LMFDB - Embedded newform 2.84.a.b.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2,84,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, 84, names="a")

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

chi := DirichletCharacter("2.1");

S:= CuspForms(chi, 84);

N := Newforms(S);

Level:	$ N $	$=$	$ 2 $
Weight:	$ k $	$=$	$ 84 $
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:	$87.2544256533$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	$\mathbb{Q}[x]/(x^{3} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 76392209863211857938006422774x + 4214151671129618412000783695211690286445664 $ x^3 - x^2 - 76392209863211857938006422774*x + 4214151671129618412000783695211690286445664
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{24}\cdot 3^{11}\cdot 5^{2}\cdot 7 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$2.43002e14$ 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)

$f(q)$	$=$	$q+2.19902e12 q^{2} -8.12053e19 q^{3} +4.83570e24 q^{4} -9.96318e28 q^{5} -1.78572e32 q^{6} -5.66053e34 q^{7} +1.06338e37 q^{8} +2.60347e39 q^{9} +O(q^{10})$	\(q+2.19902e12 q^{2} -8.12053e19 q^{3} +4.83570e24 q^{4} -9.96318e28 q^{5} -1.78572e32 q^{6} -5.66053e34 q^{7} +1.06338e37 q^{8} +2.60347e39 q^{9} -2.19093e41 q^{10} -1.84354e42 q^{11} -3.92685e44 q^{12} +2.57649e46 q^{13} -1.24476e47 q^{14} +8.09064e48 q^{15} +2.33840e49 q^{16} +6.69632e50 q^{17} +5.72509e51 q^{18} +7.59111e52 q^{19} -4.81790e53 q^{20} +4.59665e54 q^{21} -4.05399e54 q^{22} -4.69781e56 q^{23} -8.63523e56 q^{24} -4.13261e56 q^{25} +5.66575e58 q^{26} +1.12662e59 q^{27} -2.73726e59 q^{28} +2.67824e60 q^{29} +1.77915e61 q^{30} +1.41131e62 q^{31} +5.14220e61 q^{32} +1.49705e62 q^{33} +1.47254e63 q^{34} +5.63969e63 q^{35} +1.25896e64 q^{36} -1.78238e65 q^{37} +1.66930e65 q^{38} -2.09224e66 q^{39} -1.05947e66 q^{40} +4.67079e66 q^{41} +1.01081e67 q^{42} +3.40824e67 q^{43} -8.91482e66 q^{44} -2.59388e68 q^{45} -1.03306e69 q^{46} -2.61516e69 q^{47} -1.89891e69 q^{48} -1.06998e70 q^{49} -9.08771e68 q^{50} -5.43777e70 q^{51} +1.24591e71 q^{52} +1.87235e71 q^{53} +2.47746e71 q^{54} +1.83675e71 q^{55} -6.01931e71 q^{56} -6.16439e72 q^{57} +5.88951e72 q^{58} +4.41947e73 q^{59} +3.91239e73 q^{60} -2.05477e74 q^{61} +3.10351e74 q^{62} -1.47370e74 q^{63} +1.13078e74 q^{64} -2.56700e75 q^{65} +3.29206e74 q^{66} -1.07076e76 q^{67} +3.23814e75 q^{68} +3.81487e76 q^{69} +1.24018e76 q^{70} +4.83952e76 q^{71} +2.76848e76 q^{72} -1.47922e77 q^{73} -3.91949e77 q^{74} +3.35590e76 q^{75} +3.67084e77 q^{76} +1.04354e77 q^{77} -4.60089e78 q^{78} +6.65039e78 q^{79} -2.32979e78 q^{80} -1.95388e79 q^{81} +1.02712e79 q^{82} -3.99360e79 q^{83} +2.22281e79 q^{84} -6.67166e79 q^{85} +7.49481e79 q^{86} -2.17487e80 q^{87} -1.96039e79 q^{88} -5.21870e80 q^{89} -5.70401e80 q^{90} -1.45843e81 q^{91} -2.27172e81 q^{92} -1.14606e82 q^{93} -5.75080e81 q^{94} -7.56316e81 q^{95} -4.17574e81 q^{96} +1.44659e82 q^{97} -2.35290e82 q^{98} -4.79960e81 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 6597069766656 q^{2} - 16\!\cdots\!24 q^{3}+ \cdots + 29\!\cdots\!11 q^{9}+O(q^{10}) $ 3 * q + 6597069766656 * q^2 - 16865576978405999724 * q^3 + 14507109835375550096474112 * q^4 - 89124088407700875878949881670 * q^5 - 37087795993817224716679693467648 * q^6 + 72912428890136593011598868334609288 * q^7 + 31901471898837980949691369446728269824 * q^8 + 2903564094220119569530206456786641290911 * q^9	$ 3 q + 6597069766656 q^{2} - 16\!\cdots\!24 q^{3}+ \cdots - 90\!\cdots\!68 q^{99}+O(q^{100}) $ 3 * q + 6597069766656 * q^2 - 16865576978405999724 * q^3 + 14507109835375550096474112 * q^4 - 89124088407700875878949881670 * q^5 - 37087795993817224716679693467648 * q^6 + 72912428890136593011598868334609288 * q^7 + 31901471898837980949691369446728269824 * q^8 + 2903564094220119569530206456786641290911 * q^9 - 195985943038406643942730238257008570531840 * q^10 - 24978774206464004009733924371834472527507364 * q^11 - 81556925887572376760126540365236732948381696 * q^12 - 13385495184723470250431662175810956861650939774 * q^13 + 160336126748191868906331795541891520971696766976 * q^14 - 1543056839506723738737512531611763740851131609640 * q^15 + 70152078591883340073776871970381584943484762062848 * q^16 + 149312255183231021040154145354101178805710731266198 * q^17 + 6385004967175821402287019425805650736202735127887872 * q^18 + 55293849727885716244659038787880400218220271579060900 * q^19 - 430977646502745808733769149575239604851692608872775680 * q^20 + 3645719950686395996325484168686099082668843870511440096 * q^21 - 54928905375196799499786276269448398351899949454933884928 * q^22 - 805827328635818601213715040041310117378914012956593526504 * q^23 - 179345576678102595081079770977441619615326740707847176192 * q^24 - 5030521506659548631822003886373561268610311776807186370475 * q^25 - 29435015198286225166967254491150470143619882443261763125248 * q^26 + 265222728292653992247626325353300797149922016654790765501960 * q^27 + 352582871424406990891936946778819932443205506964916642250752 * q^28 + 3816821385192456910492790601757082957064381440388168733398930 * q^29 - 3393217874713855605752045901651298015147125487613766826721280 * q^30 + 27306736762531164695904395012386760223323473997636656114733856 * q^31 + 154266052248863066452028360864751609842131487403148112188932096 * q^32 - 1869543607361303438021906043202257025987688880718639325041794288 * q^33 + 328341121486839666165836778032483790052134875558177321093431296 * q^34 + 14534999710313034659766439067001754131908491908682934888734333680 * q^35 + 14040774409634665679236919316045807802362404147214739351057465344 * q^36 - 52923027520109801062478020730582335084559828742299509796837572902 * q^37 + 121592461440618317054129411207547801649483432835228080072871116800 * q^38 - 2402178840747166455209643780042189831769498863330340255477707188808 * q^39 - 947729867282607115628856150138565833831415134900987376816210575360 * q^40 - 1630826972263179623457970100158554268531829459440506302206562479314 * q^41 + 8017022954789275420837524826046741939137681828852067331165747412992 * q^42 - 33553307012363163544032667059590733336999143846880512810825154723204 * q^43 - 120789940322073018068711022370253698499067178174972959543289505120256 * q^44 - 899390150496328129010638564824906173852269254482975703134378310929790 * q^45 - 1772033035629509215437502465864067810885814745930081005516794477150208 * q^46 - 4629910079963350350221297721597969688645786047253478838346456323692112 * q^47 - 394385093895532014185455659374224235518515431267571462303021986217984 * q^48 - 25904312213759912896573562369189009500767562783277344044247210951504581 * q^49 - 11062233780698832680856090411601584992119582950272264580591137272627200 * q^50 - 115003426553005764529308651997450424423206873228307379757058913903279384 * q^51 - 64728282948557973677781246741709000029118370892377010273402322887376896 * q^52 + 1955489350374820934426361520356408182849427388960005011763112205433066 * q^53 + 583230947416495520638665011722794275537738276087139153691506290636881920 * q^54 + 2108797874787371324281515134524355674706327291312898542556270469340517960 * q^55 + 775337933771571692582215196932671567522046479268565605290553175760175104 * q^56 + 15322000670469704774223981579586808538599472097150639315439774454541455600 * q^57 + 8393278988326410801385336257701289695718651111903517826702411402953359360 * q^58 + 17515422328677368763527856098594833667145631862459457466418222357737323660 * q^59 - 7461765017650501214602908995933776573955387698027100979270449411716546560 * q^60 - 43640380317138565765125545690879749580949226301206837258015611765251644494 * q^61 + 60048149174042762521445970801083724832034804351465379483433131655154368512 * q^62 - 457195494726045291713470857330955951313042916931677671039326900967012349144 * q^63 + 339234636437449791279993120142640355038876908200118839959348390648182996992 * q^64 - 4296913059058527224354407223174652737979058717517404072080357642037560619140 * q^65 - 4111169869856083518585062086214890004481713070750413249881098393661237886976 * q^66 + 141032868579017039252603961064071790283346383814419962362012801355450268628 * q^67 + 722029761903584901415847257151246901209113305857741485806171328892362555392 * q^68 + 8086087325412092464604398692880698235254488464939834057062449877128558876832 * q^69 + 31962802382419946386540207509068434826844079519986597775570617337831080591360 * q^70 + 182924642179429081351287474788615465829562015176370019587922663022657154084296 * q^71 + 30875989452746033356910691685482205465112656564337702401001511254596295589888 * q^72 - 263140135925842921903280041748503897229972912722022861455020469008131787988914 * q^73 - 116378968270939943880913485699410511986430903809811049684095477677110176251904 * q^74 - 219757760618324786335711731704583191459417224730184785076731310005445547763700 * q^75 + 267384650407729519496214980038734682337907814052411986234291580661246040473600 * q^76 - 343502161164788220719179625219521720334686808755722455114874104110835966197344 * q^77 - 5282447134797963330454358455854603687768954587296248341416467063293162098262016 * q^78 - 12034695994962253192018572414246476985958695027260336925439527447631547969548080 * q^79 - 2084080018135663591036327751031606335820235971481174518545639948196118234398720 * q^80 - 26829845454336398974126827639624302488735247553951918922512836067848733015875877 * q^81 - 3586226437788188460915494917492139518968529645233322509137448184439964935651328 * q^82 - 866285839618831283785116105591092087807254129011655636887946324521625748147484 * q^83 + 17629619917875826946065308701418928945125358538840626385585605987428989700931584 * q^84 + 999297217658610049915895867064394982963183108507668520498941294598608198173780 * q^85 - 73784502420862594609520517620018525607458954036403934280807974046874169516228608 * q^86 - 662304833857716625077531708289012630908112375820084997692130187355696595851208840 * q^87 - 265619887804976803598915032040941587597587362185479079384452874624780322379661312 * q^88 - 2902141249177927061116331049722970422359552504894459368572075199387222942405249570 * q^89 - 1977779856755838710879007473663666167277561233096029201267076883832405709899694080 * q^90 - 4775994167494808746040520734163298259656337652284546033077320243620956097336065104 * q^91 - 3896741854955696564651362008476430146191814207531134474918619063354144071473954816 * q^92 - 20606753022758608907040478217479874066388188968728538263924843766516850954617630848 * q^93 - 10181279936954027331988797479394607448439272243797402743258163521408005638742605824 * q^94 - 43227063853654043926776337745023206430945564224810828285113141330096591326575357000 * q^95 - 867261993119334011621140549565649365464384194439964291038400651660904451610247168 * q^96 - 37410452818623389818885816143993639408327020071141525834391520165010920135161558682 * q^97 - 56964184977137759788335145386948133810396144154523099324304459763673711303261683712 * q^98 - 90303617227381471027183650166443552736594841755621740583582132261899845439070414068 * 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 $

$2$	2.19902e12	0.707107
$2$	2.19902e12	0.707107
$3$	−8.12053e19	−1.28544	−0.642721	−	0.766100i	$-0.722195\pi$
$3$	−8.12053e19	−1.28544	−0.642721	+	0.766100i	$0.722195\pi$
$4$	4.83570e24	0.500000
$5$	−9.96318e28	−0.979812	−0.489906	−	0.871775i	$-0.662969\pi$
$5$	−9.96318e28	−0.979812	−0.489906	+	0.871775i	$0.662969\pi$
$6$	−1.78572e32	−0.908945
$7$	−5.66053e34	−0.480052	−0.240026	−	0.970766i	$-0.577156\pi$
$7$	−5.66053e34	−0.480052	−0.240026	+	0.970766i	$0.577156\pi$
$8$	1.06338e37	0.353553
$9$	2.60347e39	0.652362
$10$	−2.19093e41	−0.692832
$11$	−1.84354e42	−0.111649	−0.0558247	−	0.998441i	$-0.517779\pi$
$11$	−1.84354e42	−0.111649	−0.0558247	+	0.998441i	$0.517779\pi$
$12$	−3.92685e44	−0.642721
$13$	2.57649e46	1.52187	0.760937	−	0.648826i	$-0.224740\pi$
$13$	2.57649e46	1.52187	0.760937	+	0.648826i	$0.224740\pi$
$14$	−1.24476e47	−0.339448
$15$	8.09064e48	1.25949
$16$	2.33840e49	0.250000
$17$	6.69632e50	0.578370	0.289185	−	0.957273i	$-0.406616\pi$
$17$	6.69632e50	0.578370	0.289185	+	0.957273i	$0.406616\pi$
$18$	5.72509e51	0.461289
$19$	7.59111e52	0.648681	0.324340	−	0.945940i	$-0.394858\pi$
$19$	7.59111e52	0.648681	0.324340	+	0.945940i	$0.394858\pi$
$20$	−4.81790e53	−0.489906
$21$	4.59665e54	0.617079
$22$	−4.05399e54	−0.0789480
$23$	−4.69781e56	−1.44607	−0.723036	−	0.690810i	$-0.757254\pi$
$23$	−4.69781e56	−1.44607	−0.723036	+	0.690810i	$0.757254\pi$
$24$	−8.63523e56	−0.454472
$25$	−4.13261e56	−0.0399682
$26$	5.66575e58	1.07613
$27$	1.12662e59	0.446869
$28$	−2.73726e59	−0.240026
$29$	2.67824e60	0.547435	0.273718	−	0.961810i	$-0.411747\pi$
$29$	2.67824e60	0.547435	0.273718	+	0.961810i	$0.411747\pi$
$30$	1.77915e61	0.890595
$31$	1.41131e62	1.81181	0.905907	−	0.423477i	$-0.139191\pi$
$31$	1.41131e62	1.81181	0.905907	+	0.423477i	$0.139191\pi$
$32$	5.14220e61	0.176777
$33$	1.49705e62	0.143519
$34$	1.47254e63	0.408969
$35$	5.63969e63	0.470361
$36$	1.25896e64	0.326181
$37$	−1.78238e65	−1.48125	−0.740625	−	0.671918i	$-0.765471\pi$
$37$	−1.78238e65	−1.48125	−0.740625	+	0.671918i	$0.765471\pi$
$38$	1.66930e65	0.458687
$39$	−2.09224e66	−1.95628
$40$	−1.05947e66	−0.346416
$41$	4.67079e66	0.548101	0.274051	−	0.961715i	$-0.411636\pi$
$41$	4.67079e66	0.548101	0.274051	+	0.961715i	$0.411636\pi$
$42$	1.01081e67	0.436341
$43$	3.40824e67	0.554102	0.277051	−	0.960855i	$-0.410643\pi$
$43$	3.40824e67	0.554102	0.277051	+	0.960855i	$0.410643\pi$
$44$	−8.91482e66	−0.0558247
$45$	−2.59388e68	−0.639192
$46$	−1.03306e69	−1.02253
$47$	−2.61516e69	−1.06032	−0.530160	−	0.847897i	$-0.677868\pi$
$47$	−2.61516e69	−1.06032	−0.530160	+	0.847897i	$0.677868\pi$
$48$	−1.89891e69	−0.321361
$49$	−1.06998e70	−0.769550
$50$	−9.08771e68	−0.0282618
$51$	−5.43777e70	−0.743461
$52$	1.24591e71	0.760937
$53$	1.87235e71	0.518726	0.259363	−	0.965780i	$-0.416487\pi$
$53$	1.87235e71	0.518726	0.259363	+	0.965780i	$0.416487\pi$
$54$	2.47746e71	0.315984
$55$	1.83675e71	0.109395
$56$	−6.01931e71	−0.169724
$57$	−6.16439e72	−0.833842
$58$	5.88951e72	0.387095
$59$	4.41947e73	1.42893	0.714466	−	0.699670i	$-0.246670\pi$
$59$	4.41947e73	1.42893	0.714466	+	0.699670i	$0.246670\pi$
$60$	3.91239e73	0.629746
$61$	−2.05477e74	−1.66561	−0.832807	−	0.553563i	$-0.813268\pi$
$61$	−2.05477e74	−1.66561	−0.832807	+	0.553563i	$0.813268\pi$
$62$	3.10351e74	1.28115
$63$	−1.47370e74	−0.313168
$64$	1.13078e74	0.125000
$65$	−2.56700e75	−1.49115
$66$	3.29206e74	0.101483
$67$	−1.07076e76	−1.76842	−0.884212	−	0.467086i	$-0.845304\pi$
$67$	−1.07076e76	−1.76842	−0.884212	+	0.467086i	$0.845304\pi$
$68$	3.23814e75	0.289185
$69$	3.81487e76	1.85884
$70$	1.24018e76	0.332595
$71$	4.83952e76	0.720412	0.360206	−	0.932873i	$-0.382706\pi$
$71$	4.83952e76	0.720412	0.360206	+	0.932873i	$0.382706\pi$
$72$	2.76848e76	0.230645
$73$	−1.47922e77	−0.695237	−0.347618	−	0.937636i	$-0.613010\pi$
$73$	−1.47922e77	−0.695237	−0.347618	+	0.937636i	$0.613010\pi$
$74$	−3.91949e77	−1.04740
$75$	3.35590e76	0.0513768
$76$	3.67084e77	0.324340
$77$	1.04354e77	0.0535975
$78$	−4.60089e78	−1.38330
$79$	6.65039e78	1.17848	0.589241	−	0.807957i	$-0.299427\pi$
$79$	6.65039e78	1.17848	0.589241	+	0.807957i	$0.299427\pi$
$80$	−2.32979e78	−0.244953
$81$	−1.95388e79	−1.22679
$82$	1.02712e79	0.387566
$83$	−3.99360e79	−0.911220	−0.455610	−	0.890180i	$-0.650579\pi$
$83$	−3.99360e79	−0.911220	−0.455610	+	0.890180i	$0.650579\pi$
$84$	2.22281e79	0.308540
$85$	−6.67166e79	−0.566694
$86$	7.49481e79	0.391809
$87$	−2.17487e80	−0.703696
$88$	−1.96039e79	−0.0394740
$89$	−5.21870e80	−0.657472	−0.328736	−	0.944422i	$-0.606623\pi$
$89$	−5.21870e80	−0.657472	−0.328736	+	0.944422i	$0.606623\pi$
$90$	−5.70401e80	−0.451977
$91$	−1.45843e81	−0.730579
$92$	−2.27172e81	−0.723036
$93$	−1.14606e82	−2.32898
$94$	−5.75080e81	−0.749760
$95$	−7.56316e81	−0.635585
$96$	−4.17574e81	−0.227236
$97$	1.44659e82	0.512059	0.256029	−	0.966669i	$-0.417586\pi$
$97$	1.44659e82	0.512059	0.256029	+	0.966669i	$0.417586\pi$
$98$	−2.35290e82	−0.544154
$99$	−4.79960e81	−0.0728358
$100$	−1.99841e81	−0.0199841
$101$	−1.87438e83	−1.24028	−0.620140	−	0.784491i	$-0.712924\pi$
$101$	−1.87438e83	−1.24028	−0.620140	+	0.784491i	$0.712924\pi$
$102$	−1.19578e83	−0.525706
$103$	−5.71658e83	−1.67645	−0.838227	−	0.545321i	$-0.816408\pi$
$103$	−5.71658e83	−1.67645	−0.838227	+	0.545321i	$0.816408\pi$
$104$	2.73979e83	0.538064
$105$	−4.57973e83	−0.604622
$106$	4.11734e83	0.366794
$107$	2.44017e83	0.147229	0.0736144	−	0.997287i	$-0.476547\pi$
$107$	2.44017e83	0.147229	0.0736144	+	0.997287i	$0.476547\pi$
$108$	5.44799e83	0.223435
$109$	3.23441e84	0.904890	0.452445	−	0.891792i	$-0.350552\pi$
$109$	3.23441e84	0.904890	0.452445	+	0.891792i	$0.350552\pi$
$110$	4.03906e83	0.0773542
$111$	1.44739e85	1.90406
$112$	−1.32366e84	−0.120013
$113$	−1.14942e84	−0.0720647	−0.0360323	−	0.999351i	$-0.511472\pi$
$113$	−1.14942e84	−0.0720647	−0.0360323	+	0.999351i	$0.511472\pi$
$114$	−1.35556e85	−0.589615
$115$	4.68051e85	1.41688
$116$	1.29512e85	0.273718
$117$	6.70780e85	0.992812
$118$	9.71851e85	1.01041
$119$	−3.79047e85	−0.277648
$120$	8.60344e85	0.445298
$121$	−2.69243e86	−0.987534
$122$	−4.51848e86	−1.17777
$123$	−3.79294e86	−0.704552
$124$	6.82470e86	0.905907
$125$	1.07134e87	1.01897
$126$	−3.24071e86	−0.221443
$127$	−1.65294e87	−0.813585	−0.406792	−	0.913521i	$-0.633353\pi$
$127$	−1.65294e87	−0.813585	−0.406792	+	0.913521i	$0.633353\pi$
$128$	2.48662e86	0.0883883
$129$	−2.76768e87	−0.712266
$130$	−5.64489e87	−1.05440
$131$	−4.72634e87	−0.642342	−0.321171	−	0.947021i	$-0.604076\pi$
$131$	−4.72634e87	−0.642342	−0.321171	+	0.947021i	$0.604076\pi$
$132$	7.23931e86	0.0717594
$133$	−4.29697e87	−0.311401
$134$	−2.35462e88	−1.25046
$135$	−1.12247e88	−0.437848
$136$	7.12074e87	0.204485
$137$	3.18315e88	0.674456	0.337228	−	0.941423i	$-0.390511\pi$
$137$	3.18315e88	0.674456	0.337228	+	0.941423i	$0.390511\pi$
$138$	8.38899e88	1.31440
$139$	1.78420e88	0.207172	0.103586	−	0.994621i	$-0.466968\pi$
$139$	1.78420e88	0.207172	0.103586	+	0.994621i	$0.466968\pi$
$140$	2.72719e88	0.235181
$141$	2.12365e89	1.36298
$142$	1.06422e89	0.509408
$143$	−4.74986e88	−0.169916
$144$	6.08796e88	0.163090
$145$	−2.66838e89	−0.536384
$146$	−3.25283e89	−0.491607
$147$	8.68878e89	0.989212
$148$	−8.61906e89	−0.740625
$149$	2.16375e90	1.40597	0.702985	−	0.711204i	$-0.251850\pi$
$149$	2.16375e90	1.40597	0.702985	+	0.711204i	$0.251850\pi$
$150$	7.37971e88	0.0363289
$151$	−1.93727e90	−0.723846	−0.361923	−	0.932208i	$-0.617880\pi$
$151$	−1.93727e90	−0.723846	−0.361923	+	0.932208i	$0.617880\pi$
$152$	8.07225e89	0.229343
$153$	1.74337e90	0.377306
$154$	2.29477e89	0.0378992
$155$	−1.40612e91	−1.77524
$156$	−1.01175e91	−0.978140
$157$	−8.26782e90	−0.613134	−0.306567	−	0.951849i	$-0.599180\pi$
$157$	−8.26782e90	−0.613134	−0.306567	+	0.951849i	$0.599180\pi$
$158$	1.46244e91	0.833313
$159$	−1.52045e91	−0.666792
$160$	−5.12327e90	−0.173208
$161$	2.65921e91	0.694190
$162$	−4.29662e91	−0.867469
$163$	4.08809e90	0.0639345	0.0319672	−	0.999489i	$-0.489823\pi$
$163$	4.08809e90	0.0639345	0.0319672	+	0.999489i	$0.489823\pi$
$164$	2.25866e91	0.274051
$165$	−1.49154e91	−0.140621
$166$	−8.78201e91	−0.644330
$167$	2.32556e92	1.32982	0.664912	−	0.746922i	$-0.268469\pi$
$167$	2.32556e92	1.32982	0.664912	+	0.746922i	$0.268469\pi$
$168$	4.88800e91	0.218171
$169$	3.77213e92	1.31610
$170$	−1.46711e92	−0.400713
$171$	1.97632e92	0.423174
$172$	1.64813e92	0.277051
$173$	1.50883e93	1.99401	0.997007	−	0.0773124i	$-0.0246339\pi$
$173$	1.50883e93	1.99401	0.997007	+	0.0773124i	$0.0246339\pi$
$174$	−4.78260e92	−0.497588
$175$	2.33928e91	0.0191868
$176$	−4.31094e91	−0.0279123
$177$	−3.58884e93	−1.83681
$178$	−1.14760e93	−0.464903
$179$	4.30426e92	0.138197	0.0690983	−	0.997610i	$-0.477988\pi$
$179$	4.30426e92	0.138197	0.0690983	+	0.997610i	$0.477988\pi$
$180$	−1.25433e93	−0.319596
$181$	−6.99616e93	−1.41644	−0.708221	−	0.705991i	$-0.750502\pi$
$181$	−6.99616e93	−1.41644	−0.708221	+	0.705991i	$0.750502\pi$
$182$	−3.20712e93	−0.516597
$183$	1.66858e94	2.14105
$184$	−4.99557e93	−0.511264
$185$	1.77582e94	1.45135
$186$	−2.52022e94	−1.64684
$187$	−1.23449e93	−0.0645746
$188$	−1.26461e94	−0.530160
$189$	−6.37725e93	−0.214520
$190$	−1.66316e94	−0.449427
$191$	−1.99542e94	−0.433660	−0.216830	−	0.976209i	$-0.569572\pi$
$191$	−1.99542e94	−0.433660	−0.216830	+	0.976209i	$0.569572\pi$
$192$	−9.18256e93	−0.160680
$193$	6.79632e94	0.958617	0.479309	−	0.877646i	$-0.340887\pi$
$193$	6.79632e94	0.958617	0.479309	+	0.877646i	$0.340887\pi$
$194$	3.18109e94	0.362080
$195$	2.08454e95	1.91679
$196$	−5.17409e94	−0.384775
$197$	−2.86262e93	−0.0172352	−0.00861759	−	0.999963i	$-0.502743\pi$
$197$	−2.86262e93	−0.0172352	−0.00861759	+	0.999963i	$0.502743\pi$
$198$	−1.05544e94	−0.0515027
$199$	1.46701e95	0.580805	0.290402	−	0.956905i	$-0.406211\pi$
$199$	1.46701e95	0.580805	0.290402	+	0.956905i	$0.406211\pi$
$200$	−4.39455e93	−0.0141309
$201$	8.69511e95	2.27321
$202$	−4.12180e95	−0.877010
$203$	−1.51603e95	−0.262798
$204$	−2.62954e95	−0.371731
$205$	−4.65360e95	−0.537036
$206$	−1.25709e96	−1.18543
$207$	−1.22306e96	−0.943362
$208$	6.02486e95	0.380468
$209$	−1.39945e95	−0.0724248
$210$	−1.00709e96	−0.427532
$211$	1.42090e96	0.495268	0.247634	−	0.968854i	$-0.420347\pi$
$211$	1.42090e96	0.495268	0.247634	+	0.968854i	$0.420347\pi$
$212$	9.05412e95	0.259363
$213$	−3.92995e96	−0.926048
$214$	5.36598e95	0.104106
$215$	−3.39569e96	−0.542916
$216$	1.19803e96	0.157992
$217$	−7.98879e96	−0.869765
$218$	7.11255e96	0.639854
$219$	1.20120e97	0.893687
$220$	8.88199e95	0.0546977
$221$	1.72530e97	0.880206
$222$	3.18284e97	1.34638
$223$	−1.15805e97	−0.406513	−0.203256	−	0.979126i	$-0.565152\pi$
$223$	−1.15805e97	−0.406513	−0.203256	+	0.979126i	$0.565152\pi$
$224$	−2.91076e96	−0.0848621
$225$	−1.07591e96	−0.0260737
$226$	−2.52760e96	−0.0509574
$227$	4.73459e97	0.794711	0.397356	−	0.917665i	$-0.369928\pi$
$227$	4.73459e97	0.794711	0.397356	+	0.917665i	$0.369928\pi$
$228$	−2.98092e97	−0.416921
$229$	−1.28596e98	−1.49987	−0.749935	−	0.661511i	$-0.769915\pi$
$229$	−1.28596e98	−1.49987	−0.749935	+	0.661511i	$0.769915\pi$
$230$	1.02926e98	1.00188
$231$	−8.47412e96	−0.0688965
$232$	2.84799e97	0.193548
$233$	−2.41110e98	−1.37071	−0.685354	−	0.728210i	$-0.740353\pi$
$233$	−2.41110e98	−1.37071	−0.685354	+	0.728210i	$0.740353\pi$
$234$	1.47506e98	0.702024
$235$	2.60553e98	1.03892
$236$	2.13712e98	0.714466
$237$	−5.40047e98	−1.51487
$238$	−8.33533e97	−0.196327
$239$	−6.74885e98	−1.33572	−0.667862	−	0.744285i	$-0.732790\pi$
$239$	−6.74885e98	−1.33572	−0.667862	+	0.744285i	$0.732790\pi$
$240$	1.89192e98	0.314873
$241$	−9.92548e98	−1.39009	−0.695047	−	0.718964i	$-0.744616\pi$
$241$	−9.92548e98	−1.39009	−0.695047	+	0.718964i	$0.744616\pi$
$242$	−5.92073e98	−0.698292
$243$	1.13704e99	1.13009
$244$	−9.93624e98	−0.832807
$245$	1.06604e99	0.754014
$246$	−8.34075e98	−0.498194
$247$	1.95584e99	0.987210
$248$	1.50077e99	0.640573
$249$	3.24301e99	1.17132
$250$	2.35591e99	0.720523
$251$	2.81163e99	0.728615	0.364308	−	0.931279i	$-0.381306\pi$
$251$	2.81163e99	0.728615	0.364308	+	0.931279i	$0.381306\pi$
$252$	−7.12639e98	−0.156584
$253$	8.66060e98	0.161453
$254$	−3.63485e99	−0.575291
$255$	5.41774e99	0.728452
$256$	5.46813e98	0.0625000
$257$	−1.89182e100	−1.83931	−0.919654	−	0.392728i	$-0.871531\pi$
$257$	−1.89182e100	−1.83931	−0.919654	+	0.392728i	$0.871531\pi$
$258$	−6.08618e99	−0.503648
$259$	1.00892e100	0.711078
$260$	−1.24132e100	−0.745575
$261$	6.97272e99	0.357126
$262$	−1.03933e100	−0.454204
$263$	1.26186e100	0.470814	0.235407	−	0.971897i	$-0.424358\pi$
$263$	1.26186e100	0.470814	0.235407	+	0.971897i	$0.424358\pi$
$264$	1.59194e99	0.0507416
$265$	−1.86545e100	−0.508254
$266$	−9.44914e99	−0.220193
$267$	4.23787e100	0.845142
$268$	−5.17786e100	−0.884212
$269$	−1.17751e101	−1.72284	−0.861418	−	0.507897i	$-0.830423\pi$
$269$	−1.17751e101	−1.72284	−0.861418	+	0.507897i	$0.830423\pi$
$270$	−2.46834e100	−0.309605
$271$	7.35412e100	0.791235	0.395617	−	0.918415i	$-0.370531\pi$
$271$	7.35412e100	0.791235	0.395617	+	0.918415i	$0.370531\pi$
$272$	1.56587e100	0.144592
$273$	1.18432e101	0.939117
$274$	6.99982e100	0.476912
$275$	7.61864e98	0.00446242
$276$	1.84476e101	0.929421
$277$	−3.84695e101	−1.66804	−0.834019	−	0.551735i	$-0.813966\pi$
$277$	−3.84695e101	−1.66804	−0.834019	+	0.551735i	$0.813966\pi$
$278$	3.92351e100	0.146493
$279$	3.67431e101	1.18196
$280$	5.99715e100	0.166298
$281$	1.52983e101	0.365873	0.182936	−	0.983125i	$-0.441440\pi$
$281$	1.52983e101	0.365873	0.182936	+	0.983125i	$0.441440\pi$
$282$	4.66996e101	0.963773
$283$	−7.45279e101	−1.32795	−0.663975	−	0.747754i	$-0.731132\pi$
$283$	−7.45279e101	−1.32795	−0.663975	+	0.747754i	$0.731132\pi$
$284$	2.34025e101	0.360206
$285$	6.14169e101	0.817008
$286$	−1.04450e101	−0.120149
$287$	−2.64392e101	−0.263117
$288$	1.33876e101	0.115322
$289$	−8.92074e101	−0.665488
$290$	−5.86783e101	−0.379281
$291$	−1.17471e102	−0.658222
$292$	−7.15305e101	−0.347618
$293$	1.46451e102	0.617568	0.308784	−	0.951132i	$-0.400078\pi$
$293$	1.46451e102	0.617568	0.308784	+	0.951132i	$0.400078\pi$
$294$	1.91068e102	0.699478
$295$	−4.40320e102	−1.40008
$296$	−1.89535e102	−0.523701
$297$	−2.07697e101	−0.0498927
$298$	4.75813e102	0.994171
$299$	−1.21038e103	−2.20074
$300$	1.62281e101	0.0256884
$301$	−1.92925e102	−0.265998
$302$	−4.26009e102	−0.511836
$303$	1.52209e103	1.59431
$304$	1.77511e102	0.162170
$305$	2.04720e103	1.63199
$306$	3.83370e102	0.266796
$307$	2.15317e103	1.30868	0.654342	−	0.756199i	$-0.272946\pi$
$307$	2.15317e103	1.30868	0.654342	+	0.756199i	$0.272946\pi$
$308$	5.04626e101	0.0267988
$309$	4.64217e103	2.15498
$310$	−3.09209e103	−1.25528
$311$	−3.04066e103	−1.07997	−0.539984	−	0.841675i	$-0.681570\pi$
$311$	−3.04066e103	−1.07997	−0.539984	+	0.841675i	$0.681570\pi$
$312$	−2.22486e103	−0.691650
$313$	−2.46914e103	−0.672133	−0.336067	−	0.941838i	$-0.609097\pi$
$313$	−2.46914e103	−0.672133	−0.336067	+	0.941838i	$0.609097\pi$
$314$	−1.81811e103	−0.433551
$315$	1.46828e103	0.306845
$316$	3.21593e103	0.589241
$317$	−1.61535e103	−0.259601	−0.129800	−	0.991540i	$-0.541434\pi$
$317$	−1.61535e103	−0.259601	−0.129800	+	0.991540i	$0.541434\pi$
$318$	−3.34350e103	−0.471493
$319$	−4.93745e102	−0.0611208
$320$	−1.12662e103	−0.122477
$321$	−1.98155e103	−0.189254
$322$	5.84766e103	0.490867
$323$	5.08325e103	0.375177
$324$	−9.44837e103	−0.613393
$325$	−1.06476e103	−0.0608265
$326$	8.98981e102	0.0452085
$327$	−2.62652e104	−1.16318
$328$	4.96684e103	0.193783
$329$	1.48032e104	0.509009
$330$	−3.27993e103	−0.0994344
$331$	−3.01344e104	−0.805750	−0.402875	−	0.915255i	$-0.631989\pi$
$331$	−3.01344e104	−0.805750	−0.402875	+	0.915255i	$0.631989\pi$
$332$	−1.93118e104	−0.455610
$333$	−4.64037e104	−0.966311
$334$	5.11396e104	0.940328
$335$	1.06681e105	1.73272
$336$	1.07488e104	0.154270
$337$	4.70618e104	0.597073	0.298536	−	0.954398i	$-0.403502\pi$
$337$	4.70618e104	0.597073	0.298536	+	0.954398i	$0.403502\pi$
$338$	8.29501e104	0.930623
$339$	9.33389e103	0.0926350
$340$	−3.22622e104	−0.283347
$341$	−2.60182e104	−0.202288
$342$	4.34598e104	0.299229
$343$	1.39270e105	0.849476
$344$	3.62427e104	0.195905
$345$	−3.80082e105	−1.82132
$346$	3.31796e105	1.40998
$347$	−2.82430e105	−1.06473	−0.532363	−	0.846516i	$-0.678696\pi$
$347$	−2.82430e105	−1.06473	−0.532363	+	0.846516i	$0.678696\pi$
$348$	−1.05170e105	−0.351848
$349$	−2.83308e105	−0.841401	−0.420701	−	0.907199i	$-0.638216\pi$
$349$	−2.83308e105	−0.841401	−0.420701	+	0.907199i	$0.638216\pi$
$350$	5.14413e103	0.0135671
$351$	2.90271e105	0.680078
$352$	−9.47986e103	−0.0197370
$353$	1.61554e104	0.0298998	0.0149499	−	0.999888i	$-0.495241\pi$
$353$	1.61554e104	0.0298998	0.0149499	+	0.999888i	$0.495241\pi$
$354$	−7.89195e105	−1.29882
$355$	−4.82170e105	−0.705869
$356$	−2.52361e105	−0.328736
$357$	3.07806e105	0.356900
$358$	9.46516e104	0.0977198
$359$	7.71134e105	0.709104	0.354552	−	0.935036i	$-0.384633\pi$
$359$	7.71134e105	0.709104	0.354552	+	0.935036i	$0.384633\pi$
$360$	−2.75829e105	−0.225988
$361$	−7.93209e105	−0.579213
$362$	−1.53847e106	−1.00158
$363$	2.18640e106	1.26942
$364$	−7.05252e105	−0.365289
$365$	1.47377e106	0.681201
$366$	3.66925e106	1.51395
$367$	2.49169e106	0.918022	0.459011	−	0.888431i	$-0.348204\pi$
$367$	2.49169e106	0.918022	0.459011	+	0.888431i	$0.348204\pi$
$368$	−1.09854e106	−0.361518
$369$	1.21603e106	0.357560
$370$	3.90506e106	1.02626
$371$	−1.05985e106	−0.249015
$372$	−5.54202e106	−1.16449
$373$	3.35513e106	0.630656	0.315328	−	0.948983i	$-0.397886\pi$
$373$	3.35513e106	0.630656	0.315328	+	0.948983i	$0.397886\pi$
$374$	−2.71468e105	−0.0456612
$375$	−8.69988e106	−1.30983
$376$	−2.78092e106	−0.374880
$377$	6.90045e106	0.833127
$378$	−1.40237e106	−0.151689
$379$	−7.42621e106	−0.719847	−0.359923	−	0.932982i	$-0.617197\pi$
$379$	−7.42621e106	−0.719847	−0.359923	+	0.932982i	$0.617197\pi$
$380$	−3.65732e106	−0.317793
$381$	1.34228e107	1.04582
$382$	−4.38797e106	−0.306644
$383$	−2.06276e107	−1.29330	−0.646652	−	0.762785i	$-0.723831\pi$
$383$	−2.06276e107	−1.29330	−0.646652	+	0.762785i	$0.723831\pi$
$384$	−2.01927e106	−0.113618
$385$	−1.03970e106	−0.0525155
$386$	1.49453e107	0.677845
$387$	8.87326e106	0.361475
$388$	6.99530e106	0.256029
$389$	−4.73239e107	−1.55658	−0.778290	−	0.627905i	$-0.783913\pi$
$389$	−4.73239e107	−1.55658	−0.778290	+	0.627905i	$0.783913\pi$
$390$	4.58395e107	1.35537
$391$	−3.14580e107	−0.836365
$392$	−1.13779e107	−0.272077
$393$	3.83804e107	0.825693
$394$	−6.29497e105	−0.0121871
$395$	−6.62591e107	−1.15469
$396$	−2.32095e106	−0.0364179
$397$	−1.01510e107	−0.143451	−0.0717256	−	0.997424i	$-0.522851\pi$
$397$	−1.01510e107	−0.143451	−0.0717256	+	0.997424i	$0.522851\pi$
$398$	3.22599e107	0.410691
$399$	3.48937e107	0.400287
$400$	−9.66371e105	−0.00999204
$401$	−7.00944e107	−0.653420	−0.326710	−	0.945125i	$-0.605940\pi$
$401$	−7.00944e107	−0.653420	−0.326710	+	0.945125i	$0.605940\pi$
$402$	1.91208e108	1.60740
$403$	3.63623e108	2.75735
$404$	−9.06393e107	−0.620140
$405$	1.94668e108	1.20202
$406$	−3.33378e107	−0.185826
$407$	3.28589e107	0.165381
$408$	−5.78242e107	−0.262853
$409$	−3.93330e108	−1.61525	−0.807625	−	0.589696i	$-0.799248\pi$
$409$	−3.93330e108	−1.61525	−0.807625	+	0.589696i	$0.799248\pi$
$410$	−1.02334e108	−0.379742
$411$	−2.58489e108	−0.866974
$412$	−2.76437e108	−0.838227
$413$	−2.50165e108	−0.685962
$414$	−2.68954e108	−0.667058
$415$	3.97889e108	0.892824
$416$	1.32488e108	0.269032
$417$	−1.44887e108	−0.266307
$418$	−3.07743e107	−0.0512121
$419$	−3.00401e108	−0.452709	−0.226354	−	0.974045i	$-0.572681\pi$
$419$	−3.00401e108	−0.452709	−0.226354	+	0.974045i	$0.572681\pi$
$420$	−2.21462e108	−0.302311
$421$	8.86459e108	1.09636	0.548178	−	0.836362i	$-0.315322\pi$
$421$	8.86459e108	1.09636	0.548178	+	0.836362i	$0.315322\pi$
$422$	3.12458e108	0.350208
$423$	−6.80849e108	−0.691713
$424$	1.99102e108	0.183397
$425$	−2.76733e107	−0.0231164
$426$	−8.64206e108	−0.654815
$427$	1.16311e109	0.799582
$428$	1.17999e108	0.0736144
$429$	3.85714e108	0.218418
$430$	−7.46721e108	−0.383900
$431$	3.22121e109	1.50388	0.751938	−	0.659233i	$-0.229119\pi$
$431$	3.22121e109	1.50388	0.751938	+	0.659233i	$0.229119\pi$
$432$	2.63449e108	0.111717
$433$	1.49748e109	0.576915	0.288458	−	0.957493i	$-0.406858\pi$
$433$	1.49748e109	0.576915	0.288458	+	0.957493i	$0.406858\pi$
$434$	−1.75675e109	−0.615017
$435$	2.16687e109	0.689490
$436$	1.56407e109	0.452445
$437$	−3.56616e109	−0.938039
$438$	2.64147e109	0.631932
$439$	−1.69236e109	−0.368311	−0.184155	−	0.982897i	$-0.558955\pi$
$439$	−1.69236e109	−0.368311	−0.184155	+	0.982897i	$0.558955\pi$
$440$	1.95317e108	0.0386771
$441$	−2.78565e109	−0.502025
$442$	3.79397e109	0.622400
$443$	−1.03592e110	−1.54730	−0.773648	−	0.633616i	$-0.781570\pi$
$443$	−1.03592e110	−1.54730	−0.773648	+	0.633616i	$0.781570\pi$
$444$	6.99913e109	0.952031
$445$	5.19949e109	0.644199
$446$	−2.54657e109	−0.287448
$447$	−1.75708e110	−1.80729
$448$	−6.40083e108	−0.0600065
$449$	−1.11575e110	−0.953554	−0.476777	−	0.879024i	$-0.658195\pi$
$449$	−1.11575e110	−0.953554	−0.476777	+	0.879024i	$0.658195\pi$
$450$	−2.36596e108	−0.0184369
$451$	−8.61080e108	−0.0611952
$452$	−5.55824e108	−0.0360323
$453$	1.57316e110	0.930462
$454$	1.04115e110	0.561946
$455$	1.45306e110	0.715830
$456$	−6.55510e109	−0.294807
$457$	−6.22626e109	−0.255685	−0.127842	−	0.991794i	$-0.540805\pi$
$457$	−6.22626e109	−0.255685	−0.127842	+	0.991794i	$0.540805\pi$
$458$	−2.82785e110	−1.06057
$459$	7.54419e109	0.258456
$460$	2.26336e110	0.708440
$461$	−2.25378e110	−0.644649	−0.322325	−	0.946629i	$-0.604464\pi$
$461$	−2.25378e110	−0.644649	−0.322325	+	0.946629i	$0.604464\pi$
$462$	−1.86348e109	−0.0487172
$463$	−3.12304e110	−0.746392	−0.373196	−	0.927752i	$-0.621738\pi$
$463$	−3.12304e110	−0.746392	−0.373196	+	0.927752i	$0.621738\pi$
$464$	6.26281e109	0.136859
$465$	1.14184e111	2.28196
$466$	−5.30207e110	−0.969237
$467$	−2.35474e110	−0.393815	−0.196907	−	0.980422i	$-0.563090\pi$
$467$	−2.35474e110	−0.393815	−0.196907	+	0.980422i	$0.563090\pi$
$468$	3.24369e110	0.496406
$469$	6.06105e110	0.848936
$470$	5.72963e110	0.734624
$471$	6.71391e110	0.788148
$472$	4.69959e110	0.505204
$473$	−6.28324e109	−0.0618651
$474$	−1.18758e111	−1.07118
$475$	−3.13711e109	−0.0259266
$476$	−1.83296e110	−0.138824
$477$	4.87460e110	0.338397
$478$	−1.48409e111	−0.944499
$479$	1.95907e111	1.14321	0.571605	−	0.820529i	$-0.306321\pi$
$479$	1.95907e111	1.14321	0.571605	+	0.820529i	$0.306321\pi$
$480$	4.16037e110	0.222649
$481$	−4.59227e111	−2.25428
$482$	−2.18264e111	−0.982945
$483$	−2.15942e111	−0.892341
$484$	−1.30198e111	−0.493767
$485$	−1.44127e111	−0.501721
$486$	2.50037e111	0.799097
$487$	1.15824e111	0.339896	0.169948	−	0.985453i	$-0.445640\pi$
$487$	1.15824e111	0.339896	0.169948	+	0.985453i	$0.445640\pi$
$488$	−2.18500e111	−0.588884
$489$	−3.31975e110	−0.0821841
$490$	2.34424e111	0.533169
$491$	5.92174e111	1.23756	0.618782	−	0.785563i	$-0.287627\pi$
$491$	5.92174e111	1.23756	0.618782	+	0.785563i	$0.287627\pi$
$492$	−1.83415e111	−0.352276
$493$	1.79343e111	0.316620
$494$	4.30094e111	0.698063
$495$	4.78193e110	0.0713654
$496$	3.30022e111	0.452953
$497$	−2.73943e111	−0.345836
$498$	7.13146e111	0.828249
$499$	5.11082e111	0.546158	0.273079	−	0.961992i	$-0.411958\pi$
$499$	5.11082e111	0.546158	0.273079	+	0.961992i	$0.411958\pi$
$500$	5.18070e111	0.509487
$501$	−1.88848e112	−1.70941
$502$	6.18283e111	0.515209
$503$	−3.96005e111	−0.303829	−0.151914	−	0.988394i	$-0.548544\pi$
$503$	−3.96005e111	−0.303829	−0.151914	+	0.988394i	$0.548544\pi$
$504$	−1.56711e111	−0.110721
$505$	1.86747e112	1.21524
$506$	1.90449e111	0.114165
$507$	−3.06317e112	−1.69177
$508$	−7.99313e111	−0.406792
$509$	4.16250e111	0.195239	0.0976194	−	0.995224i	$-0.468877\pi$
$509$	4.16250e111	0.195239	0.0976194	+	0.995224i	$0.468877\pi$
$510$	1.19137e112	0.515093
$511$	8.37314e111	0.333750
$512$	1.20245e111	0.0441942
$513$	8.55228e111	0.289875
$514$	−4.16015e112	−1.30059
$515$	5.69553e112	1.64261
$516$	−1.33837e112	−0.356133
$517$	4.82116e111	0.118384
$518$	2.21864e112	0.502808
$519$	−1.22525e113	−2.56319
$520$	−2.72970e112	−0.527201
$521$	1.28309e112	0.228819	0.114410	−	0.993434i	$-0.463502\pi$
$521$	1.28309e112	0.228819	0.114410	+	0.993434i	$0.463502\pi$
$522$	1.53332e112	0.252526
$523$	−9.63360e112	−1.46544	−0.732721	−	0.680529i	$-0.761750\pi$
$523$	−9.63360e112	−1.46544	−0.732721	+	0.680529i	$0.761750\pi$
$524$	−2.28552e112	−0.321171
$525$	−1.89962e111	−0.0246635
$526$	2.77487e112	0.332916
$527$	9.45061e112	1.04790
$528$	3.50071e111	0.0358797
$529$	1.15156e113	1.09112
$530$	−4.10218e112	−0.359390
$531$	1.15060e113	0.932180
$532$	−2.07789e112	−0.155700
$533$	1.20342e113	0.834141
$534$	9.31916e112	0.597606
$535$	−2.43118e112	−0.144257
$536$	−1.13862e113	−0.625232
$537$	−3.49529e112	−0.177644
$538$	−2.58937e113	−1.21823
$539$	1.97254e112	0.0859198
$540$	−5.42793e112	−0.218924
$541$	2.16711e113	0.809460	0.404730	−	0.914436i	$-0.367365\pi$
$541$	2.16711e113	0.809460	0.404730	+	0.914436i	$0.367365\pi$
$542$	1.61719e113	0.559488
$543$	5.68125e113	1.82075
$544$	3.44338e112	0.102242
$545$	−3.22250e113	−0.886622
$546$	2.60435e113	0.664056
$547$	−4.67487e113	−1.10483	−0.552415	−	0.833569i	$-0.686294\pi$
$547$	−4.67487e113	−1.10483	−0.552415	+	0.833569i	$0.686294\pi$
$548$	1.53928e113	0.337228
$549$	−5.34952e113	−1.08658
$550$	1.67536e111	0.00315541
$551$	2.03308e113	0.355111
$552$	4.05667e113	0.657200
$553$	−3.76448e113	−0.565733
$554$	−8.45953e113	−1.17948
$555$	−1.44206e114	−1.86562
$556$	8.62789e112	0.103586
$557$	−1.50543e114	−1.67753	−0.838767	−	0.544490i	$-0.816723\pi$
$557$	−1.50543e114	−1.67753	−0.838767	+	0.544490i	$0.816723\pi$
$558$	8.07990e113	0.835770
$559$	8.78129e113	0.843273
$560$	1.31879e113	0.117590
$561$	1.00247e113	0.0830070
$562$	3.36412e113	0.258711
$563$	6.86216e112	0.0490187	0.0245094	−	0.999700i	$-0.492198\pi$
$563$	6.86216e112	0.0490187	0.0245094	+	0.999700i	$0.492198\pi$
$564$	1.02693e114	0.681491
$565$	1.14519e113	0.0706098
$566$	−1.63889e114	−0.939003
$567$	1.10600e114	0.588921
$568$	5.14626e113	0.254704
$569$	2.57202e114	1.18336	0.591679	−	0.806174i	$-0.298465\pi$
$569$	2.57202e114	1.18336	0.591679	+	0.806174i	$0.298465\pi$
$570$	1.35057e114	0.577712
$571$	2.50808e114	0.997568	0.498784	−	0.866726i	$-0.333780\pi$
$571$	2.50808e114	0.997568	0.498784	+	0.866726i	$0.333780\pi$
$572$	−2.29689e113	−0.0849581
$573$	1.62039e114	0.557445
$574$	−5.81404e113	−0.186052
$575$	1.94142e113	0.0577969
$576$	2.94396e113	0.0815452
$577$	−1.69083e114	−0.435817	−0.217909	−	0.975969i	$-0.569923\pi$
$577$	−1.69083e114	−0.435817	−0.217909	+	0.975969i	$0.569923\pi$
$578$	−1.96169e114	−0.470571
$579$	−5.51897e114	−1.23225
$580$	−1.29035e114	−0.268192
$581$	2.26059e114	0.437433
$582$	−2.58322e114	−0.465433
$583$	−3.45175e113	−0.0579154
$584$	−1.57297e114	−0.245803
$585$	−6.68310e114	−0.972769
$586$	3.22048e114	0.436687
$587$	4.57319e114	0.577747	0.288873	−	0.957367i	$-0.406719\pi$
$587$	4.57319e114	0.577747	0.288873	+	0.957367i	$0.406719\pi$
$588$	4.20164e114	0.494606
$589$	1.07134e115	1.17529
$590$	−9.68273e114	−0.990010
$591$	2.32460e113	0.0221548
$592$	−4.16792e114	−0.370313
$593$	−7.00771e114	−0.580505	−0.290253	−	0.956950i	$-0.593739\pi$
$593$	−7.00771e114	−0.580505	−0.290253	+	0.956950i	$0.593739\pi$
$594$	−4.56730e113	−0.0352794
$595$	3.77651e114	0.272043
$596$	1.04632e115	0.702985
$597$	−1.19129e115	−0.746591
$598$	−2.66166e115	−1.55616
$599$	2.11008e114	0.115103	0.0575513	−	0.998343i	$-0.481671\pi$
$599$	2.11008e114	0.115103	0.0575513	+	0.998343i	$0.481671\pi$
$600$	3.56861e113	0.0181644
$601$	1.96438e115	0.933113	0.466556	−	0.884492i	$-0.345495\pi$
$601$	1.96438e115	0.933113	0.466556	+	0.884492i	$0.345495\pi$
$602$	−4.24246e114	−0.188089
$603$	−2.78768e115	−1.15365
$604$	−9.36805e114	−0.361923
$605$	2.68252e115	0.967598
$606$	3.34712e115	1.12735
$607$	2.54578e115	0.800738	0.400369	−	0.916354i	$-0.368882\pi$
$607$	2.54578e115	0.800738	0.400369	+	0.916354i	$0.368882\pi$
$608$	3.90350e114	0.114672
$609$	1.23109e115	0.337811
$610$	4.50184e115	1.15399
$611$	−6.73792e115	−1.61367
$612$	8.43040e114	0.188653
$613$	−5.95606e114	−0.124552	−0.0622758	−	0.998059i	$-0.519836\pi$
$613$	−5.95606e114	−0.124552	−0.0622758	+	0.998059i	$0.519836\pi$
$614$	4.73486e115	0.925379
$615$	3.77897e115	0.690329
$616$	1.10968e114	0.0189496
$617$	−1.08314e115	−0.172922	−0.0864608	−	0.996255i	$-0.527556\pi$
$617$	−1.08314e115	−0.172922	−0.0864608	+	0.996255i	$0.527556\pi$
$618$	1.02082e116	1.52380
$619$	−4.00859e115	−0.559539	−0.279769	−	0.960067i	$-0.590258\pi$
$619$	−4.00859e115	−0.559539	−0.279769	+	0.960067i	$0.590258\pi$
$620$	−6.79957e115	−0.887619
$621$	−5.29263e115	−0.646205
$622$	−6.68647e115	−0.763653
$623$	2.95406e115	0.315621
$624$	−4.89251e115	−0.489070
$625$	−1.02467e116	−0.958434
$626$	−5.42969e115	−0.475270
$627$	1.13643e115	0.0930979
$628$	−3.99807e115	−0.306567
$629$	−1.19354e116	−0.856711
$630$	3.22877e115	0.216973
$631$	1.87683e116	1.18088	0.590441	−	0.807081i	$-0.298954\pi$
$631$	1.87683e116	1.18088	0.590441	+	0.807081i	$0.298954\pi$
$632$	7.07191e115	0.416656
$633$	−1.15384e116	−0.636639
$634$	−3.55218e115	−0.183566
$635$	1.64685e116	0.797160
$636$	−7.35243e115	−0.333396
$637$	−2.75678e116	−1.17116
$638$	−1.08576e115	−0.0432189
$639$	1.25996e116	0.469969
$640$	−2.47746e115	−0.0866040
$641$	3.31005e116	1.08449	0.542245	−	0.840220i	$-0.317574\pi$
$641$	3.31005e116	1.08449	0.542245	+	0.840220i	$0.317574\pi$
$642$	−4.35746e115	−0.133823
$643$	−1.59351e116	−0.458776	−0.229388	−	0.973335i	$-0.573672\pi$
$643$	−1.59351e116	−0.458776	−0.229388	+	0.973335i	$0.573672\pi$
$644$	1.28591e116	0.347095
$645$	2.75749e116	0.697887
$646$	1.11782e116	0.265290
$647$	4.66600e116	1.03853	0.519263	−	0.854614i	$-0.326206\pi$
$647$	4.66600e116	1.03853	0.519263	+	0.854614i	$0.326206\pi$
$648$	−2.07772e116	−0.433734
$649$	−8.14747e115	−0.159539
$650$	−2.34144e115	−0.0430108
$651$	6.48732e116	1.11803
$652$	1.97688e115	0.0319672
$653$	4.82664e116	0.732400	0.366200	−	0.930536i	$-0.380659\pi$
$653$	4.82664e116	0.732400	0.366200	+	0.930536i	$0.380659\pi$
$654$	−5.77577e116	−0.822495
$655$	4.70894e116	0.629374
$656$	1.09222e116	0.137025
$657$	−3.85109e116	−0.453546
$658$	3.25526e116	0.359924
$659$	−1.21923e117	−1.26573	−0.632867	−	0.774260i	$-0.718122\pi$
$659$	−1.21923e117	−1.26573	−0.632867	+	0.774260i	$0.718122\pi$
$660$	−7.21265e115	−0.0703107
$661$	−8.37746e116	−0.766923	−0.383462	−	0.923557i	$-0.625268\pi$
$661$	−8.37746e116	−0.766923	−0.383462	+	0.923557i	$0.625268\pi$
$662$	−6.62662e116	−0.569752
$663$	−1.40103e117	−1.13145
$664$	−4.24672e116	−0.322165
$665$	4.28115e116	0.305114
$666$	−1.02043e117	−0.683285
$667$	−1.25819e117	−0.791631
$668$	1.12457e117	0.664912
$669$	9.40395e116	0.522548
$670$	2.34595e117	1.22522
$671$	3.78805e116	0.185965
$672$	2.36369e116	0.109085
$673$	3.83437e115	0.0166368	0.00831838	−	0.999965i	$-0.497352\pi$
$673$	3.83437e115	0.0166368	0.00831838	+	0.999965i	$0.497352\pi$
$674$	1.03490e117	0.422194
$675$	−4.65587e115	−0.0178605
$676$	1.82409e117	0.658050
$677$	−2.22711e117	−0.755636	−0.377818	−	0.925880i	$-0.623326\pi$
$677$	−2.22711e117	−0.755636	−0.377818	+	0.925880i	$0.623326\pi$
$678$	2.05254e116	0.0655028
$679$	−8.18849e116	−0.245815
$680$	−7.09453e116	−0.200357
$681$	−3.84474e117	−1.02156
$682$	−5.72145e116	−0.143039
$683$	−1.23614e117	−0.290810	−0.145405	−	0.989372i	$-0.546448\pi$
$683$	−1.23614e117	−0.290810	−0.145405	+	0.989372i	$0.546448\pi$
$684$	9.55691e116	0.211587
$685$	−3.17143e117	−0.660840
$686$	3.06258e117	0.600671
$687$	1.04427e118	1.92800
$688$	7.96985e116	0.138526
$689$	4.82408e117	0.789435
$690$	−8.35810e117	−1.28787
$691$	9.48066e117	1.37562	0.687812	−	0.725889i	$-0.258571\pi$
$691$	9.48066e117	1.37562	0.687812	+	0.725889i	$0.258571\pi$
$692$	7.29627e117	0.997007
$693$	2.71683e116	0.0349650
$694$	−6.21071e117	−0.752876
$695$	−1.77764e117	−0.202989
$696$	−2.31272e117	−0.248794
$697$	3.12771e117	0.317005
$698$	−6.23000e117	−0.594961
$699$	1.95795e118	1.76197
$700$	1.13121e116	0.00959340
$701$	−2.09566e118	−1.67503	−0.837516	−	0.546412i	$-0.815993\pi$
$701$	−2.09566e118	−1.67503	−0.837516	+	0.546412i	$0.815993\pi$
$702$	6.38314e117	0.480888
$703$	−1.35302e118	−0.960859
$704$	−2.08464e116	−0.0139562
$705$	−2.11583e118	−1.33547
$706$	3.55262e116	0.0211424
$707$	1.06100e118	0.595399
$708$	−1.73546e118	−0.918405
$709$	−4.56136e117	−0.227654	−0.113827	−	0.993501i	$-0.536311\pi$
$709$	−4.56136e117	−0.227654	−0.113827	+	0.993501i	$0.536311\pi$
$710$	−1.06030e118	−0.499125
$711$	1.73141e118	0.768796
$712$	−5.54948e117	−0.232451
$713$	−6.63008e118	−2.62001
$714$	6.76874e117	0.252367
$715$	4.73237e117	0.166486
$716$	2.08141e117	0.0690983
$717$	5.48042e118	1.71700
$718$	1.69574e118	0.501412
$719$	4.08138e118	1.13909	0.569545	−	0.821960i	$-0.307120\pi$
$719$	4.08138e118	1.13909	0.569545	+	0.821960i	$0.307120\pi$
$720$	−6.06554e117	−0.159798
$721$	3.23589e118	0.804786
$722$	−1.74428e118	−0.409566
$723$	8.06002e118	1.78689
$724$	−3.38313e118	−0.708221
$725$	−1.10681e117	−0.0218800
$726$	4.80795e118	0.897614
$727$	−7.10553e118	−1.25291	−0.626453	−	0.779460i	$-0.715494\pi$
$727$	−7.10553e118	−1.25291	−0.626453	+	0.779460i	$0.715494\pi$
$728$	−1.55087e118	−0.258299
$729$	−1.43575e118	−0.225884
$730$	3.24085e118	0.481682
$731$	2.28227e118	0.320476
$732$	8.06876e118	1.07053
$733$	−1.20926e119	−1.51602	−0.758010	−	0.652243i	$-0.773828\pi$
$733$	−1.20926e119	−1.51602	−0.758010	+	0.652243i	$0.773828\pi$
$734$	5.47929e118	0.649139
$735$	−8.65679e118	−0.969242
$736$	−2.41571e118	−0.255632
$737$	1.97398e118	0.197443
$738$	2.67407e118	0.252833
$739$	9.63059e118	0.860813	0.430406	−	0.902635i	$-0.358370\pi$
$739$	9.63059e118	0.860813	0.430406	+	0.902635i	$0.358370\pi$
$740$	8.58732e118	0.725674
$741$	−1.58825e119	−1.26900
$742$	−2.33063e118	−0.176081
$743$	7.35863e118	0.525728	0.262864	−	0.964833i	$-0.415333\pi$
$743$	7.35863e118	0.525728	0.262864	+	0.964833i	$0.415333\pi$
$744$	−1.21870e119	−0.823419
$745$	−2.15578e119	−1.37759
$746$	7.37800e118	0.445941
$747$	−1.03972e119	−0.594445
$748$	−5.96964e117	−0.0322873
$749$	−1.38126e118	−0.0706775
$750$	−1.91312e119	−0.926191
$751$	2.31153e119	1.05887	0.529433	−	0.848352i	$-0.322405\pi$
$751$	2.31153e119	1.05887	0.529433	+	0.848352i	$0.322405\pi$
$752$	−6.11530e118	−0.265080
$753$	−2.28319e119	−0.936593
$754$	1.51742e119	0.589110
$755$	1.93013e119	0.709233
$756$	−3.08385e118	−0.107260
$757$	6.06090e118	0.199553	0.0997765	−	0.995010i	$-0.468187\pi$
$757$	6.06090e118	0.199553	0.0997765	+	0.995010i	$0.468187\pi$
$758$	−1.63304e119	−0.509009
$759$	−7.03287e118	−0.207539
$760$	−8.04253e118	−0.224713
$761$	7.32771e119	1.93867	0.969337	−	0.245733i	$-0.0790287\pi$
$761$	7.32771e119	1.93867	0.969337	+	0.245733i	$0.0790287\pi$
$762$	2.95170e119	0.739504
$763$	−1.83085e119	−0.434394
$764$	−9.64925e118	−0.216830
$765$	−1.73695e119	−0.369689
$766$	−4.53607e119	−0.914504
$767$	1.13867e120	2.17465
$768$	−4.44041e118	−0.0803401
$769$	−6.46064e119	−1.10747	−0.553736	−	0.832692i	$-0.686798\pi$
$769$	−6.46064e119	−1.10747	−0.553736	+	0.832692i	$0.686798\pi$
$770$	−2.28632e118	−0.0371341
$771$	1.53626e120	2.36433
$772$	3.28650e119	0.479309
$773$	−1.21468e120	−1.67885	−0.839425	−	0.543475i	$-0.817108\pi$
$773$	−1.21468e120	−1.67885	−0.839425	+	0.543475i	$0.817108\pi$
$774$	1.95125e119	0.255601
$775$	−5.83242e118	−0.0724149
$776$	1.53828e119	0.181040
$777$	−8.19298e119	−0.914049
$778$	−1.04066e120	−1.10067
$779$	3.54565e119	0.355543
$780$	1.00802e120	0.958394
$781$	−8.92186e118	−0.0804336
$782$	−6.91769e119	−0.591399
$783$	3.01735e119	0.244632
$784$	−2.50203e119	−0.192387
$785$	8.23738e119	0.600756
$786$	8.43994e119	0.583853
$787$	6.90354e119	0.453023	0.226512	−	0.974008i	$-0.427268\pi$
$787$	6.90354e119	0.453023	0.226512	+	0.974008i	$0.427268\pi$
$788$	−1.38428e118	−0.00861759
$789$	−1.02470e120	−0.605204
$790$	−1.45705e120	−0.816490
$791$	6.50631e118	0.0345948
$792$	−5.10381e118	−0.0257513
$793$	−5.29408e120	−2.53485
$794$	−2.23224e119	−0.101435
$795$	1.51485e120	0.653331
$796$	7.09402e119	0.290402
$797$	−2.04606e120	−0.795058	−0.397529	−	0.917590i	$-0.630132\pi$
$797$	−2.04606e120	−0.795058	−0.397529	+	0.917590i	$0.630132\pi$
$798$	7.67321e119	0.283046
$799$	−1.75119e120	−0.613258
$800$	−2.12507e118	−0.00706544
$801$	−1.35867e120	−0.428909
$802$	−1.54139e120	−0.462037
$803$	2.72699e119	0.0776227
$804$	4.20470e120	1.13660
$805$	−2.64942e120	−0.680176
$806$	7.99616e120	1.94974
$807$	9.56199e120	2.21461
$808$	−1.99318e120	−0.438505
$809$	5.30306e120	1.10831	0.554157	−	0.832412i	$-0.313041\pi$
$809$	5.30306e120	1.10831	0.554157	+	0.832412i	$0.313041\pi$
$810$	4.28080e120	0.849956
$811$	3.22985e120	0.609280	0.304640	−	0.952467i	$-0.401464\pi$
$811$	3.22985e120	0.609280	0.304640	+	0.952467i	$0.401464\pi$
$812$	−7.33105e119	−0.131399
$813$	−5.97194e120	−1.01709
$814$	7.22574e119	0.116942
$815$	−4.07304e119	−0.0626438
$816$	−1.27157e120	−0.185865
$817$	2.58724e120	0.359435
$818$	−8.64942e120	−1.14215
$819$	−3.79697e120	−0.476602
$820$	−2.25034e120	−0.268518
$821$	1.26169e121	1.43124	0.715620	−	0.698490i	$-0.246144\pi$
$821$	1.26169e121	1.43124	0.715620	+	0.698490i	$0.246144\pi$
$822$	−5.68423e120	−0.613043
$823$	−9.58637e120	−0.983017	−0.491509	−	0.870873i	$-0.663554\pi$
$823$	−9.58637e120	−0.983017	−0.491509	+	0.870873i	$0.663554\pi$
$824$	−6.07891e120	−0.592716
$825$	−6.18674e118	−0.00573618
$826$	−5.50120e120	−0.485048
$827$	−1.54365e121	−1.29441	−0.647204	−	0.762317i	$-0.724062\pi$
$827$	−1.54365e121	−1.29441	−0.647204	+	0.762317i	$0.724062\pi$
$828$	−5.91435e120	−0.471681
$829$	5.22730e118	0.00396520	0.00198260	−	0.999998i	$-0.499369\pi$
$829$	5.22730e118	0.00396520	0.00198260	+	0.999998i	$0.499369\pi$
$830$	8.74967e120	0.631322
$831$	3.12393e121	2.14417
$832$	2.91344e120	0.190234
$833$	−7.16490e120	−0.445084
$834$	−3.18610e120	−0.188308
$835$	−2.31700e121	−1.30298
$836$	−6.76734e119	−0.0362124
$837$	1.59001e121	0.809643
$838$	−6.60588e120	−0.320114
$839$	1.41280e121	0.651568	0.325784	−	0.945444i	$-0.394372\pi$
$839$	1.41280e121	0.651568	0.325784	+	0.945444i	$0.394372\pi$
$840$	−4.87000e120	−0.213766
$841$	−1.67620e121	−0.700315
$842$	1.94934e121	0.775241
$843$	−1.24230e121	−0.470308
$844$	6.87103e120	0.247634
$845$	−3.75824e121	−1.28953
$846$	−1.49720e121	−0.489115
$847$	1.52406e121	0.474068
$848$	4.37830e120	0.129681
$849$	6.05207e121	1.70700
$850$	−6.08542e119	−0.0163458
$851$	8.37327e121	2.14200
$852$	−1.90041e121	−0.463024
$853$	−3.06794e121	−0.711971	−0.355985	−	0.934492i	$-0.615855\pi$
$853$	−3.06794e121	−0.711971	−0.355985	+	0.934492i	$0.615855\pi$
$854$	2.55770e121	0.565390
$855$	−1.96905e121	−0.414631
$856$	2.59483e120	0.0520532
$857$	−1.35952e121	−0.259825	−0.129913	−	0.991525i	$-0.541470\pi$
$857$	−1.35952e121	−0.259825	−0.129913	+	0.991525i	$0.541470\pi$
$858$	8.48193e120	0.154445
$859$	−7.13161e121	−1.23729	−0.618644	−	0.785671i	$-0.712318\pi$
$859$	−7.13161e121	−1.23729	−0.618644	+	0.785671i	$0.712318\pi$
$860$	−1.64206e121	−0.271458
$861$	2.14700e121	0.338222
$862$	7.08351e121	1.06340
$863$	1.34282e122	1.92119	0.960595	−	0.277953i	$-0.0896560\pi$
$863$	1.34282e122	1.92119	0.960595	+	0.277953i	$0.0896560\pi$
$864$	5.79329e120	0.0789960
$865$	−1.50328e122	−1.95376
$866$	3.29298e121	0.407941
$867$	7.24412e121	0.855447
$868$	−3.86314e121	−0.434883
$869$	−1.22603e121	−0.131577
$870$	4.76499e121	0.487543
$871$	−2.75879e122	−2.69132
$872$	3.43942e121	0.319927
$873$	3.76616e121	0.334047
$874$	−7.84206e121	−0.663294
$875$	−6.06437e121	−0.489160
$876$	5.80866e121	0.446843
$877$	−1.25341e122	−0.919626	−0.459813	−	0.888016i	$-0.652084\pi$
$877$	−1.25341e122	−0.919626	−0.459813	+	0.888016i	$0.652084\pi$
$878$	−3.72153e121	−0.260435
$879$	−1.18926e122	−0.793848
$880$	4.29507e120	0.0273489
$881$	3.01073e122	1.82882	0.914410	−	0.404789i	$-0.132655\pi$
$881$	3.01073e122	1.82882	0.914410	+	0.404789i	$0.132655\pi$
$882$	−6.12571e121	−0.354985
$883$	−1.25329e122	−0.692921	−0.346460	−	0.938065i	$-0.612616\pi$
$883$	−1.25329e122	−0.692921	−0.346460	+	0.938065i	$0.612616\pi$
$884$	8.34302e121	0.440103
$885$	3.57563e122	1.79973
$886$	−2.27802e122	−1.09410
$887$	−1.83684e122	−0.841862	−0.420931	−	0.907093i	$-0.638297\pi$
$887$	−1.83684e122	−0.841862	−0.420931	+	0.907093i	$0.638297\pi$
$888$	1.53913e122	0.673188
$889$	9.35652e121	0.390563
$890$	1.14338e122	0.455518
$891$	3.60205e121	0.136970
$892$	−5.59997e121	−0.203256
$893$	−1.98520e122	−0.687810
$894$	−3.86385e122	−1.27795
$895$	−4.28841e121	−0.135407
$896$	−1.40756e121	−0.0424310
$897$	9.82896e122	2.82892
$898$	−2.45357e122	−0.674265
$899$	3.77984e122	0.991851
$900$	−5.20280e120	−0.0130368
$901$	1.25378e122	0.300015
$902$	−1.89354e121	−0.0432715
$903$	1.56665e122	0.341925
$904$	−1.22227e121	−0.0254787
$905$	6.97040e122	1.38785
$906$	3.45942e122	0.657936
$907$	−3.57492e122	−0.649476	−0.324738	−	0.945804i	$-0.605276\pi$
$907$	−3.57492e122	−0.649476	−0.324738	+	0.945804i	$0.605276\pi$
$908$	2.28951e122	0.397356
$909$	−4.87988e122	−0.809111
$910$	3.19531e122	0.506168
$911$	−9.59483e122	−1.45219	−0.726097	−	0.687592i	$-0.758668\pi$
$911$	−9.59483e122	−1.45219	−0.726097	+	0.687592i	$0.758668\pi$
$912$	−1.44148e122	−0.208460
$913$	7.36236e121	0.101737
$914$	−1.36917e122	−0.180796
$915$	−1.66244e123	−2.09783
$916$	−6.21851e122	−0.749935
$917$	2.67536e122	0.308358
$918$	1.65898e122	0.182756
$919$	−1.10511e122	−0.116362	−0.0581809	−	0.998306i	$-0.518530\pi$
$919$	−1.10511e122	−0.116362	−0.0581809	+	0.998306i	$0.518530\pi$
$920$	4.97717e122	0.500942
$921$	−1.74849e123	−1.68224
$922$	−4.95612e122	−0.455836
$923$	1.24690e123	1.09638
$924$	−4.09783e121	−0.0344483
$925$	7.36588e121	0.0592029
$926$	−6.86765e122	−0.527779
$927$	−1.48830e123	−1.09365
$928$	1.37721e122	0.0967738
$929$	2.38661e123	1.60373	0.801863	−	0.597508i	$-0.203842\pi$
$929$	2.38661e123	1.60373	0.801863	+	0.597508i	$0.203842\pi$
$930$	2.51094e123	1.61359
$931$	−8.12231e122	−0.499192
$932$	−1.16594e123	−0.685354
$933$	2.46917e123	1.38824
$934$	−5.17813e122	−0.278469
$935$	1.22995e122	0.0632710
$936$	7.13296e122	0.351012
$937$	4.31860e122	0.203306	0.101653	−	0.994820i	$-0.467587\pi$
$937$	4.31860e122	0.203306	0.101653	+	0.994820i	$0.467587\pi$
$938$	1.33284e123	0.600288
$939$	2.00507e123	0.863988
$940$	1.25996e123	0.519458
$941$	−4.12168e123	−1.62594	−0.812970	−	0.582306i	$-0.802151\pi$
$941$	−4.12168e123	−1.62594	−0.812970	+	0.582306i	$0.802151\pi$
$942$	1.47640e123	0.557305
$943$	−2.19425e123	−0.792594
$944$	1.03345e123	0.357233
$945$	6.35377e122	0.210190
$946$	−1.38170e122	−0.0437453
$947$	−1.04553e123	−0.316819	−0.158409	−	0.987374i	$-0.550637\pi$
$947$	−1.04553e123	−0.316819	−0.158409	+	0.987374i	$0.550637\pi$
$948$	−2.61151e123	−0.757435
$949$	−3.81118e123	−1.05806
$950$	−6.89858e121	−0.0183329
$951$	1.31175e123	0.333702
$952$	−4.03072e122	−0.0981633
$953$	5.43588e123	1.26740	0.633701	−	0.773578i	$-0.281535\pi$
$953$	5.43588e123	1.26740	0.633701	+	0.773578i	$0.281535\pi$
$954$	1.07194e123	0.239283
$955$	1.98807e123	0.424905
$956$	−3.26354e123	−0.667862
$957$	4.00947e122	0.0785673
$958$	4.30804e123	0.808372
$959$	−1.80183e123	−0.323774
$960$	9.14875e122	0.157436
$961$	1.38504e124	2.28267
$962$	−1.00985e124	−1.59401
$963$	6.35290e122	0.0960464
$964$	−4.79967e123	−0.695047
$965$	−6.77129e123	−0.939265
$966$	−4.74861e123	−0.630981
$967$	−1.64451e123	−0.209333	−0.104666	−	0.994507i	$-0.533378\pi$
$967$	−1.64451e123	−0.209333	−0.104666	+	0.994507i	$0.533378\pi$
$968$	−2.86309e123	−0.349146
$969$	−4.12787e123	−0.482269
$970$	−3.16938e123	−0.354770
$971$	−1.16021e124	−1.24434	−0.622168	−	0.782884i	$-0.713748\pi$
$971$	−1.16021e124	−1.24434	−0.622168	+	0.782884i	$0.713748\pi$
$972$	5.49837e123	0.565047
$973$	−1.00995e123	−0.0994533
$974$	2.54699e123	0.240343
$975$	8.64643e122	0.0781890
$976$	−4.80487e123	−0.416404
$977$	1.45072e123	0.120493	0.0602463	−	0.998184i	$-0.480811\pi$
$977$	1.45072e123	0.120493	0.0602463	+	0.998184i	$0.480811\pi$
$978$	−7.30021e122	−0.0581129
$979$	9.62089e122	0.0734063
$980$	5.15504e123	0.377007
$981$	8.42069e123	0.590315
$982$	1.30220e124	0.875089
$983$	2.90910e124	1.87408	0.937040	−	0.349221i	$-0.113554\pi$
$983$	2.90910e124	1.87408	0.937040	+	0.349221i	$0.113554\pi$
$984$	−4.03334e123	−0.249097
$985$	2.85208e122	0.0168872
$986$	3.94380e123	0.223884
$987$	−1.20210e124	−0.654302
$988$	9.45786e123	0.493605
$989$	−1.60113e124	−0.801272
$990$	1.05156e123	0.0504629
$991$	1.84920e123	0.0850995	0.0425497	−	0.999094i	$-0.486452\pi$
$991$	1.84920e123	0.0850995	0.0425497	+	0.999094i	$0.486452\pi$
$992$	7.25726e123	0.320286
$993$	2.44707e124	1.03575
$994$	−6.02406e123	−0.244543
$995$	−1.46161e124	−0.569079
$996$	1.56822e124	0.585660
$997$	4.67732e123	0.167551	0.0837757	−	0.996485i	$-0.473302\pi$
$997$	4.67732e123	0.167551	0.0837757	+	0.996485i	$0.473302\pi$
$998$	1.12388e124	0.386192
$999$	−2.00806e124	−0.661925

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2.84.a.b.1.1	✓	3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2.84.a.b.1.1	✓	3	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:	\( k \)	\(=\)	\( 84 \)
Character orbit:	\([\chi]\)	\(=\)	2.a (trivial)

\(f(q)\)	\(=\)	\(q+2.19902e12 q^{2} -8.12053e19 q^{3} +4.83570e24 q^{4} -9.96318e28 q^{5} -1.78572e32 q^{6} -5.66053e34 q^{7} +1.06338e37 q^{8} +2.60347e39 q^{9} +O(q^{10})\)	\(q+2.19902e12 q^{2} -8.12053e19 q^{3} +4.83570e24 q^{4} -9.96318e28 q^{5} -1.78572e32 q^{6} -5.66053e34 q^{7} +1.06338e37 q^{8} +2.60347e39 q^{9} -2.19093e41 q^{10} -1.84354e42 q^{11} -3.92685e44 q^{12} +2.57649e46 q^{13} -1.24476e47 q^{14} +8.09064e48 q^{15} +2.33840e49 q^{16} +6.69632e50 q^{17} +5.72509e51 q^{18} +7.59111e52 q^{19} -4.81790e53 q^{20} +4.59665e54 q^{21} -4.05399e54 q^{22} -4.69781e56 q^{23} -8.63523e56 q^{24} -4.13261e56 q^{25} +5.66575e58 q^{26} +1.12662e59 q^{27} -2.73726e59 q^{28} +2.67824e60 q^{29} +1.77915e61 q^{30} +1.41131e62 q^{31} +5.14220e61 q^{32} +1.49705e62 q^{33} +1.47254e63 q^{34} +5.63969e63 q^{35} +1.25896e64 q^{36} -1.78238e65 q^{37} +1.66930e65 q^{38} -2.09224e66 q^{39} -1.05947e66 q^{40} +4.67079e66 q^{41} +1.01081e67 q^{42} +3.40824e67 q^{43} -8.91482e66 q^{44} -2.59388e68 q^{45} -1.03306e69 q^{46} -2.61516e69 q^{47} -1.89891e69 q^{48} -1.06998e70 q^{49} -9.08771e68 q^{50} -5.43777e70 q^{51} +1.24591e71 q^{52} +1.87235e71 q^{53} +2.47746e71 q^{54} +1.83675e71 q^{55} -6.01931e71 q^{56} -6.16439e72 q^{57} +5.88951e72 q^{58} +4.41947e73 q^{59} +3.91239e73 q^{60} -2.05477e74 q^{61} +3.10351e74 q^{62} -1.47370e74 q^{63} +1.13078e74 q^{64} -2.56700e75 q^{65} +3.29206e74 q^{66} -1.07076e76 q^{67} +3.23814e75 q^{68} +3.81487e76 q^{69} +1.24018e76 q^{70} +4.83952e76 q^{71} +2.76848e76 q^{72} -1.47922e77 q^{73} -3.91949e77 q^{74} +3.35590e76 q^{75} +3.67084e77 q^{76} +1.04354e77 q^{77} -4.60089e78 q^{78} +6.65039e78 q^{79} -2.32979e78 q^{80} -1.95388e79 q^{81} +1.02712e79 q^{82} -3.99360e79 q^{83} +2.22281e79 q^{84} -6.67166e79 q^{85} +7.49481e79 q^{86} -2.17487e80 q^{87} -1.96039e79 q^{88} -5.21870e80 q^{89} -5.70401e80 q^{90} -1.45843e81 q^{91} -2.27172e81 q^{92} -1.14606e82 q^{93} -5.75080e81 q^{94} -7.56316e81 q^{95} -4.17574e81 q^{96} +1.44659e82 q^{97} -2.35290e82 q^{98} -4.79960e81 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 6597069766656 q^{2} - 16\!\cdots\!24 q^{3}+ \cdots + 29\!\cdots\!11 q^{9}+O(q^{10}) \) 3 * q + 6597069766656 * q^2 - 16865576978405999724 * q^3 + 14507109835375550096474112 * q^4 - 89124088407700875878949881670 * q^5 - 37087795993817224716679693467648 * q^6 + 72912428890136593011598868334609288 * q^7 + 31901471898837980949691369446728269824 * q^8 + 2903564094220119569530206456786641290911 * q^9	\( 3 q + 6597069766656 q^{2} - 16\!\cdots\!24 q^{3}+ \cdots - 90\!\cdots\!68 q^{99}+O(q^{100}) \) 3 * q + 6597069766656 * q^2 - 16865576978405999724 * q^3 + 14507109835375550096474112 * q^4 - 89124088407700875878949881670 * q^5 - 37087795993817224716679693467648 * q^6 + 72912428890136593011598868334609288 * q^7 + 31901471898837980949691369446728269824 * q^8 + 2903564094220119569530206456786641290911 * q^9 - 195985943038406643942730238257008570531840 * q^10 - 24978774206464004009733924371834472527507364 * q^11 - 81556925887572376760126540365236732948381696 * q^12 - 13385495184723470250431662175810956861650939774 * q^13 + 160336126748191868906331795541891520971696766976 * q^14 - 1543056839506723738737512531611763740851131609640 * q^15 + 70152078591883340073776871970381584943484762062848 * q^16 + 149312255183231021040154145354101178805710731266198 * q^17 + 6385004967175821402287019425805650736202735127887872 * q^18 + 55293849727885716244659038787880400218220271579060900 * q^19 - 430977646502745808733769149575239604851692608872775680 * q^20 + 3645719950686395996325484168686099082668843870511440096 * q^21 - 54928905375196799499786276269448398351899949454933884928 * q^22 - 805827328635818601213715040041310117378914012956593526504 * q^23 - 179345576678102595081079770977441619615326740707847176192 * q^24 - 5030521506659548631822003886373561268610311776807186370475 * q^25 - 29435015198286225166967254491150470143619882443261763125248 * q^26 + 265222728292653992247626325353300797149922016654790765501960 * q^27 + 352582871424406990891936946778819932443205506964916642250752 * q^28 + 3816821385192456910492790601757082957064381440388168733398930 * q^29 - 3393217874713855605752045901651298015147125487613766826721280 * q^30 + 27306736762531164695904395012386760223323473997636656114733856 * q^31 + 154266052248863066452028360864751609842131487403148112188932096 * q^32 - 1869543607361303438021906043202257025987688880718639325041794288 * q^33 + 328341121486839666165836778032483790052134875558177321093431296 * q^34 + 14534999710313034659766439067001754131908491908682934888734333680 * q^35 + 14040774409634665679236919316045807802362404147214739351057465344 * q^36 - 52923027520109801062478020730582335084559828742299509796837572902 * q^37 + 121592461440618317054129411207547801649483432835228080072871116800 * q^38 - 2402178840747166455209643780042189831769498863330340255477707188808 * q^39 - 947729867282607115628856150138565833831415134900987376816210575360 * q^40 - 1630826972263179623457970100158554268531829459440506302206562479314 * q^41 + 8017022954789275420837524826046741939137681828852067331165747412992 * q^42 - 33553307012363163544032667059590733336999143846880512810825154723204 * q^43 - 120789940322073018068711022370253698499067178174972959543289505120256 * q^44 - 899390150496328129010638564824906173852269254482975703134378310929790 * q^45 - 1772033035629509215437502465864067810885814745930081005516794477150208 * q^46 - 4629910079963350350221297721597969688645786047253478838346456323692112 * q^47 - 394385093895532014185455659374224235518515431267571462303021986217984 * q^48 - 25904312213759912896573562369189009500767562783277344044247210951504581 * q^49 - 11062233780698832680856090411601584992119582950272264580591137272627200 * q^50 - 115003426553005764529308651997450424423206873228307379757058913903279384 * q^51 - 64728282948557973677781246741709000029118370892377010273402322887376896 * q^52 + 1955489350374820934426361520356408182849427388960005011763112205433066 * q^53 + 583230947416495520638665011722794275537738276087139153691506290636881920 * q^54 + 2108797874787371324281515134524355674706327291312898542556270469340517960 * q^55 + 775337933771571692582215196932671567522046479268565605290553175760175104 * q^56 + 15322000670469704774223981579586808538599472097150639315439774454541455600 * q^57 + 8393278988326410801385336257701289695718651111903517826702411402953359360 * q^58 + 17515422328677368763527856098594833667145631862459457466418222357737323660 * q^59 - 7461765017650501214602908995933776573955387698027100979270449411716546560 * q^60 - 43640380317138565765125545690879749580949226301206837258015611765251644494 * q^61 + 60048149174042762521445970801083724832034804351465379483433131655154368512 * q^62 - 457195494726045291713470857330955951313042916931677671039326900967012349144 * q^63 + 339234636437449791279993120142640355038876908200118839959348390648182996992 * q^64 - 4296913059058527224354407223174652737979058717517404072080357642037560619140 * q^65 - 4111169869856083518585062086214890004481713070750413249881098393661237886976 * q^66 + 141032868579017039252603961064071790283346383814419962362012801355450268628 * q^67 + 722029761903584901415847257151246901209113305857741485806171328892362555392 * q^68 + 8086087325412092464604398692880698235254488464939834057062449877128558876832 * q^69 + 31962802382419946386540207509068434826844079519986597775570617337831080591360 * q^70 + 182924642179429081351287474788615465829562015176370019587922663022657154084296 * q^71 + 30875989452746033356910691685482205465112656564337702401001511254596295589888 * q^72 - 263140135925842921903280041748503897229972912722022861455020469008131787988914 * q^73 - 116378968270939943880913485699410511986430903809811049684095477677110176251904 * q^74 - 219757760618324786335711731704583191459417224730184785076731310005445547763700 * q^75 + 267384650407729519496214980038734682337907814052411986234291580661246040473600 * q^76 - 343502161164788220719179625219521720334686808755722455114874104110835966197344 * q^77 - 5282447134797963330454358455854603687768954587296248341416467063293162098262016 * q^78 - 12034695994962253192018572414246476985958695027260336925439527447631547969548080 * q^79 - 2084080018135663591036327751031606335820235971481174518545639948196118234398720 * q^80 - 26829845454336398974126827639624302488735247553951918922512836067848733015875877 * q^81 - 3586226437788188460915494917492139518968529645233322509137448184439964935651328 * q^82 - 866285839618831283785116105591092087807254129011655636887946324521625748147484 * q^83 + 17629619917875826946065308701418928945125358538840626385585605987428989700931584 * q^84 + 999297217658610049915895867064394982963183108507668520498941294598608198173780 * q^85 - 73784502420862594609520517620018525607458954036403934280807974046874169516228608 * q^86 - 662304833857716625077531708289012630908112375820084997692130187355696595851208840 * q^87 - 265619887804976803598915032040941587597587362185479079384452874624780322379661312 * q^88 - 2902141249177927061116331049722970422359552504894459368572075199387222942405249570 * q^89 - 1977779856755838710879007473663666167277561233096029201267076883832405709899694080 * q^90 - 4775994167494808746040520734163298259656337652284546033077320243620956097336065104 * q^91 - 3896741854955696564651362008476430146191814207531134474918619063354144071473954816 * q^92 - 20606753022758608907040478217479874066388188968728538263924843766516850954617630848 * q^93 - 10181279936954027331988797479394607448439272243797402743258163521408005638742605824 * q^94 - 43227063853654043926776337745023206430945564224810828285113141330096591326575357000 * q^95 - 867261993119334011621140549565649365464384194439964291038400651660904451610247168 * q^96 - 37410452818623389818885816143993639408327020071141525834391520165010920135161558682 * q^97 - 56964184977137759788335145386948133810396144154523099324304459763673711303261683712 * q^98 - 90303617227381471027183650166443552736594841755621740583582132261899845439070414068 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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