LMFDB - Embedded newform 2.74.a.a.1.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [2,74,Mod(1,2)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://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);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2, base_ring=CyclotomicField(1)) chi = DirichletCharacter(H, H._module([])) N = Newforms(chi, 74, names="a")

Level:	$ N $	$=$	$ 2 $
Weight:	$ k $	$=$	$ 74 $
Character orbit:	$[\chi]$	$=$	2.a (trivial)

Newform invariants

comment:select newform

sage:traces = [3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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			1.1
Root			$-1.44110e13$ 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)

$f(q)$	$=$	\(q-6.87195e10 q^{2} -3.50368e17 q^{3} +4.72237e21 q^{4} -5.44340e25 q^{5} +2.40771e28 q^{6} -1.20967e31 q^{7} -3.24519e32 q^{8} +5.51727e34 q^{9} +3.74068e36 q^{10} +4.97648e37 q^{11} -1.65457e39 q^{12} -2.84466e40 q^{13} +8.31279e41 q^{14} +1.90720e43 q^{15} +2.23007e43 q^{16} -1.37840e45 q^{17} -3.79144e45 q^{18} +8.02045e45 q^{19} -2.57058e47 q^{20} +4.23830e48 q^{21} -3.41981e48 q^{22} +4.09563e49 q^{23} +1.13701e50 q^{24} +1.90427e51 q^{25} +1.95483e51 q^{26} +4.34894e51 q^{27} -5.71250e52 q^{28} +1.93908e53 q^{29} -1.31062e54 q^{30} +1.64422e54 q^{31} -1.53250e54 q^{32} -1.74360e55 q^{33} +9.47230e55 q^{34} +6.58472e56 q^{35} +2.60546e56 q^{36} -2.76462e57 q^{37} -5.51161e56 q^{38} +9.96677e57 q^{39} +1.76649e58 q^{40} +5.83879e58 q^{41} -2.91254e59 q^{42} +5.73993e59 q^{43} +2.35008e59 q^{44} -3.00327e60 q^{45} -2.81449e60 q^{46} -1.00447e61 q^{47} -7.81347e60 q^{48} +9.71083e61 q^{49} -1.30861e62 q^{50} +4.82948e62 q^{51} -1.34335e62 q^{52} -3.54191e62 q^{53} -2.98857e62 q^{54} -2.70890e63 q^{55} +3.92560e63 q^{56} -2.81011e63 q^{57} -1.33252e64 q^{58} -1.77576e64 q^{59} +9.00648e64 q^{60} -8.28520e64 q^{61} -1.12990e65 q^{62} -6.67408e65 q^{63} +1.05312e65 q^{64} +1.54846e66 q^{65} +1.19819e66 q^{66} -3.24702e66 q^{67} -6.50931e66 q^{68} -1.43498e67 q^{69} -4.52499e67 q^{70} -3.58492e67 q^{71} -1.79046e67 q^{72} +1.10301e67 q^{73} +1.89984e68 q^{74} -6.67197e68 q^{75} +3.78755e67 q^{76} -6.01990e68 q^{77} -6.84911e68 q^{78} -7.67262e68 q^{79} -1.21392e69 q^{80} -5.25259e69 q^{81} -4.01238e69 q^{82} -5.36941e69 q^{83} +2.00148e70 q^{84} +7.50319e70 q^{85} -3.94445e70 q^{86} -6.79391e70 q^{87} -1.61496e70 q^{88} +2.49415e71 q^{89} +2.06383e71 q^{90} +3.44109e71 q^{91} +1.93410e71 q^{92} -5.76082e71 q^{93} +6.90270e71 q^{94} -4.36585e71 q^{95} +5.36938e71 q^{96} +9.96943e71 q^{97} -6.67323e72 q^{98} +2.74566e72 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 206158430208 q^{2} - 30\!\cdots\!72 q^{3} + 14\!\cdots\!88 q^{4} - 32\!\cdots\!50 q^{5} + 20\!\cdots\!92 q^{6} - 23\!\cdots\!64 q^{7} - 97\!\cdots\!68 q^{8} + 74\!\cdots\!59 q^{9} + 22\!\cdots\!00 q^{10}+ \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

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
$3$	−3.50368e17	−1.34772	−0.673859	−	0.738860i	$-0.735364\pi$
$3$	−3.50368e17	−1.34772	−0.673859	+	0.738860i	$0.735364\pi$
$4$	4.72237e21	0.500000
$5$	−5.44340e25	−1.67288	−0.836441	−	0.548056i	$-0.815368\pi$
$5$	−5.44340e25	−1.67288	−0.836441	+	0.548056i	$0.815368\pi$
$6$	2.40771e28	0.952980
$7$	−1.20967e31	−1.72420	−0.862101	−	0.506736i	$-0.830852\pi$
$7$	−1.20967e31	−1.72420	−0.862101	+	0.506736i	$0.830852\pi$
$8$	−3.24519e32	−0.353553
$9$	5.51727e34	0.816343
$10$	3.74068e36	1.18291
$11$	4.97648e37	0.485388	0.242694	−	0.970103i	$-0.421969\pi$
$11$	4.97648e37	0.485388	0.242694	+	0.970103i	$0.421969\pi$
$12$	−1.65457e39	−0.673859
$13$	−2.84466e40	−0.623875	−0.311937	−	0.950103i	$-0.600978\pi$
$13$	−2.84466e40	−0.623875	−0.311937	+	0.950103i	$0.600978\pi$
$14$	8.31279e41	1.21920
$15$	1.90720e43	2.25457
$16$	2.23007e43	0.250000
$17$	−1.37840e45	−1.69040	−0.845201	−	0.534449i	$-0.820519\pi$
$17$	−1.37840e45	−1.69040	−0.845201	+	0.534449i	$0.820519\pi$
$18$	−3.79144e45	−0.577242
$19$	8.02045e45	0.169704	0.0848520	−	0.996394i	$-0.472958\pi$
$19$	8.02045e45	0.169704	0.0848520	+	0.996394i	$0.472958\pi$
$20$	−2.57058e47	−0.836441
$21$	4.23830e48	2.32374
$22$	−3.41981e48	−0.343221
$23$	4.09563e49	0.811436	0.405718	−	0.913998i	$-0.367021\pi$
$23$	4.09563e49	0.811436	0.405718	+	0.913998i	$0.367021\pi$
$24$	1.13701e50	0.476490
$25$	1.90427e51	1.79854
$26$	1.95483e51	0.441146
$27$	4.34894e51	0.247518
$28$	−5.71250e52	−0.862101
$29$	1.93908e53	0.812958	0.406479	−	0.913660i	$-0.366756\pi$
$29$	1.93908e53	0.812958	0.406479	+	0.913660i	$0.366756\pi$
$30$	−1.31062e54	−1.59422
$31$	1.64422e54	0.604307	0.302154	−	0.953259i	$-0.402294\pi$
$31$	1.64422e54	0.604307	0.302154	+	0.953259i	$0.402294\pi$
$32$	−1.53250e54	−0.176777
$33$	−1.74360e55	−0.654166
$34$	9.47230e55	1.19529
$35$	6.58472e56	2.88439
$36$	2.60546e56	0.408172
$37$	−2.76462e57	−1.59321	−0.796605	−	0.604500i	$-0.793373\pi$
$37$	−2.76462e57	−1.59321	−0.796605	+	0.604500i	$0.793373\pi$
$38$	−5.51161e56	−0.119999
$39$	9.96677e57	0.840807
$40$	1.76649e58	0.591453
$41$	5.83879e58	0.793801	0.396901	−	0.917862i	$-0.370086\pi$
$41$	5.83879e58	0.793801	0.396901	+	0.917862i	$0.370086\pi$
$42$	−2.91254e59	−1.64313
$43$	5.73993e59	1.37185	0.685927	−	0.727670i	$-0.259397\pi$
$43$	5.73993e59	1.37185	0.685927	+	0.727670i	$0.259397\pi$
$44$	2.35008e59	0.242694
$45$	−3.00327e60	−1.36565
$46$	−2.81449e60	−0.573772
$47$	−1.00447e61	−0.934044	−0.467022	−	0.884246i	$-0.654673\pi$
$47$	−1.00447e61	−0.934044	−0.467022	+	0.884246i	$0.654673\pi$
$48$	−7.81347e60	−0.336929
$49$	9.71083e61	1.97287
$50$	−1.30861e62	−1.27176
$51$	4.82948e62	2.27818
$52$	−1.34335e62	−0.311937
$53$	−3.54191e62	−0.410363	−0.205182	−	0.978724i	$-0.565779\pi$
$53$	−3.54191e62	−0.410363	−0.205182	+	0.978724i	$0.565779\pi$
$54$	−2.98857e62	−0.175021
$55$	−2.70890e63	−0.811997
$56$	3.92560e63	0.609598
$57$	−2.81011e63	−0.228713
$58$	−1.33252e64	−0.574848
$59$	−1.77576e64	−0.410475	−0.205237	−	0.978712i	$-0.565797\pi$
$59$	−1.77576e64	−0.410475	−0.205237	+	0.978712i	$0.565797\pi$
$60$	9.00648e64	1.12729
$61$	−8.28520e64	−0.567237	−0.283618	−	0.958937i	$-0.591535\pi$
$61$	−8.28520e64	−0.567237	−0.283618	+	0.958937i	$0.591535\pi$
$62$	−1.12990e65	−0.427310
$63$	−6.67408e65	−1.40754
$64$	1.05312e65	0.125000
$65$	1.54846e66	1.04367
$66$	1.19819e66	0.462565
$67$	−3.24702e66	−0.724026	−0.362013	−	0.932173i	$-0.617910\pi$
$67$	−3.24702e66	−0.724026	−0.362013	+	0.932173i	$0.617910\pi$
$68$	−6.50931e66	−0.845201
$69$	−1.43498e67	−1.09359
$70$	−4.52499e67	−2.03957
$71$	−3.58492e67	−0.962829	−0.481415	−	0.876493i	$-0.659877\pi$
$71$	−3.58492e67	−0.962829	−0.481415	+	0.876493i	$0.659877\pi$
$72$	−1.79046e67	−0.288621
$73$	1.10301e67	0.107472	0.0537359	−	0.998555i	$-0.482887\pi$
$73$	1.10301e67	0.107472	0.0537359	+	0.998555i	$0.482887\pi$
$74$	1.89984e68	1.12657
$75$	−6.67197e68	−2.42392
$76$	3.78755e67	0.0848520
$77$	−6.01990e68	−0.836908
$78$	−6.84911e68	−0.594540
$79$	−7.67262e68	−0.418364	−0.209182	−	0.977877i	$-0.567080\pi$
$79$	−7.67262e68	−0.418364	−0.209182	+	0.977877i	$0.567080\pi$
$80$	−1.21392e69	−0.418221
$81$	−5.25259e69	−1.14993
$82$	−4.01238e69	−0.561302
$83$	−5.36941e69	−0.482588	−0.241294	−	0.970452i	$-0.577572\pi$
$83$	−5.36941e69	−0.482588	−0.241294	+	0.970452i	$0.577572\pi$
$84$	2.00148e70	1.16187
$85$	7.50319e70	2.82784
$86$	−3.94445e70	−0.970048
$87$	−6.79391e70	−1.09564
$88$	−1.61496e70	−0.171611
$89$	2.49415e71	1.75464	0.877320	−	0.479906i	$-0.159329\pi$
$89$	2.49415e71	1.75464	0.877320	+	0.479906i	$0.159329\pi$
$90$	2.06383e71	0.965658
$91$	3.44109e71	1.07569
$92$	1.93410e71	0.405718
$93$	−5.76082e71	−0.814436
$94$	6.90270e71	0.660469
$95$	−4.36585e71	−0.283895
$96$	5.36938e71	0.238245
$97$	9.96943e71	0.303042	0.151521	−	0.988454i	$-0.451583\pi$
$97$	9.96943e71	0.303042	0.151521	+	0.988454i	$0.451583\pi$
$98$	−6.67323e72	−1.39503
$99$	2.74566e72	0.396243
$100$	8.99268e72	0.899268
$101$	−4.04089e72	−0.281027	−0.140513	−	0.990079i	$-0.544875\pi$
$101$	−4.04089e72	−0.281027	−0.140513	+	0.990079i	$0.544875\pi$
$102$	−3.31879e73	−1.61092
$103$	3.18220e73	1.08186	0.540928	−	0.841069i	$-0.318073\pi$
$103$	3.18220e73	1.08186	0.540928	+	0.841069i	$0.318073\pi$
$104$	9.23144e72	0.220573
$105$	−2.30708e74	−3.88734
$106$	2.43398e73	0.290171
$107$	−3.52638e73	−0.298416	−0.149208	−	0.988806i	$-0.547672\pi$
$107$	−3.52638e73	−0.298416	−0.149208	+	0.988806i	$0.547672\pi$
$108$	2.05373e73	0.123759
$109$	−6.49727e73	−0.279682	−0.139841	−	0.990174i	$-0.544659\pi$
$109$	−6.49727e73	−0.279682	−0.139841	+	0.990174i	$0.544659\pi$
$110$	1.86154e74	0.574169
$111$	9.68637e74	2.14720
$112$	−2.69765e74	−0.431051
$113$	1.24576e75	1.43904	0.719518	−	0.694473i	$-0.244363\pi$
$113$	1.24576e75	1.43904	0.719518	+	0.694473i	$0.244363\pi$
$114$	1.93109e74	0.161725
$115$	−2.22942e75	−1.35744
$116$	9.15703e74	0.406479
$117$	−1.56947e75	−0.509296
$118$	1.22029e75	0.290249
$119$	1.66741e76	2.91460
$120$	−6.18921e75	−0.797112
$121$	−8.03500e75	−0.764398
$122$	5.69355e75	0.401097
$123$	−2.04573e76	−1.06982
$124$	7.76460e75	0.302154
$125$	−4.60231e76	−1.33586
$126$	4.58639e76	0.995282
$127$	−1.96521e76	−0.319575	−0.159788	−	0.987151i	$-0.551081\pi$
$127$	−1.96521e76	−0.319575	−0.159788	+	0.987151i	$0.551081\pi$
$128$	−7.23701e75	−0.0883883
$129$	−2.01109e77	−1.84887
$130$	−1.06409e77	−0.737986
$131$	2.57954e77	1.35251	0.676254	−	0.736669i	$-0.263602\pi$
$131$	2.57954e77	1.35251	0.676254	+	0.736669i	$0.263602\pi$
$132$	−8.23392e76	−0.327083
$133$	−9.70209e76	−0.292604
$134$	2.23133e77	0.511964
$135$	−2.36730e77	−0.414068
$136$	4.47317e77	0.597647
$137$	6.46446e77	0.661045	0.330523	−	0.943798i	$-0.392775\pi$
$137$	6.46446e77	0.661045	0.330523	+	0.943798i	$0.392775\pi$
$138$	9.86109e77	0.773283
$139$	−1.93602e78	−1.16646	−0.583230	−	0.812307i	$-0.698211\pi$
$139$	−1.93602e78	−1.16646	−0.583230	+	0.812307i	$0.698211\pi$
$140$	3.10955e78	1.44219
$141$	3.51936e78	1.25883
$142$	2.46354e78	0.680823
$143$	−1.41564e78	−0.302821
$144$	1.23039e78	0.204086
$145$	−1.05552e79	−1.35998
$146$	−7.57982e77	−0.0759941
$147$	−3.40237e79	−2.65888
$148$	−1.30556e79	−0.796605
$149$	3.27361e79	1.56217	0.781084	−	0.624426i	$-0.214667\pi$
$149$	3.27361e79	1.56217	0.781084	+	0.624426i	$0.214667\pi$
$150$	4.58495e79	1.71397
$151$	−2.12822e79	−0.624250	−0.312125	−	0.950041i	$-0.601041\pi$
$151$	−2.12822e79	−0.624250	−0.312125	+	0.950041i	$0.601041\pi$
$152$	−2.60278e78	−0.0599994
$153$	−7.60501e79	−1.37995
$154$	4.13684e79	0.591783
$155$	−8.95015e79	−1.01094
$156$	4.70668e79	0.420404
$157$	−6.66095e79	−0.471193	−0.235596	−	0.971851i	$-0.575704\pi$
$157$	−6.66095e79	−0.471193	−0.235596	+	0.971851i	$0.575704\pi$
$158$	5.27258e79	0.295828
$159$	1.24097e80	0.553054
$160$	8.34199e79	0.295727
$161$	−4.95435e80	−1.39908
$162$	3.60955e80	0.813121
$163$	1.04855e81	1.88687	0.943436	−	0.331554i	$-0.107573\pi$
$163$	1.04855e81	1.88687	0.943436	+	0.331554i	$0.107573\pi$
$164$	2.75729e80	0.396901
$165$	9.49112e80	1.09434
$166$	3.68983e80	0.341241
$167$	−2.09279e80	−0.155444	−0.0777222	−	0.996975i	$-0.524765\pi$
$167$	−2.09279e80	−0.155444	−0.0777222	+	0.996975i	$0.524765\pi$
$168$	−1.37541e81	−0.821566
$169$	−1.26984e81	−0.610780
$170$	−5.15616e81	−1.99959
$171$	4.42510e80	0.138537
$172$	2.71061e81	0.685927
$173$	3.82035e81	0.782385	0.391193	−	0.920309i	$-0.372063\pi$
$173$	3.82035e81	0.782385	0.391193	+	0.920309i	$0.372063\pi$
$174$	4.66874e81	0.774733
$175$	−2.30354e82	−3.10104
$176$	1.10979e81	0.121347
$177$	6.22171e81	0.553204
$178$	−1.71397e82	−1.24072
$179$	1.66267e82	0.981002	0.490501	−	0.871441i	$-0.336814\pi$
$179$	1.66267e82	0.981002	0.490501	+	0.871441i	$0.336814\pi$
$180$	−1.41826e82	−0.682823
$181$	2.78548e82	1.09555	0.547774	−	0.836626i	$-0.315475\pi$
$181$	2.78548e82	1.09555	0.547774	+	0.836626i	$0.315475\pi$
$182$	−2.36470e82	−0.760625
$183$	2.90287e82	0.764475
$184$	−1.32911e82	−0.286886
$185$	1.50490e83	2.66525
$186$	3.95881e82	0.575893
$187$	−6.85958e82	−0.820501
$188$	−4.74350e82	−0.467022
$189$	−5.26078e82	−0.426770
$190$	3.00019e82	0.200744
$191$	−4.94811e82	−0.273351	−0.136676	−	0.990616i	$-0.543642\pi$
$191$	−4.94811e82	−0.273351	−0.136676	+	0.990616i	$0.543642\pi$
$192$	−3.68981e82	−0.168465
$193$	2.93562e83	1.10881	0.554406	−	0.832246i	$-0.312945\pi$
$193$	2.93562e83	1.10881	0.554406	+	0.832246i	$0.312945\pi$
$194$	−6.85094e82	−0.214283
$195$	−5.42532e83	−1.40657
$196$	4.58581e83	0.986437
$197$	8.01765e82	0.143229	0.0716143	−	0.997432i	$-0.477185\pi$
$197$	8.01765e82	0.143229	0.0716143	+	0.997432i	$0.477185\pi$
$198$	−1.88680e83	−0.280186
$199$	−1.06209e84	−1.31227	−0.656136	−	0.754643i	$-0.727810\pi$
$199$	−1.06209e84	−1.31227	−0.656136	+	0.754643i	$0.727810\pi$
$200$	−6.17972e83	−0.635879
$201$	1.13765e84	0.975783
$202$	2.77688e83	0.198716
$203$	−2.34564e84	−1.40170
$204$	2.28066e84	1.13909
$205$	−3.17829e84	−1.32794
$206$	−2.18679e84	−0.764987
$207$	2.25967e84	0.662410
$208$	−6.34380e83	−0.155969
$209$	3.99136e83	0.0823723
$210$	1.58541e85	2.74877
$211$	9.15310e84	1.33432	0.667158	−	0.744917i	$-0.267511\pi$
$211$	9.15310e84	1.33432	0.667158	+	0.744917i	$0.267511\pi$
$212$	−1.67262e84	−0.205182
$213$	1.25604e85	1.29762
$214$	2.42331e84	0.211012
$215$	−3.12448e85	−2.29495
$216$	−1.41131e84	−0.0875107
$217$	−1.98896e85	−1.04195
$218$	4.46489e84	0.197765
$219$	−3.86459e84	−0.144842
$220$	−1.27924e85	−0.405999
$221$	3.92108e85	1.05460
$222$	−6.65642e85	−1.51830
$223$	−5.31542e84	−0.102899	−0.0514493	−	0.998676i	$-0.516384\pi$
$223$	−5.31542e84	−0.102899	−0.0514493	+	0.998676i	$0.516384\pi$
$224$	1.85381e85	0.304799
$225$	1.05064e86	1.46822
$226$	−8.56081e85	−1.01755
$227$	−1.26453e86	−1.27934	−0.639669	−	0.768651i	$-0.720928\pi$
$227$	−1.26453e86	−1.27934	−0.639669	+	0.768651i	$0.720928\pi$
$228$	−1.32704e85	−0.114357
$229$	−1.02207e86	−0.750737	−0.375368	−	0.926876i	$-0.622484\pi$
$229$	−1.02207e86	−0.750737	−0.375368	+	0.926876i	$0.622484\pi$
$230$	1.53204e86	0.959853
$231$	2.10918e86	1.12792
$232$	−6.29266e85	−0.287424
$233$	−1.22520e86	−0.478317	−0.239159	−	0.970981i	$-0.576872\pi$
$233$	−1.22520e86	−0.478317	−0.239159	+	0.970981i	$0.576872\pi$
$234$	1.07853e86	0.360127
$235$	5.46776e86	1.56255
$236$	−8.38580e85	−0.205237
$237$	2.68824e86	0.563837
$238$	−1.14584e87	−2.06093
$239$	1.22978e87	1.89803	0.949017	−	0.315226i	$-0.102080\pi$
$239$	1.22978e87	1.89803	0.949017	+	0.315226i	$0.102080\pi$
$240$	4.25319e86	0.563643
$241$	−9.17763e86	−1.04498	−0.522491	−	0.852645i	$-0.674997\pi$
$241$	−9.17763e86	−1.04498	−0.522491	+	0.852645i	$0.674997\pi$
$242$	5.52161e86	0.540511
$243$	1.54642e87	1.30226
$244$	−3.91258e86	−0.283618
$245$	−5.28600e87	−3.30039
$246$	1.40581e87	0.756477
$247$	−2.28154e86	−0.105874
$248$	−5.33580e86	−0.213655
$249$	1.88127e87	0.650392
$250$	3.16268e87	0.944594
$251$	−2.65298e87	−0.684926	−0.342463	−	0.939531i	$-0.611261\pi$
$251$	−2.65298e87	−0.684926	−0.342463	+	0.939531i	$0.611261\pi$
$252$	−3.15174e87	−0.703771
$253$	2.03818e87	0.393861
$254$	1.35048e87	0.225974
$255$	−2.62888e88	−3.81114
$256$	4.97323e86	0.0625000
$257$	−2.26844e87	−0.247268	−0.123634	−	0.992328i	$-0.539455\pi$
$257$	−2.26844e87	−0.247268	−0.123634	+	0.992328i	$0.539455\pi$
$258$	1.38201e88	1.30735
$259$	3.34428e88	2.74702
$260$	7.31240e87	0.521835
$261$	1.06984e88	0.663653
$262$	−1.77264e88	−0.956367
$263$	2.34718e88	1.10195	0.550976	−	0.834521i	$-0.314256\pi$
$263$	2.34718e88	1.10195	0.550976	+	0.834521i	$0.314256\pi$
$264$	5.65831e87	0.231283
$265$	1.92801e88	0.686490
$266$	6.66722e87	0.206902
$267$	−8.73872e88	−2.36476
$268$	−1.53336e88	−0.362013
$269$	6.33870e88	1.30630	0.653149	−	0.757230i	$-0.273448\pi$
$269$	6.33870e88	1.30630	0.653149	+	0.757230i	$0.273448\pi$
$270$	1.62680e88	0.292790
$271$	−4.61770e88	−0.726184	−0.363092	−	0.931753i	$-0.618279\pi$
$271$	−4.61770e88	−0.726184	−0.363092	+	0.931753i	$0.618279\pi$
$272$	−3.07394e88	−0.422600
$273$	−1.20565e89	−1.44972
$274$	−4.44234e88	−0.467430
$275$	9.47658e88	0.872988
$276$	−6.77649e88	−0.546793
$277$	3.58579e87	0.0253556	0.0126778	−	0.999920i	$-0.495964\pi$
$277$	3.58579e87	0.0253556	0.0126778	+	0.999920i	$0.495964\pi$
$278$	1.33042e89	0.824812
$279$	9.07160e88	0.493322
$280$	−2.13686e89	−1.01979
$281$	1.79606e89	0.752559	0.376280	−	0.926506i	$-0.377203\pi$
$281$	1.79606e89	0.752559	0.376280	+	0.926506i	$0.377203\pi$
$282$	−2.41849e89	−0.890125
$283$	1.85008e89	0.598392	0.299196	−	0.954192i	$-0.403282\pi$
$283$	1.85008e89	0.598392	0.299196	+	0.954192i	$0.403282\pi$
$284$	−1.69293e89	−0.481415
$285$	1.52966e89	0.382610
$286$	9.72819e88	0.214127
$287$	−7.06300e89	−1.36867
$288$	−8.45519e88	−0.144310
$289$	1.23507e90	1.85746
$290$	7.25346e89	0.961653
$291$	−3.49297e89	−0.408415
$292$	5.20881e88	0.0537359
$293$	−1.04226e90	−0.949093	−0.474547	−	0.880230i	$-0.657388\pi$
$293$	−1.04226e90	−0.949093	−0.474547	+	0.880230i	$0.657388\pi$
$294$	2.33809e90	1.88011
$295$	9.66619e89	0.686676
$296$	8.97172e89	0.563285
$297$	2.16424e89	0.120142
$298$	−2.24961e90	−1.10462
$299$	−1.16507e90	−0.506235
$300$	−3.15075e90	−1.21196
$301$	−6.94342e90	−2.36536
$302$	1.46250e90	0.441411
$303$	1.41580e90	0.378744
$304$	1.78862e89	0.0424260
$305$	4.50997e90	0.948920
$306$	5.22613e90	0.975771
$307$	−3.26773e90	−0.541620	−0.270810	−	0.962633i	$-0.587292\pi$
$307$	−3.26773e90	−0.541620	−0.270810	+	0.962633i	$0.587292\pi$
$308$	−2.84282e90	−0.418454
$309$	−1.11494e91	−1.45804
$310$	6.15050e90	0.714839
$311$	−8.51312e89	−0.0879700	−0.0439850	−	0.999032i	$-0.514005\pi$
$311$	−8.51312e89	−0.0879700	−0.0439850	+	0.999032i	$0.514005\pi$
$312$	−3.23440e90	−0.297270
$313$	−1.29306e91	−1.05742	−0.528712	−	0.848801i	$-0.677325\pi$
$313$	−1.29306e91	−1.05742	−0.528712	+	0.848801i	$0.677325\pi$
$314$	4.57737e90	0.333184
$315$	3.63297e91	2.35465
$316$	−3.62329e90	−0.209182
$317$	3.14601e91	1.61844	0.809220	−	0.587505i	$-0.199890\pi$
$317$	3.14601e91	1.61844	0.809220	+	0.587505i	$0.199890\pi$
$318$	−8.52791e90	−0.391068
$319$	9.64977e90	0.394600
$320$	−5.73257e90	−0.209110
$321$	1.23553e91	0.402180
$322$	3.40461e91	0.989299
$323$	−1.10554e91	−0.286868
$324$	−2.48047e91	−0.574963
$325$	−5.41701e91	−1.12206
$326$	−7.20560e91	−1.33422
$327$	2.27644e91	0.376932
$328$	−1.89479e91	−0.280651
$329$	1.21508e92	1.61048
$330$	−6.52225e91	−0.773818
$331$	−1.21441e92	−1.29016	−0.645082	−	0.764114i	$-0.723177\pi$
$331$	−1.21441e92	−1.29016	−0.645082	+	0.764114i	$0.723177\pi$
$332$	−2.53563e91	−0.241294
$333$	−1.52532e92	−1.30061
$334$	1.43816e91	0.109916
$335$	1.76748e92	1.21121
$336$	9.45172e91	0.580935
$337$	1.64422e92	0.906709	0.453354	−	0.891330i	$-0.350227\pi$
$337$	1.64422e92	0.906709	0.453354	+	0.891330i	$0.350227\pi$
$338$	8.72629e91	0.431887
$339$	−4.36476e92	−1.93942
$340$	3.54328e92	1.41392
$341$	8.18242e91	0.293324
$342$	−3.04090e91	−0.0979602
$343$	−5.79269e92	−1.67743
$344$	−1.86271e92	−0.485024
$345$	7.81116e92	1.82944
$346$	−2.62533e92	−0.553230
$347$	8.89317e91	0.168667	0.0843336	−	0.996438i	$-0.473124\pi$
$347$	8.89317e91	0.168667	0.0843336	+	0.996438i	$0.473124\pi$
$348$	−3.20833e92	−0.547819
$349$	1.07338e92	0.165054	0.0825269	−	0.996589i	$-0.473701\pi$
$349$	1.07338e92	0.165054	0.0825269	+	0.996589i	$0.473701\pi$
$350$	1.58298e93	2.19277
$351$	−1.23712e92	−0.154420
$352$	−7.62643e91	−0.0858053
$353$	9.90414e92	1.00471	0.502354	−	0.864662i	$-0.332467\pi$
$353$	9.90414e92	1.00471	0.502354	+	0.864662i	$0.332467\pi$
$354$	−4.27552e92	−0.391174
$355$	1.95142e93	1.61070
$356$	1.17783e93	0.877320
$357$	−5.84207e93	−3.92805
$358$	−1.14258e93	−0.693673
$359$	−1.45153e93	−0.795939	−0.397969	−	0.917399i	$-0.630285\pi$
$359$	−1.45153e93	−0.795939	−0.397969	+	0.917399i	$0.630285\pi$
$360$	9.74618e92	0.482829
$361$	−2.16931e93	−0.971201
$362$	−1.91417e93	−0.774670
$363$	2.81521e93	1.03019
$364$	1.62501e93	0.537843
$365$	−6.00413e92	−0.179788
$366$	−1.99484e93	−0.540565
$367$	7.19539e92	0.176499	0.0882497	−	0.996098i	$-0.471873\pi$
$367$	7.19539e92	0.176499	0.0882497	+	0.996098i	$0.471873\pi$
$368$	9.13355e92	0.202859
$369$	3.22142e93	0.648014
$370$	−1.03416e94	−1.88462
$371$	4.28454e93	0.707550
$372$	−2.72047e93	−0.407218
$373$	1.25705e94	1.70600	0.853000	−	0.521912i	$-0.174781\pi$
$373$	1.25705e94	1.70600	0.853000	+	0.521912i	$0.174781\pi$
$374$	4.71387e93	0.580182
$375$	1.61250e94	1.80036
$376$	3.25971e93	0.330234
$377$	−5.51601e93	−0.507184
$378$	3.61518e93	0.301772
$379$	−2.19370e94	−1.66282	−0.831410	−	0.555659i	$-0.812466\pi$
$379$	−2.19370e94	−1.66282	−0.831410	+	0.555659i	$0.812466\pi$
$380$	−2.06172e93	−0.141947
$381$	6.88547e93	0.430697
$382$	3.40031e93	0.193289
$383$	−2.40171e94	−1.24098	−0.620490	−	0.784214i	$-0.713066\pi$
$383$	−2.40171e94	−1.24098	−0.620490	+	0.784214i	$0.713066\pi$
$384$	2.53562e93	0.119123
$385$	3.27687e94	1.40005
$386$	−2.01734e94	−0.784049
$387$	3.16688e94	1.11990
$388$	4.70793e93	0.151521
$389$	−5.10520e94	−1.49573	−0.747863	−	0.663853i	$-0.768920\pi$
$389$	−5.10520e94	−1.49573	−0.747863	+	0.663853i	$0.768920\pi$
$390$	3.72825e94	0.994596
$391$	−5.64542e94	−1.37165
$392$	−3.15134e94	−0.697516
$393$	−9.03788e94	−1.82280
$394$	−5.50969e93	−0.101278
$395$	4.17652e94	0.699875
$396$	1.29660e94	0.198122
$397$	−4.47580e92	−0.00623760	−0.00311880	−	0.999995i	$-0.500993\pi$
$397$	−4.47580e92	−0.00623760	−0.00311880	+	0.999995i	$0.500993\pi$
$398$	7.29862e94	0.927916
$399$	3.39930e94	0.394348
$400$	4.24667e94	0.449634
$401$	4.86109e94	0.469856	0.234928	−	0.972013i	$-0.424515\pi$
$401$	4.86109e94	0.469856	0.234928	+	0.972013i	$0.424515\pi$
$402$	−7.81788e94	−0.689983
$403$	−4.67724e94	−0.377012
$404$	−1.90826e94	−0.140513
$405$	2.85920e95	1.92369
$406$	1.61191e95	0.991154
$407$	−1.37581e95	−0.773326
$408$	−1.56726e95	−0.805460
$409$	−2.72749e95	−1.28192	−0.640962	−	0.767573i	$-0.721464\pi$
$409$	−2.72749e95	−1.28192	−0.640962	+	0.767573i	$0.721464\pi$
$410$	2.18410e95	0.938993
$411$	−2.26494e95	−0.890903
$412$	1.50275e95	0.540928
$413$	2.14808e95	0.707741
$414$	−1.55283e95	−0.468395
$415$	2.92279e95	0.807313
$416$	4.35942e94	0.110287
$417$	6.78320e95	1.57206
$418$	−2.74284e94	−0.0582460
$419$	−2.90173e94	−0.0564736	−0.0282368	−	0.999601i	$-0.508989\pi$
$419$	−2.90173e94	−0.0564736	−0.0282368	+	0.999601i	$0.508989\pi$
$420$	−1.08949e96	−1.94367
$421$	7.70995e95	1.26112	0.630558	−	0.776142i	$-0.282826\pi$
$421$	7.70995e95	1.26112	0.630558	+	0.776142i	$0.282826\pi$
$422$	−6.28996e95	−0.943503
$423$	−5.54196e95	−0.762500
$424$	1.14942e95	0.145085
$425$	−2.62485e96	−3.04025
$426$	−8.63145e95	−0.917557
$427$	1.00224e96	0.978031
$428$	−1.66529e95	−0.149208
$429$	4.95994e95	0.408118
$430$	2.14712e96	1.62278
$431$	3.40514e94	0.0236436	0.0118218	−	0.999930i	$-0.496237\pi$
$431$	3.40514e94	0.0236436	0.0118218	+	0.999930i	$0.496237\pi$
$432$	9.69846e94	0.0618794
$433$	−1.99457e96	−1.16961	−0.584806	−	0.811173i	$-0.698829\pi$
$433$	−1.99457e96	−1.16961	−0.584806	+	0.811173i	$0.698829\pi$
$434$	1.36680e96	0.736769
$435$	3.69820e96	1.83287
$436$	−3.06825e95	−0.139841
$437$	3.28487e95	0.137704
$438$	2.65573e95	0.102419
$439$	−6.92002e95	−0.245557	−0.122779	−	0.992434i	$-0.539180\pi$
$439$	−6.92002e95	−0.245557	−0.122779	+	0.992434i	$0.539180\pi$
$440$	8.79088e95	0.287084
$441$	5.35773e96	1.61054
$442$	−2.69454e96	−0.745714
$443$	6.00371e96	1.52997	0.764986	−	0.644047i	$-0.222746\pi$
$443$	6.00371e96	1.52997	0.764986	+	0.644047i	$0.222746\pi$
$444$	4.57426e96	1.07360
$445$	−1.35767e97	−2.93531
$446$	3.65273e95	0.0727604
$447$	−1.14697e97	−2.10536
$448$	−1.27393e96	−0.215525
$449$	3.52724e96	0.550102	0.275051	−	0.961430i	$-0.411305\pi$
$449$	3.52724e96	0.550102	0.275051	+	0.961430i	$0.411305\pi$
$450$	−7.21994e96	−1.03819
$451$	2.90566e96	0.385302
$452$	5.88295e96	0.719518
$453$	7.45661e96	0.841312
$454$	8.68978e96	0.904628
$455$	−1.87313e97	−1.79950
$456$	9.11933e95	0.0808623
$457$	−1.65939e95	−0.0135834	−0.00679170	−	0.999977i	$-0.502162\pi$
$457$	−1.65939e95	−0.0135834	−0.00679170	+	0.999977i	$0.502162\pi$
$458$	7.02364e96	0.530851
$459$	−5.99458e96	−0.418404
$460$	−1.05281e97	−0.678719
$461$	−4.92601e96	−0.293367	−0.146684	−	0.989183i	$-0.546860\pi$
$461$	−4.92601e96	−0.293367	−0.146684	+	0.989183i	$0.546860\pi$
$462$	−1.44942e97	−0.797556
$463$	−1.08826e97	−0.553381	−0.276691	−	0.960959i	$-0.589238\pi$
$463$	−1.08826e97	−0.553381	−0.276691	+	0.960959i	$0.589238\pi$
$464$	4.32428e96	0.203239
$465$	3.13585e97	1.36246
$466$	8.41951e96	0.338221
$467$	1.48924e97	0.553222	0.276611	−	0.960982i	$-0.410789\pi$
$467$	1.48924e97	0.553222	0.276611	+	0.960982i	$0.410789\pi$
$468$	−7.41163e96	−0.254648
$469$	3.92782e97	1.24837
$470$	−3.75742e97	−1.10489
$471$	2.33379e97	0.635035
$472$	5.76268e96	0.145125
$473$	2.85647e97	0.665882
$474$	−1.84735e97	−0.398693
$475$	1.52731e97	0.305219
$476$	7.87412e97	1.45730
$477$	−1.95417e97	−0.334997
$478$	−8.45098e97	−1.34211
$479$	−1.07420e98	−1.58067	−0.790334	−	0.612676i	$-0.790093\pi$
$479$	−1.07420e98	−1.58067	−0.790334	+	0.612676i	$0.790093\pi$
$480$	−2.92277e97	−0.398556
$481$	7.86441e97	0.993964
$482$	6.30682e97	0.738913
$483$	1.73585e98	1.88557
$484$	−3.79442e97	−0.382199
$485$	−5.42677e97	−0.506953
$486$	−1.06269e98	−0.920837
$487$	−1.92661e98	−1.54877	−0.774386	−	0.632714i	$-0.781941\pi$
$487$	−1.92661e98	−1.54877	−0.774386	+	0.632714i	$0.781941\pi$
$488$	2.68870e97	0.200548
$489$	−3.67380e98	−2.54297
$490$	3.63251e98	2.33373
$491$	1.93408e98	1.15345	0.576727	−	0.816937i	$-0.304330\pi$
$491$	1.93408e98	1.15345	0.576727	+	0.816937i	$0.304330\pi$
$492$	−9.66067e97	−0.534910
$493$	−2.67282e98	−1.37423
$494$	1.56786e97	0.0748643
$495$	−1.49457e98	−0.662869
$496$	3.66673e97	0.151077
$497$	4.33656e98	1.66011
$498$	−1.29280e98	−0.459897
$499$	−1.80489e97	−0.0596734	−0.0298367	−	0.999555i	$-0.509499\pi$
$499$	−1.80489e97	−0.0596734	−0.0298367	+	0.999555i	$0.509499\pi$
$500$	−2.17338e98	−0.667929
$501$	7.33248e97	0.209495
$502$	1.82312e98	0.484316
$503$	5.81737e97	0.143713	0.0718563	−	0.997415i	$-0.477108\pi$
$503$	5.81737e97	0.143713	0.0718563	+	0.997415i	$0.477108\pi$
$504$	2.16586e98	0.497641
$505$	2.19962e98	0.470124
$506$	−1.40063e98	−0.278502
$507$	4.44912e98	0.823159
$508$	−9.28044e97	−0.159788
$509$	1.82383e98	0.292270	0.146135	−	0.989265i	$-0.453317\pi$
$509$	1.82383e98	0.292270	0.146135	+	0.989265i	$0.453317\pi$
$510$	1.80655e99	2.69488
$511$	−1.33428e98	−0.185303
$512$	−3.41758e97	−0.0441942
$513$	3.48804e97	0.0420047
$514$	1.55886e98	0.174845
$515$	−1.73220e99	−1.80982
$516$	−9.49711e98	−0.924437
$517$	−4.99875e98	−0.453374
$518$	−2.29817e99	−1.94243
$519$	−1.33853e99	−1.05443
$520$	−5.02505e98	−0.368993
$521$	−4.97148e97	−0.0340337	−0.0170168	−	0.999855i	$-0.505417\pi$
$521$	−4.97148e97	−0.0340337	−0.0170168	+	0.999855i	$0.505417\pi$
$522$	−7.35189e98	−0.469273
$523$	1.12481e99	0.669525	0.334763	−	0.942303i	$-0.391344\pi$
$523$	1.12481e99	0.669525	0.334763	+	0.942303i	$0.391344\pi$
$524$	1.21815e99	0.676254
$525$	8.07088e99	4.17933
$526$	−1.61297e99	−0.779197
$527$	−2.26639e99	−1.02152
$528$	−3.88836e98	−0.163542
$529$	−8.70189e98	−0.341571
$530$	−1.32492e99	−0.485422
$531$	−9.79736e98	−0.335088
$532$	−4.58168e98	−0.146302
$533$	−1.66093e99	−0.495233
$534$	6.00520e99	1.67214
$535$	1.91955e99	0.499214
$536$	1.05372e99	0.255982
$537$	−5.82546e99	−1.32211
$538$	−4.35592e99	−0.923692
$539$	4.83257e99	0.957610
$540$	−1.11793e99	−0.207034
$541$	8.81484e99	1.52586	0.762929	−	0.646482i	$-0.223760\pi$
$541$	8.81484e99	1.52586	0.762929	+	0.646482i	$0.223760\pi$
$542$	3.17326e99	0.513490
$543$	−9.75943e99	−1.47649
$544$	2.11239e99	0.298824
$545$	3.53673e99	0.467875
$546$	8.28516e99	1.02511
$547$	1.73734e99	0.201070	0.100535	−	0.994934i	$-0.467945\pi$
$547$	1.73734e99	0.201070	0.100535	+	0.994934i	$0.467945\pi$
$548$	3.05275e99	0.330523
$549$	−4.57117e99	−0.463060
$550$	−6.51226e99	−0.617296
$551$	1.55523e99	0.137962
$552$	4.65677e99	0.386641
$553$	9.28133e99	0.721345
$554$	−2.46414e98	−0.0179291
$555$	−5.27268e100	−3.59201
$556$	−9.14260e99	−0.583230
$557$	1.97252e100	1.17844	0.589218	−	0.807974i	$-0.299436\pi$
$557$	1.97252e100	1.17844	0.589218	+	0.807974i	$0.299436\pi$
$558$	−6.23396e99	−0.348831
$559$	−1.63281e100	−0.855866
$560$	1.46844e100	0.721097
$561$	2.40338e100	1.10580
$562$	−1.23424e100	−0.532140
$563$	−1.25994e100	−0.509088	−0.254544	−	0.967061i	$-0.581925\pi$
$563$	−1.25994e100	−0.509088	−0.254544	+	0.967061i	$0.581925\pi$
$564$	1.66197e100	0.629414
$565$	−6.78119e100	−2.40734
$566$	−1.27137e100	−0.423127
$567$	6.35390e100	1.98271
$568$	1.16337e100	0.340412
$569$	1.86784e100	0.512556	0.256278	−	0.966603i	$-0.417504\pi$
$569$	1.86784e100	0.512556	0.256278	+	0.966603i	$0.417504\pi$
$570$	−1.05117e100	−0.270546
$571$	−3.92494e99	−0.0947579	−0.0473789	−	0.998877i	$-0.515087\pi$
$571$	−3.92494e99	−0.0947579	−0.0473789	+	0.998877i	$0.515087\pi$
$572$	−6.68516e99	−0.151411
$573$	1.73366e100	0.368401
$574$	4.85366e100	0.967799
$575$	7.79920e100	1.45940
$576$	5.81037e99	0.102043
$577$	7.50563e100	1.23728	0.618642	−	0.785673i	$-0.287683\pi$
$577$	7.50563e100	1.23728	0.618642	+	0.785673i	$0.287683\pi$
$578$	−8.48731e100	−1.31342
$579$	−1.02855e101	−1.49437
$580$	−4.98454e100	−0.679991
$581$	6.49521e100	0.832079
$582$	2.40035e100	0.288793
$583$	−1.76263e100	−0.199186
$584$	−3.57947e99	−0.0379970
$585$	8.54328e100	0.851992
$586$	7.16237e100	0.671110
$587$	8.05605e100	0.709303	0.354651	−	0.934999i	$-0.384600\pi$
$587$	8.05605e100	0.709303	0.354651	+	0.934999i	$0.384600\pi$
$588$	−1.60672e101	−1.32944
$589$	1.31874e100	0.102553
$590$	−6.64256e100	−0.485553
$591$	−2.80913e100	−0.193032
$592$	−6.16532e100	−0.398303
$593$	−5.36808e100	−0.326079	−0.163039	−	0.986620i	$-0.552130\pi$
$593$	−5.36808e100	−0.326079	−0.163039	+	0.986620i	$0.552130\pi$
$594$	−1.48725e100	−0.0849533
$595$	−9.07639e101	−4.87578
$596$	1.54592e101	0.781084
$597$	3.72122e101	1.76857
$598$	8.00627e100	0.357962
$599$	−4.04849e101	−1.70300	−0.851499	−	0.524355i	$-0.824306\pi$
$599$	−4.04849e101	−1.70300	−0.851499	+	0.524355i	$0.824306\pi$
$600$	2.16518e101	0.856985
$601$	3.95874e101	1.47448	0.737240	−	0.675631i	$-0.236129\pi$
$601$	3.95874e101	1.47448	0.737240	+	0.675631i	$0.236129\pi$
$602$	4.77148e101	1.67256
$603$	−1.79147e101	−0.591054
$604$	−1.00502e101	−0.312125
$605$	4.37377e101	1.27875
$606$	−9.72931e100	−0.267813
$607$	−2.92874e101	−0.759091	−0.379546	−	0.925173i	$-0.623920\pi$
$607$	−2.92874e101	−0.759091	−0.379546	+	0.925173i	$0.623920\pi$
$608$	−1.22913e100	−0.0299997
$609$	8.21838e101	1.88910
$610$	−3.09923e101	−0.670988
$611$	2.85739e101	0.582726
$612$	−3.59137e101	−0.689974
$613$	−9.32452e101	−1.68779	−0.843897	−	0.536505i	$-0.819744\pi$
$613$	−9.32452e101	−1.68779	−0.843897	+	0.536505i	$0.819744\pi$
$614$	2.24557e101	0.382984
$615$	1.11357e102	1.78968
$616$	1.95357e101	0.295891
$617$	−1.16030e102	−1.65639	−0.828193	−	0.560443i	$-0.810631\pi$
$617$	−1.16030e102	−1.65639	−0.828193	+	0.560443i	$0.810631\pi$
$618$	7.66183e101	1.03099
$619$	6.96429e101	0.883422	0.441711	−	0.897157i	$-0.354372\pi$
$619$	6.96429e101	0.883422	0.441711	+	0.897157i	$0.354372\pi$
$620$	−4.22659e101	−0.505468
$621$	1.78116e101	0.200845
$622$	5.85017e100	0.0622042
$623$	−3.01710e102	−3.02535
$624$	2.22266e101	0.210202
$625$	4.88994e101	0.436197
$626$	8.88582e101	0.747712
$627$	−1.39845e101	−0.111015
$628$	−3.14554e101	−0.235596
$629$	3.81076e102	2.69317
$630$	−2.49656e102	−1.66499
$631$	1.69285e102	1.06548	0.532741	−	0.846279i	$-0.321162\pi$
$631$	1.69285e102	1.06548	0.532741	+	0.846279i	$0.321162\pi$
$632$	2.48991e101	0.147914
$633$	−3.20695e102	−1.79828
$634$	−2.16192e102	−1.14441
$635$	1.06974e102	0.534612
$636$	5.86033e101	0.276527
$637$	−2.76240e102	−1.23083
$638$	−6.63127e101	−0.279024
$639$	−1.97790e102	−0.785999
$640$	3.93940e101	0.147863
$641$	1.77576e102	0.629602	0.314801	−	0.949158i	$-0.398062\pi$
$641$	1.77576e102	0.629602	0.314801	+	0.949158i	$0.398062\pi$
$642$	−8.49052e101	−0.284384
$643$	−4.67194e102	−1.47842	−0.739208	−	0.673477i	$-0.764800\pi$
$643$	−4.67194e102	−1.47842	−0.739208	+	0.673477i	$0.764800\pi$
$644$	−2.33963e102	−0.699540
$645$	1.09472e103	3.09295
$646$	7.59721e101	0.202846
$647$	3.75593e102	0.947789	0.473894	−	0.880582i	$-0.342848\pi$
$647$	3.75593e102	0.947789	0.473894	+	0.880582i	$0.342848\pi$
$648$	1.70456e102	0.406561
$649$	−8.83704e101	−0.199240
$650$	3.72254e102	0.793417
$651$	6.96869e102	1.40425
$652$	4.95165e102	0.943436
$653$	5.32582e102	0.959522	0.479761	−	0.877399i	$-0.340723\pi$
$653$	5.32582e102	0.959522	0.479761	+	0.877399i	$0.340723\pi$
$654$	−1.56436e102	−0.266531
$655$	−1.40415e103	−2.26259
$656$	1.30209e102	0.198450
$657$	6.08560e101	0.0877339
$658$	−8.34998e102	−1.13878
$659$	−5.56227e102	−0.717686	−0.358843	−	0.933398i	$-0.616829\pi$
$659$	−5.56227e102	−0.717686	−0.358843	+	0.933398i	$0.616829\pi$
$660$	4.48206e102	0.547172
$661$	−1.39952e103	−1.61669	−0.808343	−	0.588712i	$-0.799635\pi$
$661$	−1.39952e103	−1.61669	−0.808343	+	0.588712i	$0.799635\pi$
$662$	8.34538e102	0.912283
$663$	−1.37382e103	−1.42130
$664$	1.74247e102	0.170621
$665$	5.28124e102	0.489492
$666$	1.04819e103	0.919668
$667$	7.94173e102	0.659663
$668$	−9.88293e101	−0.0777222
$669$	1.86235e102	0.138678
$670$	−1.21460e103	−0.856455
$671$	−4.12311e102	−0.275330
$672$	−6.49517e102	−0.410783
$673$	−2.24347e103	−1.34391	−0.671955	−	0.740592i	$-0.734545\pi$
$673$	−2.24347e103	−1.34391	−0.671955	+	0.740592i	$0.734545\pi$
$674$	−1.12990e103	−0.641140
$675$	8.28157e102	0.445169
$676$	−5.99666e102	−0.305390
$677$	4.04088e102	0.194980	0.0974899	−	0.995237i	$-0.468919\pi$
$677$	4.04088e102	0.194980	0.0974899	+	0.995237i	$0.468919\pi$
$678$	2.99944e103	1.37137
$679$	−1.20597e103	−0.522505
$680$	−2.43493e103	−0.999794
$681$	4.43051e103	1.72419
$682$	−5.62292e102	−0.207411
$683$	3.60794e103	1.26155	0.630774	−	0.775967i	$-0.282738\pi$
$683$	3.60794e103	1.26155	0.630774	+	0.775967i	$0.282738\pi$
$684$	2.08969e102	0.0692684
$685$	−3.51886e103	−1.10585
$686$	3.98071e103	1.18612
$687$	3.58103e103	1.01178
$688$	1.28005e103	0.342964
$689$	1.00755e103	0.256015
$690$	−5.36779e103	−1.29361
$691$	−1.37292e103	−0.313830	−0.156915	−	0.987612i	$-0.550155\pi$
$691$	−1.37292e103	−0.313830	−0.156915	+	0.987612i	$0.550155\pi$
$692$	1.80411e103	0.391193
$693$	−3.32134e103	−0.683204
$694$	−6.11134e102	−0.119266
$695$	1.05385e104	1.95135
$696$	2.20475e103	0.387366
$697$	−8.04819e103	−1.34184
$698$	−7.37621e102	−0.116711
$699$	4.29271e103	0.644637
$700$	−1.08782e104	−1.55052
$701$	5.98420e103	0.809652	0.404826	−	0.914394i	$-0.367332\pi$
$701$	5.98420e103	0.809652	0.404826	+	0.914394i	$0.367332\pi$
$702$	8.50145e102	0.109191
$703$	−2.21735e103	−0.270374
$704$	5.24084e102	0.0606735
$705$	−1.91573e104	−2.10587
$706$	−6.80607e103	−0.710436
$707$	4.88815e103	0.484547
$708$	2.93812e103	0.276602
$709$	1.31408e104	1.17499	0.587493	−	0.809229i	$-0.300115\pi$
$709$	1.31408e104	1.17499	0.587493	+	0.809229i	$0.300115\pi$
$710$	−1.34100e104	−1.13894
$711$	−4.23319e103	−0.341529
$712$	−8.09399e103	−0.620359
$713$	6.73411e103	0.490357
$714$	4.01464e104	2.77755
$715$	7.70589e103	0.506585
$716$	7.85173e103	0.490501
$717$	−4.30876e104	−2.55801
$718$	9.97486e103	0.562814
$719$	−2.73501e104	−1.46674	−0.733372	−	0.679828i	$-0.762055\pi$
$719$	−2.73501e104	−1.46674	−0.733372	+	0.679828i	$0.762055\pi$
$720$	−6.69753e103	−0.341412
$721$	−3.84941e104	−1.86534
$722$	1.49074e104	0.686742
$723$	3.21555e104	1.40834
$724$	1.31540e104	0.547774
$725$	3.69253e104	1.46213
$726$	−1.93460e104	−0.728457
$727$	4.47898e104	1.60389	0.801943	−	0.597401i	$-0.203800\pi$
$727$	4.47898e104	1.60389	0.801943	+	0.597401i	$0.203800\pi$
$728$	−1.11670e104	−0.380313
$729$	−1.86818e104	−0.605151
$730$	4.12600e103	0.127129
$731$	−7.91193e104	−2.31899
$732$	1.37084e104	0.382237
$733$	4.43229e104	1.17580	0.587900	−	0.808934i	$-0.299955\pi$
$733$	4.43229e104	1.17580	0.587900	+	0.808934i	$0.299955\pi$
$734$	−4.94464e103	−0.124804
$735$	1.85205e105	4.44799
$736$	−6.27653e103	−0.143443
$737$	−1.61587e104	−0.351434
$738$	−2.21374e104	−0.458215
$739$	−8.06712e104	−1.58926	−0.794632	−	0.607091i	$-0.792336\pi$
$739$	−8.06712e104	−1.58926	−0.794632	+	0.607091i	$0.792336\pi$
$740$	7.10667e104	1.33263
$741$	7.99380e103	0.142688
$742$	−2.94432e104	−0.500313
$743$	−5.17927e104	−0.837870	−0.418935	−	0.908016i	$-0.637597\pi$
$743$	−5.17927e104	−0.837870	−0.418935	+	0.908016i	$0.637597\pi$
$744$	1.86949e104	0.287946
$745$	−1.78196e105	−2.61332
$746$	−8.63835e104	−1.20632
$747$	−2.96245e104	−0.393957
$748$	−3.23935e104	−0.410251
$749$	4.26576e104	0.514529
$750$	−1.10810e105	−1.27305
$751$	4.49473e104	0.491865	0.245933	−	0.969287i	$-0.420906\pi$
$751$	4.49473e104	0.491865	0.245933	+	0.969287i	$0.420906\pi$
$752$	−2.24005e104	−0.233511
$753$	9.29521e104	0.923087
$754$	3.79057e104	0.358633
$755$	1.15848e105	1.04430
$756$	−2.48433e104	−0.213385
$757$	2.18537e104	0.178865	0.0894324	−	0.995993i	$-0.471495\pi$
$757$	2.18537e104	0.178865	0.0894324	+	0.995993i	$0.471495\pi$
$758$	1.50750e105	1.17579
$759$	−7.14114e104	−0.530814
$760$	1.41680e104	0.100372
$761$	−1.78202e105	−1.20330	−0.601648	−	0.798762i	$-0.705489\pi$
$761$	−1.78202e105	−1.20330	−0.601648	+	0.798762i	$0.705489\pi$
$762$	−4.73166e104	−0.304549
$763$	7.85955e104	0.482228
$764$	−2.33668e104	−0.136676
$765$	4.13972e105	2.30849
$766$	1.65044e105	0.877505
$767$	5.05143e104	0.256085
$768$	−1.74246e104	−0.0842324
$769$	−1.81156e105	−0.835107	−0.417554	−	0.908652i	$-0.637112\pi$
$769$	−1.81156e105	−0.835107	−0.417554	+	0.908652i	$0.637112\pi$
$770$	−2.25185e105	−0.989984
$771$	7.94789e104	0.333248
$772$	1.38631e105	0.554406
$773$	2.69199e105	1.02689	0.513443	−	0.858124i	$-0.328370\pi$
$773$	2.69199e105	1.02689	0.513443	+	0.858124i	$0.328370\pi$
$774$	−2.17626e105	−0.791892
$775$	3.13104e105	1.08687
$776$	−3.23527e104	−0.107141
$777$	−1.17173e106	−3.70220
$778$	3.50827e105	1.05764
$779$	4.68297e104	0.134711
$780$	−2.56203e105	−0.703286
$781$	−1.78403e105	−0.467346
$782$	3.87950e105	0.969905
$783$	8.43293e104	0.201221
$784$	2.16559e105	0.493219
$785$	3.62582e105	0.788251
$786$	6.21078e105	1.28891
$787$	7.55749e104	0.149727	0.0748634	−	0.997194i	$-0.476148\pi$
$787$	7.55749e104	0.149727	0.0748634	+	0.997194i	$0.476148\pi$
$788$	3.78623e104	0.0716143
$789$	−8.22379e105	−1.48512
$790$	−2.87008e105	−0.494886
$791$	−1.50696e106	−2.48119
$792$	−8.91017e104	−0.140093
$793$	2.35686e105	0.353885
$794$	3.07575e103	0.00441065
$795$	−6.75512e105	−0.925195
$796$	−5.01558e105	−0.656136
$797$	1.39914e105	0.174836	0.0874180	−	0.996172i	$-0.472138\pi$
$797$	1.39914e105	0.174836	0.0874180	+	0.996172i	$0.472138\pi$
$798$	−2.33598e105	−0.278846
$799$	1.38457e106	1.57891
$800$	−2.91829e105	−0.317939
$801$	1.37609e106	1.43239
$802$	−3.34052e105	−0.332238
$803$	5.48910e104	0.0521656
$804$	5.37241e105	0.487891
$805$	2.69686e106	2.34050
$806$	3.21417e105	0.266588
$807$	−2.22088e106	−1.76052
$808$	1.31135e105	0.0993579
$809$	1.88586e106	1.36581	0.682903	−	0.730509i	$-0.260717\pi$
$809$	1.88586e106	1.36581	0.682903	+	0.730509i	$0.260717\pi$
$810$	−1.96483e106	−1.36026
$811$	4.33542e105	0.286926	0.143463	−	0.989656i	$-0.454176\pi$
$811$	4.33542e105	0.286926	0.143463	+	0.989656i	$0.454176\pi$
$812$	−1.10770e106	−0.700852
$813$	1.61790e106	0.978691
$814$	9.45449e105	0.546824
$815$	−5.70770e106	−3.15652
$816$	1.07701e106	0.569546
$817$	4.60368e105	0.232809
$818$	1.87432e106	0.906457
$819$	1.89855e106	0.878129
$820$	−1.50090e106	−0.663968
$821$	3.84063e106	1.62509	0.812545	−	0.582899i	$-0.198082\pi$
$821$	3.84063e106	1.62509	0.812545	+	0.582899i	$0.198082\pi$
$822$	1.55645e106	0.629963
$823$	−9.55806e105	−0.370063	−0.185032	−	0.982733i	$-0.559239\pi$
$823$	−9.55806e105	−0.370063	−0.185032	+	0.982733i	$0.559239\pi$
$824$	−1.03268e106	−0.382494
$825$	−3.32029e106	−1.17654
$826$	−1.47615e106	−0.500449
$827$	1.41672e106	0.459549	0.229774	−	0.973244i	$-0.426201\pi$
$827$	1.41672e106	0.459549	0.229774	+	0.973244i	$0.426201\pi$
$828$	1.06710e106	0.331205
$829$	3.07350e106	0.912837	0.456418	−	0.889765i	$-0.349132\pi$
$829$	3.07350e106	0.912837	0.456418	+	0.889765i	$0.349132\pi$
$830$	−2.00852e106	−0.570856
$831$	−1.25635e105	−0.0341721
$832$	−2.99577e105	−0.0779844
$833$	−1.33854e107	−3.33495
$834$	−4.66138e106	−1.11161
$835$	1.13919e106	0.260040
$836$	1.88487e105	0.0411862
$837$	7.15061e105	0.149577
$838$	1.99405e105	0.0399329
$839$	2.06238e106	0.395420	0.197710	−	0.980261i	$-0.436650\pi$
$839$	2.06238e106	0.395420	0.197710	+	0.980261i	$0.436650\pi$
$840$	7.48689e106	1.37438
$841$	−1.92922e106	−0.339100
$842$	−5.29824e106	−0.891744
$843$	−6.29283e106	−1.01424
$844$	4.32243e106	0.667158
$845$	6.91226e106	1.02176
$846$	3.80841e106	0.539169
$847$	9.71969e106	1.31798
$848$	−7.89873e105	−0.102591
$849$	−6.48209e106	−0.806463
$850$	1.80379e107	2.14978
$851$	−1.13229e107	−1.29279
$852$	5.93149e106	0.648811
$853$	8.58762e106	0.899980	0.449990	−	0.893034i	$-0.351427\pi$
$853$	8.58762e106	0.899980	0.449990	+	0.893034i	$0.351427\pi$
$854$	−6.88731e106	−0.691572
$855$	−2.40876e106	−0.231756
$856$	1.14438e106	0.105506
$857$	1.52229e107	1.34492	0.672462	−	0.740132i	$-0.265237\pi$
$857$	1.52229e107	1.34492	0.672462	+	0.740132i	$0.265237\pi$
$858$	−3.40845e106	−0.288583
$859$	4.82385e106	0.391420	0.195710	−	0.980662i	$-0.437299\pi$
$859$	4.82385e106	0.391420	0.195710	+	0.980662i	$0.437299\pi$
$860$	−1.47549e107	−1.14748
$861$	2.47465e107	1.84459
$862$	−2.33999e105	−0.0167186
$863$	−1.60372e107	−1.09834	−0.549169	−	0.835712i	$-0.685056\pi$
$863$	−1.60372e107	−1.09834	−0.549169	+	0.835712i	$0.685056\pi$
$864$	−6.66473e105	−0.0437553
$865$	−2.07957e107	−1.30884
$866$	1.37066e107	0.827041
$867$	−4.32728e107	−2.50333
$868$	−9.39260e106	−0.520974
$869$	−3.81826e106	−0.203069
$870$	−2.54138e107	−1.29604
$871$	9.23665e106	0.451702
$872$	2.10849e106	0.0988824
$873$	5.50041e106	0.247386
$874$	−2.25735e106	−0.0973714
$875$	5.56727e107	2.30329
$876$	−1.82500e106	−0.0724209
$877$	−1.62082e107	−0.616950	−0.308475	−	0.951233i	$-0.599819\pi$
$877$	−1.62082e107	−0.616950	−0.308475	+	0.951233i	$0.599819\pi$
$878$	4.75540e106	0.173635
$879$	3.65176e107	1.27911
$880$	−6.04105e106	−0.202999
$881$	1.79212e107	0.577758	0.288879	−	0.957366i	$-0.406717\pi$
$881$	1.79212e107	0.577758	0.288879	+	0.957366i	$0.406717\pi$
$882$	−3.68180e107	−1.13883
$883$	−7.45370e106	−0.221211	−0.110605	−	0.993864i	$-0.535279\pi$
$883$	−7.45370e106	−0.221211	−0.110605	+	0.993864i	$0.535279\pi$
$884$	1.85168e107	0.527300
$885$	−3.38673e107	−0.925445
$886$	−4.12572e107	−1.08185
$887$	−1.06437e107	−0.267843	−0.133922	−	0.990992i	$-0.542757\pi$
$887$	−1.06437e107	−0.267843	−0.133922	+	0.990992i	$0.542757\pi$
$888$	−3.14341e107	−0.759149
$889$	2.37725e107	0.551012
$890$	9.32983e107	2.07558
$891$	−2.61394e107	−0.558161
$892$	−2.51013e106	−0.0514493
$893$	−8.05633e106	−0.158511
$894$	7.88190e107	1.48872
$895$	−9.05057e107	−1.64110
$896$	8.75439e106	0.152399
$897$	4.08202e107	0.682261
$898$	−2.42390e107	−0.388981
$899$	3.18827e107	0.491276
$900$	4.96151e107	0.734112
$901$	4.88218e107	0.693679
$902$	−1.99675e107	−0.272450
$903$	2.43275e108	3.18783
$904$	−4.04273e107	−0.508776
$905$	−1.51625e108	−1.83272
$906$	−5.12415e107	−0.594898
$907$	−2.95754e107	−0.329811	−0.164906	−	0.986309i	$-0.552732\pi$
$907$	−2.95754e107	−0.329811	−0.164906	+	0.986309i	$0.552732\pi$
$908$	−5.97157e107	−0.639669
$909$	−2.22947e107	−0.229414
$910$	1.28720e108	1.27244
$911$	5.81750e107	0.552479	0.276239	−	0.961089i	$-0.410912\pi$
$911$	5.81750e107	0.552479	0.276239	+	0.961089i	$0.410912\pi$
$912$	−6.26675e106	−0.0571783
$913$	−2.67208e107	−0.234242
$914$	1.14033e106	0.00960491
$915$	−1.58015e108	−1.27888
$916$	−4.82661e107	−0.375368
$917$	−3.12039e108	−2.33200
$918$	4.11945e107	0.295856
$919$	−8.98934e107	−0.620457	−0.310228	−	0.950662i	$-0.600406\pi$
$919$	−8.98934e107	−0.620457	−0.310228	+	0.950662i	$0.600406\pi$
$920$	7.23487e107	0.479927
$921$	1.14491e108	0.729952
$922$	3.38513e107	0.207442
$923$	1.01979e108	0.600685
$924$	9.96032e107	0.563958
$925$	−5.26460e108	−2.86545
$926$	7.47843e107	0.391300
$927$	1.75571e108	0.883165
$928$	−2.97163e107	−0.143712
$929$	3.50337e108	1.62897	0.814484	−	0.580185i	$-0.197020\pi$
$929$	3.50337e108	1.62897	0.814484	+	0.580185i	$0.197020\pi$
$930$	−2.15494e108	−0.963401
$931$	7.78852e107	0.334805
$932$	−5.78585e107	−0.239159
$933$	2.98273e107	0.118559
$934$	−1.02340e108	−0.391187
$935$	3.73395e108	1.37260
$936$	5.09324e107	0.180063
$937$	−3.76507e108	−1.28020	−0.640100	−	0.768292i	$-0.721107\pi$
$937$	−3.76507e108	−1.28020	−0.640100	+	0.768292i	$0.721107\pi$
$938$	−2.69918e108	−0.882729
$939$	4.53046e108	1.42511
$940$	2.58208e108	0.781273
$941$	2.30818e108	0.671813	0.335906	−	0.941895i	$-0.390957\pi$
$941$	2.30818e108	0.671813	0.335906	+	0.941895i	$0.390957\pi$
$942$	−1.60377e108	−0.449038
$943$	2.39135e108	0.644119
$944$	−3.96008e107	−0.102619
$945$	2.86366e108	0.713937
$946$	−1.96295e108	−0.470850
$947$	5.61299e108	1.29545	0.647725	−	0.761875i	$-0.275721\pi$
$947$	5.61299e108	1.29545	0.647725	+	0.761875i	$0.275721\pi$
$948$	1.26949e108	0.281919
$949$	−3.13768e107	−0.0670490
$950$	−1.04956e108	−0.215822
$951$	−1.10226e109	−2.18120
$952$	−5.41105e108	−1.03046
$953$	4.06055e108	0.744207	0.372103	−	0.928191i	$-0.378637\pi$
$953$	4.06055e108	0.744207	0.372103	+	0.928191i	$0.378637\pi$
$954$	1.34290e108	0.236879
$955$	2.69346e108	0.457285
$956$	5.80747e108	0.949017
$957$	−3.38097e108	−0.531810
$958$	7.38188e108	1.11770
$959$	−7.81985e108	−1.13978
$960$	2.00851e108	0.281822
$961$	−4.69947e108	−0.634813
$962$	−5.40438e108	−0.702839
$963$	−1.94560e108	−0.243610
$964$	−4.33401e108	−0.522491
$965$	−1.59798e109	−1.85491
$966$	−1.19287e109	−1.33330
$967$	−1.07346e109	−1.15536	−0.577682	−	0.816262i	$-0.696043\pi$
$967$	−1.07346e109	−1.15536	−0.577682	+	0.816262i	$0.696043\pi$
$968$	2.60751e108	0.270256
$969$	3.87346e108	0.386617
$970$	3.72925e108	0.358470
$971$	−2.98402e108	−0.276249	−0.138124	−	0.990415i	$-0.544107\pi$
$971$	−2.98402e108	−0.276249	−0.138124	+	0.990415i	$0.544107\pi$
$972$	7.30275e108	0.651130
$973$	2.34195e109	2.01121
$974$	1.32396e109	1.09515
$975$	1.89795e109	1.51222
$976$	−1.84766e108	−0.141809
$977$	2.59448e108	0.191822	0.0959112	−	0.995390i	$-0.469424\pi$
$977$	2.59448e108	0.191822	0.0959112	+	0.995390i	$0.469424\pi$
$978$	2.52461e109	1.79815
$979$	1.24121e109	0.851681
$980$	−2.49624e109	−1.65019
$981$	−3.58472e108	−0.228316
$982$	−1.32909e109	−0.815615
$983$	−2.72768e109	−1.61283	−0.806416	−	0.591348i	$-0.798596\pi$
$983$	−2.72768e109	−1.61283	−0.806416	+	0.591348i	$0.798596\pi$
$984$	6.63876e108	0.378239
$985$	−4.36433e108	−0.239605
$986$	1.83675e109	0.971724
$987$	−4.25726e109	−2.17047
$988$	−1.07743e108	−0.0529370
$989$	2.35086e109	1.11317
$990$	1.02706e109	0.468719
$991$	−9.74884e108	−0.428810	−0.214405	−	0.976745i	$-0.568781\pi$
$991$	−9.74884e108	−0.428810	−0.214405	+	0.976745i	$0.568781\pi$
$992$	−2.51976e108	−0.106827
$993$	4.25492e109	1.73878
$994$	−2.98006e109	−1.17388
$995$	5.78138e109	2.19528
$996$	8.88405e108	0.325196
$997$	−4.43886e109	−1.56639	−0.783193	−	0.621779i	$-0.786410\pi$
$997$	−4.43886e109	−1.56639	−0.783193	+	0.621779i	$0.786410\pi$
$998$	1.24031e108	0.0421955
$999$	−1.20232e109	−0.394348

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2.74.a.a.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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 2 \)
Weight:	\( k \)	\(=\)	\( 74 \)
Character orbit:	\([\chi]\)	\(=\)	2.a (trivial)

\(f(q)\)	\(=\)	\(q-6.87195e10 q^{2} -3.50368e17 q^{3} +4.72237e21 q^{4} -5.44340e25 q^{5} +2.40771e28 q^{6} -1.20967e31 q^{7} -3.24519e32 q^{8} +5.51727e34 q^{9} +3.74068e36 q^{10} +4.97648e37 q^{11} -1.65457e39 q^{12} -2.84466e40 q^{13} +8.31279e41 q^{14} +1.90720e43 q^{15} +2.23007e43 q^{16} -1.37840e45 q^{17} -3.79144e45 q^{18} +8.02045e45 q^{19} -2.57058e47 q^{20} +4.23830e48 q^{21} -3.41981e48 q^{22} +4.09563e49 q^{23} +1.13701e50 q^{24} +1.90427e51 q^{25} +1.95483e51 q^{26} +4.34894e51 q^{27} -5.71250e52 q^{28} +1.93908e53 q^{29} -1.31062e54 q^{30} +1.64422e54 q^{31} -1.53250e54 q^{32} -1.74360e55 q^{33} +9.47230e55 q^{34} +6.58472e56 q^{35} +2.60546e56 q^{36} -2.76462e57 q^{37} -5.51161e56 q^{38} +9.96677e57 q^{39} +1.76649e58 q^{40} +5.83879e58 q^{41} -2.91254e59 q^{42} +5.73993e59 q^{43} +2.35008e59 q^{44} -3.00327e60 q^{45} -2.81449e60 q^{46} -1.00447e61 q^{47} -7.81347e60 q^{48} +9.71083e61 q^{49} -1.30861e62 q^{50} +4.82948e62 q^{51} -1.34335e62 q^{52} -3.54191e62 q^{53} -2.98857e62 q^{54} -2.70890e63 q^{55} +3.92560e63 q^{56} -2.81011e63 q^{57} -1.33252e64 q^{58} -1.77576e64 q^{59} +9.00648e64 q^{60} -8.28520e64 q^{61} -1.12990e65 q^{62} -6.67408e65 q^{63} +1.05312e65 q^{64} +1.54846e66 q^{65} +1.19819e66 q^{66} -3.24702e66 q^{67} -6.50931e66 q^{68} -1.43498e67 q^{69} -4.52499e67 q^{70} -3.58492e67 q^{71} -1.79046e67 q^{72} +1.10301e67 q^{73} +1.89984e68 q^{74} -6.67197e68 q^{75} +3.78755e67 q^{76} -6.01990e68 q^{77} -6.84911e68 q^{78} -7.67262e68 q^{79} -1.21392e69 q^{80} -5.25259e69 q^{81} -4.01238e69 q^{82} -5.36941e69 q^{83} +2.00148e70 q^{84} +7.50319e70 q^{85} -3.94445e70 q^{86} -6.79391e70 q^{87} -1.61496e70 q^{88} +2.49415e71 q^{89} +2.06383e71 q^{90} +3.44109e71 q^{91} +1.93410e71 q^{92} -5.76082e71 q^{93} +6.90270e71 q^{94} -4.36585e71 q^{95} +5.36938e71 q^{96} +9.96943e71 q^{97} -6.67323e72 q^{98} +2.74566e72 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 206158430208 q^{2} - 30\!\cdots\!72 q^{3} + 14\!\cdots\!88 q^{4} - 32\!\cdots\!50 q^{5} + 20\!\cdots\!92 q^{6} - 23\!\cdots\!64 q^{7} - 97\!\cdots\!68 q^{8} + 74\!\cdots\!59 q^{9} + 22\!\cdots\!00 q^{10}+ \cdots + 32\!\cdots\!68 q^{99}+O(q^{100}) \) 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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