785e46	0.154036
$22$	4.79889e46	0.105958
$23$	−1.05979e48	−0.482926	−0.241463	−	0.970410i	$-0.577627\pi$
$23$	−1.05979e48	−0.482926	−0.241463	+	0.970410i	$0.577627\pi$
$24$	7.73824e47	0.0778293
$25$	−2.22699e49	−0.525832
$26$	5.28374e49	0.310018
$27$	−2.79563e50	−0.429602
$28$	8.27970e50	0.349868
$29$	2.91198e51	0.354046	0.177023	−	0.984207i	$-0.443353\pi$
$29$	2.91198e51	0.354046	0.177023	+	0.984207i	$0.443353\pi$
$30$	−2.93727e51	−0.107186
$31$	−1.29140e53	−1.47137	−0.735685	−	0.677324i	$-0.763140\pi$
$31$	−1.29140e53	−1.47137	−0.735685	+	0.677324i	$0.763140\pi$
$32$	4.78905e52	0.176777
$33$	2.66431e52	0.0329867
$34$	−1.93318e54	−0.829414
$35$	−3.14279e54	−0.481837
$36$	−8.43599e54	−0.475770
$37$	−4.26561e55	−0.909536	−0.454768	−	0.890610i	$-0.650278\pi$
$37$	−4.26561e55	−0.909536	−0.454768	+	0.890610i	$0.650278\pi$
$38$	6.18276e55	0.511522
$39$	2.93349e55	0.0965141
$40$	−1.81782e56	−0.243456
$41$	−1.24989e56	−0.0696696	−0.0348348	−	0.999393i	$-0.511091\pi$
$41$	−1.24989e56	−0.0696696	−0.0348348	+	0.999393i	$0.511091\pi$
$42$	4.59682e56	0.108920
$43$	1.00872e58	1.03667	0.518335	−	0.855178i	$-0.326552\pi$
$43$	1.00872e58	1.03667	0.518335	+	0.855178i	$0.326552\pi$
$44$	1.64889e57	0.0749240
$45$	3.20212e58	0.655229
$46$	−3.64140e58	−0.341480
$47$	−1.24115e59	−0.542440	−0.271220	−	0.962517i	$-0.587427\pi$
$47$	−1.24115e59	−0.542440	−0.271220	+	0.962517i	$0.587427\pi$
$48$	2.65884e58	0.0550337
$49$	−5.12678e59	−0.510369
$50$	−7.65187e59	−0.371820
$51$	−1.07329e60	−0.258211
$52$	1.81548e60	0.219216
$53$	1.01729e61	0.624670	0.312335	−	0.949972i	$-0.398889\pi$
$53$	1.01729e61	0.624670	0.312335	+	0.949972i	$0.398889\pi$
$54$	−9.60571e60	−0.303774
$55$	−6.25882e60	−0.103185
$56$	2.84488e61	0.247394
$57$	3.43262e61	0.159246
$58$	1.00055e62	0.250348
$59$	−9.41671e62	−1.28426	−0.642130	−	0.766596i	$-0.721949\pi$
$59$	−9.41671e62	−1.28426	−0.642130	+	0.766596i	$0.721949\pi$
$60$	−1.00924e62	−0.0757922
$61$	−9.88843e62	−0.412970	−0.206485	−	0.978450i	$-0.566202\pi$
$61$	−9.88843e62	−0.412970	−0.206485	+	0.978450i	$0.566202\pi$
$62$	−4.43723e63	−1.04042
$63$	−5.01131e63	−0.665828
$64$	1.64550e63	0.125000
$65$	−6.89116e63	−0.301904
$66$	9.15448e62	0.0233251
$67$	−9.00666e64	−1.34558	−0.672788	−	0.739835i	$-0.734903\pi$
$67$	−9.00666e64	−1.34558	−0.672788	+	0.739835i	$0.734903\pi$
$68$	−6.64237e64	−0.586485
$69$	−2.02168e64	−0.106309
$70$	−1.07986e65	−0.340710
$71$	−8.82699e65	−1.68322	−0.841610	−	0.540085i	$-0.818392\pi$
$71$	−8.82699e65	−1.68322	−0.841610	+	0.540085i	$0.818392\pi$
$72$	−2.89858e65	−0.336420
$73$	−2.67264e66	−1.90099	−0.950494	−	0.310744i	$-0.899422\pi$
$73$	−2.67264e66	−1.90099	−0.950494	+	0.310744i	$0.899422\pi$
$74$	−1.46565e66	−0.643139
$75$	−4.24825e65	−0.115754
$76$	2.12438e66	0.361701
$77$	9.79503e65	0.104854
$78$	1.00794e66	0.0682458
$79$	−8.08409e66	−0.348233	−0.174116	−	0.984725i	$-0.555707\pi$
$79$	−8.08409e66	−0.348233	−0.174116	+	0.984725i	$0.555707\pi$
$80$	−6.24598e66	−0.172150
$81$	4.83264e67	0.856971
$82$	−4.29458e66	−0.0492639
$83$	4.29941e67	0.320728	0.160364	−	0.987058i	$-0.448733\pi$
$83$	4.29941e67	0.320728	0.160364	+	0.987058i	$0.448733\pi$
$84$	1.57946e67	0.0770181
$85$	2.52130e68	0.807705
$86$	3.46594e68	0.733037
$87$	5.55497e67	0.0779378
$88$	5.66553e67	0.0529792
$89$	2.26737e69	1.41964	0.709818	−	0.704385i	$-0.248777\pi$
$89$	2.26737e69	1.41964	0.709818	+	0.704385i	$0.248777\pi$
$90$	1.10024e69	0.463317
$91$	1.07847e69	0.306787
$92$	−1.25118e69	−0.241463
$93$	−2.46351e69	−0.323899
$94$	−4.26457e69	−0.383563
$95$	−8.06368e69	−0.498133
$96$	9.13571e68	0.0389147
$97$	−6.06899e70	−1.78945	−0.894726	−	0.446616i	$-0.852629\pi$
$97$	−6.06899e70	−1.78945	−0.894726	+	0.446616i	$0.852629\pi$
$98$	−1.76155e70	−0.360885
$99$	−9.97993e69	−0.142586
$100$	−2.62916e70	−0.262916
$101$	6.08774e70	0.427609	0.213805	−	0.976876i	$-0.431414\pi$
$101$	6.08774e70	0.427609	0.213805	+	0.976876i	$0.431414\pi$
$102$	−3.68779e70	−0.182583
$103$	−8.12314e70	−0.284448	−0.142224	−	0.989835i	$-0.545425\pi$
$103$	−8.12314e70	−0.284448	−0.142224	+	0.989835i	$0.545425\pi$
$104$	6.23794e70	0.155009
$105$	−5.99527e70	−0.106069
$106$	3.49537e71	0.441708
$107$	−2.52216e71	−0.228375	−0.114187	−	0.993459i	$-0.536426\pi$
$107$	−2.52216e71	−0.228375	−0.114187	+	0.993459i	$0.536426\pi$
$108$	−3.30050e71	−0.214801
$109$	3.54207e72	1.66194	0.830972	−	0.556315i	$-0.187785\pi$
$109$	3.54207e72	1.66194	0.830972	+	0.556315i	$0.187785\pi$
$110$	−2.15051e71	−0.0729628
$111$	−8.13718e71	−0.200220
$112$	9.77494e71	0.174934
$113$	1.17064e73	1.52805	0.764025	−	0.645187i	$-0.223220\pi$
$113$	1.17064e73	1.52805	0.764025	+	0.645187i	$0.223220\pi$
$114$	1.17944e72	0.112604
$115$	4.74919e72	0.332542
$116$	3.43786e72	0.177023
$117$	−1.09882e73	−0.417186
$118$	−3.23556e73	−0.908109
$119$	−3.94583e73	−0.820769
$120$	−3.46772e72	−0.0535932
$121$	−8.49215e73	−0.977546
$122$	−3.39764e73	−0.292014
$123$	−2.38431e72	−0.0153367
$124$	−1.52462e74	−0.735685
$125$	2.89586e74	1.05069
$126$	−1.72187e74	−0.470811
$127$	−3.33597e73	−0.0688955	−0.0344477	−	0.999407i	$-0.510967\pi$
$127$	−3.33597e73	−0.0688955	−0.0344477	+	0.999407i	$0.510967\pi$
$128$	5.65391e73	0.0883883
$129$	1.92426e74	0.228207
$130$	−2.36779e74	−0.213478
$131$	2.83365e75	1.94633	0.973164	−	0.230113i	$-0.0739097\pi$
$131$	2.83365e75	1.94633	0.973164	+	0.230113i	$0.0739097\pi$
$132$	3.14546e73	0.0164934
$133$	1.26196e75	0.506191
$134$	−3.09466e75	−0.951466
$135$	1.25280e75	0.295823
$136$	−2.28230e75	−0.414707
$137$	6.01022e75	0.841997	0.420999	−	0.907061i	$-0.361680\pi$
$137$	6.01022e75	0.841997	0.420999	+	0.907061i	$0.361680\pi$
$138$	−6.94642e74	−0.0751716
$139$	1.13057e76	0.946832	0.473416	−	0.880839i	$-0.343021\pi$
$139$	1.13057e76	0.946832	0.473416	+	0.880839i	$0.343021\pi$
$140$	−3.71036e75	−0.240919
$141$	−2.36766e75	−0.119410
$142$	−3.03293e76	−1.19022
$143$	2.14774e75	0.0656982
$144$	−9.95946e75	−0.237885
$145$	−1.30494e76	−0.243796
$146$	−9.18313e76	−1.34420
$147$	−9.77998e75	−0.112350
$148$	−5.03594e76	−0.454768
$149$	4.89188e76	0.347827	0.173913	−	0.984761i	$-0.444359\pi$
$149$	4.89188e76	0.347827	0.173913	+	0.984761i	$0.444359\pi$
$150$	−1.45969e76	−0.0818504
$151$	4.71076e76	0.208646	0.104323	−	0.994543i	$-0.466732\pi$
$151$	4.71076e76	0.208646	0.104323	+	0.994543i	$0.466732\pi$
$152$	7.29931e76	0.255761
$153$	4.02031e77	1.11613
$154$	3.36555e76	0.0741430
$155$	5.78713e77	1.01318
$156$	3.46325e76	0.0482571
$157$	4.64125e77	0.515463	0.257731	−	0.966217i	$-0.417025\pi$
$157$	4.64125e77	0.515463	0.257731	+	0.966217i	$0.417025\pi$
$158$	−2.77767e77	−0.246238
$159$	1.94060e77	0.137511
$160$	−2.14610e77	−0.121728
$161$	−7.43247e77	−0.337921
$162$	1.66048e78	0.605970
$163$	−4.79426e78	−1.40625	−0.703124	−	0.711067i	$-0.748212\pi$
$163$	−4.79426e78	−1.40625	−0.703124	+	0.711067i	$0.748212\pi$
$164$	−1.47560e77	−0.0348348
$165$	−1.19395e77	−0.0227146
$166$	1.47727e78	0.226789
$167$	−4.97134e78	−0.616650	−0.308325	−	0.951281i	$-0.599768\pi$
$167$	−4.97134e78	−0.616650	−0.308325	+	0.951281i	$0.599768\pi$
$168$	5.42697e77	0.0544600
$169$	−9.93733e78	−0.807777
$170$	8.66312e78	0.571133
$171$	−1.28579e79	−0.688346
$172$	1.19089e79	0.518335
$173$	−8.03628e78	−0.284720	−0.142360	−	0.989815i	$-0.545469\pi$
$173$	−8.03628e78	−0.284720	−0.142360	+	0.989815i	$0.545469\pi$
$174$	1.90867e78	0.0551104
$175$	−1.56183e79	−0.367944
$176$	1.94666e78	0.0374620
$177$	−1.79636e79	−0.282710
$178$	7.79062e79	1.00383
$179$	1.42090e80	1.50065	0.750326	−	0.661068i	$-0.229896\pi$
$179$	1.42090e80	1.50065	0.750326	+	0.661068i	$0.229896\pi$
$180$	3.78040e79	0.327615
$181$	−3.17710e79	−0.226173	−0.113087	−	0.993585i	$-0.536074\pi$
$181$	−3.17710e79	−0.226173	−0.113087	+	0.993585i	$0.536074\pi$
$182$	3.70558e79	0.216931
$183$	−1.88634e79	−0.0909089
$184$	−4.29901e79	−0.170740
$185$	1.91153e80	0.626305
$186$	−8.46457e79	−0.229032
$187$	−7.85804e79	−0.175767
$188$	−1.46530e80	−0.271220
$189$	−1.96062e80	−0.300608
$190$	−2.77066e80	−0.352233
$191$	−1.67605e81	−1.76849	−0.884243	−	0.467027i	$-0.845325\pi$
$191$	−1.67605e81	−1.76849	−0.884243	+	0.467027i	$0.845325\pi$
$192$	3.13901e79	0.0275168
$193$	8.35268e80	0.608893	0.304447	−	0.952529i	$-0.401528\pi$
$193$	8.35268e80	0.608893	0.304447	+	0.952529i	$0.401528\pi$
$194$	−2.08529e81	−1.26533
$195$	−1.31458e80	−0.0664595
$196$	−6.05264e80	−0.255184
$197$	4.37858e81	1.54093	0.770464	−	0.637484i	$-0.220025\pi$
$197$	4.37858e81	1.54093	0.770464	+	0.637484i	$0.220025\pi$
$198$	−3.42908e80	−0.100824
$199$	6.36126e81	1.56408	0.782040	−	0.623229i	$-0.214179\pi$
$199$	6.36126e81	1.56408	0.782040	+	0.623229i	$0.214179\pi$
$200$	−9.03373e80	−0.185910
$201$	−1.71813e81	−0.296208
$202$	2.09173e81	0.302366
$203$	2.04223e81	0.247739
$204$	−1.26711e81	−0.129106
$205$	5.60108e80	0.0479744
$206$	−2.79109e81	−0.201135
$207$	7.57277e81	0.459523
$208$	2.14334e81	0.109608
$209$	2.51318e81	0.108400
$210$	−2.05996e81	−0.0750022
$211$	−1.15189e82	−0.354312	−0.177156	−	0.984183i	$-0.556690\pi$
$211$	−1.15189e82	−0.354312	−0.177156	+	0.984183i	$0.556690\pi$
$212$	1.20100e82	0.312335
$213$	−1.68386e82	−0.370535
$214$	−8.66607e81	−0.161485
$215$	−4.52035e82	−0.713849
$216$	−1.13404e82	−0.151887
$217$	−9.05684e82	−1.02957
$218$	1.21705e83	1.17517
$219$	−5.09840e82	−0.418473
$220$	−7.38911e81	−0.0515925
$221$	−8.65197e82	−0.514268
$222$	−2.79591e82	−0.141577
$223$	−1.39101e83	−0.600492	−0.300246	−	0.953862i	$-0.597069\pi$
$223$	−1.39101e83	−0.600492	−0.300246	+	0.953862i	$0.597069\pi$
$224$	3.35865e82	0.123697
$225$	1.59131e83	0.500351
$226$	4.02228e83	1.08049
$227$	5.14640e83	1.18191	0.590957	−	0.806703i	$-0.298750\pi$
$227$	5.14640e83	1.18191	0.590957	+	0.806703i	$0.298750\pi$
$228$	4.05252e82	0.0796229
$229$	9.30804e82	0.156566	0.0782832	−	0.996931i	$-0.475056\pi$
$229$	9.30804e82	0.156566	0.0782832	+	0.996931i	$0.475056\pi$
$230$	1.63181e83	0.235143
$231$	1.86852e82	0.0230820
$232$	1.18124e83	0.125174
$233$	1.10477e83	0.100493	0.0502465	−	0.998737i	$-0.483999\pi$
$233$	1.10477e83	0.100493	0.0502465	+	0.998737i	$0.483999\pi$
$234$	−3.77553e83	−0.294995
$235$	5.56195e83	0.373523
$236$	−1.11173e84	−0.642130
$237$	−1.54214e83	−0.0766581
$238$	−1.35578e84	−0.580372
$239$	−3.38387e84	−1.24821	−0.624105	−	0.781340i	$-0.714536\pi$
$239$	−3.38387e84	−1.24821	−0.624105	+	0.781340i	$0.714536\pi$
$240$	−1.19150e83	−0.0378961
$241$	−3.55374e83	−0.0975170	−0.0487585	−	0.998811i	$-0.515526\pi$
$241$	−3.55374e83	−0.0975170	−0.0487585	+	0.998811i	$0.515526\pi$
$242$	−2.91788e84	−0.691229
$243$	3.02125e84	0.618251
$244$	−1.16742e84	−0.206485
$245$	2.29745e84	0.351439
$246$	−8.19244e82	−0.0108447
$247$	2.76709e84	0.317163
$248$	−5.23856e84	−0.520208
$249$	8.20166e83	0.0706033
$250$	9.95011e84	0.742947
$251$	1.74222e85	1.12898	0.564489	−	0.825441i	$-0.309073\pi$
$251$	1.74222e85	1.12898	0.564489	+	0.825441i	$0.309073\pi$
$252$	−5.91631e84	−0.332914
$253$	−1.48016e84	−0.0723654
$254$	−1.14623e84	−0.0487165
$255$	4.80969e84	0.177804
$256$	1.94267e84	0.0625000
$257$	2.21841e85	0.621465	0.310733	−	0.950497i	$-0.399426\pi$
$257$	2.21841e85	0.621465	0.310733	+	0.950497i	$0.399426\pi$
$258$	6.61171e84	0.161367
$259$	−2.99155e85	−0.636435
$260$	−8.13565e84	−0.150952
$261$	−2.08078e85	−0.336889
$262$	9.73636e85	1.37626
$263$	−9.38880e85	−1.15926	−0.579630	−	0.814880i	$-0.696803\pi$
$263$	−9.38880e85	−1.15926	−0.579630	+	0.814880i	$0.696803\pi$
$264$	1.08077e84	0.0116626
$265$	−4.55874e85	−0.430147
$266$	4.33608e85	0.357931
$267$	4.32529e85	0.312511
$268$	−1.06332e86	−0.672788
$269$	−1.29146e86	−0.715936	−0.357968	−	0.933734i	$-0.616530\pi$
$269$	−1.29146e86	−0.715936	−0.357968	+	0.933734i	$0.616530\pi$
$270$	4.30458e85	0.209178
$271$	−3.46336e86	−1.47600	−0.738002	−	0.674798i	$-0.764231\pi$
$271$	−3.46336e86	−1.47600	−0.738002	+	0.674798i	$0.764231\pi$
$272$	−7.84193e85	−0.293242
$273$	2.05731e85	0.0675344
$274$	2.06510e86	0.595382
$275$	−3.11035e85	−0.0787949
$276$	−2.38677e85	−0.0531543
$277$	4.67470e86	0.915634	0.457817	−	0.889046i	$-0.348631\pi$
$277$	4.67470e86	0.915634	0.457817	+	0.889046i	$0.348631\pi$
$278$	3.88462e86	0.669511
$279$	9.22781e86	1.40007
$280$	−1.27487e86	−0.170355
$281$	2.77285e86	0.326477	0.163238	−	0.986587i	$-0.447806\pi$
$281$	2.77285e86	0.326477	0.163238	+	0.986587i	$0.447806\pi$
$282$	−8.13520e85	−0.0844355
$283$	7.13474e86	0.653070	0.326535	−	0.945185i	$-0.394119\pi$
$283$	7.13474e86	0.653070	0.326535	+	0.945185i	$0.394119\pi$
$284$	−1.04211e87	−0.841610
$285$	−1.53825e86	−0.109656
$286$	7.37959e85	0.0464556
$287$	−8.76567e85	−0.0487504
$288$	−3.42204e86	−0.168210
$289$	8.64760e86	0.375857
$290$	−4.48373e86	−0.172390
$291$	−1.15774e87	−0.393920
$292$	−3.15530e87	−0.950494
$293$	−5.25118e87	−1.40106	−0.700529	−	0.713624i	$-0.747053\pi$
$293$	−5.25118e87	−1.40106	−0.700529	+	0.713624i	$0.747053\pi$
$294$	−3.36038e86	−0.0794434
$295$	4.21988e87	0.884339
$296$	−1.73034e87	−0.321569
$297$	−3.90455e86	−0.0643749
$298$	1.68084e87	0.245951
$299$	−1.62971e87	−0.211730
$300$	−5.01545e86	−0.0578770
$301$	7.07434e87	0.725396
$302$	1.61861e87	0.147535
$303$	1.16131e87	0.0941317
$304$	2.50802e87	0.180850
$305$	4.43127e87	0.284370
$306$	1.38137e88	0.789222
$307$	−1.72405e88	−0.877281	−0.438641	−	0.898663i	$-0.644540\pi$
$307$	−1.72405e88	−0.877281	−0.438641	+	0.898663i	$0.644540\pi$
$308$	1.15639e87	0.0524270
$309$	−1.54959e87	−0.0626168
$310$	1.98844e88	0.716429
$311$	−1.40069e88	−0.450142	−0.225071	−	0.974342i	$-0.572261\pi$
$311$	−1.40069e88	−0.450142	−0.225071	+	0.974342i	$0.572261\pi$
$312$	1.18996e87	0.0341229
$313$	3.13749e88	0.803080	0.401540	−	0.915842i	$-0.368475\pi$
$313$	3.13749e88	0.803080	0.401540	+	0.915842i	$0.368475\pi$
$314$	1.59472e88	0.364487
$315$	2.24570e88	0.458488
$316$	−9.54401e87	−0.174116
$317$	−1.01238e89	−1.65098	−0.825489	−	0.564418i	$-0.809101\pi$
$317$	−1.01238e89	−1.65098	−0.825489	+	0.564418i	$0.809101\pi$
$318$	6.66786e87	0.0972353
$319$	4.06705e87	0.0530531
$320$	−7.37395e87	−0.0860748
$321$	−4.81133e87	−0.0502732
$322$	−2.55378e88	−0.238946
$323$	−1.01241e89	−0.848528
$324$	5.70537e88	0.428485
$325$	−3.42459e88	−0.230542
$326$	−1.64730e89	−0.994367
$327$	6.75694e88	0.365851
$328$	−5.07014e87	−0.0246319
$329$	−8.70443e88	−0.379565
$330$	−4.10237e87	−0.0160616
$331$	1.17605e89	0.413553	0.206776	−	0.978388i	$-0.433703\pi$
$331$	1.17605e89	0.413553	0.206776	+	0.978388i	$0.433703\pi$
$332$	5.07585e88	0.160364
$333$	3.04802e89	0.865460
$334$	−1.70814e89	−0.436038
$335$	4.03613e89	0.926562
$336$	1.86469e88	0.0385091
$337$	1.03103e90	1.91606	0.958028	−	0.286674i	$-0.0925496\pi$
$337$	1.03103e90	1.91606	0.958028	+	0.286674i	$0.0925496\pi$
$338$	−3.41444e89	−0.571185
$339$	2.23314e89	0.336377
$340$	2.97663e89	0.403852
$341$	−1.80365e89	−0.220482
$342$	−4.41793e89	−0.486734
$343$	−1.06404e90	−1.05686
$344$	4.09186e89	0.366518
$345$	9.05967e88	0.0732040
$346$	−2.76124e89	−0.201328
$347$	−6.80688e89	−0.447973	−0.223986	−	0.974592i	$-0.571907\pi$
$347$	−6.80688e89	−0.447973	−0.223986	+	0.974592i	$0.571907\pi$
$348$	6.55815e88	0.0389689
$349$	−2.36531e90	−1.26936	−0.634681	−	0.772774i	$-0.718868\pi$
$349$	−2.36531e90	−1.26936	−0.634681	+	0.772774i	$0.718868\pi$
$350$	−5.36639e89	−0.260176
$351$	−4.29904e89	−0.188351
$352$	6.68868e88	0.0264896
$353$	−1.84794e90	−0.661737	−0.330869	−	0.943677i	$-0.607342\pi$
$353$	−1.84794e90	−0.661737	−0.330869	+	0.943677i	$0.607342\pi$
$354$	−6.17223e89	−0.199906
$355$	3.95561e90	1.15906
$356$	2.67684e90	0.709818
$357$	−7.52716e89	−0.180680
$358$	4.88217e90	1.06112
$359$	−3.91283e90	−0.770262	−0.385131	−	0.922862i	$-0.625844\pi$
$359$	−3.91283e90	−0.770262	−0.385131	+	0.922862i	$0.625844\pi$
$360$	1.29893e90	0.231659
$361$	−2.94945e90	−0.476690
$362$	−1.09164e90	−0.159929
$363$	−1.61998e90	−0.215192
$364$	1.27323e90	0.153394
$365$	1.19768e91	1.30902
$366$	−6.48142e89	−0.0642823
$367$	2.34693e90	0.211278	0.105639	−	0.994405i	$-0.466311\pi$
$367$	2.34693e90	0.211278	0.105639	+	0.994405i	$0.466311\pi$
$368$	−1.47713e90	−0.120731
$369$	8.93114e89	0.0662935
$370$	6.56798e90	0.442864
$371$	7.13442e90	0.437104
$372$	−2.90840e90	−0.161950
$373$	−1.13086e91	−0.572460	−0.286230	−	0.958161i	$-0.592402\pi$
$373$	−1.13086e91	−0.572460	−0.286230	+	0.958161i	$0.592402\pi$
$374$	−2.70000e90	−0.124286
$375$	5.52422e90	0.231292
$376$	−5.03472e90	−0.191781
$377$	4.47796e90	0.155225
$378$	−6.73666e90	−0.212562
$379$	−3.28443e91	−0.943558	−0.471779	−	0.881717i	$-0.656388\pi$
$379$	−3.28443e91	−0.943558	−0.471779	+	0.881717i	$0.656388\pi$
$380$	−9.51992e90	−0.249067
$381$	−6.36379e89	−0.0151663
$382$	−5.75885e91	−1.25051
$383$	5.29968e91	1.04880	0.524401	−	0.851472i	$-0.324289\pi$
$383$	5.29968e91	1.04880	0.524401	+	0.851472i	$0.324289\pi$
$384$	1.07855e90	0.0194573
$385$	−4.38942e90	−0.0722023
$386$	2.86996e91	0.430553
$387$	−7.20788e91	−0.986434
$388$	−7.16500e91	−0.894726
$389$	4.34517e91	0.495218	0.247609	−	0.968860i	$-0.420355\pi$
$389$	4.34517e91	0.495218	0.247609	+	0.968860i	$0.420355\pi$
$390$	−4.51685e90	−0.0469939
$391$	5.96268e91	0.566457
$392$	−2.07967e91	−0.180443
$393$	5.40555e91	0.428454
$394$	1.50447e92	1.08960
$395$	3.62270e91	0.239793
$396$	−1.17822e91	−0.0712932
$397$	1.98627e92	1.09894	0.549472	−	0.835512i	$-0.314829\pi$
$397$	1.98627e92	1.09894	0.549472	+	0.835512i	$0.314829\pi$
$398$	2.18571e92	1.10597
$399$	2.40736e91	0.111430
$400$	−3.10397e91	−0.131458
$401$	−2.20233e92	−0.853606	−0.426803	−	0.904345i	$-0.640360\pi$
$401$	−2.20233e92	−0.853606	−0.426803	+	0.904345i	$0.640360\pi$
$402$	−5.90346e91	−0.209451
$403$	−1.98588e92	−0.645096
$404$	7.18713e91	0.213805
$405$	−2.16563e92	−0.590108
$406$	7.01703e91	0.175178
$407$	−5.95761e91	−0.136292
$408$	−4.35377e91	−0.0912914
$409$	−6.30610e92	−1.21223	−0.606113	−	0.795379i	$-0.707272\pi$
$409$	−6.30610e92	−1.21223	−0.606113	+	0.795379i	$0.707272\pi$
$410$	1.92452e91	0.0339230
$411$	1.14653e92	0.185353
$412$	−9.59011e91	−0.142224
$413$	−6.60411e92	−0.898643
$414$	2.60198e92	0.324932
$415$	−1.92668e92	−0.220853
$416$	7.36446e91	0.0775046
$417$	2.15671e92	0.208430
$418$	8.63522e91	0.0766506
$419$	1.43141e92	0.116725	0.0583627	−	0.998295i	$-0.481412\pi$
$419$	1.43141e92	0.116725	0.0583627	+	0.998295i	$0.481412\pi$
$420$	−7.07797e91	−0.0530345
$421$	1.63619e93	1.12673	0.563365	−	0.826208i	$-0.309506\pi$
$421$	1.63619e93	1.12673	0.563365	+	0.826208i	$0.309506\pi$
$422$	−3.95788e92	−0.250536
$423$	8.86874e92	0.516154
$424$	4.12661e92	0.220854
$425$	1.25297e93	0.616785
$426$	−5.78569e92	−0.262008
$427$	−6.93493e92	−0.288970
$428$	−2.97764e92	−0.114187
$429$	4.09709e91	0.0144624
$430$	−1.55318e93	−0.504768
$431$	3.22367e93	0.964734	0.482367	−	0.875969i	$-0.339777\pi$
$431$	3.22367e93	0.964734	0.482367	+	0.875969i	$0.339777\pi$
$432$	−3.89654e92	−0.107400
$433$	1.58774e93	0.403142	0.201571	−	0.979474i	$-0.435395\pi$
$433$	1.58774e93	0.403142	0.201571	+	0.979474i	$0.435395\pi$
$434$	−3.11191e93	−0.728017
$435$	−2.48933e92	−0.0536679
$436$	4.18174e93	0.830972
$437$	−1.90700e93	−0.349349
$438$	−1.75180e93	−0.295905
$439$	−2.70623e92	−0.0421574	−0.0210787	−	0.999778i	$-0.506710\pi$
$439$	−2.70623e92	−0.0421574	−0.0210787	+	0.999778i	$0.506710\pi$
$440$	−2.53888e92	−0.0364814
$441$	3.66338e93	0.485637
$442$	−2.97279e93	−0.363642
$443$	−4.73007e93	−0.533993	−0.266996	−	0.963698i	$-0.586031\pi$
$443$	−4.73007e93	−0.533993	−0.266996	+	0.963698i	$0.586031\pi$
$444$	−9.60669e92	−0.100110
$445$	−1.01607e94	−0.977559
$446$	−4.77947e93	−0.424612
$447$	9.33187e92	0.0765687
$448$	1.15402e93	0.0874671
$449$	−1.66192e94	−1.16376	−0.581882	−	0.813273i	$-0.697684\pi$
$449$	−1.66192e94	−1.16376	−0.581882	+	0.813273i	$0.697684\pi$
$450$	5.46769e93	0.353801
$451$	−1.74567e92	−0.0104398
$452$	1.38204e94	0.764025
$453$	8.98637e92	0.0459302
$454$	1.76829e94	0.835740
$455$	−4.83290e93	−0.211253
$456$	1.39243e93	0.0563019
$457$	1.27437e94	0.476729	0.238365	−	0.971176i	$-0.423389\pi$
$457$	1.27437e94	0.476729	0.238365	+	0.971176i	$0.423389\pi$
$458$	3.19822e93	0.110709
$459$	1.57291e94	0.503910
$460$	5.60685e93	0.166271
$461$	7.08046e93	0.194392	0.0971961	−	0.995265i	$-0.469013\pi$
$461$	7.08046e93	0.194392	0.0971961	+	0.995265i	$0.469013\pi$
$462$	6.42020e92	0.0163214
$463$	6.01954e94	1.41722	0.708611	−	0.705599i	$-0.249322\pi$
$463$	6.01954e94	1.41722	0.708611	+	0.705599i	$0.249322\pi$
$464$	4.05871e93	0.0885115
$465$	1.10397e94	0.223037
$466$	3.79595e93	0.0710593
$467$	−9.17191e94	−1.59115	−0.795574	−	0.605857i	$-0.792830\pi$
$467$	−9.17191e94	−1.59115	−0.795574	+	0.605857i	$0.792830\pi$
$468$	−1.29726e94	−0.208593
$469$	−6.31653e94	−0.941549
$470$	1.91107e94	0.264121
$471$	8.85376e93	0.113471
$472$	−3.81987e94	−0.454054
$473$	1.40884e94	0.155343
$474$	−5.29876e93	−0.0542055
$475$	−4.00728e94	−0.380388
$476$	−4.65841e94	−0.410385
$477$	−7.26910e94	−0.594399
$478$	−1.16269e95	−0.882618
$479$	1.67835e95	1.18297	0.591483	−	0.806317i	$-0.298543\pi$
$479$	1.67835e95	1.18297	0.591483	+	0.806317i	$0.298543\pi$
$480$	−4.09396e93	−0.0267966
$481$	−6.55953e94	−0.398770
$482$	−1.22105e94	−0.0689549
$483$	−1.41784e94	−0.0743880
$484$	−1.00258e95	−0.488773
$485$	2.71968e95	1.23221
$486$	1.03810e95	0.437169
$487$	2.08937e95	0.817969	0.408984	−	0.912541i	$-0.365883\pi$
$487$	2.08937e95	0.817969	0.408984	+	0.912541i	$0.365883\pi$
$488$	−4.01122e94	−0.146007
$489$	−9.14565e94	−0.309564
$490$	7.89398e94	0.248505
$491$	4.91495e95	1.43922	0.719609	−	0.694380i	$-0.244321\pi$
$491$	4.91495e95	1.43922	0.719609	+	0.694380i	$0.244321\pi$
$492$	−2.81490e93	−0.00766835
$493$	−1.63837e95	−0.415285
$494$	9.50766e94	0.224268
$495$	4.47228e94	0.0981848
$496$	−1.79995e95	−0.367843
$497$	−6.19052e95	−1.17781
$498$	2.81807e94	0.0499241
$499$	−1.27073e95	−0.209645	−0.104822	−	0.994491i	$-0.533427\pi$
$499$	−1.27073e95	−0.209645	−0.104822	+	0.994491i	$0.533427\pi$
$500$	3.41883e95	0.525343
$501$	−9.48345e94	−0.135746
$502$	5.98622e95	0.798308
$503$	3.02447e95	0.375825	0.187912	−	0.982186i	$-0.439828\pi$
$503$	3.02447e95	0.375825	0.187912	+	0.982186i	$0.439828\pi$
$504$	−2.03283e95	−0.235406
$505$	−2.72808e95	−0.294451
$506$	−5.08580e94	−0.0511701
$507$	−1.89567e95	−0.177820
$508$	−3.93842e94	−0.0344477
$509$	−8.02186e95	−0.654326	−0.327163	−	0.944968i	$-0.606093\pi$
$509$	−8.02186e95	−0.654326	−0.327163	+	0.944968i	$0.606093\pi$
$510$	1.65260e95	0.125726
$511$	−1.87437e96	−1.33019
$512$	6.67496e94	0.0441942
$513$	−5.03051e95	−0.310775
$514$	7.62241e95	0.439442
$515$	3.64020e95	0.195870
$516$	2.27177e95	0.114104
$517$	−1.73347e95	−0.0812835
$518$	−1.02789e96	−0.450028
$519$	−1.53302e95	−0.0626768
$520$	−2.79539e95	−0.106739
$521$	−6.19273e95	−0.220873	−0.110437	−	0.993883i	$-0.535225\pi$
$521$	−6.19273e95	−0.220873	−0.110437	+	0.993883i	$0.535225\pi$
$522$	−7.14949e95	−0.238217
$523$	5.06614e96	1.57713	0.788564	−	0.614953i	$-0.210825\pi$
$523$	5.06614e96	1.57713	0.788564	+	0.614953i	$0.210825\pi$
$524$	3.34539e96	0.973164
$525$	−2.97938e95	−0.0809972
$526$	−3.22597e96	−0.819721
$527$	7.26583e96	1.72587
$528$	3.71350e94	0.00824668
$529$	−3.69274e96	−0.766783
$530$	−1.56637e96	−0.304160
$531$	6.72877e96	1.22203
$532$	1.48987e96	0.253095
$533$	−1.92204e95	−0.0305454
$534$	1.48616e96	0.220979
$535$	1.13025e96	0.157259
$536$	−3.65354e96	−0.475733
$537$	2.71054e96	0.330346
$538$	−4.43741e96	−0.506243
$539$	−7.16038e95	−0.0764777
$540$	1.47904e96	0.147912
$541$	−2.01990e97	−1.89159	−0.945794	−	0.324767i	$-0.894714\pi$
$541$	−2.01990e97	−1.89159	−0.945794	+	0.324767i	$0.894714\pi$
$542$	−1.19000e97	−1.04369
$543$	−6.06071e95	−0.0497886
$544$	−2.69447e96	−0.207354
$545$	−1.58730e97	−1.14441
$546$	7.06886e95	0.0477541
$547$	1.40780e97	0.891232	0.445616	−	0.895224i	$-0.352985\pi$
$547$	1.40780e97	0.891232	0.445616	+	0.895224i	$0.352985\pi$
$548$	7.09562e96	0.420999
$549$	7.06584e96	0.392957
$550$	−1.06871e96	−0.0557164
$551$	5.23988e96	0.256118
$552$	−8.20089e95	−0.0375858
$553$	−5.66952e96	−0.243671
$554$	1.60621e97	0.647451
$555$	3.64649e96	0.137871
$556$	1.33474e97	0.473416
$557$	−3.20316e97	−1.06591	−0.532954	−	0.846144i	$-0.678918\pi$
$557$	−3.20316e97	−1.06591	−0.532954	+	0.846144i	$0.678918\pi$
$558$	3.17065e97	0.989998
$559$	1.55118e97	0.454510
$560$	−4.38042e96	−0.120459
$561$	−1.49902e96	−0.0386924
$562$	9.52745e96	0.230854
$563$	4.66114e97	1.06034	0.530168	−	0.847892i	$-0.322129\pi$
$563$	4.66114e97	1.06034	0.530168	+	0.847892i	$0.322129\pi$
$564$	−2.79523e96	−0.0597049
$565$	−5.24594e97	−1.05221
$566$	2.45148e97	0.461790
$567$	3.38921e97	0.599653
$568$	−3.58065e97	−0.595108
$569$	−1.11220e97	−0.173659	−0.0868295	−	0.996223i	$-0.527674\pi$
$569$	−1.11220e97	−0.173659	−0.0868295	+	0.996223i	$0.527674\pi$
$570$	−5.28538e96	−0.0775388
$571$	3.30082e96	0.0455030	0.0227515	−	0.999741i	$-0.492757\pi$
$571$	3.30082e96	0.0455030	0.0227515	+	0.999741i	$0.492757\pi$
$572$	2.53561e96	0.0328491
$573$	−3.19727e97	−0.389305
$574$	−3.01186e96	−0.0344717
$575$	2.36013e97	0.253938
$576$	−1.17581e97	−0.118943
$577$	−1.45678e98	−1.38565	−0.692824	−	0.721107i	$-0.743634\pi$
$577$	−1.45678e98	−1.38565	−0.692824	+	0.721107i	$0.743634\pi$
$578$	2.97129e97	0.265771
$579$	1.59338e97	0.134039
$580$	−1.54060e97	−0.121898
$581$	3.01525e97	0.224425
$582$	−3.97795e97	−0.278544
$583$	1.42081e97	0.0936055
$584$	−1.08415e98	−0.672100
$585$	4.92413e97	0.287274
$586$	−1.80429e98	−0.990698
$587$	2.73480e98	1.41343	0.706713	−	0.707500i	$-0.250177\pi$
$587$	2.73480e98	1.41343	0.706713	+	0.707500i	$0.250177\pi$
$588$	−1.15462e97	−0.0561749
$589$	−2.32378e98	−1.06439
$590$	1.44994e98	0.625322
$591$	8.35268e97	0.339211
$592$	−5.94539e97	−0.227384
$593$	−5.45053e97	−0.196335	−0.0981673	−	0.995170i	$-0.531298\pi$
$593$	−5.45053e97	−0.196335	−0.0981673	+	0.995170i	$0.531298\pi$
$594$	−1.34159e97	−0.0455199
$595$	1.76823e98	0.565180
$596$	5.77531e97	0.173913
$597$	1.21349e98	0.344308
$598$	−5.59964e97	−0.149716
$599$	5.97121e98	1.50456	0.752281	−	0.658843i	$-0.228954\pi$
$599$	5.97121e98	1.50456	0.752281	+	0.658843i	$0.228954\pi$
$600$	−1.72330e97	−0.0409252
$601$	−5.89753e98	−1.32016	−0.660080	−	0.751195i	$-0.729478\pi$
$601$	−5.89753e98	−1.32016	−0.660080	+	0.751195i	$0.729478\pi$
$602$	2.43072e98	0.512932
$603$	6.43577e98	1.28037
$604$	5.56149e97	0.104323
$605$	3.80556e98	0.673136
$606$	3.99024e97	0.0665611
$607$	−9.22442e98	−1.45125	−0.725623	−	0.688093i	$-0.758448\pi$
$607$	−9.22442e98	−1.45125	−0.725623	+	0.688093i	$0.758448\pi$
$608$	8.61751e97	0.127881
$609$	3.89580e97	0.0545359
$610$	1.52257e98	0.201080
$611$	−1.90861e98	−0.237823
$612$	4.74635e98	0.558064
$613$	−1.61488e99	−1.79182	−0.895908	−	0.444240i	$-0.853474\pi$
$613$	−1.61488e99	−1.79182	−0.895908	+	0.444240i	$0.853474\pi$
$614$	−5.92381e98	−0.620331
$615$	1.06848e97	0.0105608
$616$	3.97334e97	0.0370715
$617$	−8.57278e98	−0.755090	−0.377545	−	0.925991i	$-0.623232\pi$
$617$	−8.57278e98	−0.755090	−0.377545	+	0.925991i	$0.623232\pi$
$618$	−5.32435e97	−0.0442768
$619$	−2.11082e99	−1.65742	−0.828710	−	0.559678i	$-0.810925\pi$
$619$	−2.11082e99	−1.65742	−0.828710	+	0.559678i	$0.810925\pi$
$620$	6.83224e98	0.506591
$621$	2.96277e98	0.207466
$622$	−4.81274e98	−0.318298
$623$	1.59015e99	0.993371
$624$	4.08869e97	0.0241285
$625$	−3.54550e98	−0.197668
$626$	1.07803e99	0.567863
$627$	4.79420e97	0.0238627
$628$	5.47942e98	0.257731
$629$	2.39996e99	1.06686
$630$	7.71618e98	0.324200
$631$	2.73510e99	1.08625	0.543127	−	0.839651i	$-0.317240\pi$
$631$	2.73510e99	1.08625	0.543127	+	0.839651i	$0.317240\pi$
$632$	−3.27930e98	−0.123119
$633$	−2.19738e98	−0.0779963
$634$	−3.47852e99	−1.16742
$635$	1.49494e98	0.0474413
$636$	2.29106e98	0.0687557
$637$	−7.88382e98	−0.223762
$638$	1.39743e98	0.0375142
$639$	6.30738e99	1.60165
$640$	−2.53367e98	−0.0608641
$641$	2.20803e99	0.501816	0.250908	−	0.968011i	$-0.419271\pi$
$641$	2.20803e99	0.501816	0.250908	+	0.968011i	$0.419271\pi$
$642$	−1.65316e98	−0.0355485
$643$	−3.14515e99	−0.639959	−0.319979	−	0.947424i	$-0.603676\pi$
$643$	−3.14515e99	−0.639959	−0.319979	+	0.947424i	$0.603676\pi$
$644$	−8.77472e98	−0.168960
$645$	−8.62313e98	−0.157143
$646$	−3.47861e99	−0.600000
$647$	−5.89822e99	−0.962984	−0.481492	−	0.876450i	$-0.659905\pi$
$647$	−5.89822e99	−0.962984	−0.481492	+	0.876450i	$0.659905\pi$
$648$	1.96035e99	0.302985
$649$	−1.31520e99	−0.192444
$650$	−1.17668e99	−0.163018
$651$	−1.72771e99	−0.226644
$652$	−5.66007e99	−0.703124
$653$	8.31458e99	0.978189	0.489094	−	0.872231i	$-0.337327\pi$
$653$	8.31458e99	0.978189	0.489094	+	0.872231i	$0.337327\pi$
$654$	2.32167e99	0.258696
$655$	−1.26984e100	−1.34024
$656$	−1.74209e98	−0.0174174
$657$	1.90975e100	1.80887
$658$	−2.99082e99	−0.268393
$659$	−5.03918e99	−0.428477	−0.214239	−	0.976781i	$-0.568727\pi$
$659$	−5.03918e99	−0.428477	−0.214239	+	0.976781i	$0.568727\pi$
$660$	−1.40956e98	−0.0113573
$661$	−1.05882e100	−0.808485	−0.404243	−	0.914652i	$-0.632465\pi$
$661$	−1.05882e100	−0.808485	−0.404243	+	0.914652i	$0.632465\pi$
$662$	4.04087e99	0.292426
$663$	−1.65047e99	−0.113208
$664$	1.74405e99	0.113394
$665$	−5.65521e99	−0.348562
$666$	1.04729e100	0.611973
$667$	−3.08608e99	−0.170978
$668$	−5.86912e99	−0.308325
$669$	−2.65352e99	−0.132189
$670$	1.38680e100	0.655178
$671$	−1.38108e99	−0.0618826
$672$	6.40703e98	0.0272300
$673$	2.22291e99	0.0896162	0.0448081	−	0.998996i	$-0.485732\pi$
$673$	2.22291e99	0.0896162	0.0448081	+	0.998996i	$0.485732\pi$
$674$	3.54258e100	1.35486
$675$	6.22583e99	0.225898
$676$	−1.17319e100	−0.403889
$677$	5.04835e100	1.64912	0.824559	−	0.565775i	$-0.191423\pi$
$677$	5.04835e100	1.64912	0.824559	+	0.565775i	$0.191423\pi$
$678$	7.67300e99	0.237854
$679$	−4.25629e100	−1.25214
$680$	1.02276e100	0.285567
$681$	9.81741e99	0.260180
$682$	−6.19731e99	−0.155904
$683$	7.27386e99	0.173712	0.0868561	−	0.996221i	$-0.472318\pi$
$683$	7.27386e99	0.173712	0.0868561	+	0.996221i	$0.472318\pi$
$684$	−1.51799e100	−0.344173
$685$	−2.69334e100	−0.579798
$686$	−3.65602e100	−0.747313
$687$	1.77562e99	0.0344657
$688$	1.40595e100	0.259168
$689$	1.56436e100	0.273875
$690$	3.11288e99	0.0517630
$691$	−7.00674e100	−1.10674	−0.553370	−	0.832936i	$-0.686658\pi$
$691$	−7.00674e100	−1.10674	−0.553370	+	0.832936i	$0.686658\pi$
$692$	−9.48756e99	−0.142360
$693$	−6.99910e99	−0.0997729
$694$	−2.33883e100	−0.316765
$695$	−5.06640e100	−0.651987
$696$	2.25336e99	0.0275552
$697$	7.03224e99	0.0817203
$698$	−8.12714e100	−0.897574
$699$	2.10748e99	0.0221220
$700$	−1.84388e100	−0.183972
$701$	1.94815e101	1.84770	0.923852	−	0.382749i	$-0.125022\pi$
$701$	1.94815e101	1.84770	0.923852	+	0.382749i	$0.125022\pi$
$702$	−1.47714e100	−0.133184
$703$	−7.67562e100	−0.657960
$704$	2.29821e99	0.0187310
$705$	1.06101e100	0.0822254
$706$	−6.34947e100	−0.467919
$707$	4.26944e100	0.299214
$708$	−2.12076e100	−0.141355
$709$	2.55634e101	1.62061	0.810303	−	0.586011i	$-0.199302\pi$
$709$	2.55634e101	1.62061	0.810303	+	0.586011i	$0.199302\pi$
$710$	1.35914e101	0.819581
$711$	5.77654e100	0.331358
$712$	9.19755e100	0.501917
$713$	1.36861e101	0.710562
$714$	−2.58631e100	−0.127760
$715$	−9.62462e99	−0.0452397
$716$	1.67750e101	0.750326
$717$	−6.45515e100	−0.274774
$718$	−1.34444e101	−0.544658
$719$	−3.43252e101	−1.32354	−0.661770	−	0.749707i	$-0.730195\pi$
$719$	−3.43252e101	−1.32354	−0.661770	+	0.749707i	$0.730195\pi$
$720$	4.46310e100	0.163807
$721$	−5.69690e100	−0.199038
$722$	−1.01342e101	−0.337071
$723$	−6.77920e99	−0.0214669
$724$	−3.75086e100	−0.113087
$725$	−6.48495e100	−0.186169
$726$	−5.56622e100	−0.152163
$727$	1.40022e100	0.0364524	0.0182262	−	0.999834i	$-0.494198\pi$
$727$	1.40022e100	0.0364524	0.0182262	+	0.999834i	$0.494198\pi$
$728$	4.37478e100	0.108466
$729$	−3.05271e101	−0.720872
$730$	4.11521e101	0.925615
$731$	−5.67537e101	−1.21598
$732$	−2.22700e100	−0.0454545
$733$	−2.76697e101	−0.538038	−0.269019	−	0.963135i	$-0.586699\pi$
$733$	−2.76697e101	−0.538038	−0.269019	+	0.963135i	$0.586699\pi$
$734$	8.06398e100	0.149396
$735$	4.38267e100	0.0773639
$736$	−5.07537e100	−0.0853700
$737$	−1.25793e101	−0.201632
$738$	3.06872e100	0.0468766
$739$	5.97405e101	0.869744	0.434872	−	0.900492i	$-0.356794\pi$
$739$	5.97405e101	0.869744	0.434872	+	0.900492i	$0.356794\pi$
$740$	2.25674e101	0.313152
$741$	5.27858e100	0.0698185
$742$	2.45137e101	0.309079
$743$	5.02528e100	0.0604029	0.0302014	−	0.999544i	$-0.490385\pi$
$743$	5.02528e100	0.0604029	0.0302014	+	0.999544i	$0.490385\pi$
$744$	−9.99320e100	−0.114516
$745$	−2.19218e101	−0.239513
$746$	−3.88561e101	−0.404791
$747$	−3.07217e101	−0.305186
$748$	−9.27714e100	−0.0878835
$749$	−1.76884e101	−0.159802
$750$	1.89811e101	0.163548
$751$	1.79687e102	1.47672	0.738359	−	0.674407i	$-0.235601\pi$
$751$	1.79687e102	1.47672	0.738359	+	0.674407i	$0.235601\pi$
$752$	−1.72992e101	−0.135610
$753$	3.32350e101	0.248527
$754$	1.53862e101	0.109761
$755$	−2.11102e101	−0.143673
$756$	−2.31470e101	−0.150304
$757$	2.58914e102	1.60418	0.802088	−	0.597206i	$-0.203723\pi$
$757$	2.58914e102	1.60418	0.802088	+	0.597206i	$0.203723\pi$
$758$	−1.12852e102	−0.667196
$759$	−2.82360e100	−0.0159301
$760$	−3.27102e101	−0.176117
$761$	1.95449e101	0.100434	0.0502168	−	0.998738i	$-0.484009\pi$
$761$	1.95449e101	0.100434	0.0502168	+	0.998738i	$0.484009\pi$
$762$	−2.18658e100	−0.0107242
$763$	2.48412e102	1.16292
$764$	−1.97873e102	−0.884243
$765$	−1.80161e102	−0.768564
$766$	1.82096e102	0.741615
$767$	−1.44807e102	−0.563061
$768$	3.70588e100	0.0137584
$769$	−1.71574e102	−0.608229	−0.304114	−	0.952635i	$-0.598361\pi$
$769$	−1.71574e102	−0.608229	−0.304114	+	0.952635i	$0.598361\pi$
$770$	−1.50819e101	−0.0510548
$771$	4.23190e101	0.136806
$772$	9.86110e101	0.304447
$773$	−6.07019e102	−1.78990	−0.894952	−	0.446162i	$-0.852791\pi$
$773$	−6.07019e102	−1.78990	−0.894952	+	0.446162i	$0.852791\pi$
$774$	−2.47661e102	−0.697514
$775$	2.87594e102	0.773694
$776$	−2.46188e102	−0.632667
$777$	−5.70675e101	−0.140101
$778$	1.49299e102	0.350172
$779$	−2.24907e101	−0.0503991
$780$	−1.55198e101	−0.0332297
$781$	−1.23283e102	−0.252227
$782$	2.04876e102	0.400546
$783$	−8.14082e101	−0.152099
$784$	−7.14569e101	−0.127592
$785$	−2.07987e102	−0.354947
$786$	1.85733e102	0.302963
$787$	3.73177e102	0.581851	0.290926	−	0.956746i	$-0.406037\pi$
$787$	3.73177e102	0.581851	0.290926	+	0.956746i	$0.406037\pi$
$788$	5.16931e102	0.770464
$789$	−1.79103e102	−0.255193
$790$	1.24475e102	0.169559
$791$	8.20989e102	1.06923
$792$	−4.04834e101	−0.0504119
$793$	−1.52061e102	−0.181059
$794$	6.82477e102	0.777070
$795$	−8.69637e101	−0.0946902
$796$	7.51005e102	0.782040
$797$	6.99189e102	0.696344	0.348172	−	0.937431i	$-0.386802\pi$
$797$	6.99189e102	0.696344	0.348172	+	0.937431i	$0.386802\pi$
$798$	8.27161e101	0.0787930
$799$	6.98311e102	0.636265
$800$	−1.06651e102	−0.0929549
$801$	−1.62016e103	−1.35084
$802$	−7.56716e102	−0.603591
$803$	−3.73278e102	−0.284859
$804$	−2.02841e102	−0.148104
$805$	3.33069e102	0.232692
$806$	−6.82344e102	−0.456152
$807$	−2.46362e102	−0.157602
$808$	2.46948e102	0.151183
$809$	−1.82558e103	−1.06962	−0.534808	−	0.844973i	$-0.679616\pi$
$809$	−1.82558e103	−1.06962	−0.534808	+	0.844973i	$0.679616\pi$
$810$	−7.44106e102	−0.417270
$811$	−5.23233e102	−0.280837	−0.140419	−	0.990092i	$-0.544845\pi$
$811$	−5.23233e102	−0.280837	−0.140419	+	0.990092i	$0.544845\pi$
$812$	2.41103e102	0.123869
$813$	−6.60679e102	−0.324920
$814$	−2.04702e102	−0.0963730
$815$	2.14844e103	0.968340
$816$	−1.49595e102	−0.0645528
$817$	1.81511e103	0.749929
$818$	−2.16676e103	−0.857173
$819$	−7.70625e102	−0.291920
$820$	6.61258e101	0.0239872
$821$	−2.71460e103	−0.943025	−0.471513	−	0.881859i	$-0.656292\pi$
$821$	−2.71460e103	−0.943025	−0.471513	+	0.881859i	$0.656292\pi$
$822$	3.93943e102	0.131064
$823$	1.62184e103	0.516790	0.258395	−	0.966039i	$-0.416806\pi$
$823$	1.62184e103	0.516790	0.258395	+	0.966039i	$0.416806\pi$
$824$	−3.29514e102	−0.100567
$825$	−5.93337e101	−0.0173455
$826$	−2.26915e103	−0.635437
$827$	4.50795e103	1.20930	0.604649	−	0.796492i	$-0.293313\pi$
$827$	4.50795e103	1.20930	0.604649	+	0.796492i	$0.293313\pi$
$828$	8.94035e102	0.229762
$829$	3.03430e103	0.747090	0.373545	−	0.927612i	$-0.378142\pi$
$829$	3.03430e103	0.747090	0.373545	+	0.927612i	$0.378142\pi$
$830$	−6.62003e102	−0.156166
$831$	8.91757e102	0.201563
$832$	2.53041e102	0.0548040
$833$	2.88449e103	0.598647
$834$	7.41039e102	0.147383
$835$	2.22779e103	0.424624
$836$	2.96704e102	0.0542001
$837$	3.61029e103	0.632103
$838$	4.91827e102	0.0825373
$839$	−1.12091e104	−1.80311	−0.901553	−	0.432669i	$-0.857572\pi$
$839$	−1.12091e104	−1.80311	−0.901553	+	0.432669i	$0.857572\pi$
$840$	−2.43197e102	−0.0375011
$841$	−5.91688e103	−0.874651
$842$	5.62191e103	0.796719
$843$	5.28956e102	0.0718688
$844$	−1.35992e103	−0.177156
$845$	4.45318e103	0.556234
$846$	3.04728e103	0.364976
$847$	−5.95570e103	−0.684024
$848$	1.41789e103	0.156167
$849$	1.36104e103	0.143763
$850$	4.30517e103	0.436133
$851$	4.52063e103	0.439238
$852$	−1.98795e103	−0.185268
$853$	−1.22029e104	−1.09087	−0.545434	−	0.838154i	$-0.683635\pi$
$853$	−1.22029e104	−1.09087	−0.545434	+	0.838154i	$0.683635\pi$
$854$	−2.38282e103	−0.204333
$855$	5.76196e103	0.473994
$856$	−1.02311e103	−0.0807427
$857$	−2.33553e102	−0.0176834	−0.00884172	−	0.999961i	$-0.502814\pi$
$857$	−2.33553e102	−0.0176834	−0.00884172	+	0.999961i	$0.502814\pi$
$858$	1.40775e102	0.0102265
$859$	−2.09702e104	−1.46166	−0.730828	−	0.682561i	$-0.760866\pi$
$859$	−2.09702e104	−1.46166	−0.730828	+	0.682561i	$0.760866\pi$
$860$	−5.33669e103	−0.356925
$861$	−1.67216e102	−0.0107316
$862$	1.10765e104	0.682170
$863$	−2.21573e104	−1.30958	−0.654792	−	0.755809i	$-0.727244\pi$
$863$	−2.21573e104	−1.30958	−0.654792	+	0.755809i	$0.727244\pi$
$864$	−1.33884e103	−0.0759436
$865$	3.60127e103	0.196058
$866$	5.45542e103	0.285064
$867$	1.64964e103	0.0827391
$868$	−1.06924e104	−0.514786
$869$	−1.12907e103	−0.0521820
$870$	−8.55328e102	−0.0379489
$871$	−1.38502e104	−0.589944
$872$	1.43683e104	0.587586
$873$	4.33664e104	1.70274
$874$	−6.55240e103	−0.247027
$875$	2.03092e104	0.735203
$876$	−6.01912e103	−0.209237
$877$	4.77899e104	1.59533	0.797665	−	0.603101i	$-0.206068\pi$
$877$	4.77899e104	1.59533	0.797665	+	0.603101i	$0.206068\pi$
$878$	−9.29852e102	−0.0298098
$879$	−1.00173e104	−0.308421
$880$	−8.72352e102	−0.0257963
$881$	3.56273e104	1.01190	0.505951	−	0.862563i	$-0.331142\pi$
$881$	3.56273e104	1.01190	0.505951	+	0.862563i	$0.331142\pi$
$882$	1.25873e104	0.343397
$883$	−3.22733e104	−0.845744	−0.422872	−	0.906189i	$-0.638978\pi$
$883$	−3.22733e104	−0.845744	−0.422872	+	0.906189i	$0.638978\pi$
$884$	−1.02144e104	−0.257134
$885$	8.04995e103	0.194674
$886$	−1.62524e104	−0.377590
$887$	4.55556e104	1.01684	0.508421	−	0.861109i	$-0.330229\pi$
$887$	4.55556e104	1.01684	0.508421	+	0.861109i	$0.330229\pi$
$888$	−3.30083e103	−0.0707886
$889$	−2.33958e103	−0.0482087
$890$	−3.49119e104	−0.691239
$891$	6.74956e103	0.128415
$892$	−1.64221e104	−0.300246
$893$	−2.23336e104	−0.392402
$894$	3.20641e103	0.0541423
$895$	−6.36743e104	−1.03335
$896$	3.96519e103	0.0618485
$897$	−3.10887e103	−0.0466091
$898$	−5.71031e104	−0.822906
$899$	−3.76055e104	−0.520933
$900$	1.87868e104	0.250175
$901$	−5.72357e104	−0.732718
$902$	−5.99807e102	−0.00738209
$903$	1.34952e104	0.159685
$904$	4.74867e104	0.540247
$905$	1.42374e104	0.155743
$906$	3.08769e103	0.0324775
$907$	−1.09564e105	−1.10818	−0.554090	−	0.832457i	$-0.686934\pi$
$907$	−1.09564e105	−1.10818	−0.554090	+	0.832457i	$0.686934\pi$
$908$	6.07580e104	0.590957
$909$	−4.35003e104	−0.406888
$910$	−1.66057e104	−0.149378
$911$	1.47035e105	1.27209	0.636047	−	0.771650i	$-0.280568\pi$
$911$	1.47035e105	1.27209	0.636047	+	0.771650i	$0.280568\pi$
$912$	4.78437e103	0.0398114
$913$	6.00482e103	0.0480604
$914$	4.37872e104	0.337099
$915$	8.45320e103	0.0625997
$916$	1.09890e104	0.0782832
$917$	1.98729e105	1.36192
$918$	5.40447e104	0.356318
$919$	−1.19597e105	−0.758612	−0.379306	−	0.925271i	$-0.623837\pi$
$919$	−1.19597e105	−0.758612	−0.379306	+	0.925271i	$0.623837\pi$
$920$	1.92650e104	0.117571
$921$	−3.28885e104	−0.193120
$922$	2.43283e104	0.137456
$923$	−1.35739e105	−0.737978
$924$	2.20596e103	0.0115410
$925$	9.49945e104	0.478263
$926$	2.06830e105	1.00213
$927$	5.80444e104	0.270664
$928$	1.39456e104	0.0625871
$929$	−5.35843e104	−0.231462	−0.115731	−	0.993281i	$-0.536921\pi$
$929$	−5.35843e104	−0.231462	−0.115731	+	0.993281i	$0.536921\pi$
$930$	3.79320e104	0.157711
$931$	−9.22524e104	−0.369202
$932$	1.30428e104	0.0502465
$933$	−2.67200e104	−0.0990918
$934$	−3.15144e105	−1.12511
$935$	3.52140e104	0.121033
$936$	−4.45736e104	−0.147498
$937$	9.10176e104	0.289981	0.144991	−	0.989433i	$-0.453685\pi$
$937$	9.10176e104	0.289981	0.144991	+	0.989433i	$0.453685\pi$
$938$	−2.17034e105	−0.665775
$939$	5.98516e104	0.176786
$940$	6.56639e104	0.186762
$941$	−1.97081e105	−0.539776	−0.269888	−	0.962892i	$-0.586987\pi$
$941$	−1.97081e105	−0.539776	−0.269888	+	0.962892i	$0.586987\pi$
$942$	3.04213e104	0.0802363
$943$	1.32461e104	0.0336452
$944$	−1.31250e105	−0.321065
$945$	8.78609e104	0.206998
$946$	4.84074e104	0.109844
$947$	5.44036e105	1.18906	0.594530	−	0.804074i	$-0.297338\pi$
$947$	5.44036e105	1.18906	0.594530	+	0.804074i	$0.297338\pi$
$948$	−1.82064e104	−0.0383290
$949$	−4.10991e105	−0.833454
$950$	−1.37689e105	−0.268975
$951$	−1.93125e105	−0.363437
$952$	−1.60062e105	−0.290186
$953$	−9.89331e105	−1.72800	−0.864000	−	0.503492i	$-0.832048\pi$
$953$	−9.89331e105	−1.72800	−0.864000	+	0.503492i	$0.832048\pi$
$954$	−2.49764e105	−0.420303
$955$	7.51082e105	1.21778
$956$	−3.99496e105	−0.624105
$957$	7.75841e103	0.0116788
$958$	5.76678e105	0.836484
$959$	4.21508e105	0.589176
$960$	−1.40667e104	−0.0189480
$961$	8.97387e105	1.16493
$962$	−2.25384e105	−0.281973
$963$	1.80222e105	0.217308
$964$	−4.19551e104	−0.0487585
$965$	−3.74306e105	−0.419283
$966$	−4.87165e104	−0.0526003
$967$	9.63368e105	1.00266	0.501329	−	0.865257i	$-0.332845\pi$
$967$	9.63368e105	1.00266	0.501329	+	0.865257i	$0.332845\pi$
$968$	−3.44483e105	−0.345615
$969$	−1.93130e105	−0.186790
$970$	9.34475e105	0.871306
$971$	−8.70731e104	−0.0782711	−0.0391356	−	0.999234i	$-0.512460\pi$
$971$	−8.70731e104	−0.0782711	−0.0391356	+	0.999234i	$0.512460\pi$
$972$	3.56687e105	0.309125
$973$	7.92890e105	0.662533
$974$	7.17901e105	0.578391
$975$	−6.53284e104	−0.0507502
$976$	−1.37825e105	−0.103242
$977$	−3.79045e105	−0.273800	−0.136900	−	0.990585i	$-0.543714\pi$
$977$	−3.79045e105	−0.273800	−0.136900	+	0.990585i	$0.543714\pi$
$978$	−3.14242e105	−0.218895
$979$	3.16675e105	0.212730
$980$	2.71235e105	0.175720
$981$	−2.53101e106	−1.58141
$982$	1.68876e106	1.01768
$983$	−3.48725e105	−0.202691	−0.101345	−	0.994851i	$-0.532315\pi$
$983$	−3.48725e105	−0.202691	−0.101345	+	0.994851i	$0.532315\pi$
$984$	−9.67192e103	−0.00542234
$985$	−1.96216e106	−1.06108
$986$	−5.62940e105	−0.293651
$987$	−1.66048e105	−0.0835554
$988$	3.26681e105	0.158581
$989$	−1.06903e106	−0.500635
$990$	1.53666e105	0.0694271
$991$	−3.81947e105	−0.166490	−0.0832451	−	0.996529i	$-0.526528\pi$
$991$	−3.81947e105	−0.166490	−0.0832451	+	0.996529i	$0.526528\pi$
$992$	−6.18460e105	−0.260104
$993$	2.24346e105	0.0910373
$994$	−2.12705e106	−0.832838
$995$	−2.85065e106	−1.07702
$996$	9.68281e104	0.0353016
$997$	−1.76939e106	−0.622508	−0.311254	−	0.950327i	$-0.600749\pi$
$997$	−1.76939e106	−0.622508	−0.311254	+	0.950327i	$0.600749\pi$
$998$	−4.36620e105	−0.148241
$999$	1.19251e106	0.390738

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2.72.a.a.1.2	✓	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2.72.a.a.1.2	✓	2	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 2 \)
Weight:	\( k \)	\(=\)	\( 72 \)
Character orbit:	\([\chi]\)	\(=\)	2.a (trivial)

\(f(q)\)	\(=\)	\(q+3.43597e10 q^{2} +1.90762e16 q^{3} +1.18059e21 q^{4} -4.48127e24 q^{5} +6.55455e26 q^{6} +7.01318e29 q^{7} +4.05648e31 q^{8} -7.14556e33 q^{9} +O(q^{10})\)	\(q+3.43597e10 q^{2} +1.90762e16 q^{3} +1.18059e21 q^{4} -4.48127e24 q^{5} +6.55455e26 q^{6} +7.01318e29 q^{7} +4.05648e31 q^{8} -7.14556e33 q^{9} -1.53975e35 q^{10} +1.39666e36 q^{11} +2.25213e37 q^{12} +1.53777e39 q^{13} +2.40971e40 q^{14} -8.54858e40 q^{15} +1.39380e42 q^{16} -5.62631e43 q^{17} -2.45520e44 q^{18} +1.79942e45 q^{19} -5.29055e45 q^{20} +1.33785e46 q^{21} +4.79889e46 q^{22} -1.05979e48 q^{23} +7.73824e47 q^{24} -2.22699e49 q^{25} +5.28374e49 q^{26} -2.79563e50 q^{27} +8.27970e50 q^{28} +2.91198e51 q^{29} -2.93727e51 q^{30} -1.29140e53 q^{31} +4.78905e52 q^{32} +2.66431e52 q^{33} -1.93318e54 q^{34} -3.14279e54 q^{35} -8.43599e54 q^{36} -4.26561e55 q^{37} +6.18276e55 q^{38} +2.93349e55 q^{39} -1.81782e56 q^{40} -1.24989e56 q^{41} +4.59682e56 q^{42} +1.00872e58 q^{43} +1.64889e57 q^{44} +3.20212e58 q^{45} -3.64140e58 q^{46} -1.24115e59 q^{47} +2.65884e58 q^{48} -5.12678e59 q^{49} -7.65187e59 q^{50} -1.07329e60 q^{51} +1.81548e60 q^{52} +1.01729e61 q^{53} -9.60571e60 q^{54} -6.25882e60 q^{55} +2.84488e61 q^{56} +3.43262e61 q^{57} +1.00055e62 q^{58} -9.41671e62 q^{59} -1.00924e62 q^{60} -9.88843e62 q^{61} -4.43723e63 q^{62} -5.01131e63 q^{63} +1.64550e63 q^{64} -6.89116e63 q^{65} +9.15448e62 q^{66} -9.00666e64 q^{67} -6.64237e64 q^{68} -2.02168e64 q^{69} -1.07986e65 q^{70} -8.82699e65 q^{71} -2.89858e65 q^{72} -2.67264e66 q^{73} -1.46565e66 q^{74} -4.24825e65 q^{75} +2.12438e66 q^{76} +9.79503e65 q^{77} +1.00794e66 q^{78} -8.08409e66 q^{79} -6.24598e66 q^{80} +4.83264e67 q^{81} -4.29458e66 q^{82} +4.29941e67 q^{83} +1.57946e67 q^{84} +2.52130e68 q^{85} +3.46594e68 q^{86} +5.55497e67 q^{87} +5.66553e67 q^{88} +2.26737e69 q^{89} +1.10024e69 q^{90} +1.07847e69 q^{91} -1.25118e69 q^{92} -2.46351e69 q^{93} -4.26457e69 q^{94} -8.06368e69 q^{95} +9.13571e68 q^{96} -6.06899e70 q^{97} -1.76155e70 q^{98} -9.97993e69 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 68719476736 q^{2} - 73\!\cdots\!24 q^{3}+ \cdots - 61\!\cdots\!06 q^{9}+O(q^{10}) \) 2 * q + 68719476736 * q^2 - 73290552574846824 * q^3 + 2361183241434822606848 * q^4 + 4017561682270957567057500 * q^5 - 2518244211317885610315743232 * q^6 - 291238690173693964386145313552 * q^7 + 81129638414606681695789005144064 * q^8 - 6123404334975269213441745958191606 * q^9	\( 2 q + 68719476736 q^{2} - 73\!\cdots\!24 q^{3}+ \cdots - 25\!\cdots\!12 q^{99}+O(q^{100}) \) 2 * q + 68719476736 * q^2 - 73290552574846824 * q^3 + 2361183241434822606848 * q^4 + 4017561682270957567057500 * q^5 - 2518244211317885610315743232 * q^6 - 291238690173693964386145313552 * q^7 + 81129638414606681695789005144064 * q^8 - 6123404334975269213441745958191606 * q^9 + 138042368280132046088925515612160000 * q^10 + 8684021980716172090887525376850576904 * q^11 - 86526212247613054049400939322986725376 * q^12 - 1127526476847602121775517379388630880564 * q^13 - 10006885197007137092408662697676044763136 * q^14 - 870495707981432852912957098986798794190000 * q^15 + 2787593149816327892691964784081045188247552 * q^16 - 25310632831657129209270924115310927130954012 * q^17 - 210398570871227281924223539932585048573739008 * q^18 - 1515676621589311845828943656442220865774179720 * q^19 + 4743099657804439236107998378673316959354880000 * q^20 + 105057783932094120306762036640883833267054319424 * q^21 + 298380723239368814309358888863546426251303452672 * q^22 + 2203172021093641748810865503399372374910614063056 * q^23 - 2973018014802021769638859222271266932256426426368 * q^24 + 7608631123084092334620703396661508984732192968750 * q^25 - 38741514747476418312368452783630352849904496279552 * q^26 + 319648868947993055224983298099305125670447984140400 * q^27 - 343833957247777367123869889228909979682409491202048 * q^28 - 9698728689773075098486688545271532504346978353044820 * q^29 - 29910004776708962227849032598394684454226278481920000 * q^30 - 40152449056044233071756067933578167284289756136602176 * q^31 + 95780971304118053647396689196894323976171195136475136 * q^32 - 646467126733774659938188551326031765296979936890156448 * q^33 - 869666722024249947512519672631665319191092726559932416 * q^34 - 11578366136761156330569053956326057915336741584188620000 * q^35 - 7229239848136475225980096433630422626902243870395858944 * q^36 - 111302567218665505327715068364071188329715510661736133092 * q^37 - 52078252168302895367845656117167986656871260949011496960 * q^38 + 275519833227064980098009665274252977678408104840329524368 * q^39 + 162971663295510861461624602883383361666170966864035840000 * q^40 + 1293621751110559774763864122730511857252280974968281452724 * q^41 + 3609757969428628252091459480215598083336921089452940460032 * q^42 - 1570188515420028543133617556744083017145937257828102471224 * q^43 + 10252283584559329897127946035166644058616193652784990519296 * q^44 + 40708357615001912362112184537766135586032750500530146327500 * q^45 + 75700414224475307717463313812439049417335506592825614532608 * q^46 - 385166682154840572374711553898575384547395544426269119145312 * q^47 - 102152121151948219322231568723224690516220791896645696487424 * q^48 - 532035159715732504433438538355987707216238966761163005601134 * q^49 + 261430574727791417880321677225418373371479456953139200000000 * q^50 - 3932264303948319406691865647256788003255613422904957101311056 * q^51 - 1331148310703303321462704136062500237146241665952236108251136 * q^52 - 3099963518619652809000040240867303977580091183911870344857604 * q^53 + 10983051506680160776211401499861875800637953324417157378867200 * q^54 + 55675237030386993027088191557939523809594236008364091073990000 * q^55 - 11814044813067727683888054041578488163711785849542367105777664 * q^56 + 340530979210937295973262581310223186047069690231491850122484640 * q^57 - 333245780282818297674818451146232380367769998901979551377653760 * q^58 - 1634769282638530993938532031464170850734659495713497861208919640 * q^59 - 1027699938713350202229687163482744574649131800509079418306560000 * q^60 - 4880654092824262768274295733939273946937692231886071744774910356 * q^61 - 1379627644400128417380751464514180229965133097556173235859488768 * q^62 - 6025861853395026499121119084837033105792949783823904688557137744 * q^63 + 3291009114642412084309938365114701009965471731267159726697218048 * q^64 - 29543075418903360367582342730855024802992366467179006798718215000 * q^65 - 22212441338085195704544329675415390923261412452090927107868196864 * q^66 - 134179938663497929036082688157452363116312631094129088359318071272 * q^67 - 29881521036109411547967908356077030399545155480627042485522137088 * q^68 - 321605797179791219242936222377661308526135728863885795131895787072 * q^69 - 397829631188024238423499614496638648471785935450346828762972160000 * q^70 - 1460877510745740582710287713995347696234833946793802259869191016336 * q^71 - 248394789781489341122389789834951197865628377698933413906472763392 * q^72 - 3294544566820717164014310852275588208456751477490323839459061757324 * q^73 - 3824327089320080209166799848240719802335879866208768081693146873856 * q^74 - 3184606446584112229377097409458775389197568519591749999600534375000 * q^75 - 1789395119165616187416055863991190774635411515666290423769627361280 * q^76 - 6253614148334332819110227681464586033924531964755455804402474941504 * q^77 + 9466789384876945852702739096358587279675046525044436872190360551424 * q^78 + 32545937316211131695260490720524848524451973434380542886241294936160 * q^79 + 5599663712231541868723715427304950721493954977805868890975109120000 * q^80 - 14696790322123460114208775627144901209272992806663832631738624054318 * q^81 + 44448504915312847302911380237722229185910137671134107814183600914432 * q^82 + 29029289096582559444238889025865399025664140946681211932408984041976 * q^83 + 124030339401370609190995696547481222376098869028264558454981080907776 * q^84 + 515189414072415878332203587875687294826517223054383338648578942155000 * q^85 - 53951266578270514369163302115098086401206462253116960829150888722432 * q^86 + 1220360737986859838823441297151020036222068694550765089326808848685840 * q^87 + 352265781639999779838716580389548817134634070037714508800371015548928 * q^88 + 3892840256317115370330682179701204942142442453315338735392476328046420 * q^89 + 1398728517042446180581839536582579433906499662277636873109656043520000 * q^90 + 3723923831232087792375243174156474165096790899907919377283839137781664 * q^91 + 2601046427102197195248330727233686361926270850206227221189229484703744 * q^92 - 10683042981025141340950338658167930386609577245004285723682658026015488 * q^93 - 13234226426910936531546457451421780620973501002295527600190740093730816 * q^94 - 36238128778010894690559462260868212446184933626918861697256245230950000 * q^95 - 3509920156517179589395358987240212171415117269690520628101025242284032 * q^96 - 57797943272861961641603344152467986900234375803899254441558412075626172 * q^97 - 18280588890409662105806348248520070466174156498880209215855482804109312 * q^98 - 2531090145827533343099848313526915248178613009899410920700202513213912 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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