LMFDB - Embedded newform 1.44.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1,44,Mod(1,1)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

N = Newforms(chi, 44, names="a")

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

chi := DirichletCharacter("1.1");

S:= CuspForms(chi, 44);

N := Newforms(S);

Level:	$ N $	$=$	$ 1 $
Weight:	$ k $	$=$	$ 44 $
Character orbit:	$[\chi]$	$=$	1.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:	$11.7110395346$
Analytic rank:	$0$
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} - 11258260111x - 264759545317170 $ x^3 - 11258260111*x - 264759545317170
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{11}\cdot 3^{4}\cdot 5\cdot 7 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-24885.9$ of defining polynomial
Character	$\chi$	$=$	1.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-4.65343e6 q^{2} +3.22027e10 q^{3} +1.28583e13 q^{4} +5.54482e14 q^{5} -1.49853e17 q^{6} -5.57604e17 q^{7} -1.89031e19 q^{8} +7.08758e20 q^{9} +O(q^{10})$	\(q-4.65343e6 q^{2} +3.22027e10 q^{3} +1.28583e13 q^{4} +5.54482e14 q^{5} -1.49853e17 q^{6} -5.57604e17 q^{7} -1.89031e19 q^{8} +7.08758e20 q^{9} -2.58024e21 q^{10} -1.13059e22 q^{11} +4.14071e23 q^{12} +5.07130e23 q^{13} +2.59477e24 q^{14} +1.78558e25 q^{15} -2.51386e25 q^{16} +8.73610e25 q^{17} -3.29815e27 q^{18} +5.55222e27 q^{19} +7.12968e27 q^{20} -1.79564e28 q^{21} +5.26114e28 q^{22} +1.85137e29 q^{23} -6.08730e29 q^{24} -8.29418e29 q^{25} -2.35989e30 q^{26} +1.22532e31 q^{27} -7.16982e30 q^{28} +4.19782e31 q^{29} -8.30908e31 q^{30} -9.30312e31 q^{31} +2.83254e32 q^{32} -3.64082e32 q^{33} -4.06528e32 q^{34} -3.09181e32 q^{35} +9.11340e33 q^{36} -3.20928e33 q^{37} -2.58368e34 q^{38} +1.63309e34 q^{39} -1.04814e34 q^{40} +6.48857e33 q^{41} +8.35585e34 q^{42} +3.51189e33 q^{43} -1.45375e35 q^{44} +3.92993e35 q^{45} -8.61520e35 q^{46} +6.21410e35 q^{47} -8.09530e35 q^{48} -1.87289e36 q^{49} +3.85963e36 q^{50} +2.81326e36 q^{51} +6.52081e36 q^{52} +8.28552e36 q^{53} -5.70191e37 q^{54} -6.26895e36 q^{55} +1.05404e37 q^{56} +1.78797e38 q^{57} -1.95342e38 q^{58} -7.48073e36 q^{59} +2.29595e38 q^{60} -2.24824e38 q^{61} +4.32914e38 q^{62} -3.95206e38 q^{63} -1.09698e39 q^{64} +2.81194e38 q^{65} +1.69423e39 q^{66} -1.89786e39 q^{67} +1.12331e39 q^{68} +5.96191e39 q^{69} +1.43875e39 q^{70} -9.53945e39 q^{71} -1.33977e40 q^{72} +2.48260e39 q^{73} +1.49341e40 q^{74} -2.67095e40 q^{75} +7.13920e40 q^{76} +6.30424e39 q^{77} -7.59948e40 q^{78} -3.50244e39 q^{79} -1.39389e40 q^{80} +1.61930e41 q^{81} -3.01941e40 q^{82} -2.23114e41 q^{83} -2.30888e41 q^{84} +4.84401e40 q^{85} -1.63423e40 q^{86} +1.35181e42 q^{87} +2.13717e41 q^{88} -4.38099e41 q^{89} -1.82877e42 q^{90} -2.82777e41 q^{91} +2.38054e42 q^{92} -2.99586e42 q^{93} -2.89169e42 q^{94} +3.07861e42 q^{95} +9.12154e42 q^{96} -6.11565e42 q^{97} +8.71537e42 q^{98} -8.01318e42 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 2209944 q^{2} + 24401437812 q^{3} + 9822618421824 q^{4} + 535205380774170 q^{5} - 91\!\cdots\!24 q^{6}+ \cdots + 47\!\cdots\!31 q^{9}+O(q^{10}) $ 3 * q - 2209944 * q^2 + 24401437812 * q^3 + 9822618421824 * q^4 + 535205380774170 * q^5 - 91793974758443424 * q^6 + 301971425665478856 * q^7 - 15830863913787348480 * q^8 + 477482125171066743231 * q^9	$ 3 q - 2209944 q^{2} + 24401437812 q^{3} + 9822618421824 q^{4} + 535205380774170 q^{5} - 91\!\cdots\!24 q^{6}+ \cdots - 14\!\cdots\!08 q^{99}+O(q^{100}) $ 3 * q - 2209944 * q^2 + 24401437812 * q^3 + 9822618421824 * q^4 + 535205380774170 * q^5 - 91793974758443424 * q^6 + 301971425665478856 * q^7 - 15830863913787348480 * q^8 + 477482125171066743231 * q^9 + 424411733447436982320 * q^10 + 26665053285822824598396 * q^11 + 591067459530801007163136 * q^12 + 2675160683143344673595682 * q^13 + 14021968617857741064904128 * q^14 + 35619426649405115420082840 * q^15 - 79484355831457348071124992 * q^16 - 408654222932442443796841194 * q^17 - 4107998354973953853903433848 * q^18 + 1577331357975519701176464900 * q^19 + 14558304937461364568422335360 * q^20 + 39305230121617849136195725536 * q^21 + 139626647360508967807005852192 * q^22 - 1215339635928561142484811048 * q^23 - 1116055600560337571570968012800 * q^24 - 2310484082897201607166539950475 * q^25 - 1738302877111230473099097494544 * q^26 + 12636088863973677226324883265480 * q^27 + 16881555000174595924306194912768 * q^28 + 57118989018136587596191009705650 * q^29 - 73851642261923451351367502727360 * q^30 - 255565972342397832812135282963424 * q^31 - 144698056390774688063435943542784 * q^32 - 274896238871162964163796672607216 * q^33 + 460541119788760022406607937310288 * q^34 + 2398213530857285851552147980593520 * q^35 + 8176018057545637654201506848470848 * q^36 - 2320645576165979428293572256842694 * q^37 - 30659398199572233844432077267455520 * q^38 - 3966989860384498209469308423541128 * q^39 - 32703585947405178164040064943232000 * q^40 + 25742376604739002042016577514061166 * q^41 + 142089722887598025677946391121586432 * q^42 + 240714339689128182512406300123419292 * q^43 - 103743099769332204870397943787455232 * q^44 + 257230496455952342677786043056557090 * q^45 - 1897545066442972080018141849284700864 * q^46 + 308713553347399687962182796433367856 * q^47 - 2551621376300181083415582718933352448 * q^48 + 3434980292250886821160584750829904379 * q^49 + 1991781591031845842073119994352349400 * q^50 + 13352566627975131351422398848669478056 * q^51 - 1723278372049486147633277645433304704 * q^52 + 15000497558784669132889458695112796362 * q^53 - 84497407838510132201868358325218843200 * q^54 + 3996571389110251928625895283213506440 * q^55 - 64188456562605926675684864956824883200 * q^56 + 194498189404429212580032012092952587760 * q^57 - 103653602500512241322054964115851073680 * q^58 + 226996261182733939538282061249836505900 * q^59 + 172179025249459513233108554074130526720 * q^60 - 9393429368478033721028929889113591854 * q^61 - 208603081649583360642384119938663534848 * q^62 - 967475285671148246145956691206790781848 * q^63 - 1119010168436659689243622515721507700736 * q^64 - 270218921102297342477494789001032451460 * q^65 + 2927960709398652565212160365298168924032 * q^66 - 733015616887151283726086660162187354444 * q^67 + 5475599618745313926138424496016357744768 * q^68 + 1967042253746083561325124578559972227232 * q^69 + 5947953535225896394715748735968145697920 * q^70 - 18523878066158899993345833814569898287864 * q^71 - 9888656801008664055042728388175401192960 * q^72 - 20251106025908798058937016734369224029298 * q^73 + 16747422277652165725566811926177721225008 * q^74 - 21273380043530396090723723962888745519700 * q^75 + 77507609539490133886259513865936229344000 * q^76 + 59055613160181778232413942942559747685792 * q^77 - 19617648418411520686241571637167142696896 * q^78 + 15233568018599764739559826813006999294800 * q^79 - 100962488695267720109813470111835940986880 * q^80 + 73114835779397486920654645241710822062363 * q^81 - 320808727539069549327137360482471983405168 * q^82 - 89206610196719670053085531955706819434428 * q^83 - 345724182543475881552276196164469715392512 * q^84 + 438725373228516358990025164547060204838420 * q^85 + 251282426033382455934203370485070655838496 * q^86 + 1720273148596604243726575204332689696886840 * q^87 - 25677613216166441601684725395949811087360 * q^88 + 203691422331055117225246388044508249665950 * q^89 - 2339725556415524057280625761410723956665360 * q^90 - 1168954967602248602369466051364648836229584 * q^91 + 688199578839743838535125048241381149958656 * q^92 - 4949189234312030019905814954548842124935296 * q^93 - 1324027207656692012199753325229034662658432 * q^94 + 3125746305909018830165692627580442029979000 * q^95 + 10923904714711076554208778658628955663630336 * q^96 - 3881062021784775072625368160679539917597594 * q^97 + 24120041445786820251814869563279238673540008 * q^98 - 14255275025472043026078170466415579823927508 * 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 $

$2$	−4.65343e6	−1.56902	−0.784509	−	0.620118i	$-0.787085\pi$
$2$	−4.65343e6	−1.56902	−0.784509	+	0.620118i	$0.787085\pi$
$3$	3.22027e10	1.77740	0.888701	−	0.458488i	$-0.151609\pi$
$3$	3.22027e10	1.77740	0.888701	+	0.458488i	$0.151609\pi$
$4$	1.28583e13	1.46182
$5$	5.54482e14	0.520035	0.260017	−	0.965604i	$-0.416272\pi$
$5$	5.54482e14	0.520035	0.260017	+	0.965604i	$0.416272\pi$
$6$	−1.49853e17	−2.78877
$7$	−5.57604e17	−0.377327	−0.188663	−	0.982042i	$-0.560416\pi$
$7$	−5.57604e17	−0.377327	−0.188663	+	0.982042i	$0.560416\pi$
$8$	−1.89031e19	−0.724599
$9$	7.08758e20	2.15915
$10$	−2.58024e21	−0.815944
$11$	−1.13059e22	−0.460643	−0.230321	−	0.973115i	$-0.573978\pi$
$11$	−1.13059e22	−0.460643	−0.230321	+	0.973115i	$0.573978\pi$
$12$	4.14071e23	2.59823
$13$	5.07130e23	0.569294	0.284647	−	0.958632i	$-0.408124\pi$
$13$	5.07130e23	0.569294	0.284647	+	0.958632i	$0.408124\pi$
$14$	2.59477e24	0.592033
$15$	1.78558e25	0.924311
$16$	−2.51386e25	−0.324909
$17$	8.73610e25	0.306666	0.153333	−	0.988175i	$-0.450999\pi$
$17$	8.73610e25	0.306666	0.153333	+	0.988175i	$0.450999\pi$
$18$	−3.29815e27	−3.38775
$19$	5.55222e27	1.78346	0.891732	−	0.452564i	$-0.149491\pi$
$19$	5.55222e27	1.78346	0.891732	+	0.452564i	$0.149491\pi$
$20$	7.12968e27	0.760196
$21$	−1.79564e28	−0.670661
$22$	5.26114e28	0.722757
$23$	1.85137e29	0.978012	0.489006	−	0.872280i	$-0.337360\pi$
$23$	1.85137e29	0.978012	0.489006	+	0.872280i	$0.337360\pi$
$24$	−6.08730e29	−1.28790
$25$	−8.29418e29	−0.729564
$26$	−2.35989e30	−0.893233
$27$	1.22532e31	2.06028
$28$	−7.16982e30	−0.551583
$29$	4.19782e31	1.51868	0.759340	−	0.650694i	$-0.225522\pi$
$29$	4.19782e31	1.51868	0.759340	+	0.650694i	$0.225522\pi$
$30$	−8.30908e31	−1.45026
$31$	−9.30312e31	−0.802329	−0.401164	−	0.916006i	$-0.631394\pi$
$31$	−9.30312e31	−0.802329	−0.401164	+	0.916006i	$0.631394\pi$
$32$	2.83254e32	1.23439
$33$	−3.64082e32	−0.818747
$34$	−4.06528e32	−0.481165
$35$	−3.09181e32	−0.196223
$36$	9.11340e33	3.15629
$37$	−3.20928e33	−0.616695	−0.308347	−	0.951274i	$-0.599776\pi$
$37$	−3.20928e33	−0.616695	−0.308347	+	0.951274i	$0.599776\pi$
$38$	−2.58368e34	−2.79829
$39$	1.63309e34	1.01186
$40$	−1.04814e34	−0.376817
$41$	6.48857e33	0.137182	0.0685908	−	0.997645i	$-0.478150\pi$
$41$	6.48857e33	0.137182	0.0685908	+	0.997645i	$0.478150\pi$
$42$	8.35585e34	1.05228
$43$	3.51189e33	0.0266667	0.0133333	−	0.999911i	$-0.495756\pi$
$43$	3.51189e33	0.0266667	0.0133333	+	0.999911i	$0.495756\pi$
$44$	−1.45375e35	−0.673375
$45$	3.92993e35	1.12284
$46$	−8.61520e35	−1.53452
$47$	6.21410e35	0.697067	0.348533	−	0.937296i	$-0.386680\pi$
$47$	6.21410e35	0.697067	0.348533	+	0.937296i	$0.386680\pi$
$48$	−8.09530e35	−0.577493
$49$	−1.87289e36	−0.857624
$50$	3.85963e36	1.14470
$51$	2.81326e36	0.545069
$52$	6.52081e36	0.832204
$53$	8.28552e36	0.702083	0.351042	−	0.936360i	$-0.385828\pi$
$53$	8.28552e36	0.702083	0.351042	+	0.936360i	$0.385828\pi$
$54$	−5.70191e37	−3.23262
$55$	−6.26895e36	−0.239550
$56$	1.05404e37	0.273411
$57$	1.78797e38	3.16993
$58$	−1.95342e38	−2.38284
$59$	−7.48073e36	−0.0631867	−0.0315933	−	0.999501i	$-0.510058\pi$
$59$	−7.48073e36	−0.0631867	−0.0315933	+	0.999501i	$0.510058\pi$
$60$	2.29595e38	1.35117
$61$	−2.24824e38	−0.927366	−0.463683	−	0.886001i	$-0.653472\pi$
$61$	−2.24824e38	−0.927366	−0.463683	+	0.886001i	$0.653472\pi$
$62$	4.32914e38	1.25887
$63$	−3.95206e38	−0.814707
$64$	−1.09698e39	−1.61186
$65$	2.81194e38	0.296053
$66$	1.69423e39	1.28463
$67$	−1.89786e39	−1.04149	−0.520745	−	0.853712i	$-0.674346\pi$
$67$	−1.89786e39	−1.04149	−0.520745	+	0.853712i	$0.674346\pi$
$68$	1.12331e39	0.448290
$69$	5.96191e39	1.73832
$70$	1.43875e39	0.307878
$71$	−9.53945e39	−1.50476	−0.752382	−	0.658727i	$-0.771095\pi$
$71$	−9.53945e39	−1.50476	−0.752382	+	0.658727i	$0.771095\pi$
$72$	−1.33977e40	−1.56452
$73$	2.48260e39	0.215509	0.107755	−	0.994178i	$-0.465634\pi$
$73$	2.48260e39	0.215509	0.107755	+	0.994178i	$0.465634\pi$
$74$	1.49341e40	0.967605
$75$	−2.67095e40	−1.29673
$76$	7.13920e40	2.60710
$77$	6.30424e39	0.173813
$78$	−7.59948e40	−1.58763
$79$	−3.50244e39	−0.0556402	−0.0278201	−	0.999613i	$-0.508857\pi$
$79$	−3.50244e39	−0.0556402	−0.0278201	+	0.999613i	$0.508857\pi$
$80$	−1.39389e40	−0.168964
$81$	1.61930e41	1.50280
$82$	−3.01941e40	−0.215240
$83$	−2.23114e41	−1.22560	−0.612799	−	0.790239i	$-0.709957\pi$
$83$	−2.23114e41	−1.22560	−0.612799	+	0.790239i	$0.709957\pi$
$84$	−2.30888e41	−0.980384
$85$	4.84401e40	0.159477
$86$	−1.63423e40	−0.0418405
$87$	1.35181e42	2.69930
$88$	2.13717e41	0.333781
$89$	−4.38099e41	−0.536645	−0.268323	−	0.963329i	$-0.586469\pi$
$89$	−4.38099e41	−0.536645	−0.268323	+	0.963329i	$0.586469\pi$
$90$	−1.82877e42	−1.76175
$91$	−2.82777e41	−0.214810
$92$	2.38054e42	1.42967
$93$	−2.99586e42	−1.42606
$94$	−2.89169e42	−1.09371
$95$	3.07861e42	0.927463
$96$	9.12154e42	2.19400
$97$	−6.11565e42	−1.17720	−0.588600	−	0.808424i	$-0.700321\pi$
$97$	−6.11565e42	−1.17720	−0.588600	+	0.808424i	$0.700321\pi$
$98$	8.71537e42	1.34563
$99$	−8.01318e42	−0.994599
$100$	−1.06649e43	−1.06649
$101$	8.20815e42	0.662728	0.331364	−	0.943503i	$-0.392491\pi$
$101$	8.20815e42	0.662728	0.331364	+	0.943503i	$0.392491\pi$
$102$	−1.30913e43	−0.855222
$103$	2.72199e43	1.44174	0.720868	−	0.693072i	$-0.243743\pi$
$103$	2.72199e43	1.44174	0.720868	+	0.693072i	$0.243743\pi$
$104$	−9.58630e42	−0.412510
$105$	−9.95648e42	−0.348767
$106$	−3.85561e43	−1.10158
$107$	−4.26383e43	−0.995517	−0.497758	−	0.867316i	$-0.665843\pi$
$107$	−4.26383e43	−0.995517	−0.497758	+	0.867316i	$0.665843\pi$
$108$	1.57554e44	3.01176
$109$	2.42680e43	0.380508	0.190254	−	0.981735i	$-0.439069\pi$
$109$	2.42680e43	0.380508	0.190254	+	0.981735i	$0.439069\pi$
$110$	2.91721e43	0.375859
$111$	−1.03347e44	−1.09611
$112$	1.40174e43	0.122597
$113$	1.73831e44	1.25586	0.627931	−	0.778269i	$-0.283902\pi$
$113$	1.73831e44	1.25586	0.627931	+	0.778269i	$0.283902\pi$
$114$	−8.32016e44	−4.97368
$115$	1.02655e44	0.508600
$116$	5.39767e44	2.22003
$117$	3.59432e44	1.22919
$118$	3.48110e43	0.0991410
$119$	−4.87128e43	−0.115713
$120$	−3.37530e44	−0.669754
$121$	−4.74576e44	−0.787808
$122$	1.04620e45	1.45505
$123$	2.08949e44	0.243827
$124$	−1.19622e45	−1.17286
$125$	−1.09027e45	−0.899433
$126$	1.83906e45	1.27829
$127$	−2.81930e45	−1.65334	−0.826669	−	0.562688i	$-0.809767\pi$
$127$	−2.81930e45	−1.65334	−0.826669	+	0.562688i	$0.809767\pi$
$128$	2.61318e45	1.29466
$129$	1.13092e44	0.0473974
$130$	−1.30852e45	−0.464512
$131$	5.22187e45	1.57215	0.786073	−	0.618133i	$-0.212111\pi$
$131$	5.22187e45	1.57215	0.786073	+	0.618133i	$0.212111\pi$
$132$	−4.68147e45	−1.19686
$133$	−3.09594e45	−0.672949
$134$	8.83154e45	1.63412
$135$	6.79416e45	1.07142
$136$	−1.65139e45	−0.222210
$137$	−1.17929e46	−1.35559	−0.677794	−	0.735252i	$-0.737064\pi$
$137$	−1.17929e46	−1.35559	−0.677794	+	0.735252i	$0.737064\pi$
$138$	−2.77433e46	−2.72745
$139$	7.89914e45	0.664908	0.332454	−	0.943119i	$-0.392123\pi$
$139$	7.89914e45	0.664908	0.332454	+	0.943119i	$0.392123\pi$
$140$	−3.97554e45	−0.286842
$141$	2.00111e46	1.23897
$142$	4.43911e46	2.36100
$143$	−5.73358e45	−0.262241
$144$	−1.78172e46	−0.701528
$145$	2.32761e46	0.789767
$146$	−1.15526e46	−0.338138
$147$	−6.03122e46	−1.52434
$148$	−4.12658e46	−0.901495
$149$	5.77438e45	0.109144	0.0545721	−	0.998510i	$-0.482621\pi$
$149$	5.77438e45	0.109144	0.0545721	+	0.998510i	$0.482621\pi$
$150$	1.24291e47	2.03459
$151$	−1.97310e46	−0.279992	−0.139996	−	0.990152i	$-0.544709\pi$
$151$	−1.97310e46	−0.279992	−0.139996	+	0.990152i	$0.544709\pi$
$152$	−1.04954e47	−1.29230
$153$	6.19178e46	0.662140
$154$	−2.93363e46	−0.272715
$155$	−5.15842e46	−0.417239
$156$	2.09988e47	1.47916
$157$	−1.33604e47	−0.820306	−0.410153	−	0.912017i	$-0.634525\pi$
$157$	−1.33604e47	−0.820306	−0.410153	+	0.912017i	$0.634525\pi$
$158$	1.62984e46	0.0873005
$159$	2.66816e47	1.24788
$160$	1.57059e47	0.641924
$161$	−1.03233e47	−0.369030
$162$	−7.53530e47	−2.35791
$163$	−1.04926e47	−0.287641	−0.143820	−	0.989604i	$-0.545939\pi$
$163$	−1.04926e47	−0.287641	−0.143820	+	0.989604i	$0.545939\pi$
$164$	8.34318e46	0.200534
$165$	−2.01877e47	−0.425777
$166$	1.03825e48	1.92299
$167$	−6.74904e47	−1.09860	−0.549298	−	0.835627i	$-0.685105\pi$
$167$	−6.74904e47	−1.09860	−0.549298	+	0.835627i	$0.685105\pi$
$168$	3.39430e47	0.485960
$169$	−5.36351e47	−0.675904
$170$	−2.25412e47	−0.250222
$171$	3.93518e48	3.85077
$172$	4.51569e46	0.0389818
$173$	−4.15452e47	−0.316614	−0.158307	−	0.987390i	$-0.550603\pi$
$173$	−4.15452e47	−0.316614	−0.158307	+	0.987390i	$0.550603\pi$
$174$	−6.29055e48	−4.23526
$175$	4.62486e47	0.275284
$176$	2.84215e47	0.149667
$177$	−2.40900e47	−0.112308
$178$	2.03866e48	0.842006
$179$	−6.34938e47	−0.232483	−0.116241	−	0.993221i	$-0.537085\pi$
$179$	−6.34938e47	−0.232483	−0.116241	+	0.993221i	$0.537085\pi$
$180$	5.05322e48	1.64138
$181$	5.38506e47	0.155275	0.0776375	−	0.996982i	$-0.475262\pi$
$181$	5.38506e47	0.155275	0.0776375	+	0.996982i	$0.475262\pi$
$182$	1.31588e48	0.337041
$183$	−7.23994e48	−1.64830
$184$	−3.49965e48	−0.708666
$185$	−1.77949e48	−0.320703
$186$	1.39410e49	2.23751
$187$	−9.87699e47	−0.141263
$188$	7.99026e48	1.01898
$189$	−6.83240e48	−0.777400
$190$	−1.43261e49	−1.45521
$191$	1.22017e49	1.10714	0.553572	−	0.832802i	$-0.313265\pi$
$191$	1.22017e49	1.10714	0.553572	+	0.832802i	$0.313265\pi$
$192$	−3.53257e49	−2.86493
$193$	8.36996e46	0.00607073	0.00303537	−	0.999995i	$-0.499034\pi$
$193$	8.36996e46	0.00607073	0.00303537	+	0.999995i	$0.499034\pi$
$194$	2.84587e49	1.84705
$195$	9.05522e48	0.526205
$196$	−2.40822e49	−1.25369
$197$	1.24344e49	0.580229	0.290115	−	0.956992i	$-0.406307\pi$
$197$	1.24344e49	0.580229	0.290115	+	0.956992i	$0.406307\pi$
$198$	3.72887e49	1.56054
$199$	2.54032e49	0.953997	0.476999	−	0.878904i	$-0.341725\pi$
$199$	2.54032e49	0.953997	0.476999	+	0.878904i	$0.341725\pi$
$200$	1.56785e49	0.528641
$201$	−6.11161e49	−1.85115
$202$	−3.81960e49	−1.03983
$203$	−2.34072e49	−0.573039
$204$	3.61737e49	0.796790
$205$	3.59779e48	0.0713392
$206$	−1.26666e50	−2.26211
$207$	1.31217e50	2.11168
$208$	−1.27485e49	−0.184969
$209$	−6.27731e49	−0.821540
$210$	4.63317e49	0.547222
$211$	1.72327e50	1.83772	0.918861	−	0.394582i	$-0.129110\pi$
$211$	1.72327e50	1.83772	0.918861	+	0.394582i	$0.129110\pi$
$212$	1.06538e50	1.02632
$213$	−3.07196e50	−2.67457
$214$	1.98414e50	1.56198
$215$	1.94728e48	0.0138676
$216$	−2.31622e50	−1.49288
$217$	5.18746e49	0.302740
$218$	−1.12929e50	−0.597024
$219$	7.99465e49	0.383046
$220$	−8.06078e49	−0.350179
$221$	4.43033e49	0.174583
$222$	4.80920e50	1.71982
$223$	−1.43740e50	−0.466683	−0.233342	−	0.972395i	$-0.574966\pi$
$223$	−1.43740e50	−0.466683	−0.233342	+	0.972395i	$0.574966\pi$
$224$	−1.57943e50	−0.465767
$225$	−5.87856e50	−1.57524
$226$	−8.08911e50	−1.97047
$227$	−7.21848e48	−0.0159915	−0.00799576	−	0.999968i	$-0.502545\pi$
$227$	−7.21848e48	−0.0159915	−0.00799576	+	0.999968i	$0.502545\pi$
$228$	2.29902e51	4.63386
$229$	8.60814e50	1.57923	0.789617	−	0.613600i	$-0.210279\pi$
$229$	8.60814e50	1.57923	0.789617	+	0.613600i	$0.210279\pi$
$230$	−4.77698e50	−0.798003
$231$	2.03014e50	0.308935
$232$	−7.93516e50	−1.10043
$233$	−8.15789e50	−1.03140	−0.515698	−	0.856770i	$-0.672467\pi$
$233$	−8.15789e50	−1.03140	−0.515698	+	0.856770i	$0.672467\pi$
$234$	−1.67259e51	−1.92863
$235$	3.44561e50	0.362499
$236$	−9.61892e49	−0.0923673
$237$	−1.12788e50	−0.0988950
$238$	2.26681e50	0.181556
$239$	1.19865e51	0.877276	0.438638	−	0.898664i	$-0.355461\pi$
$239$	1.19865e51	0.877276	0.438638	+	0.898664i	$0.355461\pi$
$240$	−4.48870e50	−0.300316
$241$	1.15117e51	0.704326	0.352163	−	0.935939i	$-0.385446\pi$
$241$	1.15117e51	0.704326	0.352163	+	0.935939i	$0.385446\pi$
$242$	2.20841e51	1.23609
$243$	1.19241e51	0.610786
$244$	−2.89085e51	−1.35564
$245$	−1.03849e51	−0.445995
$246$	−9.72331e50	−0.382568
$247$	2.81570e51	1.01532
$248$	1.75858e51	0.581366
$249$	−7.18488e51	−2.17838
$250$	5.07349e51	1.41123
$251$	−3.52535e51	−0.899948	−0.449974	−	0.893042i	$-0.648567\pi$
$251$	−3.52535e51	−0.899948	−0.449974	+	0.893042i	$0.648567\pi$
$252$	−5.08167e51	−1.19095
$253$	−2.09315e51	−0.450514
$254$	1.31194e52	2.59412
$255$	1.55990e51	0.283455
$256$	−2.51112e51	−0.419478
$257$	−9.00901e51	−1.38393	−0.691967	−	0.721930i	$-0.743255\pi$
$257$	−9.00901e51	−1.38393	−0.691967	+	0.721930i	$0.743255\pi$
$258$	−5.26267e50	−0.0743674
$259$	1.78951e51	0.232696
$260$	3.61567e51	0.432775
$261$	2.97523e52	3.27907
$262$	−2.42996e52	−2.46673
$263$	−8.70831e51	−0.814489	−0.407245	−	0.913319i	$-0.633510\pi$
$263$	−8.70831e51	−0.814489	−0.407245	+	0.913319i	$0.633510\pi$
$264$	6.88227e51	0.593263
$265$	4.59417e51	0.365108
$266$	1.44067e52	1.05587
$267$	−1.41080e52	−0.953834
$268$	−2.44032e52	−1.52247
$269$	2.29589e52	1.32214	0.661071	−	0.750324i	$-0.270102\pi$
$269$	2.29589e52	1.32214	0.661071	+	0.750324i	$0.270102\pi$
$270$	−3.16161e52	−1.68108
$271$	−2.04437e52	−1.00397	−0.501983	−	0.864877i	$-0.667396\pi$
$271$	−2.04437e52	−1.00397	−0.501983	+	0.864877i	$0.667396\pi$
$272$	−2.19613e51	−0.0996384
$273$	−9.10620e51	−0.381804
$274$	5.48773e52	2.12694
$275$	9.37735e51	0.336068
$276$	7.66598e52	2.54110
$277$	3.67190e52	1.12610	0.563049	−	0.826424i	$-0.309628\pi$
$277$	3.67190e52	1.12610	0.563049	+	0.826424i	$0.309628\pi$
$278$	−3.67581e52	−1.04325
$279$	−6.59366e52	−1.73235
$280$	5.84447e51	0.142183
$281$	−3.21289e52	−0.723952	−0.361976	−	0.932187i	$-0.617898\pi$
$281$	−3.21289e52	−0.723952	−0.361976	+	0.932187i	$0.617898\pi$
$282$	−9.31201e52	−1.94396
$283$	7.76513e52	1.50224	0.751121	−	0.660164i	$-0.229513\pi$
$283$	7.76513e52	1.50224	0.751121	+	0.660164i	$0.229513\pi$
$284$	−1.22661e53	−2.19969
$285$	9.91395e52	1.64847
$286$	2.66808e52	0.411461
$287$	−3.61805e51	−0.0517623
$288$	2.00758e53	2.66523
$289$	−7.35209e52	−0.905956
$290$	−1.08314e53	−1.23916
$291$	−1.96940e53	−2.09236
$292$	3.19220e52	0.315035
$293$	7.07016e52	0.648299	0.324150	−	0.946006i	$-0.394922\pi$
$293$	7.07016e52	0.648299	0.324150	+	0.946006i	$0.394922\pi$
$294$	2.80658e53	2.39172
$295$	−4.14793e51	−0.0328593
$296$	6.06652e52	0.446856
$297$	−1.38533e53	−0.949054
$298$	−2.68707e52	−0.171249
$299$	9.38883e52	0.556777
$300$	−3.43438e53	−1.89558
$301$	−1.95824e51	−0.0100621
$302$	9.18168e52	0.439312
$303$	2.64325e53	1.17793
$304$	−1.39575e53	−0.579463
$305$	−1.24661e53	−0.482263
$306$	−2.88130e53	−1.03891
$307$	−4.17987e53	−1.40504	−0.702518	−	0.711666i	$-0.747941\pi$
$307$	−4.17987e53	−1.40504	−0.702518	+	0.711666i	$0.747941\pi$
$308$	8.10616e52	0.254083
$309$	8.76554e53	2.56255
$310$	2.40043e53	0.654655
$311$	1.08737e53	0.276714	0.138357	−	0.990382i	$-0.455818\pi$
$311$	1.08737e53	0.276714	0.138357	+	0.990382i	$0.455818\pi$
$312$	−3.08705e53	−0.733196
$313$	5.09671e52	0.113002	0.0565011	−	0.998403i	$-0.482006\pi$
$313$	5.09671e52	0.113002	0.0565011	+	0.998403i	$0.482006\pi$
$314$	6.21715e53	1.28707
$315$	−2.19135e53	−0.423676
$316$	−4.50354e52	−0.0813358
$317$	5.92996e53	1.00064	0.500320	−	0.865841i	$-0.333216\pi$
$317$	5.92996e53	1.00064	0.500320	+	0.865841i	$0.333216\pi$
$318$	−1.24161e54	−1.95795
$319$	−4.74603e53	−0.699569
$320$	−6.08255e53	−0.838226
$321$	−1.37307e54	−1.76943
$322$	4.80387e53	0.579015
$323$	4.85047e53	0.546928
$324$	2.08214e54	2.19681
$325$	−4.20622e53	−0.415336
$326$	4.88266e53	0.451313
$327$	7.81494e53	0.676315
$328$	−1.22654e53	−0.0994016
$329$	−3.46501e53	−0.263022
$330$	9.39420e53	0.668052
$331$	4.62094e53	0.307913	0.153957	−	0.988078i	$-0.450798\pi$
$331$	4.62094e53	0.307913	0.153957	+	0.988078i	$0.450798\pi$
$332$	−2.86886e54	−1.79160
$333$	−2.27460e54	−1.33154
$334$	3.14061e54	1.72372
$335$	−1.05233e54	−0.541611
$336$	4.51397e53	0.217904
$337$	−2.44988e54	−1.10943	−0.554717	−	0.832039i	$-0.687173\pi$
$337$	−2.44988e54	−1.10943	−0.554717	+	0.832039i	$0.687173\pi$
$338$	2.49587e54	1.06051
$339$	5.59784e54	2.23217
$340$	6.22856e53	0.233126
$341$	1.05181e54	0.369587
$342$	−1.83121e55	−6.04193
$343$	2.26203e54	0.700932
$344$	−6.63855e52	−0.0193227
$345$	3.30577e54	0.903987
$346$	1.93327e54	0.496772
$347$	2.06865e54	0.499579	0.249789	−	0.968300i	$-0.419639\pi$
$347$	2.06865e54	0.499579	0.249789	+	0.968300i	$0.419639\pi$
$348$	1.73820e55	3.94589
$349$	−9.24540e54	−1.97324	−0.986618	−	0.163050i	$-0.947867\pi$
$349$	−9.24540e54	−1.97324	−0.986618	+	0.163050i	$0.947867\pi$
$350$	−2.15215e54	−0.431926
$351$	6.21394e54	1.17291
$352$	−3.20245e54	−0.568611
$353$	−3.55103e54	−0.593196	−0.296598	−	0.955002i	$-0.595852\pi$
$353$	−3.55103e54	−0.593196	−0.296598	+	0.955002i	$0.595852\pi$
$354$	1.12101e54	0.176213
$355$	−5.28945e54	−0.782530
$356$	−5.63320e54	−0.784477
$357$	−1.56868e54	−0.205669
$358$	2.95463e54	0.364770
$359$	−6.37557e54	−0.741291	−0.370645	−	0.928774i	$-0.620863\pi$
$359$	−6.37557e54	−0.741291	−0.370645	+	0.928774i	$0.620863\pi$
$360$	−7.42878e54	−0.813605
$361$	2.11353e55	2.18074
$362$	−2.50590e54	−0.243629
$363$	−1.52826e55	−1.40025
$364$	−3.63603e54	−0.314013
$365$	1.37656e54	0.112072
$366$	3.36905e55	2.58621
$367$	1.19284e55	0.863502	0.431751	−	0.901993i	$-0.357896\pi$
$367$	1.19284e55	0.863502	0.431751	+	0.901993i	$0.357896\pi$
$368$	−4.65408e54	−0.317764
$369$	4.59882e54	0.296196
$370$	8.28071e54	0.503189
$371$	−4.62004e54	−0.264915
$372$	−3.85216e55	−2.08464
$373$	−6.58590e54	−0.336415	−0.168208	−	0.985752i	$-0.553798\pi$
$373$	−6.58590e54	−0.336415	−0.168208	+	0.985752i	$0.553798\pi$
$374$	4.59618e54	0.221645
$375$	−3.51097e55	−1.59865
$376$	−1.17466e55	−0.505094
$377$	2.12884e55	0.864576
$378$	3.17941e55	1.21975
$379$	4.25975e55	1.54398	0.771989	−	0.635636i	$-0.219262\pi$
$379$	4.25975e55	1.54398	0.771989	+	0.635636i	$0.219262\pi$
$380$	3.95856e55	1.35578
$381$	−9.07892e55	−2.93865
$382$	−5.67798e55	−1.73713
$383$	−1.85965e53	−0.00537846	−0.00268923	−	0.999996i	$-0.500856\pi$
$383$	−1.85965e53	−0.00537846	−0.00268923	+	0.999996i	$0.500856\pi$
$384$	8.41515e55	2.30113
$385$	3.49559e54	0.0903888
$386$	−3.89490e53	−0.00952509
$387$	2.48908e54	0.0575775
$388$	−7.86367e55	−1.72085
$389$	7.73460e55	1.60148	0.800740	−	0.599012i	$-0.204440\pi$
$389$	7.73460e55	1.60148	0.800740	+	0.599012i	$0.204440\pi$
$390$	−4.21378e55	−0.825625
$391$	1.61737e55	0.299923
$392$	3.54034e55	0.621434
$393$	1.68158e56	2.79434
$394$	−5.78624e55	−0.910390
$395$	−1.94204e54	−0.0289349
$396$	−1.03036e56	−1.45392
$397$	−5.40998e55	−0.723102	−0.361551	−	0.932352i	$-0.617753\pi$
$397$	−5.40998e55	−0.723102	−0.361551	+	0.932352i	$0.617753\pi$
$398$	−1.18212e56	−1.49684
$399$	−9.96976e55	−1.19610
$400$	2.08504e55	0.237041
$401$	−1.27603e56	−1.37486	−0.687429	−	0.726252i	$-0.741261\pi$
$401$	−1.27603e56	−1.37486	−0.687429	+	0.726252i	$0.741261\pi$
$402$	2.84399e56	2.90448
$403$	−4.71789e55	−0.456761
$404$	1.05543e56	0.968787
$405$	8.97874e55	0.781506
$406$	1.08924e56	0.899108
$407$	3.62839e55	0.284076
$408$	−5.31793e55	−0.394956
$409$	1.15025e56	0.810481	0.405240	−	0.914210i	$-0.367188\pi$
$409$	1.15025e56	0.810481	0.405240	+	0.914210i	$0.367188\pi$
$410$	−1.67421e55	−0.111932
$411$	−3.79763e56	−2.40942
$412$	3.50001e56	2.10756
$413$	4.17128e54	0.0238420
$414$	−6.10609e56	−3.31326
$415$	−1.23713e56	−0.637354
$416$	1.43646e56	0.702729
$417$	2.54374e56	1.18181
$418$	2.92110e56	1.28901
$419$	−3.32264e55	−0.139278	−0.0696389	−	0.997572i	$-0.522185\pi$
$419$	−3.32264e55	−0.139278	−0.0696389	+	0.997572i	$0.522185\pi$
$420$	−1.28023e56	−0.509834
$421$	−3.83623e55	−0.145158	−0.0725788	−	0.997363i	$-0.523123\pi$
$421$	−3.83623e55	−0.145158	−0.0725788	+	0.997363i	$0.523123\pi$
$422$	−8.01909e56	−2.88342
$423$	4.40429e56	1.50507
$424$	−1.56622e56	−0.508729
$425$	−7.24588e55	−0.223732
$426$	1.42951e57	4.19645
$427$	1.25363e56	0.349920
$428$	−5.48255e56	−1.45526
$429$	−1.84637e56	−0.466108
$430$	−9.06153e54	−0.0217585
$431$	2.91528e56	0.665916	0.332958	−	0.942942i	$-0.391953\pi$
$431$	2.91528e56	0.665916	0.332958	+	0.942942i	$0.391953\pi$
$432$	−3.08027e56	−0.669404
$433$	−8.91932e56	−1.84434	−0.922172	−	0.386780i	$-0.873587\pi$
$433$	−8.91932e56	−1.84434	−0.922172	+	0.386780i	$0.873587\pi$
$434$	−2.41394e56	−0.475005
$435$	7.49555e56	1.40373
$436$	3.12044e56	0.556233
$437$	1.02792e57	1.74425
$438$	−3.72025e56	−0.601006
$439$	−4.59768e56	−0.707216	−0.353608	−	0.935394i	$-0.615045\pi$
$439$	−4.59768e56	−0.707216	−0.353608	+	0.935394i	$0.615045\pi$
$440$	1.18502e56	0.173578
$441$	−1.32743e57	−1.85174
$442$	−2.06162e56	−0.273924
$443$	7.17753e56	0.908437	0.454219	−	0.890890i	$-0.349918\pi$
$443$	7.17753e56	0.908437	0.454219	+	0.890890i	$0.349918\pi$
$444$	−1.32887e57	−1.60232
$445$	−2.42918e56	−0.279074
$446$	6.68882e56	0.732234
$447$	1.85951e56	0.193993
$448$	6.11679e56	0.608200
$449$	−2.56945e56	−0.243526	−0.121763	−	0.992559i	$-0.538855\pi$
$449$	−2.56945e56	−0.243526	−0.121763	+	0.992559i	$0.538855\pi$
$450$	2.73555e57	2.47158
$451$	−7.33594e55	−0.0631917
$452$	2.23517e57	1.83584
$453$	−6.35392e56	−0.497657
$454$	3.35907e55	0.0250910
$455$	−1.56795e56	−0.111709
$456$	−3.37980e57	−2.29693
$457$	−1.11475e57	−0.722733	−0.361367	−	0.932424i	$-0.617690\pi$
$457$	−1.11475e57	−0.722733	−0.361367	+	0.932424i	$0.617690\pi$
$458$	−4.00574e57	−2.47785
$459$	1.07045e57	0.631819
$460$	1.31997e57	0.743481
$461$	2.02024e57	1.08601	0.543003	−	0.839731i	$-0.317287\pi$
$461$	2.02024e57	1.08601	0.543003	+	0.839731i	$0.317287\pi$
$462$	−9.44708e56	−0.484725
$463$	−2.86426e56	−0.140288	−0.0701442	−	0.997537i	$-0.522346\pi$
$463$	−2.86426e56	−0.140288	−0.0701442	+	0.997537i	$0.522346\pi$
$464$	−1.05527e57	−0.493432
$465$	−1.66115e57	−0.741601
$466$	3.79621e57	1.61828
$467$	1.63037e57	0.663701	0.331850	−	0.943332i	$-0.392327\pi$
$467$	1.63037e57	0.663701	0.331850	+	0.943332i	$0.392327\pi$
$468$	4.62168e57	1.79686
$469$	1.05825e57	0.392982
$470$	−1.60339e57	−0.568767
$471$	−4.30240e57	−1.45801
$472$	1.41409e56	0.0457850
$473$	−3.97052e55	−0.0122838
$474$	5.24852e56	0.155168
$475$	−4.60511e57	−1.30115
$476$	−6.26363e56	−0.169152
$477$	5.87243e57	1.51591
$478$	−5.57781e57	−1.37646
$479$	7.76358e57	1.83168	0.915838	−	0.401548i	$-0.131528\pi$
$479$	7.76358e57	1.83168	0.915838	+	0.401548i	$0.131528\pi$
$480$	5.05773e57	1.14096
$481$	−1.62752e57	−0.351081
$482$	−5.35690e57	−1.10510
$483$	−3.32438e57	−0.655915
$484$	−6.10223e57	−1.15163
$485$	−3.39102e57	−0.612185
$486$	−5.54877e57	−0.958335
$487$	1.02143e58	1.68786	0.843932	−	0.536451i	$-0.180235\pi$
$487$	1.02143e58	1.68786	0.843932	+	0.536451i	$0.180235\pi$
$488$	4.24986e57	0.671968
$489$	−3.37891e57	−0.511253
$490$	4.83251e57	0.699773
$491$	4.75337e57	0.658794	0.329397	−	0.944192i	$-0.393155\pi$
$491$	4.75337e57	0.658794	0.329397	+	0.944192i	$0.393155\pi$
$492$	2.68673e57	0.356430
$493$	3.66725e57	0.465728
$494$	−1.31026e58	−1.59305
$495$	−4.44316e57	−0.517226
$496$	2.33867e57	0.260683
$497$	5.31923e57	0.567788
$498$	3.34343e58	3.41792
$499$	−6.28971e57	−0.615841	−0.307921	−	0.951412i	$-0.599633\pi$
$499$	−6.28971e57	−0.615841	−0.307921	+	0.951412i	$0.599633\pi$
$500$	−1.40190e58	−1.31481
$501$	−2.17337e58	−1.95264
$502$	1.64050e58	1.41203
$503$	−2.08189e58	−1.71690	−0.858451	−	0.512896i	$-0.828573\pi$
$503$	−2.08189e58	−1.71690	−0.858451	+	0.512896i	$0.828573\pi$
$504$	7.47060e57	0.590336
$505$	4.55127e57	0.344642
$506$	9.74030e57	0.706865
$507$	−1.72720e58	−1.20135
$508$	−3.62514e58	−2.41688
$509$	4.65765e57	0.297669	0.148835	−	0.988862i	$-0.452448\pi$
$509$	4.65765e57	0.297669	0.148835	+	0.988862i	$0.452448\pi$
$510$	−7.25889e57	−0.444745
$511$	−1.38431e57	−0.0813174
$512$	−1.13005e58	−0.636491
$513$	6.80322e58	3.67444
$514$	4.19228e58	2.17142
$515$	1.50929e58	0.749754
$516$	1.45417e57	0.0692863
$517$	−7.02563e57	−0.321099
$518$	−8.32733e57	−0.365104
$519$	−1.33787e58	−0.562749
$520$	−5.31543e57	−0.214520
$521$	4.15022e57	0.160716	0.0803582	−	0.996766i	$-0.474394\pi$
$521$	4.15022e57	0.160716	0.0803582	+	0.996766i	$0.474394\pi$
$522$	−1.38450e59	−5.14491
$523$	−3.61441e57	−0.128899	−0.0644497	−	0.997921i	$-0.520529\pi$
$523$	−3.61441e57	−0.128899	−0.0644497	+	0.997921i	$0.520529\pi$
$524$	6.71442e58	2.29819
$525$	1.48933e58	0.489290
$526$	4.05235e58	1.27795
$527$	−8.12730e57	−0.246047
$528$	9.15251e57	0.266018
$529$	−1.55852e57	−0.0434925
$530$	−2.13787e58	−0.572861
$531$	−5.30202e57	−0.136430
$532$	−3.98084e58	−0.983728
$533$	3.29054e57	0.0780967
$534$	6.56504e58	1.49658
$535$	−2.36422e58	−0.517703
$536$	3.58753e58	0.754662
$537$	−2.04467e58	−0.413215
$538$	−1.06838e59	−2.07446
$539$	2.11748e58	0.395058
$540$	8.73611e58	1.56622
$541$	−4.79722e58	−0.826511	−0.413256	−	0.910615i	$-0.635608\pi$
$541$	−4.79722e58	−0.826511	−0.413256	+	0.910615i	$0.635608\pi$
$542$	9.51331e58	1.57524
$543$	1.73414e58	0.275986
$544$	2.47453e58	0.378544
$545$	1.34562e58	0.197877
$546$	4.23750e58	0.599057
$547$	3.67046e58	0.498877	0.249439	−	0.968391i	$-0.419754\pi$
$547$	3.67046e58	0.498877	0.249439	+	0.968391i	$0.419754\pi$
$548$	−1.51636e59	−1.98162
$549$	−1.59346e59	−2.00233
$550$	−4.36368e58	−0.527297
$551$	2.33072e59	2.70851
$552$	−1.12698e59	−1.25958
$553$	1.95298e57	0.0209946
$554$	−1.70869e59	−1.76687
$555$	−5.73043e58	−0.570018
$556$	1.01569e59	0.971974
$557$	−1.44377e59	−1.32926	−0.664632	−	0.747171i	$-0.731412\pi$
$557$	−1.44377e59	−1.32926	−0.664632	+	0.747171i	$0.731412\pi$
$558$	3.06831e59	2.71809
$559$	1.78098e57	0.0151812
$560$	7.77238e57	0.0637546
$561$	−3.18066e58	−0.251082
$562$	1.49509e59	1.13589
$563$	−1.85030e58	−0.135304	−0.0676521	−	0.997709i	$-0.521551\pi$
$563$	−1.85030e58	−0.135304	−0.0676521	+	0.997709i	$0.521551\pi$
$564$	2.57308e59	1.81114
$565$	9.63864e58	0.653092
$566$	−3.61344e59	−2.35705
$567$	−9.02928e58	−0.567045
$568$	1.80325e59	1.09035
$569$	7.55839e58	0.440064	0.220032	−	0.975493i	$-0.429384\pi$
$569$	7.55839e58	0.440064	0.220032	+	0.975493i	$0.429384\pi$
$570$	−4.61338e59	−2.58649
$571$	1.65354e59	0.892767	0.446384	−	0.894842i	$-0.352712\pi$
$571$	1.65354e59	0.892767	0.446384	+	0.894842i	$0.352712\pi$
$572$	−7.37239e58	−0.383349
$573$	3.92929e59	1.96784
$574$	1.68363e58	0.0812160
$575$	−1.53556e59	−0.713522
$576$	−7.77492e59	−3.48027
$577$	−4.04625e59	−1.74491	−0.872453	−	0.488697i	$-0.837472\pi$
$577$	−4.04625e59	−1.74491	−0.872453	+	0.488697i	$0.837472\pi$
$578$	3.42124e59	1.42146
$579$	2.69535e57	0.0107901
$580$	2.99291e59	1.15449
$581$	1.24409e59	0.462451
$582$	9.16448e59	3.28294
$583$	−9.36757e58	−0.323410
$584$	−4.69288e58	−0.156158
$585$	1.99299e59	0.639224
$586$	−3.29005e59	−1.01719
$587$	3.79894e59	1.13225	0.566126	−	0.824319i	$-0.308442\pi$
$587$	3.79894e59	1.13225	0.566126	+	0.824319i	$0.308442\pi$
$588$	−7.75511e59	−2.22831
$589$	−5.16530e59	−1.43092
$590$	1.93021e58	0.0515568
$591$	4.00420e59	1.03130
$592$	8.06767e58	0.200369
$593$	−4.79450e59	−1.14833	−0.574166	−	0.818739i	$-0.694674\pi$
$593$	−4.79450e59	−1.14833	−0.574166	+	0.818739i	$0.694674\pi$
$594$	6.44655e59	1.48908
$595$	−2.70104e58	−0.0601750
$596$	7.42486e58	0.159549
$597$	8.18052e59	1.69564
$598$	−4.36902e59	−0.873592
$599$	−4.48279e59	−0.864713	−0.432356	−	0.901703i	$-0.642318\pi$
$599$	−4.48279e59	−0.864713	−0.432356	+	0.901703i	$0.642318\pi$
$600$	5.04892e59	0.939607
$601$	−1.41250e59	−0.253621	−0.126811	−	0.991927i	$-0.540474\pi$
$601$	−1.41250e59	−0.253621	−0.126811	+	0.991927i	$0.540474\pi$
$602$	9.11254e57	0.0157876
$603$	−1.34512e60	−2.24874
$604$	−2.53707e59	−0.409296
$605$	−2.63144e59	−0.409688
$606$	−1.23001e60	−1.84820
$607$	7.01925e59	1.01797	0.508984	−	0.860776i	$-0.330021\pi$
$607$	7.01925e59	1.01797	0.508984	+	0.860776i	$0.330021\pi$
$608$	1.57269e60	2.20148
$609$	−7.53775e59	−1.01852
$610$	5.80100e59	0.756679
$611$	3.15135e59	0.396836
$612$	7.96156e59	0.967927
$613$	1.03814e60	1.21858	0.609292	−	0.792946i	$-0.291454\pi$
$613$	1.03814e60	1.21858	0.609292	+	0.792946i	$0.291454\pi$
$614$	1.94507e60	2.20453
$615$	1.15859e59	0.126798
$616$	−1.19169e59	−0.125945
$617$	−1.00931e60	−1.03014	−0.515069	−	0.857149i	$-0.672234\pi$
$617$	−1.00931e60	−1.03014	−0.515069	+	0.857149i	$0.672234\pi$
$618$	−4.07898e60	−4.02068
$619$	1.22876e59	0.116981	0.0584907	−	0.998288i	$-0.481371\pi$
$619$	1.22876e59	0.116981	0.0584907	+	0.998288i	$0.481371\pi$
$620$	−6.63283e59	−0.609927
$621$	2.26851e60	2.01498
$622$	−5.06001e59	−0.434169
$623$	2.44286e59	0.202491
$624$	−4.10537e59	−0.328763
$625$	3.38403e59	0.261827
$626$	−2.37172e59	−0.177302
$627$	−2.02146e60	−1.46021
$628$	−1.71791e60	−1.19914
$629$	−2.80366e59	−0.189119
$630$	1.01973e60	0.664755
$631$	2.36287e60	1.48870	0.744352	−	0.667787i	$-0.232758\pi$
$631$	2.36287e60	1.48870	0.744352	+	0.667787i	$0.232758\pi$
$632$	6.62069e58	0.0403168
$633$	5.54939e60	3.26637
$634$	−2.75946e60	−1.57002
$635$	−1.56325e60	−0.859794
$636$	3.43080e60	1.82418
$637$	−9.49799e59	−0.488241
$638$	2.20853e60	1.09764
$639$	−6.76116e60	−3.24902
$640$	1.44896e60	0.673268
$641$	−3.06701e60	−1.37806	−0.689029	−	0.724734i	$-0.741963\pi$
$641$	−3.06701e60	−1.37806	−0.689029	+	0.724734i	$0.741963\pi$
$642$	6.38947e60	2.77627
$643$	8.63761e59	0.362959	0.181479	−	0.983395i	$-0.441911\pi$
$643$	8.63761e59	0.362959	0.181479	+	0.983395i	$0.441911\pi$
$644$	−1.32740e60	−0.539455
$645$	6.27077e58	0.0246483
$646$	−2.25713e60	−0.858139
$647$	−1.57232e60	−0.578228	−0.289114	−	0.957295i	$-0.593361\pi$
$647$	−1.57232e60	−0.578228	−0.289114	+	0.957295i	$0.593361\pi$
$648$	−3.06098e60	−1.08892
$649$	8.45767e58	0.0291065
$650$	1.95733e60	0.651670
$651$	1.67050e60	0.538091
$652$	−1.34917e60	−0.420478
$653$	1.42220e60	0.428870	0.214435	−	0.976738i	$-0.431209\pi$
$653$	1.42220e60	0.428870	0.214435	+	0.976738i	$0.431209\pi$
$654$	−3.63663e60	−1.06115
$655$	2.89543e60	0.817571
$656$	−1.63113e59	−0.0445715
$657$	1.75956e60	0.465317
$658$	1.61241e60	0.412686
$659$	2.37773e60	0.589015	0.294507	−	0.955649i	$-0.404844\pi$
$659$	2.37773e60	0.589015	0.294507	+	0.955649i	$0.404844\pi$
$660$	−2.59579e60	−0.622408
$661$	−7.09142e60	−1.64589	−0.822947	−	0.568119i	$-0.807671\pi$
$661$	−7.09142e60	−1.64589	−0.822947	+	0.568119i	$0.807671\pi$
$662$	−2.15032e60	−0.483121
$663$	1.42669e60	0.310304
$664$	4.21754e60	0.888067
$665$	−1.71664e60	−0.349957
$666$	1.05847e61	2.08921
$667$	7.77170e60	1.48529
$668$	−8.67810e60	−1.60595
$669$	−4.62881e60	−0.829483
$670$	4.89693e60	0.849798
$671$	2.54185e60	0.427184
$672$	−5.08620e60	−0.827855
$673$	7.62590e60	1.20217	0.601086	−	0.799184i	$-0.294735\pi$
$673$	7.62590e60	1.20217	0.601086	+	0.799184i	$0.294735\pi$
$674$	1.14003e61	1.74072
$675$	−1.01630e61	−1.50311
$676$	−6.89655e60	−0.988048
$677$	−1.33549e61	−1.85347	−0.926735	−	0.375717i	$-0.877397\pi$
$677$	−1.33549e61	−1.85347	−0.926735	+	0.375717i	$0.877397\pi$
$678$	−2.60491e61	−3.50231
$679$	3.41011e60	0.444189
$680$	−9.15667e59	−0.115557
$681$	−2.32455e59	−0.0284233
$682$	−4.89450e60	−0.579888
$683$	7.17925e60	0.824202	0.412101	−	0.911138i	$-0.364795\pi$
$683$	7.17925e60	0.824202	0.412101	+	0.911138i	$0.364795\pi$
$684$	5.05996e61	5.62913
$685$	−6.53894e60	−0.704953
$686$	−1.05262e61	−1.09977
$687$	2.77206e61	2.80693
$688$	−8.82839e58	−0.00866424
$689$	4.20183e60	0.399692
$690$	−1.53832e61	−1.41837
$691$	−1.17437e61	−1.04961	−0.524803	−	0.851224i	$-0.675861\pi$
$691$	−1.17437e61	−1.04961	−0.524803	+	0.851224i	$0.675861\pi$
$692$	−5.34200e60	−0.462831
$693$	4.46818e60	0.375289
$694$	−9.62632e60	−0.783848
$695$	4.37993e60	0.345776
$696$	−2.55534e61	−1.95591
$697$	5.66848e59	0.0420689
$698$	4.30228e61	3.09604
$699$	−2.62706e61	−1.83320
$700$	5.94678e60	0.402415
$701$	1.27675e61	0.837854	0.418927	−	0.908020i	$-0.362406\pi$
$701$	1.27675e61	0.837854	0.418927	+	0.908020i	$0.362406\pi$
$702$	−2.89161e61	−1.84031
$703$	−1.78186e61	−1.09985
$704$	1.24024e61	0.742494
$705$	1.10958e61	0.644306
$706$	1.65245e61	0.930735
$707$	−4.57689e60	−0.250065
$708$	−3.09755e60	−0.164174
$709$	−2.73809e61	−1.40784	−0.703921	−	0.710278i	$-0.748569\pi$
$709$	−2.73809e61	−1.40784	−0.703921	+	0.710278i	$0.748569\pi$
$710$	2.46141e61	1.22780
$711$	−2.48238e60	−0.120136
$712$	8.28142e60	0.388852
$713$	−1.72235e61	−0.784687
$714$	7.29976e60	0.322698
$715$	−3.17917e60	−0.136375
$716$	−8.16420e60	−0.339847
$717$	3.85997e61	1.55927
$718$	2.96683e61	1.16310
$719$	2.16831e61	0.824993	0.412496	−	0.910959i	$-0.364657\pi$
$719$	2.16831e61	0.824993	0.412496	+	0.910959i	$0.364657\pi$
$720$	−9.87930e60	−0.364819
$721$	−1.51779e61	−0.544006
$722$	−9.83518e61	−3.42162
$723$	3.70709e61	1.25187
$724$	6.92426e60	0.226984
$725$	−3.48174e61	−1.10797
$726$	7.11166e61	2.19702
$727$	1.57652e61	0.472835	0.236418	−	0.971652i	$-0.424027\pi$
$727$	1.57652e61	0.472835	0.236418	+	0.971652i	$0.424027\pi$
$728$	5.34536e60	0.155651
$729$	−1.47560e61	−0.417183
$730$	−6.40571e60	−0.175843
$731$	3.06802e59	0.00817777
$732$	−9.30931e61	−2.40951
$733$	2.88722e61	0.725679	0.362840	−	0.931852i	$-0.381807\pi$
$733$	2.88722e61	0.725679	0.362840	+	0.931852i	$0.381807\pi$
$734$	−5.55081e61	−1.35485
$735$	−3.34420e61	−0.792711
$736$	5.24407e61	1.20724
$737$	2.14571e61	0.479755
$738$	−2.14003e61	−0.464737
$739$	7.66659e60	0.161714	0.0808568	−	0.996726i	$-0.474234\pi$
$739$	7.66659e60	0.161714	0.0808568	+	0.996726i	$0.474234\pi$
$740$	−2.28811e61	−0.468809
$741$	9.06730e61	1.80462
$742$	2.14990e61	0.415656
$743$	5.63267e61	1.05792	0.528962	−	0.848645i	$-0.322581\pi$
$743$	5.63267e61	1.05792	0.528962	+	0.848645i	$0.322581\pi$
$744$	5.66309e61	1.03332
$745$	3.20179e60	0.0567588
$746$	3.06470e61	0.527841
$747$	−1.58134e62	−2.64626
$748$	−1.27001e61	−0.206501
$749$	2.37753e61	0.375635
$750$	1.63380e62	2.50832
$751$	−5.65647e60	−0.0843892	−0.0421946	−	0.999109i	$-0.513435\pi$
$751$	−5.65647e60	−0.0843892	−0.0421946	+	0.999109i	$0.513435\pi$
$752$	−1.56214e61	−0.226483
$753$	−1.13526e62	−1.59957
$754$	−9.90638e61	−1.35654
$755$	−1.09405e61	−0.145605
$756$	−8.78529e61	−1.13642
$757$	4.86809e61	0.612065	0.306032	−	0.952021i	$-0.400998\pi$
$757$	4.86809e61	0.612065	0.306032	+	0.952021i	$0.400998\pi$
$758$	−1.98224e62	−2.42253
$759$	−6.74050e61	−0.800744
$760$	−5.81951e61	−0.672039
$761$	5.98651e61	0.672053	0.336026	−	0.941853i	$-0.390917\pi$
$761$	5.98651e61	0.672053	0.336026	+	0.941853i	$0.390917\pi$
$762$	4.22481e62	4.61079
$763$	−1.35319e61	−0.143576
$764$	1.56893e62	1.61844
$765$	3.43323e61	0.344336
$766$	8.65375e59	0.00843890
$767$	−3.79370e60	−0.0359718
$768$	−8.08650e61	−0.745580
$769$	−2.53056e61	−0.226882	−0.113441	−	0.993545i	$-0.536187\pi$
$769$	−2.53056e61	−0.226882	−0.113441	+	0.993545i	$0.536187\pi$
$770$	−1.62665e61	−0.141822
$771$	−2.90115e62	−2.45980
$772$	1.07623e60	0.00887430
$773$	1.22577e62	0.982992	0.491496	−	0.870880i	$-0.336450\pi$
$773$	1.22577e62	0.982992	0.491496	+	0.870880i	$0.336450\pi$
$774$	−1.15827e61	−0.0903402
$775$	7.71618e61	0.585350
$776$	1.15605e62	0.852998
$777$	5.76269e61	0.413593
$778$	−3.59924e62	−2.51275
$779$	3.60260e61	0.244658
$780$	1.16434e62	0.769215
$781$	1.07852e62	0.693159
$782$	−7.52633e61	−0.470585
$783$	5.14365e62	3.12891
$784$	4.70819e61	0.278649
$785$	−7.40809e61	−0.426588
$786$	−7.82512e62	−4.38436
$787$	−5.88188e61	−0.320671	−0.160335	−	0.987063i	$-0.551258\pi$
$787$	−5.88188e61	−0.320671	−0.160335	+	0.987063i	$0.551258\pi$
$788$	1.59884e62	0.848189
$789$	−2.80431e62	−1.44767
$790$	9.03715e60	0.0453993
$791$	−9.69290e61	−0.473870
$792$	1.51474e62	0.720685
$793$	−1.14015e62	−0.527944
$794$	2.51749e62	1.13456
$795$	1.47945e62	0.648943
$796$	3.26641e62	1.39457
$797$	−1.91183e62	−0.794504	−0.397252	−	0.917710i	$-0.630036\pi$
$797$	−1.91183e62	−0.794504	−0.397252	+	0.917710i	$0.630036\pi$
$798$	4.63935e62	1.87670
$799$	5.42870e61	0.213767
$800$	−2.34936e62	−0.900563
$801$	−3.10506e62	−1.15870
$802$	5.93792e62	2.15718
$803$	−2.80682e61	−0.0992727
$804$	−7.85848e62	−2.70604
$805$	−5.72408e61	−0.191909
$806$	2.19543e62	0.716667
$807$	7.39340e62	2.34998
$808$	−1.55159e62	−0.480212
$809$	3.32609e62	1.00240	0.501200	−	0.865332i	$-0.332892\pi$
$809$	3.32609e62	1.00240	0.501200	+	0.865332i	$0.332892\pi$
$810$	−4.17819e62	−1.22620
$811$	2.53671e61	0.0724974	0.0362487	−	0.999343i	$-0.488459\pi$
$811$	2.53671e61	0.0724974	0.0362487	+	0.999343i	$0.488459\pi$
$812$	−3.00976e62	−0.837678
$813$	−6.58342e62	−1.78445
$814$	−1.68845e62	−0.445720
$815$	−5.81797e61	−0.149583
$816$	−7.07214e61	−0.177097
$817$	1.94988e61	0.0475591
$818$	−5.35262e62	−1.27166
$819$	−2.00421e62	−0.463808
$820$	4.62614e61	0.104285
$821$	8.50693e62	1.86808	0.934039	−	0.357170i	$-0.116258\pi$
$821$	8.50693e62	1.86808	0.934039	+	0.357170i	$0.116258\pi$
$822$	1.76720e63	3.78043
$823$	−5.42465e62	−1.13051	−0.565256	−	0.824915i	$-0.691223\pi$
$823$	−5.42465e62	−1.13051	−0.565256	+	0.824915i	$0.691223\pi$
$824$	−5.14539e62	−1.04468
$825$	3.01976e62	0.597328
$826$	−1.94107e61	−0.0374086
$827$	−7.20567e62	−1.35303	−0.676513	−	0.736431i	$-0.736510\pi$
$827$	−7.20567e62	−1.35303	−0.676513	+	0.736431i	$0.736510\pi$
$828$	1.68723e63	3.08689
$829$	−8.50026e62	−1.51534	−0.757669	−	0.652639i	$-0.773662\pi$
$829$	−8.50026e62	−1.51534	−0.757669	+	0.652639i	$0.773662\pi$
$830$	5.75689e62	1.00002
$831$	1.18245e63	2.00153
$832$	−5.56310e62	−0.917626
$833$	−1.63618e62	−0.263004
$834$	−1.18371e63	−1.85428
$835$	−3.74222e62	−0.571308
$836$	−8.07154e62	−1.20094
$837$	−1.13993e63	−1.65302
$838$	1.54617e62	0.218529
$839$	5.84952e62	0.805820	0.402910	−	0.915240i	$-0.367999\pi$
$839$	5.84952e62	0.805820	0.402910	+	0.915240i	$0.367999\pi$
$840$	1.88208e62	0.252716
$841$	9.98130e62	1.30639
$842$	1.78516e62	0.227755
$843$	−1.03464e63	−1.28675
$844$	2.21582e63	2.68641
$845$	−2.97397e62	−0.351494
$846$	−2.04950e63	−2.36149
$847$	2.64625e62	0.297261
$848$	−2.08286e62	−0.228113
$849$	2.50058e63	2.67009
$850$	3.37181e62	0.351040
$851$	−5.94155e62	−0.603135
$852$	−3.95001e63	−3.90973
$853$	6.11541e62	0.590230	0.295115	−	0.955462i	$-0.404642\pi$
$853$	6.11541e62	0.590230	0.295115	+	0.955462i	$0.404642\pi$
$854$	−5.83366e62	−0.549031
$855$	2.18199e63	2.00254
$856$	8.05994e62	0.721350
$857$	−3.04840e62	−0.266063	−0.133032	−	0.991112i	$-0.542471\pi$
$857$	−3.04840e62	−0.266063	−0.133032	+	0.991112i	$0.542471\pi$
$858$	8.59194e62	0.731332
$859$	−4.98228e62	−0.413595	−0.206798	−	0.978384i	$-0.566304\pi$
$859$	−4.98228e62	−0.413595	−0.206798	+	0.978384i	$0.566304\pi$
$860$	2.50387e61	0.0202719
$861$	−1.16511e62	−0.0920024
$862$	−1.35661e63	−1.04483
$863$	2.55705e61	0.0192091	0.00960454	−	0.999954i	$-0.496943\pi$
$863$	2.55705e61	0.0192091	0.00960454	+	0.999954i	$0.496943\pi$
$864$	3.47075e63	2.54318
$865$	−2.30361e62	−0.164650
$866$	4.15054e63	2.89381
$867$	−2.36757e63	−1.61025
$868$	6.67017e62	0.442551
$869$	3.95985e61	0.0256303
$870$	−3.48800e63	−2.20248
$871$	−9.62459e62	−0.592914
$872$	−4.58739e62	−0.275715
$873$	−4.33451e63	−2.54176
$874$	−4.78335e63	−2.73676
$875$	6.07939e62	0.339380
$876$	1.02797e63	0.559943
$877$	2.16419e63	1.15028	0.575141	−	0.818054i	$-0.304947\pi$
$877$	2.16419e63	1.15028	0.575141	+	0.818054i	$0.304947\pi$
$878$	2.13950e63	1.10963
$879$	2.27678e63	1.15229
$880$	1.57592e62	0.0778319
$881$	−8.01449e62	−0.386273	−0.193136	−	0.981172i	$-0.561866\pi$
$881$	−8.01449e62	−0.386273	−0.193136	+	0.981172i	$0.561866\pi$
$882$	6.17708e63	2.90542
$883$	−1.13427e62	−0.0520667	−0.0260334	−	0.999661i	$-0.508288\pi$
$883$	−1.13427e62	−0.0520667	−0.0260334	+	0.999661i	$0.508288\pi$
$884$	5.69665e62	0.255209
$885$	−1.33575e62	−0.0584041
$886$	−3.34001e63	−1.42535
$887$	−2.15665e63	−0.898299	−0.449150	−	0.893457i	$-0.648273\pi$
$887$	−2.15665e63	−0.898299	−0.449150	+	0.893457i	$0.648273\pi$
$888$	1.95358e63	0.794243
$889$	1.57205e63	0.623849
$890$	1.13040e63	0.437872
$891$	−1.83077e63	−0.692252
$892$	−1.84825e63	−0.682205
$893$	3.45021e63	1.24319
$894$	−8.65308e62	−0.304378
$895$	−3.52062e62	−0.120899
$896$	−1.45712e63	−0.488510
$897$	3.02346e63	0.989616
$898$	1.19568e63	0.382096
$899$	−3.90528e63	−1.21848
$900$	−7.55882e63	−2.30271
$901$	7.23832e62	0.215305
$902$	3.41372e62	0.0991489
$903$	−6.30607e61	−0.0178843
$904$	−3.28595e63	−0.909995
$905$	2.98592e62	0.0807484
$906$	2.95675e63	0.780833
$907$	7.76445e62	0.200241	0.100121	−	0.994975i	$-0.468077\pi$
$907$	7.76445e62	0.200241	0.100121	+	0.994975i	$0.468077\pi$
$908$	−9.28172e61	−0.0233767
$909$	5.81759e63	1.43093
$910$	7.29634e62	0.175273
$911$	−2.02334e62	−0.0474704	−0.0237352	−	0.999718i	$-0.507556\pi$
$911$	−2.02334e62	−0.0474704	−0.0237352	+	0.999718i	$0.507556\pi$
$912$	−4.49469e63	−1.02994
$913$	2.52252e63	0.564563
$914$	5.18739e63	1.13398
$915$	−4.01442e63	−0.857174
$916$	1.10686e64	2.30855
$917$	−2.91173e63	−0.593213
$918$	−4.98125e63	−0.991335
$919$	9.59396e63	1.86515	0.932577	−	0.360972i	$-0.117555\pi$
$919$	9.59396e63	1.86515	0.932577	+	0.360972i	$0.117555\pi$
$920$	−1.94049e63	−0.368531
$921$	−1.34603e64	−2.49731
$922$	−9.40102e63	−1.70396
$923$	−4.83773e63	−0.856654
$924$	2.61040e63	0.451607
$925$	2.66183e63	0.449918
$926$	1.33286e63	0.220115
$927$	1.92923e64	3.11293
$928$	1.18905e64	1.87464
$929$	−7.48220e63	−1.15263	−0.576317	−	0.817226i	$-0.695511\pi$
$929$	−7.48220e63	−1.15263	−0.576317	+	0.817226i	$0.695511\pi$
$930$	7.73004e63	1.16359
$931$	−1.03987e64	−1.52954
$932$	−1.04896e64	−1.50771
$933$	3.50164e63	0.491831
$934$	−7.58679e63	−1.04136
$935$	−5.47661e62	−0.0734619
$936$	−6.79437e63	−0.890673
$937$	−5.90450e63	−0.756453	−0.378227	−	0.925713i	$-0.623466\pi$
$937$	−5.90450e63	−0.756453	−0.378227	+	0.925713i	$0.623466\pi$
$938$	−4.92450e63	−0.616596
$939$	1.64128e63	0.200850
$940$	4.43046e63	0.529907
$941$	−1.10650e64	−1.29352	−0.646759	−	0.762694i	$-0.723876\pi$
$941$	−1.10650e64	−1.29352	−0.646759	+	0.762694i	$0.723876\pi$
$942$	2.00209e64	2.28765
$943$	1.20127e63	0.134165
$944$	1.88055e62	0.0205299
$945$	−3.78845e63	−0.404275
$946$	1.84765e62	0.0192735
$947$	7.68969e63	0.784123	0.392062	−	0.919939i	$-0.371762\pi$
$947$	7.68969e63	0.784123	0.392062	+	0.919939i	$0.371762\pi$
$948$	−1.45026e63	−0.144566
$949$	1.25900e63	0.122688
$950$	2.14295e64	2.04153
$951$	1.90961e64	1.77854
$952$	9.20821e62	0.0838457
$953$	5.87345e63	0.522873	0.261436	−	0.965221i	$-0.415804\pi$
$953$	5.87345e63	0.522873	0.261436	+	0.965221i	$0.415804\pi$
$954$	−2.73269e64	−2.37849
$955$	6.76564e63	0.575753
$956$	1.54125e64	1.28242
$957$	−1.52835e64	−1.24341
$958$	−3.61273e64	−2.87393
$959$	6.57576e63	0.511500
$960$	−1.95875e64	−1.48986
$961$	−4.78994e63	−0.356268
$962$	7.57354e63	0.550852
$963$	−3.02202e64	−2.14947
$964$	1.48021e64	1.02960
$965$	4.64099e61	0.00315699
$966$	1.54698e64	1.02914
$967$	−1.95511e64	−1.27205	−0.636023	−	0.771670i	$-0.719422\pi$
$967$	−1.95511e64	−1.27205	−0.636023	+	0.771670i	$0.719422\pi$
$968$	8.97095e63	0.570845
$969$	1.56198e64	0.972110
$970$	1.57799e64	0.960529
$971$	2.50785e64	1.49310	0.746549	−	0.665330i	$-0.231709\pi$
$971$	2.50785e64	1.49310	0.746549	+	0.665330i	$0.231709\pi$
$972$	1.53323e64	0.892858
$973$	−4.40459e63	−0.250888
$974$	−4.75316e64	−2.64829
$975$	−1.35452e64	−0.738220
$976$	5.65175e63	0.301309
$977$	3.39735e64	1.77177	0.885884	−	0.463906i	$-0.153553\pi$
$977$	3.39735e64	1.77177	0.885884	+	0.463906i	$0.153553\pi$
$978$	1.57235e64	0.802165
$979$	4.95312e63	0.247202
$980$	−1.33531e64	−0.651962
$981$	1.72001e64	0.821575
$982$	−2.21195e64	−1.03366
$983$	−2.21328e64	−1.01189	−0.505947	−	0.862565i	$-0.668857\pi$
$983$	−2.21328e64	−1.01189	−0.505947	+	0.862565i	$0.668857\pi$
$984$	−3.94979e63	−0.176677
$985$	6.89463e63	0.301739
$986$	−1.70653e64	−0.730735
$987$	−1.11583e64	−0.467496
$988$	3.62050e64	1.48421
$989$	6.50180e62	0.0260803
$990$	2.06759e64	0.811537
$991$	2.88177e64	1.10682	0.553408	−	0.832910i	$-0.313327\pi$
$991$	2.88177e64	1.10682	0.553408	+	0.832910i	$0.313327\pi$
$992$	−2.63514e64	−0.990383
$993$	1.48807e64	0.547285
$994$	−2.47526e64	−0.890870
$995$	1.40856e64	0.496112
$996$	−9.23852e64	−3.18439
$997$	−2.97127e64	−1.00230	−0.501148	−	0.865361i	$-0.667089\pi$
$997$	−2.97127e64	−1.00230	−0.501148	+	0.865361i	$0.667089\pi$
$998$	2.92687e64	0.966266
$999$	−3.93238e64	−1.27057

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1.44.a.a.1.1	✓	3
3.2	odd	2		9.44.a.b.1.3		3
4.3	odd	2		16.44.a.c.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.44.a.a.1.1	✓	3	1.1	even	1	trivial
9.44.a.b.1.3		3	3.2	odd	2
16.44.a.c.1.1		3	4.3	odd	2

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:	\( N \)	\(=\)	\( 1 \)
Weight:	\( k \)	\(=\)	\( 44 \)
Character orbit:	\([\chi]\)	\(=\)	1.a (trivial)

\(f(q)\)	\(=\)	\(q-4.65343e6 q^{2} +3.22027e10 q^{3} +1.28583e13 q^{4} +5.54482e14 q^{5} -1.49853e17 q^{6} -5.57604e17 q^{7} -1.89031e19 q^{8} +7.08758e20 q^{9} +O(q^{10})\)	\(q-4.65343e6 q^{2} +3.22027e10 q^{3} +1.28583e13 q^{4} +5.54482e14 q^{5} -1.49853e17 q^{6} -5.57604e17 q^{7} -1.89031e19 q^{8} +7.08758e20 q^{9} -2.58024e21 q^{10} -1.13059e22 q^{11} +4.14071e23 q^{12} +5.07130e23 q^{13} +2.59477e24 q^{14} +1.78558e25 q^{15} -2.51386e25 q^{16} +8.73610e25 q^{17} -3.29815e27 q^{18} +5.55222e27 q^{19} +7.12968e27 q^{20} -1.79564e28 q^{21} +5.26114e28 q^{22} +1.85137e29 q^{23} -6.08730e29 q^{24} -8.29418e29 q^{25} -2.35989e30 q^{26} +1.22532e31 q^{27} -7.16982e30 q^{28} +4.19782e31 q^{29} -8.30908e31 q^{30} -9.30312e31 q^{31} +2.83254e32 q^{32} -3.64082e32 q^{33} -4.06528e32 q^{34} -3.09181e32 q^{35} +9.11340e33 q^{36} -3.20928e33 q^{37} -2.58368e34 q^{38} +1.63309e34 q^{39} -1.04814e34 q^{40} +6.48857e33 q^{41} +8.35585e34 q^{42} +3.51189e33 q^{43} -1.45375e35 q^{44} +3.92993e35 q^{45} -8.61520e35 q^{46} +6.21410e35 q^{47} -8.09530e35 q^{48} -1.87289e36 q^{49} +3.85963e36 q^{50} +2.81326e36 q^{51} +6.52081e36 q^{52} +8.28552e36 q^{53} -5.70191e37 q^{54} -6.26895e36 q^{55} +1.05404e37 q^{56} +1.78797e38 q^{57} -1.95342e38 q^{58} -7.48073e36 q^{59} +2.29595e38 q^{60} -2.24824e38 q^{61} +4.32914e38 q^{62} -3.95206e38 q^{63} -1.09698e39 q^{64} +2.81194e38 q^{65} +1.69423e39 q^{66} -1.89786e39 q^{67} +1.12331e39 q^{68} +5.96191e39 q^{69} +1.43875e39 q^{70} -9.53945e39 q^{71} -1.33977e40 q^{72} +2.48260e39 q^{73} +1.49341e40 q^{74} -2.67095e40 q^{75} +7.13920e40 q^{76} +6.30424e39 q^{77} -7.59948e40 q^{78} -3.50244e39 q^{79} -1.39389e40 q^{80} +1.61930e41 q^{81} -3.01941e40 q^{82} -2.23114e41 q^{83} -2.30888e41 q^{84} +4.84401e40 q^{85} -1.63423e40 q^{86} +1.35181e42 q^{87} +2.13717e41 q^{88} -4.38099e41 q^{89} -1.82877e42 q^{90} -2.82777e41 q^{91} +2.38054e42 q^{92} -2.99586e42 q^{93} -2.89169e42 q^{94} +3.07861e42 q^{95} +9.12154e42 q^{96} -6.11565e42 q^{97} +8.71537e42 q^{98} -8.01318e42 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 2209944 q^{2} + 24401437812 q^{3} + 9822618421824 q^{4} + 535205380774170 q^{5} - 91\!\cdots\!24 q^{6}+ \cdots + 47\!\cdots\!31 q^{9}+O(q^{10}) \) 3 * q - 2209944 * q^2 + 24401437812 * q^3 + 9822618421824 * q^4 + 535205380774170 * q^5 - 91793974758443424 * q^6 + 301971425665478856 * q^7 - 15830863913787348480 * q^8 + 477482125171066743231 * q^9	\( 3 q - 2209944 q^{2} + 24401437812 q^{3} + 9822618421824 q^{4} + 535205380774170 q^{5} - 91\!\cdots\!24 q^{6}+ \cdots - 14\!\cdots\!08 q^{99}+O(q^{100}) \) 3 * q - 2209944 * q^2 + 24401437812 * q^3 + 9822618421824 * q^4 + 535205380774170 * q^5 - 91793974758443424 * q^6 + 301971425665478856 * q^7 - 15830863913787348480 * q^8 + 477482125171066743231 * q^9 + 424411733447436982320 * q^10 + 26665053285822824598396 * q^11 + 591067459530801007163136 * q^12 + 2675160683143344673595682 * q^13 + 14021968617857741064904128 * q^14 + 35619426649405115420082840 * q^15 - 79484355831457348071124992 * q^16 - 408654222932442443796841194 * q^17 - 4107998354973953853903433848 * q^18 + 1577331357975519701176464900 * q^19 + 14558304937461364568422335360 * q^20 + 39305230121617849136195725536 * q^21 + 139626647360508967807005852192 * q^22 - 1215339635928561142484811048 * q^23 - 1116055600560337571570968012800 * q^24 - 2310484082897201607166539950475 * q^25 - 1738302877111230473099097494544 * q^26 + 12636088863973677226324883265480 * q^27 + 16881555000174595924306194912768 * q^28 + 57118989018136587596191009705650 * q^29 - 73851642261923451351367502727360 * q^30 - 255565972342397832812135282963424 * q^31 - 144698056390774688063435943542784 * q^32 - 274896238871162964163796672607216 * q^33 + 460541119788760022406607937310288 * q^34 + 2398213530857285851552147980593520 * q^35 + 8176018057545637654201506848470848 * q^36 - 2320645576165979428293572256842694 * q^37 - 30659398199572233844432077267455520 * q^38 - 3966989860384498209469308423541128 * q^39 - 32703585947405178164040064943232000 * q^40 + 25742376604739002042016577514061166 * q^41 + 142089722887598025677946391121586432 * q^42 + 240714339689128182512406300123419292 * q^43 - 103743099769332204870397943787455232 * q^44 + 257230496455952342677786043056557090 * q^45 - 1897545066442972080018141849284700864 * q^46 + 308713553347399687962182796433367856 * q^47 - 2551621376300181083415582718933352448 * q^48 + 3434980292250886821160584750829904379 * q^49 + 1991781591031845842073119994352349400 * q^50 + 13352566627975131351422398848669478056 * q^51 - 1723278372049486147633277645433304704 * q^52 + 15000497558784669132889458695112796362 * q^53 - 84497407838510132201868358325218843200 * q^54 + 3996571389110251928625895283213506440 * q^55 - 64188456562605926675684864956824883200 * q^56 + 194498189404429212580032012092952587760 * q^57 - 103653602500512241322054964115851073680 * q^58 + 226996261182733939538282061249836505900 * q^59 + 172179025249459513233108554074130526720 * q^60 - 9393429368478033721028929889113591854 * q^61 - 208603081649583360642384119938663534848 * q^62 - 967475285671148246145956691206790781848 * q^63 - 1119010168436659689243622515721507700736 * q^64 - 270218921102297342477494789001032451460 * q^65 + 2927960709398652565212160365298168924032 * q^66 - 733015616887151283726086660162187354444 * q^67 + 5475599618745313926138424496016357744768 * q^68 + 1967042253746083561325124578559972227232 * q^69 + 5947953535225896394715748735968145697920 * q^70 - 18523878066158899993345833814569898287864 * q^71 - 9888656801008664055042728388175401192960 * q^72 - 20251106025908798058937016734369224029298 * q^73 + 16747422277652165725566811926177721225008 * q^74 - 21273380043530396090723723962888745519700 * q^75 + 77507609539490133886259513865936229344000 * q^76 + 59055613160181778232413942942559747685792 * q^77 - 19617648418411520686241571637167142696896 * q^78 + 15233568018599764739559826813006999294800 * q^79 - 100962488695267720109813470111835940986880 * q^80 + 73114835779397486920654645241710822062363 * q^81 - 320808727539069549327137360482471983405168 * q^82 - 89206610196719670053085531955706819434428 * q^83 - 345724182543475881552276196164469715392512 * q^84 + 438725373228516358990025164547060204838420 * q^85 + 251282426033382455934203370485070655838496 * q^86 + 1720273148596604243726575204332689696886840 * q^87 - 25677613216166441601684725395949811087360 * q^88 + 203691422331055117225246388044508249665950 * q^89 - 2339725556415524057280625761410723956665360 * q^90 - 1168954967602248602369466051364648836229584 * q^91 + 688199578839743838535125048241381149958656 * q^92 - 4949189234312030019905814954548842124935296 * q^93 - 1324027207656692012199753325229034662658432 * q^94 + 3125746305909018830165692627580442029979000 * q^95 + 10923904714711076554208778658628955663630336 * q^96 - 3881062021784775072625368160679539917597594 * q^97 + 24120041445786820251814869563279238673540008 * q^98 - 14255275025472043026078170466415579823927508 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more