LMFDB - Embedded newform 2.74.a.a.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2,74,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, 74, names="a")

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

chi := DirichletCharacter("2.1");

S:= CuspForms(chi, 74);

N := Newforms(S);

Level:	$ N $	$=$	$ 2 $
Weight:	$ k $	$=$	$ 74 $
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:	$67.4967947474$
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} - 413501459186944860372404680x - 2966140105783309949999568694815716833028 $ x^3 - x^2 - 413501459186944860372404680*x - 2966140105783309949999568694815716833028
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{23}\cdot 3^{7}\cdot 5^{3} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$2.32599e13$ 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)

$f(q)$	$=$	$q-6.87195e10 q^{2} +3.00585e17 q^{3} +4.72237e21 q^{4} -1.10375e25 q^{5} -2.06560e28 q^{6} +7.83423e29 q^{7} -3.24519e32 q^{8} +2.27660e34 q^{9} +O(q^{10})$	\(q-6.87195e10 q^{2} +3.00585e17 q^{3} +4.72237e21 q^{4} -1.10375e25 q^{5} -2.06560e28 q^{6} +7.83423e29 q^{7} -3.24519e32 q^{8} +2.27660e34 q^{9} +7.58489e35 q^{10} +3.40887e36 q^{11} +1.41947e39 q^{12} +3.80927e40 q^{13} -5.38364e40 q^{14} -3.31769e42 q^{15} +2.23007e43 q^{16} -2.38211e44 q^{17} -1.56447e45 q^{18} -4.58511e46 q^{19} -5.21229e46 q^{20} +2.35485e47 q^{21} -2.34256e47 q^{22} -5.99384e49 q^{23} -9.75453e49 q^{24} -9.36966e50 q^{25} -2.61771e51 q^{26} -1.34720e52 q^{27} +3.69961e51 q^{28} +3.66647e53 q^{29} +2.27990e53 q^{30} +1.75180e54 q^{31} -1.53250e54 q^{32} +1.02465e54 q^{33} +1.63697e55 q^{34} -8.64700e54 q^{35} +1.07509e56 q^{36} +1.64193e57 q^{37} +3.15086e57 q^{38} +1.14501e58 q^{39} +3.58186e57 q^{40} +1.95654e58 q^{41} -1.61824e58 q^{42} -7.77238e59 q^{43} +1.60979e58 q^{44} -2.51279e59 q^{45} +4.11894e60 q^{46} -5.34256e60 q^{47} +6.70326e60 q^{48} -4.86080e61 q^{49} +6.43878e61 q^{50} -7.16026e61 q^{51} +1.79888e62 q^{52} +5.17851e62 q^{53} +9.25787e62 q^{54} -3.76253e61 q^{55} -2.54235e62 q^{56} -1.37821e64 q^{57} -2.51958e64 q^{58} -1.88861e63 q^{59} -1.56674e64 q^{60} +1.49443e65 q^{61} -1.20383e65 q^{62} +1.78354e64 q^{63} +1.05312e65 q^{64} -4.20447e65 q^{65} -7.04137e64 q^{66} -8.11124e66 q^{67} -1.12492e66 q^{68} -1.80166e67 q^{69} +5.94218e65 q^{70} -2.29663e67 q^{71} -7.38798e66 q^{72} -1.30543e68 q^{73} -1.12832e68 q^{74} -2.81638e68 q^{75} -2.16526e68 q^{76} +2.67059e66 q^{77} -7.86844e68 q^{78} -7.20690e67 q^{79} -2.46144e68 q^{80} -5.58811e69 q^{81} -1.34452e69 q^{82} -1.10136e70 q^{83} +1.11205e69 q^{84} +2.62925e69 q^{85} +5.34114e70 q^{86} +1.10208e71 q^{87} -1.10624e69 q^{88} +1.46084e71 q^{89} +1.72677e70 q^{90} +2.98427e70 q^{91} -2.83051e71 q^{92} +5.26565e71 q^{93} +3.67138e71 q^{94} +5.06080e71 q^{95} -4.60645e71 q^{96} +7.46916e71 q^{97} +3.34032e72 q^{98} +7.76062e70 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 206158430208 q^{2} - 30\!\cdots\!72 q^{3}+ \cdots + 74\!\cdots\!59 q^{9}+O(q^{10}) $ 3 * q - 206158430208 * q^2 - 304039201019733972 * q^3 + 14167099448608935641088 * q^4 - 32711891603319524297119950 * q^5 + 20893414801307636165762875392 * q^6 - 2317351391358079018994287149864 * q^7 - 973555660975280180349468061728768 * q^8 + 74999430902894237070706277077434759 * q^9	$ 3 q - 206158430208 q^{2} - 30\!\cdots\!72 q^{3}+ \cdots + 32\!\cdots\!68 q^{99}+O(q^{100}) $ 3 * q - 206158430208 * q^2 - 304039201019733972 * q^3 + 14167099448608935641088 * q^4 - 32711891603319524297119950 * q^5 + 20893414801307636165762875392 * q^6 - 2317351391358079018994287149864 * q^7 - 973555660975280180349468061728768 * q^8 + 74999430902894237070706277077434759 * q^9 + 2247944074024869790310521155826483200 * q^10 - 80375859598797955703316945252313090044 * q^11 - 1435784532374058165872294155193010880512 * q^12 + 15026661416812586037400802096858217302538 * q^13 + 159247175027568742591427617911982893563904 * q^14 + 7424951702099224865385711195171330840721800 * q^15 + 66902235595591869424607154817945084517941248 * q^16 - 2021347643337102701650698954881277124608770634 * q^17 - 5153921647144679999448868794711947991658266624 * q^18 - 41519603636932196567332785885639339838588921380 * q^19 - 154477540498781101440673056783853843115094835200 * q^20 + 2186519362115879326463070410595449406900134231136 * q^21 + 5523387013835598410518447337300915041466931216384 * q^22 + 78904625597138588218784441638852494338574996350088 * q^23 + 98666361770387728979571947344734884793139259768832 * q^24 + 981710467323228821808618065764062137601115897768125 * q^25 - 1032624309652401305469162845602788282612192764755968 * q^26 + 8808207209598604044615652223279905336946557309792440 * q^27 - 10943382539580730365152382542130405349894665057337344 * q^28 + 166169304839024523153256155301347408902947424090145210 * q^29 - 510238795758331285500506112143391025243141056548044800 * q^30 + 954831074549949113941638258046298891637893269618118496 * q^31 - 4597486622597666575075041081450927550856217366550806528 * q^32 + 17544371641343847605198741899708079964205455873834669456 * q^33 + 138905952351672454511727955628103437006521386684722970624 * q^34 + 944528033393088066738035187184051695420046345746643971600 * q^35 + 354174798730125638048291031959724069834002175330053259264 * q^36 + 95831145035300740325039173416127783864165954459868024466 * q^37 + 2853205436216103072418204437238261770524309377840243015680 * q^38 + 20048825363764869028111320157141908997200830310277187046888 * q^39 + 10615615750540485736808788209840051152371953297960153907200 * q^40 + 150686231920032912821976395324429812389071948843348708195646 * q^41 - 150256466437735729111062316244043953424938772171827598852096 * q^42 - 473903333795313868852861303848307239502353736089051202446492 * q^43 - 379564265401199915100261019494491376223599255037612470042624 * q^44 - 3350842048629098689796948549122862280644512526482879102711350 * q^45 - 5422284583085355321268641115399873698435276169071157227552768 * q^46 - 12516424326520457880934881888127294200274501425051317572353264 * q^47 - 6780300752305919315311567454794725887629773534092511361892352 * q^48 + 80205164513526274948509534215913453598538485989498574623052011 * q^49 - 67462629620706311212682018614582786129738314784316420259840000 * q^50 + 514251632907479503542992104878952048928310680088916651551144216 * q^51 + 70961402224186251757724165733796369283701974007595263693160448 * q^52 + 1430548926948567355941996145547633585160394945423663769186222658 * q^53 - 605295390425878746542040819019150132418581186325572325568675840 * q^54 - 7121556178756880336995070499297110193922212727411086674935031400 * q^55 + 752023521841866599521977937198902930320336375458205717112029184 * q^56 - 15654317649185594603288320010783267868078052464546138261971761680 * q^57 - 11419067678122637943763679726879746335559974791593859725456834560 * q^58 - 38710586306395695712277475638393838858193803462160314268223532780 * q^59 + 35063343054919302252133003889663566655347220579019825099885772800 * q^60 - 133023502656151161720833761205788214903429689958710055454248963814 * q^61 - 65615491814345109805496223535540201494812791477573269589963309056 * q^62 - 676013503772547172347240007080849436653347156788941846276439197192 * q^63 + 315936875005671560093754083051011296956685286201647333762932932608 * q^64 + 1304279076912397427943938897940602441228625233151093819412708578300 * q^65 - 1205640038855066671282184256633457846291444537646256118791841775616 * q^66 - 10079574725514314413922516603802294422053580576623992539839093997844 * q^67 - 9545544361122679728510707485946294407171287912567280346400779403264 * q^68 - 57254624867981027449877853695190995327525407937353126334506438578912 * q^69 - 64907472217256146545403624452043845833639232604578312956440844697600 * q^70 - 115560233707768569360415193898496587754138245400713479870885379282024 * q^71 - 24338706841812351126216692015313690705936951869366988071633424482304 * q^72 - 154467257799518470489462616345503055869489343767852516092429168112482 * q^73 - 6585466141837591123530106555858262890456788491548136152921565822976 * q^74 - 952496562905106180077615512164377636529129991330375732809810503347500 * q^75 - 196070784597081226953620923087686701828623448812959213840608243220480 * q^76 - 1800719846849724861947803912683649646585331632872965881331191256968928 * q^77 - 1377744788169366654551382795556961279583771547626976816980140457197568 * q^78 - 4090300229098013083258477274117496841157332448206465760698517921562000 * q^79 - 729499559607582089016771340266454481446474435878051272680809902899200 * q^80 - 15201171092964708833522221028549040215131141432253228096270731424296917 * q^81 - 10355079008864202365024123008038293664935674369170683661186347833491456 * q^82 + 4825306524476108361839066204321180630013251338979638337731931270725788 * q^83 + 10325545749801545229163644801378853355946547476486310873919351376838656 * q^84 + 64402214916599555092605132019399363126870275972818152260490003075220100 * q^85 + 32566389121859913996452357376838376617962377784414237730834533278810112 * q^86 + 142543957488352500896861000833280505529834792013096113880266858327752360 * q^87 + 26083457706054687272217562236679342608550252540744140940077596896395264 * q^88 + 451463179833471932378016997715778802210673362338548837237321638477742670 * q^89 + 230268112206777928106149486385237487700482481649700794401073170848153600 * q^90 + 422354934089645630580068981961457451511973101688314707373850544534133456 * q^91 + 372616559263305534102214189136054711956961240302220591827410698788405248 * q^92 + 571168450314051543320826159340295464004746879040928540630191772427149696 * q^93 + 860122130324227073176972473842071348402391325492812865519478122221666304 * q^94 - 51353744965069329589794354056658553367168025175850659034300728742247000 * q^95 + 465938719811169920743646308301460897290471172557018837405377160200323072 * q^96 + 76854610208052175214348870937789175369657249934277291200976504477234726 * q^97 - 5511656936894321608648840534424660575554180971556009239113982639232516096 * q^98 + 3215801878115629026673420709123093980129069916698003588659485833337177268 * 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 $

$2$	−6.87195e10	−0.707107
$2$	−6.87195e10	−0.707107
$3$	3.00585e17	1.15622	0.578111	−	0.815958i	$-0.303790\pi$
$3$	3.00585e17	1.15622	0.578111	+	0.815958i	$0.303790\pi$
$4$	4.72237e21	0.500000
$5$	−1.10375e25	−0.339206	−0.169603	−	0.985512i	$-0.554249\pi$
$5$	−1.10375e25	−0.339206	−0.169603	+	0.985512i	$0.554249\pi$
$6$	−2.06560e28	−0.817572
$7$	7.83423e29	0.111665	0.0558326	−	0.998440i	$-0.482219\pi$
$7$	7.83423e29	0.111665	0.0558326	+	0.998440i	$0.482219\pi$
$8$	−3.24519e32	−0.353553
$9$	2.27660e34	0.336848
$10$	7.58489e35	0.239855
$11$	3.40887e36	0.0332489	0.0166245	−	0.999862i	$-0.494708\pi$
$11$	3.40887e36	0.0332489	0.0166245	+	0.999862i	$0.494708\pi$
$12$	1.41947e39	0.578111
$13$	3.80927e40	0.835429	0.417714	−	0.908578i	$-0.362831\pi$
$13$	3.80927e40	0.835429	0.417714	+	0.908578i	$0.362831\pi$
$14$	−5.38364e40	−0.0789592
$15$	−3.31769e42	−0.392198
$16$	2.23007e43	0.250000
$17$	−2.38211e44	−0.292130	−0.146065	−	0.989275i	$-0.546661\pi$
$17$	−2.38211e44	−0.292130	−0.146065	+	0.989275i	$0.546661\pi$
$18$	−1.56447e45	−0.238188
$19$	−4.58511e46	−0.970160	−0.485080	−	0.874470i	$-0.661210\pi$
$19$	−4.58511e46	−0.970160	−0.485080	+	0.874470i	$0.661210\pi$
$20$	−5.21229e46	−0.169603
$21$	2.35485e47	0.129110
$22$	−2.34256e47	−0.0235105
$23$	−5.99384e49	−1.18752	−0.593758	−	0.804644i	$-0.702356\pi$
$23$	−5.99384e49	−1.18752	−0.593758	+	0.804644i	$0.702356\pi$
$24$	−9.75453e49	−0.408786
$25$	−9.36966e50	−0.884939
$26$	−2.61771e51	−0.590737
$27$	−1.34720e52	−0.766750
$28$	3.69961e51	0.0558326
$29$	3.66647e53	1.53717	0.768583	−	0.639750i	$-0.220962\pi$
$29$	3.66647e53	1.53717	0.768583	+	0.639750i	$0.220962\pi$
$30$	2.27990e53	0.277326
$31$	1.75180e54	0.643847	0.321924	−	0.946766i	$-0.395671\pi$
$31$	1.75180e54	0.643847	0.321924	+	0.946766i	$0.395671\pi$
$32$	−1.53250e54	−0.176777
$33$	1.02465e54	0.0384431
$34$	1.63697e55	0.206567
$35$	−8.64700e54	−0.0378776
$36$	1.07509e56	0.168424
$37$	1.64193e57	0.946217	0.473109	−	0.881004i	$-0.343132\pi$
$37$	1.64193e57	0.946217	0.473109	+	0.881004i	$0.343132\pi$
$38$	3.15086e57	0.686007
$39$	1.14501e58	0.965941
$40$	3.58186e57	0.119928
$41$	1.95654e58	0.265998	0.132999	−	0.991116i	$-0.457539\pi$
$41$	1.95654e58	0.265998	0.132999	+	0.991116i	$0.457539\pi$
$42$	−1.61824e58	−0.0912944
$43$	−7.77238e59	−1.85761	−0.928806	−	0.370565i	$-0.879164\pi$
$43$	−7.77238e59	−1.85761	−0.928806	+	0.370565i	$0.879164\pi$
$44$	1.60979e58	0.0166245
$45$	−2.51279e59	−0.114261
$46$	4.11894e60	0.839700
$47$	−5.34256e60	−0.496795	−0.248398	−	0.968658i	$-0.579904\pi$
$47$	−5.34256e60	−0.496795	−0.248398	+	0.968658i	$0.579904\pi$
$48$	6.70326e60	0.289055
$49$	−4.86080e61	−0.987531
$50$	6.43878e61	0.625746
$51$	−7.16026e61	−0.337767
$52$	1.79888e62	0.417714
$53$	5.17851e62	0.599979	0.299989	−	0.953943i	$-0.403017\pi$
$53$	5.17851e62	0.599979	0.299989	+	0.953943i	$0.403017\pi$
$54$	9.25787e62	0.542174
$55$	−3.76253e61	−0.0112782
$56$	−2.54235e62	−0.0394796
$57$	−1.37821e64	−1.12172
$58$	−2.51958e64	−1.08694
$59$	−1.88861e63	−0.0436560	−0.0218280	−	0.999762i	$-0.506949\pi$
$59$	−1.88861e63	−0.0436560	−0.0218280	+	0.999762i	$0.506949\pi$
$60$	−1.56674e64	−0.196099
$61$	1.49443e65	1.02315	0.511573	−	0.859240i	$-0.329063\pi$
$61$	1.49443e65	1.02315	0.511573	+	0.859240i	$0.329063\pi$
$62$	−1.20383e65	−0.455269
$63$	1.78354e64	0.0376143
$64$	1.05312e65	0.125000
$65$	−4.20447e65	−0.283383
$66$	−7.04137e64	−0.0271834
$67$	−8.11124e66	−1.80866	−0.904330	−	0.426834i	$-0.859629\pi$
$67$	−8.11124e66	−1.80866	−0.904330	+	0.426834i	$0.859629\pi$
$68$	−1.12492e66	−0.146065
$69$	−1.80166e67	−1.37303
$70$	5.94218e65	0.0267835
$71$	−2.29663e67	−0.616823	−0.308412	−	0.951253i	$-0.599797\pi$
$71$	−2.29663e67	−0.616823	−0.308412	+	0.951253i	$0.599797\pi$
$72$	−7.38798e66	−0.119094
$73$	−1.30543e68	−1.27195	−0.635974	−	0.771711i	$-0.719401\pi$
$73$	−1.30543e68	−1.27195	−0.635974	+	0.771711i	$0.719401\pi$
$74$	−1.12832e68	−0.669077
$75$	−2.81638e68	−1.02319
$76$	−2.16526e68	−0.485080
$77$	2.67059e66	0.00371275
$78$	−7.86844e68	−0.683023
$79$	−7.20690e67	−0.0392970	−0.0196485	−	0.999807i	$-0.506255\pi$
$79$	−7.20690e67	−0.0392970	−0.0196485	+	0.999807i	$0.506255\pi$
$80$	−2.46144e68	−0.0848016
$81$	−5.58811e69	−1.22338
$82$	−1.34452e69	−0.188089
$83$	−1.10136e70	−0.989876	−0.494938	−	0.868928i	$-0.664809\pi$
$83$	−1.10136e70	−0.989876	−0.494938	+	0.868928i	$0.664809\pi$
$84$	1.11205e69	0.0645549
$85$	2.62925e69	0.0990924
$86$	5.34114e70	1.31353
$87$	1.10208e71	1.77731
$88$	−1.10624e69	−0.0117553
$89$	1.46084e71	1.02770	0.513851	−	0.857879i	$-0.328218\pi$
$89$	1.46084e71	1.02770	0.513851	+	0.857879i	$0.328218\pi$
$90$	1.72677e70	0.0807949
$91$	2.98427e70	0.0932883
$92$	−2.83051e71	−0.593758
$93$	5.26565e71	0.744430
$94$	3.67138e71	0.351287
$95$	5.06080e71	0.329085
$96$	−4.60645e71	−0.204393
$97$	7.46916e71	0.227040	0.113520	−	0.993536i	$-0.463787\pi$
$97$	7.46916e71	0.227040	0.113520	+	0.993536i	$0.463787\pi$
$98$	3.34032e72	0.698290
$99$	7.76062e70	0.0111998
$100$	−4.42469e72	−0.442469
$101$	−2.51591e73	−1.74971	−0.874854	−	0.484387i	$-0.839043\pi$
$101$	−2.51591e73	−1.74971	−0.874854	+	0.484387i	$0.839043\pi$
$102$	4.92049e72	0.238837
$103$	−2.90445e73	−0.987428	−0.493714	−	0.869624i	$-0.664361\pi$
$103$	−2.90445e73	−0.987428	−0.493714	+	0.869624i	$0.664361\pi$
$104$	−1.23618e73	−0.295369
$105$	−2.59916e72	−0.0437949
$106$	−3.55865e73	−0.424249
$107$	−5.02253e73	−0.425025	−0.212513	−	0.977158i	$-0.568165\pi$
$107$	−5.02253e73	−0.425025	−0.212513	+	0.977158i	$0.568165\pi$
$108$	−6.36196e73	−0.383375
$109$	1.37500e73	0.0591885	0.0295942	−	0.999562i	$-0.490578\pi$
$109$	1.37500e73	0.0591885	0.0295942	+	0.999562i	$0.490578\pi$
$110$	2.58559e72	0.00797492
$111$	4.93538e74	1.09404
$112$	1.74709e73	0.0279163
$113$	2.27517e74	0.262816	0.131408	−	0.991328i	$-0.458050\pi$
$113$	2.27517e74	0.262816	0.131408	+	0.991328i	$0.458050\pi$
$114$	9.47102e74	0.793176
$115$	6.61568e74	0.402813
$116$	1.73144e75	0.768583
$117$	8.67217e74	0.281413
$118$	1.29784e74	0.0308694
$119$	−1.86620e74	−0.0326208
$120$	1.07665e75	0.138663
$121$	−1.04999e76	−0.998895
$122$	−1.02697e76	−0.723473
$123$	5.88106e75	0.307552
$124$	8.27265e75	0.321924
$125$	2.20281e76	0.639383
$126$	−1.22564e75	−0.0265973
$127$	−3.15624e76	−0.513256	−0.256628	−	0.966510i	$-0.582611\pi$
$127$	−3.15624e76	−0.513256	−0.256628	+	0.966510i	$0.582611\pi$
$128$	−7.23701e75	−0.0883883
$129$	−2.33626e77	−2.14781
$130$	2.88929e76	0.200382
$131$	−2.21932e77	−1.16364	−0.581820	−	0.813318i	$-0.697659\pi$
$131$	−2.21932e77	−1.16364	−0.581820	+	0.813318i	$0.697659\pi$
$132$	4.83879e75	0.0192216
$133$	−3.59208e76	−0.108333
$134$	5.57400e77	1.27892
$135$	1.48696e77	0.260087
$136$	7.73039e76	0.103284
$137$	1.27232e78	1.30105	0.650526	−	0.759484i	$-0.274549\pi$
$137$	1.27232e78	1.30105	0.650526	+	0.759484i	$0.274549\pi$
$138$	1.23809e78	0.970880
$139$	−5.43939e75	−0.00327726	−0.00163863	−	0.999999i	$-0.500522\pi$
$139$	−5.43939e75	−0.00327726	−0.00163863	+	0.999999i	$0.500522\pi$
$140$	−4.08343e76	−0.0189388
$141$	−1.60589e78	−0.574405
$142$	1.57823e78	0.436160
$143$	1.29853e77	0.0277771
$144$	5.07698e77	0.0842121
$145$	−4.04685e78	−0.521417
$146$	8.97085e78	0.899403
$147$	−1.46108e79	−1.14180
$148$	7.75378e78	0.473109
$149$	−3.22048e79	−1.53682	−0.768408	−	0.639960i	$-0.778951\pi$
$149$	−3.22048e79	−1.53682	−0.768408	+	0.639960i	$0.778951\pi$
$150$	1.93540e79	0.723501
$151$	−5.09160e79	−1.49347	−0.746734	−	0.665123i	$-0.768379\pi$
$151$	−5.09160e79	−1.49347	−0.746734	+	0.665123i	$0.768379\pi$
$152$	1.48795e79	0.343003
$153$	−5.42311e78	−0.0984036
$154$	−1.83521e77	−0.00262531
$155$	−1.93354e79	−0.218397
$156$	5.40715e79	0.482970
$157$	−4.68516e79	−0.331427	−0.165713	−	0.986174i	$-0.552993\pi$
$157$	−4.68516e79	−0.331427	−0.165713	+	0.986174i	$0.552993\pi$
$158$	4.95254e78	0.0277872
$159$	1.55658e80	0.693709
$160$	1.69149e79	0.0599638
$161$	−4.69572e79	−0.132604
$162$	3.84012e80	0.865061
$163$	−5.74321e79	−0.103349	−0.0516746	−	0.998664i	$-0.516456\pi$
$163$	−5.74321e79	−0.103349	−0.0516746	+	0.998664i	$0.516456\pi$
$164$	9.23950e79	0.132999
$165$	−1.13096e79	−0.0130401
$166$	7.56852e80	0.699948
$167$	1.49912e81	1.11349	0.556743	−	0.830685i	$-0.312051\pi$
$167$	1.49912e81	1.11349	0.556743	+	0.830685i	$0.312051\pi$
$168$	−7.64193e79	−0.0456472
$169$	−6.27995e80	−0.302059
$170$	−1.80680e80	−0.0700689
$171$	−1.04385e81	−0.326797
$172$	−3.67040e81	−0.928806
$173$	−3.84638e81	−0.787716	−0.393858	−	0.919171i	$-0.628860\pi$
$173$	−3.84638e81	−0.787716	−0.393858	+	0.919171i	$0.628860\pi$
$174$	−7.57346e81	−1.25674
$175$	−7.34041e80	−0.0988169
$176$	7.60203e79	0.00831223
$177$	−5.67687e80	−0.0504760
$178$	−1.00388e82	−0.726695
$179$	2.01708e82	1.19011	0.595057	−	0.803684i	$-0.297129\pi$
$179$	2.01708e82	1.19011	0.595057	+	0.803684i	$0.297129\pi$
$180$	−1.18663e81	−0.0571306
$181$	2.00764e82	0.789621	0.394810	−	0.918763i	$-0.370810\pi$
$181$	2.00764e82	0.789621	0.394810	+	0.918763i	$0.370810\pi$
$182$	−2.05077e81	−0.0659648
$183$	4.49204e82	1.18298
$184$	1.94511e82	0.419850
$185$	−1.81227e82	−0.320963
$186$	−3.61852e82	−0.526392
$187$	−8.12031e80	−0.00971301
$188$	−2.52295e82	−0.248398
$189$	−1.05543e82	−0.0856193
$190$	−3.47775e82	−0.232698
$191$	3.45352e83	1.90785	0.953924	−	0.300049i	$-0.0970031\pi$
$191$	3.45352e83	1.90785	0.953924	+	0.300049i	$0.0970031\pi$
$192$	3.16553e82	0.144528
$193$	6.03025e82	0.227768	0.113884	−	0.993494i	$-0.463671\pi$
$193$	6.03025e82	0.227768	0.113884	+	0.993494i	$0.463671\pi$
$194$	−5.13276e82	−0.160542
$195$	−1.26380e83	−0.327653
$196$	−2.29545e83	−0.493765
$197$	−9.47960e83	−1.69345	−0.846726	−	0.532030i	$-0.821430\pi$
$197$	−9.47960e83	−1.69345	−0.846726	+	0.532030i	$0.821430\pi$
$198$	−5.33306e81	−0.00791949
$199$	1.05949e83	0.130906	0.0654530	−	0.997856i	$-0.479151\pi$
$199$	1.05949e83	0.130906	0.0654530	+	0.997856i	$0.479151\pi$
$200$	3.04063e83	0.312873
$201$	−2.43811e84	−2.09121
$202$	1.72892e84	1.23723
$203$	2.87240e83	0.171648
$204$	−3.38134e83	−0.168884
$205$	−2.15952e83	−0.0902282
$206$	1.99592e84	0.698217
$207$	−1.36456e84	−0.400013
$208$	8.49496e83	0.208857
$209$	−1.56300e83	−0.0322568
$210$	1.78613e83	0.0309676
$211$	1.32481e85	1.93127	0.965636	−	0.259898i	$-0.0836889\pi$
$211$	1.32481e85	1.93127	0.965636	+	0.259898i	$0.0836889\pi$
$212$	2.44548e84	0.299989
$213$	−6.90331e84	−0.713184
$214$	3.45146e84	0.300538
$215$	8.57873e84	0.630114
$216$	4.37191e84	0.271087
$217$	1.37240e84	0.0718954
$218$	−9.44896e83	−0.0418526
$219$	−3.92392e85	−1.47065
$220$	−1.77680e83	−0.00563912
$221$	−9.07410e84	−0.244054
$222$	−3.39157e85	−0.773601
$223$	−5.18131e85	−1.00303	−0.501513	−	0.865150i	$-0.667223\pi$
$223$	−5.18131e85	−1.00303	−0.501513	+	0.865150i	$0.667223\pi$
$224$	−1.20059e84	−0.0197398
$225$	−2.13309e85	−0.298090
$226$	−1.56349e85	−0.185839
$227$	1.31843e86	1.33387	0.666934	−	0.745117i	$-0.267606\pi$
$227$	1.31843e86	1.33387	0.666934	+	0.745117i	$0.267606\pi$
$228$	−6.50843e85	−0.560860
$229$	1.61169e86	1.18382	0.591911	−	0.806003i	$-0.298374\pi$
$229$	1.61169e86	1.18382	0.591911	+	0.806003i	$0.298374\pi$
$230$	−4.54626e85	−0.284832
$231$	8.02738e83	0.00429276
$232$	−1.18984e86	−0.543470
$233$	2.90032e86	1.13228	0.566142	−	0.824308i	$-0.308435\pi$
$233$	2.90032e86	1.13228	0.566142	+	0.824308i	$0.308435\pi$
$234$	−5.95947e85	−0.198989
$235$	5.89683e85	0.168516
$236$	−8.91870e84	−0.0218280
$237$	−2.16628e85	−0.0454361
$238$	1.28244e85	0.0230664
$239$	−9.99267e85	−0.154226	−0.0771131	−	0.997022i	$-0.524570\pi$
$239$	−9.99267e85	−0.154226	−0.0771131	+	0.997022i	$0.524570\pi$
$240$	−7.39870e85	−0.0980495
$241$	9.58884e86	1.09180	0.545901	−	0.837850i	$-0.316187\pi$
$241$	9.58884e86	1.09180	0.545901	+	0.837850i	$0.316187\pi$
$242$	7.21548e86	0.706325
$243$	−7.69195e86	−0.647750
$244$	7.05726e86	0.511573
$245$	5.36509e86	0.334977
$246$	−4.04143e86	−0.217472
$247$	−1.74659e87	−0.810500
$248$	−5.68492e86	−0.227634
$249$	−3.31053e87	−1.14452
$250$	−1.51376e87	−0.452112
$251$	−4.43152e87	−1.14410	−0.572048	−	0.820220i	$-0.693851\pi$
$251$	−4.43152e87	−1.14410	−0.572048	+	0.820220i	$0.693851\pi$
$252$	8.42253e85	0.0188071
$253$	−2.04322e86	−0.0394836
$254$	2.16895e87	0.362927
$255$	7.90311e86	0.114573
$256$	4.97323e86	0.0625000
$257$	8.23323e85	0.00897452	0.00448726	−	0.999990i	$-0.498572\pi$
$257$	8.23323e85	0.00897452	0.00448726	+	0.999990i	$0.498572\pi$
$258$	1.60546e88	1.51873
$259$	1.28632e87	0.105660
$260$	−1.98550e87	−0.141691
$261$	8.34707e87	0.517792
$262$	1.52511e88	0.822818
$263$	−7.47321e87	−0.350851	−0.175425	−	0.984493i	$-0.556130\pi$
$263$	−7.47321e87	−0.350851	−0.175425	+	0.984493i	$0.556130\pi$
$264$	−3.32519e86	−0.0135917
$265$	−5.71577e87	−0.203517
$266$	2.46846e87	0.0766031
$267$	4.39106e88	1.18825
$268$	−3.83042e88	−0.904330
$269$	−1.88616e88	−0.388704	−0.194352	−	0.980932i	$-0.562260\pi$
$269$	−1.88616e88	−0.388704	−0.194352	+	0.980932i	$0.562260\pi$
$270$	−1.02183e88	−0.183909
$271$	3.28777e88	0.517038	0.258519	−	0.966006i	$-0.416766\pi$
$271$	3.28777e88	0.517038	0.258519	+	0.966006i	$0.416766\pi$
$272$	−5.31229e87	−0.0730325
$273$	8.97026e87	0.107862
$274$	−8.74329e88	−0.919982
$275$	−3.19399e87	−0.0294233
$276$	−8.50809e88	−0.686516
$277$	−2.09853e89	−1.48390	−0.741948	−	0.670458i	$-0.766098\pi$
$277$	−2.09853e89	−1.48390	−0.741948	+	0.670458i	$0.766098\pi$
$278$	3.73792e86	0.00231737
$279$	3.98814e88	0.216879
$280$	2.80611e87	0.0133917
$281$	9.69508e88	0.406229	0.203114	−	0.979155i	$-0.434894\pi$
$281$	9.69508e88	0.406229	0.203114	+	0.979155i	$0.434894\pi$
$282$	1.10356e89	0.406166
$283$	3.94495e89	1.27596	0.637980	−	0.770053i	$-0.279770\pi$
$283$	3.94495e89	1.27596	0.637980	+	0.770053i	$0.279770\pi$
$284$	−1.08455e89	−0.308412
$285$	1.52120e89	0.380495
$286$	−8.92343e87	−0.0196414
$287$	1.53280e88	0.0297027
$288$	−3.48888e88	−0.0595470
$289$	−6.08178e89	−0.914660
$290$	2.78097e89	0.368697
$291$	2.24511e89	0.262509
$292$	−6.16472e89	−0.635974
$293$	1.44439e90	1.31527	0.657637	−	0.753335i	$-0.271556\pi$
$293$	1.44439e90	1.31527	0.657637	+	0.753335i	$0.271556\pi$
$294$	1.00405e90	0.807378
$295$	2.08454e88	0.0148084
$296$	−5.32836e89	−0.334538
$297$	−4.59242e88	−0.0254936
$298$	2.21310e90	1.08669
$299$	−2.28322e90	−0.992085
$300$	−1.33000e90	−0.511593
$301$	−6.08906e89	−0.207431
$302$	3.49892e90	1.05604
$303$	−7.56245e90	−2.02305
$304$	−1.02251e90	−0.242540
$305$	−1.64948e90	−0.347058
$306$	3.72673e89	0.0695819
$307$	−5.93114e90	−0.983077	−0.491538	−	0.870856i	$-0.663565\pi$
$307$	−5.93114e90	−0.983077	−0.491538	+	0.870856i	$0.663565\pi$
$308$	1.26115e88	0.00185637
$309$	−8.73034e90	−1.14169
$310$	1.32872e90	0.154430
$311$	1.55230e91	1.60406	0.802031	−	0.597282i	$-0.203753\pi$
$311$	1.55230e91	1.60406	0.802031	+	0.597282i	$0.203753\pi$
$312$	−3.71576e90	−0.341512
$313$	2.15089e91	1.75893	0.879467	−	0.475960i	$-0.157899\pi$
$313$	2.15089e91	1.75893	0.879467	+	0.475960i	$0.157899\pi$
$314$	3.21962e90	0.234354
$315$	−1.96857e89	−0.0127590
$316$	−3.40336e89	−0.0196485
$317$	3.35164e91	1.72423	0.862114	−	0.506714i	$-0.169140\pi$
$317$	3.35164e91	1.72423	0.862114	+	0.506714i	$0.169140\pi$
$318$	−1.06968e91	−0.490526
$319$	1.24985e90	0.0511091
$320$	−1.16238e90	−0.0424008
$321$	−1.50970e91	−0.491423
$322$	3.22687e90	0.0937653
$323$	1.09222e91	0.283413
$324$	−2.63891e91	−0.611691
$325$	−3.56915e91	−0.739303
$326$	3.94671e90	0.0730790
$327$	4.13305e90	0.0684350
$328$	−6.34934e90	−0.0940444
$329$	−4.18548e90	−0.0554747
$330$	7.77189e89	0.00922078
$331$	−1.07776e91	−0.114499	−0.0572493	−	0.998360i	$-0.518233\pi$
$331$	−1.07776e91	−0.114499	−0.0572493	+	0.998360i	$0.518233\pi$
$332$	−5.20105e91	−0.494938
$333$	3.73801e91	0.318732
$334$	−1.03019e92	−0.787354
$335$	8.95275e91	0.613509
$336$	5.25149e90	0.0322774
$337$	−2.38012e92	−1.31252	−0.656262	−	0.754533i	$-0.727863\pi$
$337$	−2.38012e92	−1.31252	−0.656262	+	0.754533i	$0.727863\pi$
$338$	4.31555e91	0.213588
$339$	6.83882e91	0.303873
$340$	1.24163e91	0.0495462
$341$	5.97166e90	0.0214072
$342$	7.17325e91	0.231080
$343$	−7.66421e91	−0.221938
$344$	2.52228e92	0.656765
$345$	1.98857e92	0.465741
$346$	2.64321e92	0.556999
$347$	3.41200e92	0.647117	0.323559	−	0.946208i	$-0.395121\pi$
$347$	3.41200e92	0.647117	0.323559	+	0.946208i	$0.395121\pi$
$348$	5.20444e92	0.888653
$349$	−5.66523e92	−0.871143	−0.435572	−	0.900154i	$-0.643454\pi$
$349$	−5.66523e92	−0.871143	−0.435572	+	0.900154i	$0.643454\pi$
$350$	5.04429e91	0.0698741
$351$	−5.13184e92	−0.640565
$352$	−5.22408e90	−0.00587763
$353$	−2.42064e92	−0.245557	−0.122779	−	0.992434i	$-0.539181\pi$
$353$	−2.42064e92	−0.245557	−0.122779	+	0.992434i	$0.539181\pi$
$354$	3.90111e91	0.0356919
$355$	2.53489e92	0.209230
$356$	6.89862e92	0.513851
$357$	−5.60952e91	−0.0377169
$358$	−1.38613e93	−0.841538
$359$	4.04247e92	0.221666	0.110833	−	0.993839i	$-0.464648\pi$
$359$	4.04247e92	0.221666	0.110833	+	0.993839i	$0.464648\pi$
$360$	8.15446e91	0.0403974
$361$	−1.31314e92	−0.0587894
$362$	−1.37964e93	−0.558346
$363$	−3.15611e93	−1.15494
$364$	1.40928e92	0.0466442
$365$	1.44086e93	0.431453
$366$	−3.08691e93	−0.836496
$367$	−1.78274e93	−0.437297	−0.218649	−	0.975804i	$-0.570165\pi$
$367$	−1.78274e93	−0.437297	−0.218649	+	0.975804i	$0.570165\pi$
$368$	−1.33667e93	−0.296879
$369$	4.45425e92	0.0896010
$370$	1.24538e93	0.226955
$371$	4.05697e92	0.0669968
$372$	2.48663e93	0.372215
$373$	1.06369e94	1.44358	0.721791	−	0.692111i	$-0.243319\pi$
$373$	1.06369e94	1.44358	0.721791	+	0.692111i	$0.243319\pi$
$374$	5.58023e91	0.00686813
$375$	6.62131e93	0.739269
$376$	1.73376e93	0.175644
$377$	1.39666e94	1.28419
$378$	7.25283e92	0.0605420
$379$	9.65049e93	0.731506	0.365753	−	0.930712i	$-0.380811\pi$
$379$	9.65049e93	0.731506	0.365753	+	0.930712i	$0.380811\pi$
$380$	2.38989e93	0.164542
$381$	−9.48717e93	−0.593437
$382$	−2.37324e94	−1.34905
$383$	−1.87302e94	−0.967805	−0.483902	−	0.875122i	$-0.660781\pi$
$383$	−1.87302e94	−0.967805	−0.483902	+	0.875122i	$0.660781\pi$
$384$	−2.17533e93	−0.102197
$385$	−2.94765e91	−0.00125939
$386$	−4.14396e93	−0.161057
$387$	−1.76946e94	−0.625734
$388$	3.52721e93	0.113520
$389$	−6.73964e93	−0.197459	−0.0987294	−	0.995114i	$-0.531478\pi$
$389$	−6.73964e93	−0.197459	−0.0987294	+	0.995114i	$0.531478\pi$
$390$	8.68476e93	0.231686
$391$	1.42780e94	0.346909
$392$	1.57742e94	0.349145
$393$	−6.67095e94	−1.34543
$394$	6.51433e94	1.19745
$395$	7.95459e92	0.0133298
$396$	3.66485e92	0.00559992
$397$	−7.26937e94	−1.01308	−0.506539	−	0.862217i	$-0.669075\pi$
$397$	−7.26937e94	−1.01308	−0.506539	+	0.862217i	$0.669075\pi$
$398$	−7.28076e93	−0.0925645
$399$	−1.07973e94	−0.125257
$400$	−2.08950e94	−0.221235
$401$	−2.50487e94	−0.242111	−0.121056	−	0.992646i	$-0.538628\pi$
$401$	−2.50487e94	−0.242111	−0.121056	+	0.992646i	$0.538628\pi$
$402$	1.67546e95	1.47871
$403$	6.67308e94	0.537888
$404$	−1.18811e95	−0.874854
$405$	6.16786e94	0.414979
$406$	−1.97390e94	−0.121373
$407$	5.59711e93	0.0314607
$408$	2.32364e94	0.119419
$409$	8.94100e94	0.420229	0.210114	−	0.977677i	$-0.432616\pi$
$409$	8.94100e94	0.420229	0.210114	+	0.977677i	$0.432616\pi$
$410$	1.48401e94	0.0638009
$411$	3.82439e95	1.50430
$412$	−1.37159e95	−0.493714
$413$	−1.47958e93	−0.00487485
$414$	9.37716e94	0.282852
$415$	1.21563e95	0.335772
$416$	−5.83769e94	−0.147684
$417$	−1.63500e93	−0.00378923
$418$	1.07409e94	0.0228090
$419$	−9.04238e95	−1.75983	−0.879916	−	0.475130i	$-0.842401\pi$
$419$	−9.04238e95	−1.75983	−0.879916	+	0.475130i	$0.842401\pi$
$420$	−1.22742e94	−0.0218974
$421$	−2.03426e94	−0.0332744	−0.0166372	−	0.999862i	$-0.505296\pi$
$421$	−2.03426e94	−0.0332744	−0.0166372	+	0.999862i	$0.505296\pi$
$422$	−9.10402e95	−1.36562
$423$	−1.21628e95	−0.167345
$424$	−1.68052e95	−0.212125
$425$	2.23196e95	0.258517
$426$	4.74392e95	0.504297
$427$	1.17077e95	0.114250
$428$	−2.37182e95	−0.212513
$429$	3.90318e94	0.0321165
$430$	−5.89526e95	−0.445558
$431$	2.07560e95	0.144120	0.0720600	−	0.997400i	$-0.477043\pi$
$431$	2.07560e95	0.144120	0.0720600	+	0.997400i	$0.477043\pi$
$432$	−3.00435e95	−0.191688
$433$	1.66164e96	0.974382	0.487191	−	0.873295i	$-0.338022\pi$
$433$	1.66164e96	0.974382	0.487191	+	0.873295i	$0.338022\pi$
$434$	−9.43107e94	−0.0508377
$435$	−1.21642e96	−0.602873
$436$	6.49328e94	0.0295942
$437$	2.74824e96	1.15208
$438$	2.69650e96	1.03991
$439$	−1.34901e95	−0.0478698	−0.0239349	−	0.999714i	$-0.507619\pi$
$439$	−1.34901e95	−0.0478698	−0.0239349	+	0.999714i	$0.507619\pi$
$440$	1.22101e94	0.00398746
$441$	−1.10661e96	−0.332648
$442$	6.23568e95	0.172572
$443$	3.93171e96	1.00195	0.500974	−	0.865462i	$-0.332975\pi$
$443$	3.93171e96	1.00195	0.500974	+	0.865462i	$0.332975\pi$
$444$	2.33067e96	0.547018
$445$	−1.61240e96	−0.348603
$446$	3.56057e96	0.709246
$447$	−9.68027e96	−1.77690
$448$	8.25041e94	0.0139582
$449$	−3.39101e96	−0.528856	−0.264428	−	0.964405i	$-0.585183\pi$
$449$	−3.39101e96	−0.528856	−0.264428	+	0.964405i	$0.585183\pi$
$450$	1.46585e96	0.210782
$451$	6.66959e94	0.00884414
$452$	1.07442e96	0.131408
$453$	−1.53046e97	−1.72678
$454$	−9.06017e96	−0.943187
$455$	−3.29388e95	−0.0316440
$456$	4.47256e96	0.396588
$457$	5.34948e95	0.0437896	0.0218948	−	0.999760i	$-0.493030\pi$
$457$	5.34948e95	0.0437896	0.0218948	+	0.999760i	$0.493030\pi$
$458$	−1.10755e97	−0.837089
$459$	3.20917e96	0.223991
$460$	3.12417e96	0.201407
$461$	2.66238e97	1.58557	0.792787	−	0.609498i	$-0.208629\pi$
$461$	2.66238e97	1.58557	0.792787	+	0.609498i	$0.208629\pi$
$462$	−5.51637e94	−0.00303544
$463$	1.21242e97	0.616518	0.308259	−	0.951302i	$-0.400254\pi$
$463$	1.21242e97	0.616518	0.308259	+	0.951302i	$0.400254\pi$
$464$	8.17650e96	0.384292
$465$	−5.81194e96	−0.252516
$466$	−1.99309e97	−0.800646
$467$	1.17202e97	0.435381	0.217690	−	0.976018i	$-0.430148\pi$
$467$	1.17202e97	0.435381	0.217690	+	0.976018i	$0.430148\pi$
$468$	4.09532e96	0.140706
$469$	−6.35453e96	−0.201964
$470$	−4.05227e96	−0.119159
$471$	−1.40829e97	−0.383203
$472$	6.12889e95	0.0154347
$473$	−2.64950e96	−0.0617636
$474$	1.48866e96	0.0321281
$475$	4.29609e97	0.858532
$476$	−8.81289e95	−0.0163104
$477$	1.17894e97	0.202102
$478$	6.86691e96	0.109054
$479$	7.40786e97	1.09005	0.545025	−	0.838420i	$-0.316520\pi$
$479$	7.40786e97	1.09005	0.545025	+	0.838420i	$0.316520\pi$
$480$	5.08435e96	0.0693314
$481$	6.25454e97	0.790497
$482$	−6.58940e97	−0.772021
$483$	−1.41146e97	−0.153320
$484$	−4.95844e97	−0.499447
$485$	−8.24405e96	−0.0770136
$486$	5.28587e97	0.458029
$487$	−2.37959e98	−1.91291	−0.956456	−	0.291877i	$-0.905720\pi$
$487$	−2.37959e98	−1.91291	−0.956456	+	0.291877i	$0.905720\pi$
$488$	−4.84971e97	−0.361737
$489$	−1.72632e97	−0.119495
$490$	−3.68686e97	−0.236864
$491$	−1.97492e98	−1.17781	−0.588906	−	0.808202i	$-0.700441\pi$
$491$	−1.97492e98	−1.17781	−0.588906	+	0.808202i	$0.700441\pi$
$492$	2.77725e97	0.153776
$493$	−8.73393e97	−0.449053
$494$	1.20025e98	0.573110
$495$	−8.56576e95	−0.00379906
$496$	3.90665e97	0.160962
$497$	−1.79923e97	−0.0688777
$498$	2.27498e98	0.809295
$499$	−1.14951e98	−0.380052	−0.190026	−	0.981779i	$-0.560857\pi$
$499$	−1.14951e98	−0.380052	−0.190026	+	0.981779i	$0.560857\pi$
$500$	1.04025e98	0.319692
$501$	4.50612e98	1.28744
$502$	3.04532e98	0.808998
$503$	−5.91076e97	−0.146020	−0.0730100	−	0.997331i	$-0.523260\pi$
$503$	−5.91076e97	−0.146020	−0.0730100	+	0.997331i	$0.523260\pi$
$504$	−5.78792e96	−0.0132987
$505$	2.77693e98	0.593512
$506$	1.40409e97	0.0279191
$507$	−1.88766e98	−0.349247
$508$	−1.49049e98	−0.256628
$509$	1.52382e98	0.244194	0.122097	−	0.992518i	$-0.461038\pi$
$509$	1.52382e98	0.244194	0.122097	+	0.992518i	$0.461038\pi$
$510$	−5.43098e97	−0.0810152
$511$	−1.02270e98	−0.142032
$512$	−3.41758e97	−0.0441942
$513$	6.17705e98	0.743870
$514$	−5.65783e96	−0.00634595
$515$	3.20578e98	0.334942
$516$	−1.10327e99	−1.07391
$517$	−1.82121e97	−0.0165179
$518$	−8.83955e97	−0.0747126
$519$	−1.15616e99	−0.910774
$520$	1.36443e98	0.100191
$521$	−1.55565e99	−1.06497	−0.532483	−	0.846441i	$-0.678741\pi$
$521$	−1.55565e99	−1.06497	−0.532483	+	0.846441i	$0.678741\pi$
$522$	−5.73606e98	−0.366134
$523$	1.35187e99	0.804677	0.402339	−	0.915491i	$-0.368197\pi$
$523$	1.35187e99	0.804677	0.402339	+	0.915491i	$0.368197\pi$
$524$	−1.04805e99	−0.581820
$525$	−2.20641e98	−0.114254
$526$	5.13555e98	0.248089
$527$	−4.17298e98	−0.188087
$528$	2.28505e97	0.00961078
$529$	1.04501e99	0.410194
$530$	3.92784e98	0.143908
$531$	−4.29960e97	−0.0147054
$532$	−1.69631e98	−0.0541666
$533$	7.45299e98	0.222222
$534$	−3.01751e99	−0.840221
$535$	5.54360e98	0.144171
$536$	2.63225e99	0.639458
$537$	6.06305e99	1.37604
$538$	1.29616e99	0.274855
$539$	−1.65698e98	−0.0328343
$540$	7.02199e98	0.130043
$541$	−5.01024e98	−0.0867279	−0.0433639	−	0.999059i	$-0.513807\pi$
$541$	−5.01024e98	−0.0867279	−0.0433639	+	0.999059i	$0.513807\pi$
$542$	−2.25934e99	−0.365601
$543$	6.03467e99	0.912977
$544$	3.65057e98	0.0516418
$545$	−1.51766e98	−0.0200771
$546$	−6.16432e98	−0.0762699
$547$	−1.48570e100	−1.71946	−0.859731	−	0.510746i	$-0.829369\pi$
$547$	−1.48570e100	−1.71946	−0.859731	+	0.510746i	$0.829369\pi$
$548$	6.00834e99	0.650526
$549$	3.40222e99	0.344645
$550$	2.19490e98	0.0208054
$551$	−1.68112e100	−1.49130
$552$	5.84671e99	0.485440
$553$	−5.64605e97	−0.00438811
$554$	1.44210e100	1.04927
$555$	−5.44741e99	−0.371104
$556$	−2.56868e97	−0.00163863
$557$	1.80353e100	1.07748	0.538740	−	0.842472i	$-0.318900\pi$
$557$	1.80353e100	1.07748	0.538740	+	0.842472i	$0.318900\pi$
$558$	−2.74063e99	−0.153357
$559$	−2.96071e100	−1.55190
$560$	−1.92835e98	−0.00946939
$561$	−2.44084e98	−0.0112304
$562$	−6.66241e99	−0.287247
$563$	−2.47834e100	−1.00139	−0.500697	−	0.865623i	$-0.666923\pi$
$563$	−2.47834e100	−1.00139	−0.500697	+	0.865623i	$0.666923\pi$
$564$	−7.58360e99	−0.287203
$565$	−2.51121e99	−0.0891488
$566$	−2.71095e100	−0.902240
$567$	−4.37786e99	−0.136609
$568$	7.45298e99	0.218080
$569$	6.22010e100	1.70687	0.853433	−	0.521202i	$-0.174516\pi$
$569$	6.22010e100	1.70687	0.853433	+	0.521202i	$0.174516\pi$
$570$	−1.04536e100	−0.269050
$571$	−3.07431e100	−0.742216	−0.371108	−	0.928590i	$-0.621022\pi$
$571$	−3.07431e100	−0.742216	−0.371108	+	0.928590i	$0.621022\pi$
$572$	6.13214e98	0.0138885
$573$	1.03807e101	2.20589
$574$	−1.05333e99	−0.0210030
$575$	5.61603e100	1.05088
$576$	2.39754e99	0.0421061
$577$	2.06343e100	0.340152	0.170076	−	0.985431i	$-0.445599\pi$
$577$	2.06343e100	0.340152	0.170076	+	0.985431i	$0.445599\pi$
$578$	4.17937e100	0.646762
$579$	1.81260e100	0.263351
$580$	−1.91107e100	−0.260708
$581$	−8.62835e99	−0.110535
$582$	−1.54283e100	−0.185622
$583$	1.76529e99	0.0199486
$584$	4.23636e100	0.449701
$585$	−9.57188e99	−0.0954571
$586$	−9.92577e100	−0.930040
$587$	−1.15251e101	−1.01474	−0.507368	−	0.861729i	$-0.669382\pi$
$587$	−1.15251e101	−1.01474	−0.507368	+	0.861729i	$0.669382\pi$
$588$	−6.89976e100	−0.570902
$589$	−8.03220e100	−0.624635
$590$	−1.43249e99	−0.0104711
$591$	−2.84942e101	−1.95801
$592$	3.66162e100	0.236554
$593$	2.83611e101	1.72277	0.861385	−	0.507953i	$-0.169598\pi$
$593$	2.83611e101	1.72277	0.861385	+	0.507953i	$0.169598\pi$
$594$	3.15589e99	0.0180267
$595$	2.05981e99	0.0110652
$596$	−1.52083e101	−0.768408
$597$	3.18466e100	0.151356
$598$	1.56901e101	0.701510
$599$	1.40873e101	0.592584	0.296292	−	0.955097i	$-0.404250\pi$
$599$	1.40873e101	0.592584	0.296292	+	0.955097i	$0.404250\pi$
$600$	9.13966e100	0.361751
$601$	−1.94434e101	−0.724191	−0.362096	−	0.932141i	$-0.617939\pi$
$601$	−1.94434e101	−0.724191	−0.362096	+	0.932141i	$0.617939\pi$
$602$	4.18437e100	0.146676
$603$	−1.84660e101	−0.609244
$604$	−2.40444e101	−0.746734
$605$	1.15892e101	0.338831
$606$	5.19688e101	1.43051
$607$	−3.29029e101	−0.852800	−0.426400	−	0.904535i	$-0.640218\pi$
$607$	−3.29029e101	−0.852800	−0.426400	+	0.904535i	$0.640218\pi$
$608$	7.02666e100	0.171502
$609$	8.63398e100	0.198463
$610$	1.13351e101	0.245407
$611$	−2.03512e101	−0.415037
$612$	−2.56099e100	−0.0492018
$613$	7.67313e101	1.38888	0.694440	−	0.719550i	$-0.255652\pi$
$613$	7.67313e101	1.38888	0.694440	+	0.719550i	$0.255652\pi$
$614$	4.07585e101	0.695140
$615$	−6.49120e100	−0.104324
$616$	−8.66655e98	−0.00131265
$617$	1.49318e101	0.213159	0.106580	−	0.994304i	$-0.466010\pi$
$617$	1.49318e101	0.213159	0.106580	+	0.994304i	$0.466010\pi$
$618$	5.99944e101	0.807294
$619$	−1.23916e102	−1.57187	−0.785936	−	0.618308i	$-0.787818\pi$
$619$	−1.23916e102	−1.57187	−0.785936	+	0.618308i	$0.787818\pi$
$620$	−9.13090e100	−0.109199
$621$	8.07489e101	0.910528
$622$	−1.06673e102	−1.13424
$623$	1.14446e101	0.114759
$624$	2.55345e101	0.241485
$625$	7.48917e101	0.668056
$626$	−1.47808e102	−1.24375
$627$	−4.69815e100	−0.0372960
$628$	−2.21251e101	−0.165713
$629$	−3.91125e101	−0.276419
$630$	1.35279e100	0.00902198
$631$	−2.75337e102	−1.73298	−0.866490	−	0.499195i	$-0.833629\pi$
$631$	−2.75337e102	−1.73298	−0.866490	+	0.499195i	$0.833629\pi$
$632$	2.33877e100	0.0138936
$633$	3.98217e102	2.23298
$634$	−2.30323e102	−1.21921
$635$	3.48369e101	0.174100
$636$	7.35075e101	0.346854
$637$	−1.85161e102	−0.825012
$638$	−8.58891e100	−0.0361396
$639$	−5.22849e101	−0.207776
$640$	7.98782e100	0.0299819
$641$	5.79044e101	0.205302	0.102651	−	0.994717i	$-0.467267\pi$
$641$	5.79044e101	0.205302	0.102651	+	0.994717i	$0.467267\pi$
$642$	1.03745e102	0.347489
$643$	−3.89322e101	−0.123199	−0.0615996	−	0.998101i	$-0.519620\pi$
$643$	−3.89322e101	−0.123199	−0.0615996	+	0.998101i	$0.519620\pi$
$644$	−2.21749e101	−0.0663021
$645$	2.57864e102	0.728552
$646$	−7.50571e101	−0.200403
$647$	−1.64739e102	−0.415708	−0.207854	−	0.978160i	$-0.566648\pi$
$647$	−1.64739e102	−0.415708	−0.207854	+	0.978160i	$0.566648\pi$
$648$	1.81345e102	0.432531
$649$	−6.43802e99	−0.00145151
$650$	2.45270e102	0.522766
$651$	4.12523e101	0.0831270
$652$	−2.71216e101	−0.0516746
$653$	9.50113e102	1.71177	0.855883	−	0.517170i	$-0.173015\pi$
$653$	9.50113e102	1.71177	0.855883	+	0.517170i	$0.173015\pi$
$654$	−2.84021e101	−0.0483908
$655$	2.44957e102	0.394714
$656$	4.36323e101	0.0664994
$657$	−2.97194e102	−0.428454
$658$	2.87624e101	0.0392266
$659$	7.31327e102	0.943614	0.471807	−	0.881702i	$-0.343602\pi$
$659$	7.31327e102	0.943614	0.471807	+	0.881702i	$0.343602\pi$
$660$	−5.34080e100	−0.00652007
$661$	−1.56804e103	−1.81136	−0.905680	−	0.423963i	$-0.860639\pi$
$661$	−1.56804e103	−1.81136	−0.905680	+	0.423963i	$0.860639\pi$
$662$	7.40631e101	0.0809627
$663$	−2.72754e102	−0.282180
$664$	3.57413e102	0.349974
$665$	3.96475e101	0.0367473
$666$	−2.56874e102	−0.225377
$667$	−2.19762e103	−1.82541
$668$	7.07939e102	0.556743
$669$	−1.55742e103	−1.15972
$670$	−6.15228e102	−0.433816
$671$	5.09433e101	0.0340185
$672$	−3.60880e101	−0.0228236
$673$	−2.13281e103	−1.27762	−0.638812	−	0.769363i	$-0.720574\pi$
$673$	−2.13281e103	−1.27762	−0.638812	+	0.769363i	$0.720574\pi$
$674$	1.63560e103	0.928094
$675$	1.26228e103	0.678527
$676$	−2.96562e102	−0.151030
$677$	4.75816e102	0.229590	0.114795	−	0.993389i	$-0.463379\pi$
$677$	4.75816e102	0.229590	0.114795	+	0.993389i	$0.463379\pi$
$678$	−4.69960e102	−0.214871
$679$	5.85151e101	0.0253525
$680$	−8.53239e101	−0.0350345
$681$	3.96300e103	1.54225
$682$	−4.10369e101	−0.0151372
$683$	4.75457e103	1.66248	0.831238	−	0.555916i	$-0.187632\pi$
$683$	4.75457e103	1.66248	0.831238	+	0.555916i	$0.187632\pi$
$684$	−4.92942e102	−0.163398
$685$	−1.40431e103	−0.441325
$686$	5.26680e102	0.156934
$687$	4.84450e103	1.36876
$688$	−1.73330e103	−0.464403
$689$	1.97264e103	0.501240
$690$	−1.36654e103	−0.329329
$691$	−6.23923e103	−1.42621	−0.713103	−	0.701059i	$-0.752711\pi$
$691$	−6.23923e103	−1.42621	−0.713103	+	0.701059i	$0.752711\pi$
$692$	−1.81640e103	−0.393858
$693$	6.07985e100	0.00125063
$694$	−2.34471e103	−0.457581
$695$	6.00371e100	0.00111167
$696$	−3.57647e103	−0.628372
$697$	−4.66070e102	−0.0777060
$698$	3.89312e103	0.615991
$699$	8.71793e103	1.30917
$700$	−3.46641e102	−0.0494085
$701$	2.75532e103	0.372790	0.186395	−	0.982475i	$-0.440320\pi$
$701$	2.75532e103	0.372790	0.186395	+	0.982475i	$0.440320\pi$
$702$	3.52657e103	0.452948
$703$	−7.52842e103	−0.917982
$704$	3.58996e101	0.00415611
$705$	1.77250e103	0.194842
$706$	1.66345e103	0.173635
$707$	−1.97103e103	−0.195382
$708$	−2.68083e102	−0.0252380
$709$	−1.90532e104	−1.70365	−0.851823	−	0.523830i	$-0.824503\pi$
$709$	−1.90532e104	−1.70365	−0.851823	+	0.523830i	$0.824503\pi$
$710$	−1.74197e103	−0.147948
$711$	−1.64072e102	−0.0132371
$712$	−4.74070e103	−0.363348
$713$	−1.05000e104	−0.764579
$714$	3.85483e102	0.0266698
$715$	−1.43325e102	−0.00942217
$716$	9.52541e103	0.595057
$717$	−3.00364e103	−0.178320
$718$	−2.77796e103	−0.156741
$719$	5.28737e103	0.283553	0.141777	−	0.989899i	$-0.454719\pi$
$719$	5.28737e103	0.283553	0.141777	+	0.989899i	$0.454719\pi$
$720$	−5.60370e102	−0.0285653
$721$	−2.27542e103	−0.110261
$722$	9.02385e102	0.0415704
$723$	2.88226e104	1.26237
$724$	9.48083e103	0.394810
$725$	−3.43535e104	−1.36030
$726$	2.16886e104	0.816668
$727$	4.43475e104	1.58805	0.794023	−	0.607888i	$-0.207983\pi$
$727$	4.43475e104	1.58805	0.794023	+	0.607888i	$0.207983\pi$
$728$	−9.68451e102	−0.0329824
$729$	1.46465e104	0.474439
$730$	−9.90154e103	−0.305083
$731$	1.85147e104	0.542665
$732$	2.12131e104	0.591492
$733$	−6.26266e104	−1.66136	−0.830681	−	0.556749i	$-0.812048\pi$
$733$	−6.26266e104	−1.66136	−0.830681	+	0.556749i	$0.812048\pi$
$734$	1.22509e104	0.309216
$735$	1.61266e104	0.387307
$736$	9.18554e103	0.209925
$737$	−2.76502e103	−0.0601360
$738$	−3.06094e103	−0.0633574
$739$	−1.72996e104	−0.340811	−0.170406	−	0.985374i	$-0.554508\pi$
$739$	−1.72996e104	−0.340811	−0.170406	+	0.985374i	$0.554508\pi$
$740$	−8.55821e103	−0.160481
$741$	−5.24999e104	−0.937117
$742$	−2.78793e103	−0.0473739
$743$	3.33964e104	0.540267	0.270134	−	0.962823i	$-0.412932\pi$
$743$	3.33964e104	0.540267	0.270134	+	0.962823i	$0.412932\pi$
$744$	−1.70880e104	−0.263196
$745$	3.55459e104	0.521298
$746$	−7.30960e104	−1.02077
$747$	−2.50736e104	−0.333438
$748$	−3.83471e102	−0.00485650
$749$	−3.93477e103	−0.0474605
$750$	−4.55013e104	−0.522742
$751$	9.73411e104	1.06522	0.532609	−	0.846362i	$-0.321212\pi$
$751$	9.73411e104	1.06522	0.532609	+	0.846362i	$0.321212\pi$
$752$	−1.19143e104	−0.124199
$753$	−1.33205e105	−1.32283
$754$	−9.59775e104	−0.908061
$755$	5.61984e104	0.506594
$756$	−4.98411e103	−0.0428097
$757$	−4.34695e104	−0.355783	−0.177891	−	0.984050i	$-0.556928\pi$
$757$	−4.34695e104	−0.355783	−0.177891	+	0.984050i	$0.556928\pi$
$758$	−6.63177e104	−0.517253
$759$	−6.14162e103	−0.0456518
$760$	−1.64232e104	−0.116349
$761$	2.66509e105	1.79958	0.899792	−	0.436319i	$-0.143718\pi$
$761$	2.66509e105	1.79958	0.899792	+	0.436319i	$0.143718\pi$
$762$	6.51953e104	0.419624
$763$	1.07721e103	0.00660929
$764$	1.63088e105	0.953924
$765$	5.98574e103	0.0333791
$766$	1.28713e105	0.684341
$767$	−7.19422e103	−0.0364714
$768$	1.49488e104	0.0722639
$769$	3.43153e105	1.58189	0.790944	−	0.611888i	$-0.209590\pi$
$769$	3.43153e105	1.58189	0.790944	+	0.611888i	$0.209590\pi$
$770$	2.02561e102	0.000890522 0
$771$	2.47478e103	0.0103765
$772$	2.84771e104	0.113884
$773$	−4.29363e105	−1.63785	−0.818924	−	0.573902i	$-0.805429\pi$
$773$	−4.29363e105	−1.63785	−0.818924	+	0.573902i	$0.805429\pi$
$774$	1.21596e105	0.442461
$775$	−1.64138e105	−0.569766
$776$	−2.42388e104	−0.0802709
$777$	3.86649e104	0.122166
$778$	4.63145e104	0.139624
$779$	−8.97095e104	−0.258060
$780$	−5.96812e104	−0.163827
$781$	−7.82890e103	−0.0205087
$782$	−9.81177e104	−0.245302
$783$	−4.93946e105	−1.17862
$784$	−1.08399e105	−0.246883
$785$	5.17123e104	0.112422
$786$	4.58424e105	0.951359
$787$	−5.62421e104	−0.111425	−0.0557127	−	0.998447i	$-0.517743\pi$
$787$	−5.62421e104	−0.111425	−0.0557127	+	0.998447i	$0.517743\pi$
$788$	−4.47661e105	−0.846726
$789$	−2.24633e105	−0.405661
$790$	−5.46635e103	−0.00942559
$791$	1.78242e104	0.0293474
$792$	−2.51847e103	−0.00395974
$793$	5.69270e105	0.854765
$794$	4.99547e105	0.716355
$795$	−1.71807e105	−0.235310
$796$	5.00330e104	0.0654530
$797$	−8.98427e105	−1.12267	−0.561337	−	0.827587i	$-0.689713\pi$
$797$	−8.98427e105	−1.12267	−0.561337	+	0.827587i	$0.689713\pi$
$798$	7.41981e104	0.0885702
$799$	1.27266e105	0.145129
$800$	1.43590e105	0.156437
$801$	3.32574e105	0.346180
$802$	1.72133e105	0.171198
$803$	−4.45004e104	−0.0422909
$804$	−1.15137e106	−1.04561
$805$	5.18288e104	0.0449802
$806$	−4.58571e105	−0.380345
$807$	−5.66950e105	−0.449428
$808$	8.16461e105	0.618615
$809$	1.36941e106	0.991770	0.495885	−	0.868388i	$-0.334844\pi$
$809$	1.36941e106	0.991770	0.495885	+	0.868388i	$0.334844\pi$
$810$	−4.23852e105	−0.293434
$811$	1.27012e106	0.840590	0.420295	−	0.907387i	$-0.361927\pi$
$811$	1.27012e106	0.840590	0.420295	+	0.907387i	$0.361927\pi$
$812$	1.35645e105	0.0858240
$813$	9.88254e105	0.597811
$814$	−3.84631e104	−0.0222461
$815$	6.33905e104	0.0350567
$816$	−1.59679e105	−0.0844418
$817$	3.56372e106	1.80218
$818$	−6.14421e105	−0.297146
$819$	6.79398e104	0.0314240
$820$	−1.01981e105	−0.0451141
$821$	−7.14465e105	−0.302312	−0.151156	−	0.988510i	$-0.548300\pi$
$821$	−7.14465e105	−0.302312	−0.151156	+	0.988510i	$0.548300\pi$
$822$	−2.62810e106	−1.06370
$823$	2.85583e106	1.10570	0.552851	−	0.833280i	$-0.313540\pi$
$823$	2.85583e106	1.10570	0.552851	+	0.833280i	$0.313540\pi$
$824$	9.42549e105	0.349109
$825$	−9.60066e104	−0.0340198
$826$	1.01676e104	0.00344704
$827$	−5.39859e106	−1.75118	−0.875588	−	0.483059i	$-0.839526\pi$
$827$	−5.39859e106	−1.75118	−0.875588	+	0.483059i	$0.839526\pi$
$828$	−6.44394e105	−0.200006
$829$	−2.39224e106	−0.710499	−0.355250	−	0.934771i	$-0.615604\pi$
$829$	−2.39224e106	−0.710499	−0.355250	+	0.934771i	$0.615604\pi$
$830$	−8.35373e105	−0.237427
$831$	−6.30786e106	−1.71571
$832$	4.01163e105	0.104429
$833$	1.15790e106	0.288488
$834$	1.12356e104	0.00267939
$835$	−1.65465e106	−0.377702
$836$	−7.38108e104	−0.0161284
$837$	−2.36002e106	−0.493670
$838$	6.21388e106	1.24439
$839$	−6.91196e106	−1.32522	−0.662612	−	0.748963i	$-0.730552\pi$
$839$	−6.91196e106	−1.32522	−0.662612	+	0.748963i	$0.730552\pi$
$840$	8.43475e104	0.0154838
$841$	7.75375e106	1.36288
$842$	1.39793e105	0.0235285
$843$	2.91419e106	0.469690
$844$	6.25623e106	0.965636
$845$	6.93148e105	0.102460
$846$	8.35825e105	0.118331
$847$	−8.22587e105	−0.111542
$848$	1.15485e106	0.149995
$849$	1.18579e107	1.47529
$850$	−1.53379e106	−0.182799
$851$	−9.84145e106	−1.12365
$852$	−3.26000e106	−0.356592
$853$	4.32735e106	0.453505	0.226753	−	0.973952i	$-0.427189\pi$
$853$	4.32735e106	0.453505	0.226753	+	0.973952i	$0.427189\pi$
$854$	−8.04550e105	−0.0807868
$855$	1.15214e106	0.110852
$856$	1.62990e106	0.150269
$857$	−2.66836e106	−0.235746	−0.117873	−	0.993029i	$-0.537608\pi$
$857$	−2.66836e106	−0.235746	−0.117873	+	0.993029i	$0.537608\pi$
$858$	−2.68225e105	−0.0227098
$859$	8.23486e106	0.668199	0.334100	−	0.942538i	$-0.391568\pi$
$859$	8.23486e106	0.668199	0.334100	+	0.942538i	$0.391568\pi$
$860$	4.05119e106	0.315057
$861$	4.60736e105	0.0343429
$862$	−1.42634e106	−0.101908
$863$	8.24432e106	0.564626	0.282313	−	0.959322i	$-0.408898\pi$
$863$	8.24432e106	0.564626	0.282313	+	0.959322i	$0.408898\pi$
$864$	2.06457e106	0.135544
$865$	4.24543e106	0.267198
$866$	−1.14187e107	−0.688992
$867$	−1.82809e107	−1.05755
$868$	6.48098e105	0.0359477
$869$	−2.45674e104	−0.00130658
$870$	8.35918e106	0.426296
$871$	−3.08979e107	−1.51101
$872$	−4.46215e105	−0.0209263
$873$	1.70043e106	0.0764782
$874$	−1.88858e107	−0.814644
$875$	1.72573e106	0.0713969
$876$	−1.85302e107	−0.735327
$877$	−3.47099e107	−1.32120	−0.660600	−	0.750738i	$-0.729698\pi$
$877$	−3.47099e107	−1.32120	−0.660600	+	0.750738i	$0.729698\pi$
$878$	9.27035e105	0.0338491
$879$	4.34162e107	1.52075
$880$	−8.39072e104	−0.00281956
$881$	−5.58005e106	−0.179894	−0.0899472	−	0.995947i	$-0.528670\pi$
$881$	−5.58005e106	−0.179894	−0.0899472	+	0.995947i	$0.528670\pi$
$882$	7.60455e106	0.235218
$883$	4.50047e107	1.33565	0.667824	−	0.744320i	$-0.267226\pi$
$883$	4.50047e107	1.33565	0.667824	+	0.744320i	$0.267226\pi$
$884$	−4.28512e106	−0.122027
$885$	6.26582e105	0.0171218
$886$	−2.70185e107	−0.708484
$887$	5.29484e107	1.33242	0.666209	−	0.745765i	$-0.267916\pi$
$887$	5.29484e107	1.33242	0.666209	+	0.745765i	$0.267916\pi$
$888$	−1.60162e107	−0.386800
$889$	−2.47267e106	−0.0573128
$890$	1.10803e107	0.246500
$891$	−1.90491e106	−0.0406761
$892$	−2.44680e107	−0.501513
$893$	2.44962e107	0.481971
$894$	6.65223e107	1.25646
$895$	−2.22635e107	−0.403694
$896$	−5.66964e105	−0.00986991
$897$	−6.86300e107	−1.14707
$898$	2.33028e107	0.373958
$899$	6.42292e107	0.989701
$900$	−1.00732e107	−0.149045
$901$	−1.23358e107	−0.175272
$902$	−4.58331e105	−0.00625375
$903$	−1.83028e107	−0.239836
$904$	−7.38336e106	−0.0929194
$905$	−2.21593e107	−0.267844
$906$	1.05172e108	1.22102
$907$	−7.96720e107	−0.888464	−0.444232	−	0.895912i	$-0.646523\pi$
$907$	−7.96720e107	−0.888464	−0.444232	+	0.895912i	$0.646523\pi$
$908$	6.22610e107	0.666934
$909$	−5.72772e107	−0.589387
$910$	2.26354e106	0.0223757
$911$	9.49752e107	0.901965	0.450982	−	0.892533i	$-0.351074\pi$
$911$	9.49752e107	0.901965	0.450982	+	0.892533i	$0.351074\pi$
$912$	−3.07352e107	−0.280430
$913$	−3.75441e106	−0.0329123
$914$	−3.67614e106	−0.0309639
$915$	−4.95807e107	−0.401276
$916$	7.61099e107	0.591911
$917$	−1.73867e107	−0.129938
$918$	−2.20533e107	−0.158385
$919$	4.69059e106	0.0323751	0.0161876	−	0.999869i	$-0.494847\pi$
$919$	4.69059e106	0.0323751	0.0161876	+	0.999869i	$0.494847\pi$
$920$	−2.14691e107	−0.142416
$921$	−1.78281e108	−1.13665
$922$	−1.82958e108	−1.12117
$923$	−8.74847e107	−0.515312
$924$	3.79082e105	0.00214638
$925$	−1.53843e108	−0.837345
$926$	−8.33167e107	−0.435944
$927$	−6.61227e107	−0.332614
$928$	−5.61884e107	−0.271735
$929$	9.33420e107	0.434014	0.217007	−	0.976170i	$-0.430371\pi$
$929$	9.33420e107	0.434014	0.217007	+	0.976170i	$0.430371\pi$
$930$	3.99393e107	0.178555
$931$	2.22873e108	0.958063
$932$	1.36964e108	0.566142
$933$	4.66597e108	1.85465
$934$	−8.05407e107	−0.307861
$935$	8.96276e105	0.00329472
$936$	−2.81428e107	−0.0994945
$937$	−3.60458e108	−1.22563	−0.612815	−	0.790227i	$-0.709963\pi$
$937$	−3.60458e108	−1.22563	−0.612815	+	0.790227i	$0.709963\pi$
$938$	4.36680e107	0.142810
$939$	6.46524e108	2.03372
$940$	2.78470e107	0.0842580
$941$	4.97283e108	1.44738	0.723690	−	0.690125i	$-0.242445\pi$
$941$	4.97283e108	1.44738	0.723690	+	0.690125i	$0.242445\pi$
$942$	9.67768e107	0.270965
$943$	−1.17272e108	−0.315877
$944$	−4.21174e106	−0.0109140
$945$	1.16492e107	0.0290426
$946$	1.82072e107	0.0436735
$947$	−2.44879e107	−0.0565169	−0.0282584	−	0.999601i	$-0.508996\pi$
$947$	−2.44879e107	−0.0565169	−0.0282584	+	0.999601i	$0.508996\pi$
$948$	−1.02300e107	−0.0227180
$949$	−4.97273e108	−1.06262
$950$	−2.95225e108	−0.607074
$951$	1.00745e109	1.99359
$952$	6.05617e106	0.0115332
$953$	−9.43485e108	−1.72920	−0.864598	−	0.502464i	$-0.832427\pi$
$953$	−9.43485e108	−1.72920	−0.864598	+	0.502464i	$0.832427\pi$
$954$	−8.10161e107	−0.142908
$955$	−3.81181e108	−0.647154
$956$	−4.71891e107	−0.0771131
$957$	3.75686e107	0.0590935
$958$	−5.09064e108	−0.770782
$959$	9.96762e107	0.145282
$960$	−3.49394e107	−0.0490247
$961$	−4.33412e108	−0.585461
$962$	−4.29809e108	−0.558966
$963$	−1.14343e108	−0.143169
$964$	4.52820e108	0.545901
$965$	−6.65587e107	−0.0772605
$966$	9.69948e107	0.108414
$967$	−1.61324e108	−0.173633	−0.0868164	−	0.996224i	$-0.527669\pi$
$967$	−1.61324e108	−0.173633	−0.0868164	+	0.996224i	$0.527669\pi$
$968$	3.40742e108	0.353163
$969$	3.28306e108	0.327688
$970$	5.66527e107	0.0544568
$971$	3.21844e108	0.297950	0.148975	−	0.988841i	$-0.452403\pi$
$971$	3.21844e108	0.297950	0.148975	+	0.988841i	$0.452403\pi$
$972$	−3.63242e108	−0.323875
$973$	−4.26135e105	−0.000365955 0
$974$	1.63524e109	1.35263
$975$	−1.07283e109	−0.854799
$976$	3.33270e108	0.255787
$977$	−1.43332e109	−1.05972	−0.529862	−	0.848084i	$-0.677756\pi$
$977$	−1.43332e109	−1.05972	−0.529862	+	0.848084i	$0.677756\pi$
$978$	1.18632e108	0.0844955
$979$	4.97981e107	0.0341700
$980$	2.53359e108	0.167488
$981$	3.13033e107	0.0199375
$982$	1.35716e109	0.832838
$983$	−1.45244e109	−0.858805	−0.429403	−	0.903113i	$-0.641276\pi$
$983$	−1.45244e109	−0.858805	−0.429403	+	0.903113i	$0.641276\pi$
$984$	−1.90851e108	−0.108736
$985$	1.04631e109	0.574430
$986$	6.00191e108	0.317528
$987$	−1.25809e108	−0.0641411
$988$	−8.24805e108	−0.405250
$989$	4.65864e109	2.20594
$990$	5.88634e106	0.00268634
$991$	8.66392e108	0.381089	0.190544	−	0.981679i	$-0.438975\pi$
$991$	8.66392e108	0.381089	0.190544	+	0.981679i	$0.438975\pi$
$992$	−2.68463e108	−0.113817
$993$	−3.23958e108	−0.132386
$994$	1.23642e108	0.0487039
$995$	−1.16941e108	−0.0444042
$996$	−1.56336e109	−0.572258
$997$	1.09926e109	0.387905	0.193953	−	0.981011i	$-0.437869\pi$
$997$	1.09926e109	0.387905	0.193953	+	0.981011i	$0.437869\pi$
$998$	7.89938e108	0.268738
$999$	−2.21200e109	−0.725512

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2.74.a.a.1.3	✓	3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2.74.a.a.1.3	✓	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:	\( k \)	\(=\)	\( 74 \)
Character orbit:	\([\chi]\)	\(=\)	2.a (trivial)

\(f(q)\)	\(=\)	\(q-6.87195e10 q^{2} +3.00585e17 q^{3} +4.72237e21 q^{4} -1.10375e25 q^{5} -2.06560e28 q^{6} +7.83423e29 q^{7} -3.24519e32 q^{8} +2.27660e34 q^{9} +O(q^{10})\)	\(q-6.87195e10 q^{2} +3.00585e17 q^{3} +4.72237e21 q^{4} -1.10375e25 q^{5} -2.06560e28 q^{6} +7.83423e29 q^{7} -3.24519e32 q^{8} +2.27660e34 q^{9} +7.58489e35 q^{10} +3.40887e36 q^{11} +1.41947e39 q^{12} +3.80927e40 q^{13} -5.38364e40 q^{14} -3.31769e42 q^{15} +2.23007e43 q^{16} -2.38211e44 q^{17} -1.56447e45 q^{18} -4.58511e46 q^{19} -5.21229e46 q^{20} +2.35485e47 q^{21} -2.34256e47 q^{22} -5.99384e49 q^{23} -9.75453e49 q^{24} -9.36966e50 q^{25} -2.61771e51 q^{26} -1.34720e52 q^{27} +3.69961e51 q^{28} +3.66647e53 q^{29} +2.27990e53 q^{30} +1.75180e54 q^{31} -1.53250e54 q^{32} +1.02465e54 q^{33} +1.63697e55 q^{34} -8.64700e54 q^{35} +1.07509e56 q^{36} +1.64193e57 q^{37} +3.15086e57 q^{38} +1.14501e58 q^{39} +3.58186e57 q^{40} +1.95654e58 q^{41} -1.61824e58 q^{42} -7.77238e59 q^{43} +1.60979e58 q^{44} -2.51279e59 q^{45} +4.11894e60 q^{46} -5.34256e60 q^{47} +6.70326e60 q^{48} -4.86080e61 q^{49} +6.43878e61 q^{50} -7.16026e61 q^{51} +1.79888e62 q^{52} +5.17851e62 q^{53} +9.25787e62 q^{54} -3.76253e61 q^{55} -2.54235e62 q^{56} -1.37821e64 q^{57} -2.51958e64 q^{58} -1.88861e63 q^{59} -1.56674e64 q^{60} +1.49443e65 q^{61} -1.20383e65 q^{62} +1.78354e64 q^{63} +1.05312e65 q^{64} -4.20447e65 q^{65} -7.04137e64 q^{66} -8.11124e66 q^{67} -1.12492e66 q^{68} -1.80166e67 q^{69} +5.94218e65 q^{70} -2.29663e67 q^{71} -7.38798e66 q^{72} -1.30543e68 q^{73} -1.12832e68 q^{74} -2.81638e68 q^{75} -2.16526e68 q^{76} +2.67059e66 q^{77} -7.86844e68 q^{78} -7.20690e67 q^{79} -2.46144e68 q^{80} -5.58811e69 q^{81} -1.34452e69 q^{82} -1.10136e70 q^{83} +1.11205e69 q^{84} +2.62925e69 q^{85} +5.34114e70 q^{86} +1.10208e71 q^{87} -1.10624e69 q^{88} +1.46084e71 q^{89} +1.72677e70 q^{90} +2.98427e70 q^{91} -2.83051e71 q^{92} +5.26565e71 q^{93} +3.67138e71 q^{94} +5.06080e71 q^{95} -4.60645e71 q^{96} +7.46916e71 q^{97} +3.34032e72 q^{98} +7.76062e70 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 206158430208 q^{2} - 30\!\cdots\!72 q^{3}+ \cdots + 74\!\cdots\!59 q^{9}+O(q^{10}) \) 3 * q - 206158430208 * q^2 - 304039201019733972 * q^3 + 14167099448608935641088 * q^4 - 32711891603319524297119950 * q^5 + 20893414801307636165762875392 * q^6 - 2317351391358079018994287149864 * q^7 - 973555660975280180349468061728768 * q^8 + 74999430902894237070706277077434759 * q^9	\( 3 q - 206158430208 q^{2} - 30\!\cdots\!72 q^{3}+ \cdots + 32\!\cdots\!68 q^{99}+O(q^{100}) \) 3 * q - 206158430208 * q^2 - 304039201019733972 * q^3 + 14167099448608935641088 * q^4 - 32711891603319524297119950 * q^5 + 20893414801307636165762875392 * q^6 - 2317351391358079018994287149864 * q^7 - 973555660975280180349468061728768 * q^8 + 74999430902894237070706277077434759 * q^9 + 2247944074024869790310521155826483200 * q^10 - 80375859598797955703316945252313090044 * q^11 - 1435784532374058165872294155193010880512 * q^12 + 15026661416812586037400802096858217302538 * q^13 + 159247175027568742591427617911982893563904 * q^14 + 7424951702099224865385711195171330840721800 * q^15 + 66902235595591869424607154817945084517941248 * q^16 - 2021347643337102701650698954881277124608770634 * q^17 - 5153921647144679999448868794711947991658266624 * q^18 - 41519603636932196567332785885639339838588921380 * q^19 - 154477540498781101440673056783853843115094835200 * q^20 + 2186519362115879326463070410595449406900134231136 * q^21 + 5523387013835598410518447337300915041466931216384 * q^22 + 78904625597138588218784441638852494338574996350088 * q^23 + 98666361770387728979571947344734884793139259768832 * q^24 + 981710467323228821808618065764062137601115897768125 * q^25 - 1032624309652401305469162845602788282612192764755968 * q^26 + 8808207209598604044615652223279905336946557309792440 * q^27 - 10943382539580730365152382542130405349894665057337344 * q^28 + 166169304839024523153256155301347408902947424090145210 * q^29 - 510238795758331285500506112143391025243141056548044800 * q^30 + 954831074549949113941638258046298891637893269618118496 * q^31 - 4597486622597666575075041081450927550856217366550806528 * q^32 + 17544371641343847605198741899708079964205455873834669456 * q^33 + 138905952351672454511727955628103437006521386684722970624 * q^34 + 944528033393088066738035187184051695420046345746643971600 * q^35 + 354174798730125638048291031959724069834002175330053259264 * q^36 + 95831145035300740325039173416127783864165954459868024466 * q^37 + 2853205436216103072418204437238261770524309377840243015680 * q^38 + 20048825363764869028111320157141908997200830310277187046888 * q^39 + 10615615750540485736808788209840051152371953297960153907200 * q^40 + 150686231920032912821976395324429812389071948843348708195646 * q^41 - 150256466437735729111062316244043953424938772171827598852096 * q^42 - 473903333795313868852861303848307239502353736089051202446492 * q^43 - 379564265401199915100261019494491376223599255037612470042624 * q^44 - 3350842048629098689796948549122862280644512526482879102711350 * q^45 - 5422284583085355321268641115399873698435276169071157227552768 * q^46 - 12516424326520457880934881888127294200274501425051317572353264 * q^47 - 6780300752305919315311567454794725887629773534092511361892352 * q^48 + 80205164513526274948509534215913453598538485989498574623052011 * q^49 - 67462629620706311212682018614582786129738314784316420259840000 * q^50 + 514251632907479503542992104878952048928310680088916651551144216 * q^51 + 70961402224186251757724165733796369283701974007595263693160448 * q^52 + 1430548926948567355941996145547633585160394945423663769186222658 * q^53 - 605295390425878746542040819019150132418581186325572325568675840 * q^54 - 7121556178756880336995070499297110193922212727411086674935031400 * q^55 + 752023521841866599521977937198902930320336375458205717112029184 * q^56 - 15654317649185594603288320010783267868078052464546138261971761680 * q^57 - 11419067678122637943763679726879746335559974791593859725456834560 * q^58 - 38710586306395695712277475638393838858193803462160314268223532780 * q^59 + 35063343054919302252133003889663566655347220579019825099885772800 * q^60 - 133023502656151161720833761205788214903429689958710055454248963814 * q^61 - 65615491814345109805496223535540201494812791477573269589963309056 * q^62 - 676013503772547172347240007080849436653347156788941846276439197192 * q^63 + 315936875005671560093754083051011296956685286201647333762932932608 * q^64 + 1304279076912397427943938897940602441228625233151093819412708578300 * q^65 - 1205640038855066671282184256633457846291444537646256118791841775616 * q^66 - 10079574725514314413922516603802294422053580576623992539839093997844 * q^67 - 9545544361122679728510707485946294407171287912567280346400779403264 * q^68 - 57254624867981027449877853695190995327525407937353126334506438578912 * q^69 - 64907472217256146545403624452043845833639232604578312956440844697600 * q^70 - 115560233707768569360415193898496587754138245400713479870885379282024 * q^71 - 24338706841812351126216692015313690705936951869366988071633424482304 * q^72 - 154467257799518470489462616345503055869489343767852516092429168112482 * q^73 - 6585466141837591123530106555858262890456788491548136152921565822976 * q^74 - 952496562905106180077615512164377636529129991330375732809810503347500 * q^75 - 196070784597081226953620923087686701828623448812959213840608243220480 * q^76 - 1800719846849724861947803912683649646585331632872965881331191256968928 * q^77 - 1377744788169366654551382795556961279583771547626976816980140457197568 * q^78 - 4090300229098013083258477274117496841157332448206465760698517921562000 * q^79 - 729499559607582089016771340266454481446474435878051272680809902899200 * q^80 - 15201171092964708833522221028549040215131141432253228096270731424296917 * q^81 - 10355079008864202365024123008038293664935674369170683661186347833491456 * q^82 + 4825306524476108361839066204321180630013251338979638337731931270725788 * q^83 + 10325545749801545229163644801378853355946547476486310873919351376838656 * q^84 + 64402214916599555092605132019399363126870275972818152260490003075220100 * q^85 + 32566389121859913996452357376838376617962377784414237730834533278810112 * q^86 + 142543957488352500896861000833280505529834792013096113880266858327752360 * q^87 + 26083457706054687272217562236679342608550252540744140940077596896395264 * q^88 + 451463179833471932378016997715778802210673362338548837237321638477742670 * q^89 + 230268112206777928106149486385237487700482481649700794401073170848153600 * q^90 + 422354934089645630580068981961457451511973101688314707373850544534133456 * q^91 + 372616559263305534102214189136054711956961240302220591827410698788405248 * q^92 + 571168450314051543320826159340295464004746879040928540630191772427149696 * q^93 + 860122130324227073176972473842071348402391325492812865519478122221666304 * q^94 - 51353744965069329589794354056658553367168025175850659034300728742247000 * q^95 + 465938719811169920743646308301460897290471172557018837405377160200323072 * q^96 + 76854610208052175214348870937789175369657249934277291200976504477234726 * q^97 - 5511656936894321608648840534424660575554180971556009239113982639232516096 * q^98 + 3215801878115629026673420709123093980129069916698003588659485833337177268 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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