LMFDB - Embedded newform 1.44.a.a.1.2

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			1.2
Root			$116336.$ 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)

$f(q)$	$=$	$q-1.18359e6 q^{2} -1.79507e10 q^{3} -7.39521e12 q^{4} -6.39116e14 q^{5} +2.12463e16 q^{6} -1.72730e18 q^{7} +1.91639e19 q^{8} -6.02939e18 q^{9} +O(q^{10})$	\(q-1.18359e6 q^{2} -1.79507e10 q^{3} -7.39521e12 q^{4} -6.39116e14 q^{5} +2.12463e16 q^{6} -1.72730e18 q^{7} +1.91639e19 q^{8} -6.02939e18 q^{9} +7.56451e20 q^{10} +1.05408e22 q^{11} +1.32749e23 q^{12} +1.50541e24 q^{13} +2.04442e24 q^{14} +1.14726e25 q^{15} +4.23668e25 q^{16} -5.54217e26 q^{17} +7.13632e24 q^{18} -1.99446e27 q^{19} +4.72640e27 q^{20} +3.10063e28 q^{21} -1.24760e28 q^{22} +7.48572e28 q^{23} -3.44005e29 q^{24} -7.28399e29 q^{25} -1.78179e30 q^{26} +6.00067e30 q^{27} +1.27738e31 q^{28} -7.64381e30 q^{29} -1.35788e31 q^{30} +1.08077e31 q^{31} -2.18712e32 q^{32} -1.89215e32 q^{33} +6.55966e32 q^{34} +1.10395e33 q^{35} +4.45886e31 q^{36} +2.93069e32 q^{37} +2.36062e33 q^{38} -2.70232e34 q^{39} -1.22479e34 q^{40} +7.49273e34 q^{41} -3.66987e34 q^{42} +1.23211e35 q^{43} -7.79515e34 q^{44} +3.85348e33 q^{45} -8.86002e34 q^{46} -5.61634e35 q^{47} -7.60514e35 q^{48} +7.99756e35 q^{49} +8.62125e35 q^{50} +9.94859e36 q^{51} -1.11328e37 q^{52} +2.77981e36 q^{53} -7.10233e36 q^{54} -6.73680e36 q^{55} -3.31018e37 q^{56} +3.58019e37 q^{57} +9.04713e36 q^{58} +1.73860e38 q^{59} -8.48422e37 q^{60} -1.16569e38 q^{61} -1.27918e37 q^{62} +1.04146e37 q^{63} -1.13797e38 q^{64} -9.62132e38 q^{65} +2.23953e38 q^{66} +9.18410e38 q^{67} +4.09855e39 q^{68} -1.34374e39 q^{69} -1.30662e39 q^{70} -3.76161e39 q^{71} -1.15546e38 q^{72} -9.44690e39 q^{73} -3.46873e38 q^{74} +1.30753e40 q^{75} +1.47494e40 q^{76} -1.82072e40 q^{77} +3.19843e40 q^{78} +3.86685e40 q^{79} -2.70773e40 q^{80} -1.05737e41 q^{81} -8.86831e40 q^{82} +1.39471e41 q^{83} -2.29298e41 q^{84} +3.54209e41 q^{85} -1.45831e41 q^{86} +1.37212e41 q^{87} +2.02002e41 q^{88} +9.05928e41 q^{89} -4.56094e39 q^{90} -2.60030e42 q^{91} -5.53585e41 q^{92} -1.94005e41 q^{93} +6.64744e41 q^{94} +1.27469e42 q^{95} +3.92603e42 q^{96} -1.23492e42 q^{97} -9.46583e41 q^{98} -6.35546e40 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.18359e6	−0.399077	−0.199538	−	0.979890i	$-0.563944\pi$
$2$	−1.18359e6	−0.399077	−0.199538	+	0.979890i	$0.563944\pi$
$3$	−1.79507e10	−0.990773	−0.495387	−	0.868673i	$-0.664974\pi$
$3$	−1.79507e10	−0.990773	−0.495387	+	0.868673i	$0.664974\pi$
$4$	−7.39521e12	−0.840738
$5$	−6.39116e14	−0.599411	−0.299706	−	0.954032i	$-0.596888\pi$
$5$	−6.39116e14	−0.599411	−0.299706	+	0.954032i	$0.596888\pi$
$6$	2.12463e16	0.395394
$7$	−1.72730e18	−1.16885	−0.584427	−	0.811446i	$-0.698681\pi$
$7$	−1.72730e18	−1.16885	−0.584427	+	0.811446i	$0.698681\pi$
$8$	1.91639e19	0.734595
$9$	−6.02939e18	−0.0183679
$10$	7.56451e20	0.239211
$11$	1.05408e22	0.429468	0.214734	−	0.976673i	$-0.431111\pi$
$11$	1.05408e22	0.429468	0.214734	+	0.976673i	$0.431111\pi$
$12$	1.32749e23	0.832981
$13$	1.50541e24	1.68995	0.844973	−	0.534809i	$-0.179617\pi$
$13$	1.50541e24	1.68995	0.844973	+	0.534809i	$0.179617\pi$
$14$	2.04442e24	0.466462
$15$	1.14726e25	0.593881
$16$	4.23668e25	0.547578
$17$	−5.54217e26	−1.94549	−0.972743	−	0.231884i	$-0.925511\pi$
$17$	−5.54217e26	−1.94549	−0.972743	+	0.231884i	$0.925511\pi$
$18$	7.13632e24	0.00733019
$19$	−1.99446e27	−0.640652	−0.320326	−	0.947307i	$-0.603792\pi$
$19$	−1.99446e27	−0.640652	−0.320326	+	0.947307i	$0.603792\pi$
$20$	4.72640e27	0.503948
$21$	3.10063e28	1.15807
$22$	−1.24760e28	−0.171391
$23$	7.48572e28	0.395444	0.197722	−	0.980258i	$-0.436646\pi$
$23$	7.48572e28	0.395444	0.197722	+	0.980258i	$0.436646\pi$
$24$	−3.44005e29	−0.727818
$25$	−7.28399e29	−0.640706
$26$	−1.78179e30	−0.674418
$27$	6.00067e30	1.00897
$28$	1.27738e31	0.982700
$29$	−7.64381e30	−0.276537	−0.138268	−	0.990395i	$-0.544154\pi$
$29$	−7.64381e30	−0.276537	−0.138268	+	0.990395i	$0.544154\pi$
$30$	−1.35788e31	−0.237004
$31$	1.08077e31	0.0932085	0.0466043	−	0.998913i	$-0.485160\pi$
$31$	1.08077e31	0.0932085	0.0466043	+	0.998913i	$0.485160\pi$
$32$	−2.18712e32	−0.953121
$33$	−1.89215e32	−0.425506
$34$	6.55966e32	0.776398
$35$	1.10395e33	0.700624
$36$	4.45886e31	0.0154426
$37$	2.93069e32	0.0563161	0.0281580	−	0.999603i	$-0.491036\pi$
$37$	2.93069e32	0.0563161	0.0281580	+	0.999603i	$0.491036\pi$
$38$	2.36062e33	0.255669
$39$	−2.70232e34	−1.67435
$40$	−1.22479e34	−0.440325
$41$	7.49273e34	1.58412	0.792058	−	0.610446i	$-0.209010\pi$
$41$	7.49273e34	1.58412	0.792058	+	0.610446i	$0.209010\pi$
$42$	−3.66987e34	−0.462158
$43$	1.23211e35	0.935572	0.467786	−	0.883842i	$-0.345052\pi$
$43$	1.23211e35	0.935572	0.467786	+	0.883842i	$0.345052\pi$
$44$	−7.79515e34	−0.361070
$45$	3.85348e33	0.0110099
$46$	−8.86002e34	−0.157812
$47$	−5.61634e35	−0.630013	−0.315006	−	0.949090i	$-0.602007\pi$
$47$	−5.61634e35	−0.630013	−0.315006	+	0.949090i	$0.602007\pi$
$48$	−7.60514e35	−0.542526
$49$	7.99756e35	0.366220
$50$	8.62125e35	0.255691
$51$	9.94859e36	1.92754
$52$	−1.11328e37	−1.42080
$53$	2.77981e36	0.235551	0.117775	−	0.993040i	$-0.462424\pi$
$53$	2.77981e36	0.235551	0.117775	+	0.993040i	$0.462424\pi$
$54$	−7.10233e36	−0.402657
$55$	−6.73680e36	−0.257428
$56$	−3.31018e37	−0.858635
$57$	3.58019e37	0.634741
$58$	9.04713e36	0.110359
$59$	1.73860e38	1.46852	0.734262	−	0.678866i	$-0.237528\pi$
$59$	1.73860e38	1.46852	0.734262	+	0.678866i	$0.237528\pi$
$60$	−8.48422e37	−0.499298
$61$	−1.16569e38	−0.480829	−0.240414	−	0.970670i	$-0.577283\pi$
$61$	−1.16569e38	−0.480829	−0.240414	+	0.970670i	$0.577283\pi$
$62$	−1.27918e37	−0.0371973
$63$	1.04146e37	0.0214694
$64$	−1.13797e38	−0.167210
$65$	−9.62132e38	−1.01297
$66$	2.23953e38	0.169809
$67$	9.18410e38	0.503998	0.251999	−	0.967728i	$-0.418912\pi$
$67$	9.18410e38	0.503998	0.251999	+	0.967728i	$0.418912\pi$
$68$	4.09855e39	1.63564
$69$	−1.34374e39	−0.391796
$70$	−1.30662e39	−0.279603
$71$	−3.76161e39	−0.593361	−0.296681	−	0.954977i	$-0.595880\pi$
$71$	−3.76161e39	−0.593361	−0.296681	+	0.954977i	$0.595880\pi$
$72$	−1.15546e38	−0.0134930
$73$	−9.44690e39	−0.820065	−0.410032	−	0.912071i	$-0.634483\pi$
$73$	−9.44690e39	−0.820065	−0.410032	+	0.912071i	$0.634483\pi$
$74$	−3.46873e38	−0.0224744
$75$	1.30753e40	0.634795
$76$	1.47494e40	0.538620
$77$	−1.82072e40	−0.501986
$78$	3.19843e40	0.668195
$79$	3.86685e40	0.614293	0.307146	−	0.951662i	$-0.400626\pi$
$79$	3.86685e40	0.614293	0.307146	+	0.951662i	$0.400626\pi$
$80$	−2.70773e40	−0.328224
$81$	−1.05737e41	−0.981295
$82$	−8.86831e40	−0.632183
$83$	1.39471e41	0.766137	0.383068	−	0.923720i	$-0.374867\pi$
$83$	1.39471e41	0.766137	0.383068	+	0.923720i	$0.374867\pi$
$84$	−2.29298e41	−0.973633
$85$	3.54209e41	1.16615
$86$	−1.45831e41	−0.373365
$87$	1.37212e41	0.273985
$88$	2.02002e41	0.315485
$89$	9.05928e41	1.10971	0.554854	−	0.831948i	$-0.312774\pi$
$89$	9.05928e41	1.10971	0.554854	+	0.831948i	$0.312774\pi$
$90$	−4.56094e39	−0.00439380
$91$	−2.60030e42	−1.97530
$92$	−5.53585e41	−0.332465
$93$	−1.94005e41	−0.0923486
$94$	6.64744e41	0.251423
$95$	1.27469e42	0.384014
$96$	3.92603e42	0.944327
$97$	−1.23492e42	−0.237709	−0.118855	−	0.992912i	$-0.537922\pi$
$97$	−1.23492e42	−0.237709	−0.118855	+	0.992912i	$0.537922\pi$
$98$	−9.46583e41	−0.146150
$99$	−6.35546e40	−0.00788842
$100$	5.38666e42	0.538666
$101$	9.34212e41	0.0754286	0.0377143	−	0.999289i	$-0.487992\pi$
$101$	9.34212e41	0.0754286	0.0377143	+	0.999289i	$0.487992\pi$
$102$	−1.17750e43	−0.769235
$103$	−2.71649e43	−1.43882	−0.719412	−	0.694584i	$-0.755589\pi$
$103$	−2.71649e43	−1.43882	−0.719412	+	0.694584i	$0.755589\pi$
$104$	2.88495e43	1.24143
$105$	−1.98166e43	−0.694160
$106$	−3.29016e42	−0.0940027
$107$	7.12131e43	1.66268	0.831340	−	0.555764i	$-0.187574\pi$
$107$	7.12131e43	1.66268	0.831340	+	0.555764i	$0.187574\pi$
$108$	−4.43762e43	−0.848281
$109$	5.74242e43	0.900379	0.450190	−	0.892933i	$-0.351356\pi$
$109$	5.74242e43	0.900379	0.450190	+	0.892933i	$0.351356\pi$
$110$	7.97361e42	0.102733
$111$	−5.26079e42	−0.0557965
$112$	−7.31803e43	−0.640039
$113$	−6.84403e43	−0.494454	−0.247227	−	0.968958i	$-0.579519\pi$
$113$	−6.84403e43	−0.494454	−0.247227	+	0.968958i	$0.579519\pi$
$114$	−4.23747e43	−0.253310
$115$	−4.78425e43	−0.237034
$116$	5.65275e43	0.232495
$117$	−9.07670e42	−0.0310407
$118$	−2.05779e44	−0.586053
$119$	9.57300e44	2.27399
$120$	2.19859e44	0.436262
$121$	−4.91292e44	−0.815557
$122$	1.37969e44	0.191888
$123$	−1.34500e45	−1.56950
$124$	−7.99250e43	−0.0783640
$125$	1.19212e45	0.983458
$126$	−1.23266e43	−0.00856792
$127$	−2.23889e45	−1.31297	−0.656483	−	0.754341i	$-0.727957\pi$
$127$	−2.23889e45	−1.31297	−0.656483	+	0.754341i	$0.727957\pi$
$128$	2.05850e45	1.01985
$129$	−2.21172e45	−0.926940
$130$	1.13877e45	0.404253
$131$	2.93570e45	0.883850	0.441925	−	0.897052i	$-0.354296\pi$
$131$	2.93570e45	0.883850	0.441925	+	0.897052i	$0.354296\pi$
$132$	1.39928e45	0.357739
$133$	3.44503e45	0.748829
$134$	−1.08702e45	−0.201134
$135$	−3.83513e45	−0.604789
$136$	−1.06209e46	−1.42915
$137$	1.51920e45	0.174631	0.0873157	−	0.996181i	$-0.472171\pi$
$137$	1.51920e45	0.174631	0.0873157	+	0.996181i	$0.472171\pi$
$138$	1.59044e45	0.156356
$139$	6.55245e44	0.0551551	0.0275775	−	0.999620i	$-0.491221\pi$
$139$	6.55245e44	0.0551551	0.0275775	+	0.999620i	$0.491221\pi$
$140$	−8.16392e45	−0.589041
$141$	1.00817e46	0.624200
$142$	4.45220e45	0.236797
$143$	1.58682e46	0.725778
$144$	−2.55446e44	−0.0100579
$145$	4.88528e45	0.165759
$146$	1.11813e46	0.327269
$147$	−1.43562e46	−0.362841
$148$	−2.16730e45	−0.0473470
$149$	−8.85478e46	−1.67368	−0.836841	−	0.547446i	$-0.815600\pi$
$149$	−8.85478e46	−1.67368	−0.836841	+	0.547446i	$0.815600\pi$
$150$	−1.54757e46	−0.253332
$151$	8.54056e46	1.21194	0.605971	−	0.795486i	$-0.292785\pi$
$151$	8.54056e46	1.21194	0.605971	+	0.795486i	$0.292785\pi$
$152$	−3.82215e46	−0.470620
$153$	3.34159e45	0.0357345
$154$	2.15498e46	0.200331
$155$	−6.90736e45	−0.0558702
$156$	1.99842e47	1.40769
$157$	−6.33166e46	−0.388754	−0.194377	−	0.980927i	$-0.562269\pi$
$157$	−6.33166e46	−0.388754	−0.194377	+	0.980927i	$0.562269\pi$
$158$	−4.57677e46	−0.245150
$159$	−4.98996e46	−0.233377
$160$	1.39782e47	0.571311
$161$	−1.29301e47	−0.462217
$162$	1.25149e47	0.391612
$163$	−2.42368e47	−0.664419	−0.332210	−	0.943206i	$-0.607794\pi$
$163$	−2.42368e47	−0.664419	−0.332210	+	0.943206i	$0.607794\pi$
$164$	−5.54103e47	−1.33183
$165$	1.20930e47	0.255053
$166$	−1.65077e47	−0.305747
$167$	2.12976e47	0.346677	0.173339	−	0.984862i	$-0.444544\pi$
$167$	2.12976e47	0.346677	0.173339	+	0.984862i	$0.444544\pi$
$168$	5.94200e47	0.850713
$169$	1.47273e48	1.85592
$170$	−4.19238e47	−0.465382
$171$	1.20253e46	0.0117674
$172$	−9.11170e47	−0.786571
$173$	−9.17738e47	−0.699403	−0.349702	−	0.936861i	$-0.613717\pi$
$173$	−9.17738e47	−0.699403	−0.349702	+	0.936861i	$0.613717\pi$
$174$	−1.62402e47	−0.109341
$175$	1.25816e48	0.748892
$176$	4.46580e47	0.235167
$177$	−3.12091e48	−1.45497
$178$	−1.07225e48	−0.442858
$179$	1.88488e48	0.690150	0.345075	−	0.938575i	$-0.387853\pi$
$179$	1.88488e48	0.690150	0.345075	+	0.938575i	$0.387853\pi$
$180$	−2.84973e46	−0.00925645
$181$	−1.01885e47	−0.0293779	−0.0146889	−	0.999892i	$-0.504676\pi$
$181$	−1.01885e47	−0.0293779	−0.0146889	+	0.999892i	$0.504676\pi$
$182$	3.07768e48	0.788296
$183$	2.09249e48	0.476392
$184$	1.43455e48	0.290491
$185$	−1.87305e47	−0.0337565
$186$	2.29623e47	0.0368541
$187$	−5.84190e48	−0.835525
$188$	4.15340e48	0.529676
$189$	−1.03650e49	−1.17934
$190$	−1.50871e48	−0.153251
$191$	8.44008e48	0.765824	0.382912	−	0.923785i	$-0.374921\pi$
$191$	8.44008e48	0.765824	0.382912	+	0.923785i	$0.374921\pi$
$192$	2.04274e48	0.165667
$193$	−2.13716e49	−1.55008	−0.775042	−	0.631909i	$-0.782272\pi$
$193$	−2.13716e49	−1.55008	−0.775042	+	0.631909i	$0.782272\pi$
$194$	1.46164e48	0.0948641
$195$	1.72709e49	1.00363
$196$	−5.91436e48	−0.307895
$197$	1.92220e49	0.896963	0.448482	−	0.893792i	$-0.351965\pi$
$197$	1.92220e49	0.896963	0.448482	+	0.893792i	$0.351965\pi$
$198$	7.52225e46	0.00314808
$199$	3.32032e49	1.24692	0.623460	−	0.781855i	$-0.285726\pi$
$199$	3.32032e49	1.24692	0.623460	+	0.781855i	$0.285726\pi$
$200$	−1.39589e49	−0.470660
$201$	−1.64861e49	−0.499347
$202$	−1.10572e48	−0.0301018
$203$	1.32032e49	0.323231
$204$	−7.35719e49	−1.62055
$205$	−4.78872e49	−0.949537
$206$	3.21521e49	0.574201
$207$	−4.51343e47	−0.00726347
$208$	6.37794e49	0.925377
$209$	−2.10232e49	−0.275140
$210$	2.34547e49	0.277023
$211$	7.61623e49	0.812208	0.406104	−	0.913827i	$-0.366887\pi$
$211$	7.61623e49	0.812208	0.406104	+	0.913827i	$0.366887\pi$
$212$	−2.05573e49	−0.198036
$213$	6.75235e49	0.587887
$214$	−8.42871e49	−0.663537
$215$	−7.87460e49	−0.560792
$216$	1.14996e50	0.741186
$217$	−1.86681e49	−0.108947
$218$	−6.79667e49	−0.359320
$219$	1.69579e50	0.812498
$220$	4.98200e49	0.216430
$221$	−8.34324e50	−3.28777
$222$	6.22661e48	0.0222671
$223$	2.81313e50	0.913344	0.456672	−	0.889635i	$-0.349041\pi$
$223$	2.81313e50	0.913344	0.456672	+	0.889635i	$0.349041\pi$
$224$	3.77782e50	1.11406
$225$	4.39180e48	0.0117684
$226$	8.10052e49	0.197325
$227$	4.74569e50	1.05134	0.525670	−	0.850689i	$-0.323815\pi$
$227$	4.74569e50	1.05134	0.525670	+	0.850689i	$0.323815\pi$
$228$	−2.64762e50	−0.533651
$229$	−1.73705e50	−0.318676	−0.159338	−	0.987224i	$-0.550936\pi$
$229$	−1.73705e50	−0.318676	−0.159338	+	0.987224i	$0.550936\pi$
$230$	5.66258e49	0.0945946
$231$	3.26831e50	0.497354
$232$	−1.46485e50	−0.203143
$233$	−3.86377e50	−0.488494	−0.244247	−	0.969713i	$-0.578541\pi$
$233$	−3.86377e50	−0.488494	−0.244247	+	0.969713i	$0.578541\pi$
$234$	1.07431e49	0.0123876
$235$	3.58949e50	0.377637
$236$	−1.28573e51	−1.23464
$237$	−6.94127e50	−0.608625
$238$	−1.13305e51	−0.907496
$239$	1.53965e51	1.12685	0.563427	−	0.826166i	$-0.309483\pi$
$239$	1.53965e51	1.12685	0.563427	+	0.826166i	$0.309483\pi$
$240$	4.86057e50	0.325196
$241$	1.69305e51	1.03586	0.517932	−	0.855422i	$-0.326702\pi$
$241$	1.69305e51	1.03586	0.517932	+	0.855422i	$0.326702\pi$
$242$	5.81488e50	0.325470
$243$	−7.17082e49	−0.0367311
$244$	8.62050e50	0.404251
$245$	−5.11137e50	−0.219516
$246$	1.59192e51	0.626351
$247$	−3.00247e51	−1.08267
$248$	2.07117e50	0.0684706
$249$	−2.50361e51	−0.759068
$250$	−1.41098e51	−0.392475
$251$	1.12233e51	0.286506	0.143253	−	0.989686i	$-0.454244\pi$
$251$	1.12233e51	0.286506	0.143253	+	0.989686i	$0.454244\pi$
$252$	−7.70179e49	−0.0180501
$253$	7.89055e50	0.169831
$254$	2.64993e51	0.523974
$255$	−6.35830e51	−1.15539
$256$	−1.43545e51	−0.239788
$257$	5.15162e51	0.791374	0.395687	−	0.918385i	$-0.370506\pi$
$257$	5.15162e51	0.791374	0.395687	+	0.918385i	$0.370506\pi$
$258$	2.61777e51	0.369920
$259$	−5.06218e50	−0.0658252
$260$	7.11517e51	0.851644
$261$	4.60875e49	0.00507939
$262$	−3.47466e51	−0.352724
$263$	9.78033e51	0.914755	0.457377	−	0.889273i	$-0.348789\pi$
$263$	9.78033e51	0.914755	0.457377	+	0.889273i	$0.348789\pi$
$264$	−3.62609e51	−0.312575
$265$	−1.77662e51	−0.141192
$266$	−4.07750e51	−0.298840
$267$	−1.62620e52	−1.09947
$268$	−6.79184e51	−0.423730
$269$	−1.17046e52	−0.674037	−0.337019	−	0.941498i	$-0.609419\pi$
$269$	−1.17046e52	−0.674037	−0.337019	+	0.941498i	$0.609419\pi$
$270$	4.53922e51	0.241357
$271$	1.90564e52	0.935839	0.467919	−	0.883771i	$-0.345004\pi$
$271$	1.90564e52	0.935839	0.467919	+	0.883771i	$0.345004\pi$
$272$	−2.34804e52	−1.06531
$273$	4.66771e52	1.95707
$274$	−1.79811e51	−0.0696913
$275$	−7.67791e51	−0.275163
$276$	9.93723e51	0.329397
$277$	3.73097e51	0.114421	0.0572106	−	0.998362i	$-0.481779\pi$
$277$	3.73097e51	0.114421	0.0572106	+	0.998362i	$0.481779\pi$
$278$	−7.75541e50	−0.0220111
$279$	−6.51636e49	−0.00171204
$280$	2.11559e52	0.514675
$281$	3.03658e51	0.0684225	0.0342112	−	0.999415i	$-0.489108\pi$
$281$	3.03658e51	0.0684225	0.0342112	+	0.999415i	$0.489108\pi$
$282$	−1.19326e52	−0.249104
$283$	−6.91493e52	−1.33776	−0.668882	−	0.743369i	$-0.733227\pi$
$283$	−6.91493e52	−1.33776	−0.668882	+	0.743369i	$0.733227\pi$
$284$	2.78179e52	0.498861
$285$	−2.28816e52	−0.380471
$286$	−1.87815e52	−0.289641
$287$	−1.29422e53	−1.85160
$288$	1.31870e51	0.0175068
$289$	2.26004e53	2.78492
$290$	−5.78217e51	−0.0661506
$291$	2.21676e52	0.235516
$292$	6.98618e52	0.689459
$293$	−7.58660e52	−0.695654	−0.347827	−	0.937559i	$-0.613080\pi$
$293$	−7.58660e52	−0.695654	−0.347827	+	0.937559i	$0.613080\pi$
$294$	1.69918e52	0.144801
$295$	−1.11117e53	−0.880250
$296$	5.61632e51	0.0413695
$297$	6.32519e52	0.433321
$298$	1.04804e53	0.667927
$299$	1.12691e53	0.668279
$300$	−9.66943e52	−0.533696
$301$	−2.12822e53	−1.09355
$302$	−1.01085e53	−0.483658
$303$	−1.67698e52	−0.0747326
$304$	−8.44988e52	−0.350807
$305$	7.45010e52	0.288214
$306$	−3.95507e51	−0.0142608
$307$	−3.17728e53	−1.06802	−0.534011	−	0.845478i	$-0.679316\pi$
$307$	−3.17728e53	−1.06802	−0.534011	+	0.845478i	$0.679316\pi$
$308$	1.34646e53	0.422038
$309$	4.87629e53	1.42555
$310$	8.17548e51	0.0222965
$311$	6.14862e53	1.56469	0.782347	−	0.622843i	$-0.214022\pi$
$311$	6.14862e53	1.56469	0.782347	+	0.622843i	$0.214022\pi$
$312$	−5.17868e53	−1.22997
$313$	3.42329e53	0.758997	0.379498	−	0.925192i	$-0.376097\pi$
$313$	3.42329e53	0.758997	0.379498	+	0.925192i	$0.376097\pi$
$314$	7.49409e52	0.155143
$315$	−6.65612e51	−0.0128690
$316$	−2.85962e53	−0.516459
$317$	−5.98968e53	−1.01072	−0.505358	−	0.862909i	$-0.668640\pi$
$317$	−5.98968e53	−1.01072	−0.505358	+	0.862909i	$0.668640\pi$
$318$	5.90606e52	0.0931354
$319$	−8.05719e52	−0.118764
$320$	7.27296e52	0.100228
$321$	−1.27833e54	−1.64734
$322$	1.53039e53	0.184460
$323$	1.10536e54	1.24638
$324$	7.81948e53	0.825012
$325$	−1.09654e54	−1.08276
$326$	2.86864e53	0.265154
$327$	−1.03081e54	−0.892072
$328$	1.43590e54	1.16368
$329$	9.70111e53	0.736393
$330$	−1.43132e53	−0.101786
$331$	1.33462e54	0.889317	0.444659	−	0.895700i	$-0.353325\pi$
$331$	1.33462e54	0.889317	0.444659	+	0.895700i	$0.353325\pi$
$332$	−1.03142e54	−0.644120
$333$	−1.76702e51	−0.00103441
$334$	−2.52076e53	−0.138351
$335$	−5.86971e53	−0.302102
$336$	1.31364e54	0.634134
$337$	−2.37074e54	−1.07359	−0.536797	−	0.843711i	$-0.680366\pi$
$337$	−2.37074e54	−1.07359	−0.536797	+	0.843711i	$0.680366\pi$
$338$	−1.74310e54	−0.740652
$339$	1.22855e54	0.489891
$340$	−2.61945e54	−0.980423
$341$	1.13922e53	0.0400301
$342$	−1.42331e52	−0.00469610
$343$	2.39069e54	0.740796
$344$	2.36119e54	0.687266
$345$	8.58806e53	0.234847
$346$	1.08623e54	0.279115
$347$	−5.56591e54	−1.34417	−0.672083	−	0.740476i	$-0.734600\pi$
$347$	−5.56591e54	−1.34417	−0.672083	+	0.740476i	$0.734600\pi$
$348$	−1.01471e54	−0.230350
$349$	5.55165e54	1.18488	0.592441	−	0.805614i	$-0.298164\pi$
$349$	5.55165e54	1.18488	0.592441	+	0.805614i	$0.298164\pi$
$350$	−1.48915e54	−0.298865
$351$	9.03347e54	1.70511
$352$	−2.30540e54	−0.409335
$353$	−2.79315e54	−0.466592	−0.233296	−	0.972406i	$-0.574951\pi$
$353$	−2.79315e54	−0.466592	−0.233296	+	0.972406i	$0.574951\pi$
$354$	3.69387e54	0.580646
$355$	2.40411e54	0.355667
$356$	−6.69952e54	−0.932973
$357$	−1.71842e55	−2.25301
$358$	−2.23092e54	−0.275423
$359$	4.56336e54	0.530584	0.265292	−	0.964168i	$-0.414532\pi$
$359$	4.56336e54	0.530584	0.265292	+	0.964168i	$0.414532\pi$
$360$	7.38475e52	0.00808783
$361$	−5.71395e54	−0.589565
$362$	1.20590e53	0.0117240
$363$	8.81904e54	0.808032
$364$	1.92297e55	1.66071
$365$	6.03767e54	0.491556
$366$	−2.47665e54	−0.190117
$367$	−9.24553e54	−0.669286	−0.334643	−	0.942345i	$-0.608616\pi$
$367$	−9.24553e54	−0.669286	−0.334643	+	0.942345i	$0.608616\pi$
$368$	3.17146e54	0.216537
$369$	−4.51765e53	−0.0290969
$370$	2.21692e53	0.0134714
$371$	−4.80157e54	−0.275324
$372$	1.43471e54	0.0776409
$373$	9.10042e54	0.464859	0.232430	−	0.972613i	$-0.425332\pi$
$373$	9.10042e54	0.464859	0.232430	+	0.972613i	$0.425332\pi$
$374$	6.91441e54	0.333438
$375$	−2.13994e55	−0.974384
$376$	−1.07631e55	−0.462804
$377$	−1.15071e55	−0.467332
$378$	1.22679e55	0.470647
$379$	−2.67644e55	−0.970096	−0.485048	−	0.874488i	$-0.661198\pi$
$379$	−2.67644e55	−0.970096	−0.485048	+	0.874488i	$0.661198\pi$
$380$	−9.42660e54	−0.322855
$381$	4.01897e55	1.30085
$382$	−9.98959e54	−0.305622
$383$	2.36692e55	0.684556	0.342278	−	0.939599i	$-0.388801\pi$
$383$	2.36692e55	0.684556	0.342278	+	0.939599i	$0.388801\pi$
$384$	−3.69515e55	−1.01044
$385$	1.16365e55	0.300896
$386$	2.52952e55	0.618603
$387$	−7.42886e53	−0.0171845
$388$	9.13247e54	0.199851
$389$	9.04290e55	1.87237	0.936184	−	0.351509i	$-0.114331\pi$
$389$	9.04290e55	1.87237	0.936184	+	0.351509i	$0.114331\pi$
$390$	−2.04417e55	−0.400524
$391$	−4.14872e55	−0.769331
$392$	1.53264e55	0.269023
$393$	−5.26978e55	−0.875695
$394$	−2.27510e55	−0.357957
$395$	−2.47137e55	−0.368214
$396$	4.69999e53	0.00663210
$397$	5.22770e55	0.698738	0.349369	−	0.936985i	$-0.386396\pi$
$397$	5.22770e55	0.698738	0.349369	+	0.936985i	$0.386396\pi$
$398$	−3.92990e55	−0.497617
$399$	−6.18407e55	−0.741920
$400$	−3.08599e55	−0.350837
$401$	2.74708e55	0.295983	0.147992	−	0.988989i	$-0.452719\pi$
$401$	2.74708e55	0.295983	0.147992	+	0.988989i	$0.452719\pi$
$402$	1.95128e55	0.199278
$403$	1.62700e55	0.157517
$404$	−6.90869e54	−0.0634156
$405$	6.75783e55	0.588199
$406$	−1.56271e55	−0.128994
$407$	3.08918e54	0.0241860
$408$	1.90653e56	1.41596
$409$	−2.29499e55	−0.161708	−0.0808538	−	0.996726i	$-0.525765\pi$
$409$	−2.29499e55	−0.161708	−0.0808538	+	0.996726i	$0.525765\pi$
$410$	5.66788e55	0.378938
$411$	−2.72707e55	−0.173020
$412$	2.00890e56	1.20967
$413$	−3.00308e56	−1.71649
$414$	5.34205e53	0.00289868
$415$	−8.91385e55	−0.459231
$416$	−3.29251e56	−1.61072
$417$	−1.17621e55	−0.0546462
$418$	2.48828e55	0.109802
$419$	−3.63801e54	−0.0152497	−0.00762487	−	0.999971i	$-0.502427\pi$
$419$	−3.63801e54	−0.0152497	−0.00762487	+	0.999971i	$0.502427\pi$
$420$	1.46548e56	0.583606
$421$	1.16447e56	0.440620	0.220310	−	0.975430i	$-0.429293\pi$
$421$	1.16447e56	0.440620	0.220310	+	0.975430i	$0.429293\pi$
$422$	−9.01449e55	−0.324133
$423$	3.38631e54	0.0115720
$424$	5.32719e55	0.173034
$425$	4.03691e56	1.24649
$426$	−7.99201e55	−0.234612
$427$	2.01349e56	0.562019
$428$	−5.26636e56	−1.39788
$429$	−2.84846e56	−0.719082
$430$	9.32030e55	0.223799
$431$	5.90924e56	1.34980	0.674901	−	0.737908i	$-0.264186\pi$
$431$	5.90924e56	1.34980	0.674901	+	0.737908i	$0.264186\pi$
$432$	2.54229e56	0.552491
$433$	1.91269e56	0.395507	0.197754	−	0.980252i	$-0.436635\pi$
$433$	1.91269e56	0.395507	0.197754	+	0.980252i	$0.436635\pi$
$434$	2.20954e55	0.0434783
$435$	−8.76942e55	−0.164230
$436$	−4.24664e56	−0.756983
$437$	−1.49299e56	−0.253342
$438$	−2.00711e56	−0.324249
$439$	−1.21770e57	−1.87307	−0.936537	−	0.350569i	$-0.885988\pi$
$439$	−1.21770e57	−1.87307	−0.936537	+	0.350569i	$0.885988\pi$
$440$	−1.29103e56	−0.189105
$441$	−4.82204e54	−0.00672669
$442$	9.87497e56	1.31207
$443$	2.89543e56	0.366465	0.183233	−	0.983070i	$-0.441344\pi$
$443$	2.89543e56	0.366465	0.183233	+	0.983070i	$0.441344\pi$
$444$	3.89046e55	0.0469102
$445$	−5.78993e56	−0.665171
$446$	−3.32959e56	−0.364494
$447$	1.58949e57	1.65824
$448$	1.96562e56	0.195444
$449$	−7.37718e55	−0.0699188	−0.0349594	−	0.999389i	$-0.511130\pi$
$449$	−7.37718e55	−0.0699188	−0.0349594	+	0.999389i	$0.511130\pi$
$450$	−5.19809e54	−0.00469650
$451$	7.89794e56	0.680327
$452$	5.06130e56	0.415706
$453$	−1.53309e57	−1.20076
$454$	−5.61694e56	−0.419565
$455$	1.66189e57	1.18402
$456$	6.86102e56	0.466278
$457$	−1.57216e57	−1.01929	−0.509646	−	0.860384i	$-0.670224\pi$
$457$	−1.57216e57	−1.01929	−0.509646	+	0.860384i	$0.670224\pi$
$458$	2.05596e56	0.127176
$459$	−3.32568e57	−1.96294
$460$	3.53805e56	0.199283
$461$	4.69628e56	0.252455	0.126228	−	0.992001i	$-0.459713\pi$
$461$	4.69628e56	0.252455	0.126228	+	0.992001i	$0.459713\pi$
$462$	−3.86834e56	−0.198482
$463$	−3.45809e56	−0.169373	−0.0846866	−	0.996408i	$-0.526989\pi$
$463$	−3.45809e56	−0.169373	−0.0846866	+	0.996408i	$0.526989\pi$
$464$	−3.23844e56	−0.151425
$465$	1.23992e56	0.0553547
$466$	4.57312e56	0.194946
$467$	3.48051e57	1.41687	0.708436	−	0.705775i	$-0.249401\pi$
$467$	3.48051e57	1.41687	0.708436	+	0.705775i	$0.249401\pi$
$468$	6.71241e55	0.0260971
$469$	−1.58637e57	−0.589100
$470$	−4.24849e56	−0.150706
$471$	1.13658e57	0.385167
$472$	3.33182e57	1.07877
$473$	1.29874e57	0.401798
$474$	8.21562e56	0.242888
$475$	1.45276e57	0.410470
$476$	−7.07944e57	−1.91183
$477$	−1.67606e55	−0.00432657
$478$	−1.82232e57	−0.449701
$479$	3.13467e56	0.0739567	0.0369784	−	0.999316i	$-0.488227\pi$
$479$	3.13467e56	0.0739567	0.0369784	+	0.999316i	$0.488227\pi$
$480$	−2.50919e57	−0.566040
$481$	4.41188e56	0.0951711
$482$	−2.00387e57	−0.413389
$483$	2.32104e57	0.457952
$484$	3.63321e57	0.685670
$485$	7.89256e56	0.142485
$486$	8.48731e55	0.0146585
$487$	−8.38372e57	−1.38536	−0.692682	−	0.721243i	$-0.743571\pi$
$487$	−8.38372e57	−1.38536	−0.692682	+	0.721243i	$0.743571\pi$
$488$	−2.23391e57	−0.353215
$489$	4.35068e57	0.658289
$490$	6.04977e56	0.0876038
$491$	−5.79408e57	−0.803031	−0.401516	−	0.915852i	$-0.631516\pi$
$491$	−5.79408e57	−0.803031	−0.401516	+	0.915852i	$0.631516\pi$
$492$	9.94653e57	1.31954
$493$	4.23633e57	0.537998
$494$	3.55370e57	0.432067
$495$	4.06188e55	0.00472841
$496$	4.57887e56	0.0510390
$497$	6.49743e57	0.693553
$498$	2.96325e57	0.302926
$499$	6.67553e56	0.0653618	0.0326809	−	0.999466i	$-0.489595\pi$
$499$	6.67553e56	0.0653618	0.0326809	+	0.999466i	$0.489595\pi$
$500$	−8.81600e57	−0.826830
$501$	−3.82306e57	−0.343479
$502$	−1.32837e57	−0.114338
$503$	−2.00370e58	−1.65242	−0.826212	−	0.563359i	$-0.809509\pi$
$503$	−2.00370e58	−1.65242	−0.826212	+	0.563359i	$0.809509\pi$
$504$	1.99583e56	0.0157713
$505$	−5.97070e56	−0.0452127
$506$	−9.33918e56	−0.0677755
$507$	−2.64365e58	−1.83879
$508$	1.65571e58	1.10386
$509$	2.35405e58	1.50447	0.752233	−	0.658897i	$-0.228977\pi$
$509$	2.35405e58	1.50447	0.752233	+	0.658897i	$0.228977\pi$
$510$	7.52562e57	0.461088
$511$	1.63177e58	0.958536
$512$	−1.64078e58	−0.924157
$513$	−1.19681e58	−0.646400
$514$	−6.09741e57	−0.315819
$515$	1.73615e58	0.862447
$516$	1.63561e58	0.779313
$517$	−5.92007e57	−0.270571
$518$	5.99154e56	0.0262693
$519$	1.64740e58	0.692950
$520$	−1.84382e58	−0.744125
$521$	1.49380e58	0.578471	0.289236	−	0.957258i	$-0.406599\pi$
$521$	1.49380e58	0.578471	0.289236	+	0.957258i	$0.406599\pi$
$522$	−5.45486e55	−0.00202707
$523$	1.11209e58	0.396602	0.198301	−	0.980141i	$-0.436458\pi$
$523$	1.11209e58	0.396602	0.198301	+	0.980141i	$0.436458\pi$
$524$	−2.17101e58	−0.743086
$525$	−2.25849e58	−0.741983
$526$	−1.15759e58	−0.365057
$527$	−5.98980e57	−0.181336
$528$	−8.01643e57	−0.232998
$529$	−3.02305e58	−0.843624
$530$	2.10279e57	0.0563463
$531$	−1.04827e57	−0.0269737
$532$	−2.54767e58	−0.629569
$533$	1.12796e59	2.67707
$534$	1.92476e58	0.438772
$535$	−4.55135e58	−0.996629
$536$	1.76003e58	0.370234
$537$	−3.38349e58	−0.683782
$538$	1.38535e58	0.268992
$539$	8.43008e57	0.157280
$540$	2.83616e58	0.508469
$541$	8.34052e57	0.143698	0.0718492	−	0.997416i	$-0.477110\pi$
$541$	8.34052e57	0.143698	0.0718492	+	0.997416i	$0.477110\pi$
$542$	−2.25550e58	−0.373471
$543$	1.82891e57	0.0291068
$544$	1.21214e59	1.85428
$545$	−3.67008e58	−0.539697
$546$	−5.52466e58	−0.781023
$547$	−6.38951e58	−0.868440	−0.434220	−	0.900807i	$-0.642976\pi$
$547$	−6.38951e58	−0.868440	−0.434220	+	0.900807i	$0.642976\pi$
$548$	−1.12348e58	−0.146819
$549$	7.02838e56	0.00883181
$550$	9.08749e57	0.109811
$551$	1.52452e58	0.177164
$552$	−2.57512e58	−0.287811
$553$	−6.67922e58	−0.718019
$554$	−4.41593e57	−0.0456628
$555$	3.36225e57	0.0334450
$556$	−4.84567e57	−0.0463710
$557$	−1.47103e59	−1.35436	−0.677181	−	0.735816i	$-0.736799\pi$
$557$	−1.47103e59	−1.35436	−0.677181	+	0.735816i	$0.736799\pi$
$558$	7.71270e55	0.000683237 0
$559$	1.85483e59	1.58107
$560$	4.67707e58	0.383646
$561$	1.04866e59	0.827816
$562$	−3.59406e57	−0.0273058
$563$	9.38359e58	0.686181	0.343090	−	0.939302i	$-0.388526\pi$
$563$	9.38359e58	0.686181	0.343090	+	0.939302i	$0.388526\pi$
$564$	−7.45564e58	−0.524789
$565$	4.37413e58	0.296381
$566$	8.18444e58	0.533870
$567$	1.82640e59	1.14699
$568$	−7.20869e58	−0.435880
$569$	−2.42417e59	−1.41140	−0.705698	−	0.708513i	$-0.749366\pi$
$569$	−2.42417e59	−1.41140	−0.705698	+	0.708513i	$0.749366\pi$
$570$	2.70824e58	0.151837
$571$	−2.26275e59	−1.22169	−0.610844	−	0.791751i	$-0.709170\pi$
$571$	−2.26275e59	−1.22169	−0.610844	+	0.791751i	$0.709170\pi$
$572$	−1.17349e59	−0.610189
$573$	−1.51505e59	−0.758758
$574$	1.53182e59	0.738930
$575$	−5.45259e58	−0.253364
$576$	6.86127e56	0.00307129
$577$	2.80486e59	1.20957	0.604786	−	0.796388i	$-0.293259\pi$
$577$	2.80486e59	1.20957	0.604786	+	0.796388i	$0.293259\pi$
$578$	−2.67496e59	−1.11140
$579$	3.83636e59	1.53578
$580$	−3.61277e58	−0.139360
$581$	−2.40909e59	−0.895502
$582$	−2.62374e58	−0.0939888
$583$	2.93015e58	0.101162
$584$	−1.81039e59	−0.602416
$585$	5.80107e57	0.0186062
$586$	8.97942e58	0.277619
$587$	6.13483e59	1.82845	0.914226	−	0.405204i	$-0.132800\pi$
$587$	6.13483e59	1.82845	0.914226	+	0.405204i	$0.132800\pi$
$588$	1.06167e59	0.305054
$589$	−2.15554e58	−0.0597142
$590$	1.31517e59	0.351287
$591$	−3.45048e59	−0.888687
$592$	1.24164e58	0.0308374
$593$	3.38684e59	0.811183	0.405591	−	0.914055i	$-0.367066\pi$
$593$	3.38684e59	0.811183	0.405591	+	0.914055i	$0.367066\pi$
$594$	−7.48643e58	−0.172928
$595$	−6.11826e59	−1.36305
$596$	6.54829e59	1.40713
$597$	−5.96021e59	−1.23542
$598$	−1.33380e59	−0.266694
$599$	−8.69352e59	−1.67695	−0.838473	−	0.544944i	$-0.816551\pi$
$599$	−8.69352e59	−1.67695	−0.838473	+	0.544944i	$0.816551\pi$
$600$	2.50573e59	0.466317
$601$	2.05552e59	0.369080	0.184540	−	0.982825i	$-0.440920\pi$
$601$	2.05552e59	0.369080	0.184540	+	0.982825i	$0.440920\pi$
$602$	2.51894e59	0.436409
$603$	−5.53745e57	−0.00925737
$604$	−6.31592e59	−1.01893
$605$	3.13993e59	0.488854
$606$	1.98485e58	0.0298240
$607$	7.51891e59	1.09043	0.545215	−	0.838296i	$-0.316448\pi$
$607$	7.51891e59	1.09043	0.545215	+	0.838296i	$0.316448\pi$
$608$	4.36211e59	0.610619
$609$	−2.37006e59	−0.320249
$610$	−8.81785e58	−0.115020
$611$	−8.45489e59	−1.06469
$612$	−2.47118e58	−0.0300433
$613$	6.96117e59	0.817112	0.408556	−	0.912733i	$-0.366032\pi$
$613$	6.96117e59	0.817112	0.408556	+	0.912733i	$0.366032\pi$
$614$	3.76059e59	0.426222
$615$	8.59609e59	0.940776
$616$	−3.48919e59	−0.368756
$617$	1.68634e60	1.72113	0.860567	−	0.509337i	$-0.170109\pi$
$617$	1.68634e60	1.72113	0.860567	+	0.509337i	$0.170109\pi$
$618$	−5.77152e59	−0.568903
$619$	−1.32244e60	−1.25901	−0.629503	−	0.776998i	$-0.716742\pi$
$619$	−1.32244e60	−1.25901	−0.629503	+	0.776998i	$0.716742\pi$
$620$	5.10814e58	0.0469722
$621$	4.49194e59	0.398992
$622$	−7.27744e59	−0.624433
$623$	−1.56481e60	−1.29709
$624$	−1.14489e60	−0.916839
$625$	6.61886e58	0.0512110
$626$	−4.05176e59	−0.302898
$627$	3.77381e59	0.272601
$628$	4.68240e59	0.326840
$629$	−1.62424e59	−0.109562
$630$	7.87811e57	0.00513571
$631$	1.50474e60	0.948048	0.474024	−	0.880512i	$-0.342801\pi$
$631$	1.50474e60	0.948048	0.474024	+	0.880512i	$0.342801\pi$
$632$	7.41038e59	0.451257
$633$	−1.36717e60	−0.804714
$634$	7.08932e59	0.403353
$635$	1.43091e60	0.787007
$636$	3.69018e59	0.196209
$637$	1.20396e60	0.618892
$638$	9.53640e58	0.0473958
$639$	2.26802e58	0.0108988
$640$	−1.31562e60	−0.611310
$641$	−1.27833e60	−0.574373	−0.287187	−	0.957875i	$-0.592720\pi$
$641$	−1.27833e60	−0.574373	−0.287187	+	0.957875i	$0.592720\pi$
$642$	1.51301e60	0.657415
$643$	−1.28540e60	−0.540134	−0.270067	−	0.962842i	$-0.587046\pi$
$643$	−1.28540e60	−0.540134	−0.270067	+	0.962842i	$0.587046\pi$
$644$	9.56208e59	0.388603
$645$	1.41355e60	0.555618
$646$	−1.30830e60	−0.497401
$647$	−3.49078e60	−1.28375	−0.641875	−	0.766809i	$-0.721843\pi$
$647$	−3.49078e60	−1.28375	−0.641875	+	0.766809i	$0.721843\pi$
$648$	−2.02633e60	−0.720855
$649$	1.83262e60	0.630684
$650$	1.29785e60	0.432104
$651$	3.35106e59	0.107942
$652$	1.79236e60	0.558602
$653$	−4.91548e60	−1.48229	−0.741143	−	0.671347i	$-0.765716\pi$
$653$	−4.91548e60	−1.48229	−0.741143	+	0.671347i	$0.765716\pi$
$654$	1.22005e60	0.356005
$655$	−1.87625e60	−0.529790
$656$	3.17443e60	0.867427
$657$	5.69590e58	0.0150629
$658$	−1.14821e60	−0.293877
$659$	−4.43095e60	−1.09764	−0.548821	−	0.835940i	$-0.684923\pi$
$659$	−4.43095e60	−1.09764	−0.548821	+	0.835940i	$0.684923\pi$
$660$	−8.94305e59	−0.214433
$661$	3.53419e60	0.820274	0.410137	−	0.912024i	$-0.365481\pi$
$661$	3.53419e60	0.820274	0.410137	+	0.912024i	$0.365481\pi$
$662$	−1.57965e60	−0.354906
$663$	1.49767e61	3.25743
$664$	2.67281e60	0.562800
$665$	−2.20177e60	−0.448856
$666$	2.09143e57	0.000412807 0
$667$	−5.72194e59	−0.109355
$668$	−1.57500e60	−0.291465
$669$	−5.04976e60	−0.904917
$670$	6.94733e59	0.120562
$671$	−1.22873e60	−0.206501
$672$	−6.78144e60	−1.10378
$673$	3.42060e60	0.539236	0.269618	−	0.962967i	$-0.413103\pi$
$673$	3.42060e60	0.539236	0.269618	+	0.962967i	$0.413103\pi$
$674$	2.80598e60	0.428446
$675$	−4.37088e60	−0.646455
$676$	−1.08911e61	−1.56034
$677$	6.63114e60	0.920305	0.460152	−	0.887840i	$-0.347795\pi$
$677$	6.63114e60	0.920305	0.460152	+	0.887840i	$0.347795\pi$
$678$	−1.45410e60	−0.195504
$679$	2.13307e60	0.277847
$680$	6.78802e60	0.856646
$681$	−8.51884e60	−1.04164
$682$	−1.34836e59	−0.0159751
$683$	4.07501e60	0.467825	0.233913	−	0.972258i	$-0.424847\pi$
$683$	4.07501e60	0.467825	0.233913	+	0.972258i	$0.424847\pi$
$684$	−8.89300e58	−0.00989332
$685$	−9.70945e59	−0.104676
$686$	−2.82959e60	−0.295634
$687$	3.11813e60	0.315736
$688$	5.22005e60	0.512299
$689$	4.18476e60	0.398068
$690$	−1.01647e60	−0.0937218
$691$	1.23638e61	1.10503	0.552514	−	0.833504i	$-0.313669\pi$
$691$	1.23638e61	1.10503	0.552514	+	0.833504i	$0.313669\pi$
$692$	6.78687e60	0.588015
$693$	1.09778e59	0.00922042
$694$	6.58776e60	0.536425
$695$	−4.18778e59	−0.0330606
$696$	2.62950e60	0.201268
$697$	−4.15260e61	−3.08188
$698$	−6.57087e60	−0.472859
$699$	6.93574e60	0.483987
$700$	−9.30439e60	−0.629622
$701$	1.41956e61	0.931574	0.465787	−	0.884897i	$-0.345771\pi$
$701$	1.41956e61	0.931574	0.465787	+	0.884897i	$0.345771\pi$
$702$	−1.06919e61	−0.680468
$703$	−5.84513e59	−0.0360790
$704$	−1.19951e60	−0.0718114
$705$	−6.44339e60	−0.374152
$706$	3.30594e60	0.186206
$707$	−1.61367e60	−0.0881650
$708$	2.30797e61	1.22325
$709$	−6.77303e60	−0.348248	−0.174124	−	0.984724i	$-0.555709\pi$
$709$	−6.77303e60	−0.348248	−0.174124	+	0.984724i	$0.555709\pi$
$710$	−2.84547e60	−0.141938
$711$	−2.33148e59	−0.0112833
$712$	1.73611e61	0.815186
$713$	8.09032e59	0.0368588
$714$	2.03391e61	0.899123
$715$	−1.01416e61	−0.435039
$716$	−1.39391e61	−0.580235
$717$	−2.76378e61	−1.11646
$718$	−5.40114e60	−0.211744
$719$	3.64283e61	1.38601	0.693006	−	0.720931i	$-0.256286\pi$
$719$	3.64283e61	1.38601	0.693006	+	0.720931i	$0.256286\pi$
$720$	1.63260e59	0.00602879
$721$	4.69219e61	1.68177
$722$	6.76297e60	0.235282
$723$	−3.03914e61	−1.02631
$724$	7.53460e59	0.0246991
$725$	5.56774e60	0.177179
$726$	−1.04381e61	−0.322467
$727$	−1.87172e61	−0.561372	−0.280686	−	0.959800i	$-0.590562\pi$
$727$	−1.87172e61	−0.561372	−0.280686	+	0.959800i	$0.590562\pi$
$728$	−4.98317e61	−1.45105
$729$	3.59962e61	1.01769
$730$	−7.14612e60	−0.196168
$731$	−6.82856e61	−1.82014
$732$	−1.54744e61	−0.400521
$733$	4.58324e61	1.15196	0.575980	−	0.817464i	$-0.304621\pi$
$733$	4.58324e61	1.15196	0.575980	+	0.817464i	$0.304621\pi$
$734$	1.09429e61	0.267096
$735$	9.17527e60	0.217491
$736$	−1.63722e61	−0.376906
$737$	9.68078e60	0.216451
$738$	5.34705e59	0.0116119
$739$	−6.45765e59	−0.0136213	−0.00681066	−	0.999977i	$-0.502168\pi$
$739$	−6.45765e59	−0.0136213	−0.00681066	+	0.999977i	$0.502168\pi$
$740$	1.38516e60	0.0283803
$741$	5.38965e61	1.07268
$742$	5.68309e60	0.109875
$743$	3.46765e61	0.651291	0.325646	−	0.945492i	$-0.394418\pi$
$743$	3.46765e61	0.651291	0.325646	+	0.945492i	$0.394418\pi$
$744$	−3.71789e60	−0.0678388
$745$	5.65923e61	1.00322
$746$	−1.07712e61	−0.185514
$747$	−8.40927e59	−0.0140723
$748$	4.32020e61	0.702457
$749$	−1.23007e62	−1.94343
$750$	2.53281e61	0.388854
$751$	−3.57168e61	−0.532861	−0.266430	−	0.963854i	$-0.585844\pi$
$751$	−3.57168e61	−0.532861	−0.266430	+	0.963854i	$0.585844\pi$
$752$	−2.37946e61	−0.344981
$753$	−2.01465e61	−0.283863
$754$	1.36196e61	0.186501
$755$	−5.45841e61	−0.726452
$756$	7.66511e61	0.991517
$757$	−1.06737e62	−1.34200	−0.671002	−	0.741456i	$-0.734136\pi$
$757$	−1.06737e62	−1.34200	−0.671002	+	0.741456i	$0.734136\pi$
$758$	3.16781e61	0.387142
$759$	−1.41641e61	−0.168264
$760$	2.44280e61	0.282095
$761$	9.90270e61	1.11169	0.555845	−	0.831286i	$-0.312395\pi$
$761$	9.90270e61	1.11169	0.555845	+	0.831286i	$0.312395\pi$
$762$	−4.75681e61	−0.519140
$763$	−9.91890e61	−1.05241
$764$	−6.24161e61	−0.643857
$765$	−2.13566e60	−0.0214196
$766$	−2.80146e61	−0.273190
$767$	2.61730e62	2.48173
$768$	2.57673e61	0.237576
$769$	−2.55003e61	−0.228628	−0.114314	−	0.993445i	$-0.536467\pi$
$769$	−2.55003e61	−0.228628	−0.114314	+	0.993445i	$0.536467\pi$
$770$	−1.37728e61	−0.120080
$771$	−9.24752e61	−0.784073
$772$	1.58048e62	1.30322
$773$	1.50600e62	1.20772	0.603861	−	0.797090i	$-0.293628\pi$
$773$	1.50600e62	1.20772	0.603861	+	0.797090i	$0.293628\pi$
$774$	8.79272e59	0.00685792
$775$	−7.87229e60	−0.0597193
$776$	−2.36658e61	−0.174620
$777$	9.08696e60	0.0652179
$778$	−1.07031e62	−0.747219
$779$	−1.49439e62	−1.01487
$780$	−1.27722e62	−0.843786
$781$	−3.96504e61	−0.254830
$782$	4.91038e61	0.307022
$783$	−4.58680e61	−0.279018
$784$	3.38831e61	0.200534
$785$	4.04667e61	0.233024
$786$	6.23726e61	0.349469
$787$	1.74985e62	0.953989	0.476994	−	0.878906i	$-0.341726\pi$
$787$	1.74985e62	0.953989	0.476994	+	0.878906i	$0.341726\pi$
$788$	−1.42151e62	−0.754111
$789$	−1.75564e62	−0.906315
$790$	2.92509e61	0.146946
$791$	1.18217e62	0.577944
$792$	−1.21795e60	−0.00579480
$793$	−1.75484e62	−0.812575
$794$	−6.18745e61	−0.278850
$795$	3.18916e61	0.139889
$796$	−2.45545e62	−1.04833
$797$	3.53459e62	1.46888	0.734438	−	0.678676i	$-0.237446\pi$
$797$	3.53459e62	1.46888	0.734438	+	0.678676i	$0.237446\pi$
$798$	7.31939e61	0.296083
$799$	3.11267e62	1.22568
$800$	1.59310e62	0.610671
$801$	−5.46219e60	−0.0203830
$802$	−3.25142e61	−0.118120
$803$	−9.95780e61	−0.352192
$804$	1.21918e62	0.419820
$805$	8.26384e61	0.277058
$806$	−1.92570e61	−0.0628615
$807$	2.10106e62	0.667818
$808$	1.79031e61	0.0554095
$809$	−4.31937e62	−1.30175	−0.650875	−	0.759185i	$-0.725598\pi$
$809$	−4.31937e62	−1.30175	−0.650875	+	0.759185i	$0.725598\pi$
$810$	−7.99850e61	−0.234736
$811$	−5.78809e62	−1.65419	−0.827097	−	0.562059i	$-0.810010\pi$
$811$	−5.78809e62	−1.65419	−0.827097	+	0.562059i	$0.810010\pi$
$812$	−9.76401e61	−0.271753
$813$	−3.42076e62	−0.927204
$814$	−3.65632e60	−0.00965205
$815$	1.54901e62	0.398260
$816$	4.21490e62	1.05548
$817$	−2.45739e62	−0.599376
$818$	2.71633e61	0.0645337
$819$	1.56782e61	0.0362821
$820$	3.54136e62	0.798311
$821$	−1.86128e62	−0.408727	−0.204364	−	0.978895i	$-0.565512\pi$
$821$	−1.86128e62	−0.408727	−0.204364	+	0.978895i	$0.565512\pi$
$822$	3.22773e61	0.0690483
$823$	6.65210e62	1.38632	0.693158	−	0.720785i	$-0.256219\pi$
$823$	6.65210e62	1.38632	0.693158	+	0.720785i	$0.256219\pi$
$824$	−5.20584e62	−1.05695
$825$	1.37824e62	0.272624
$826$	3.55442e62	0.685011
$827$	−6.49406e61	−0.121940	−0.0609702	−	0.998140i	$-0.519419\pi$
$827$	−6.49406e61	−0.121940	−0.0609702	+	0.998140i	$0.519419\pi$
$828$	3.33778e60	0.00610668
$829$	4.83956e62	0.862746	0.431373	−	0.902174i	$-0.358029\pi$
$829$	4.83956e62	0.862746	0.431373	+	0.902174i	$0.358029\pi$
$830$	1.05503e62	0.183268
$831$	−6.69735e61	−0.113365
$832$	−1.71311e62	−0.282576
$833$	−4.43239e62	−0.712476
$834$	1.39215e61	0.0218080
$835$	−1.36116e62	−0.207802
$836$	1.55471e62	0.231320
$837$	6.48533e61	0.0940448
$838$	4.30591e60	0.00608582
$839$	5.22756e62	0.720140	0.360070	−	0.932925i	$-0.382753\pi$
$839$	5.22756e62	0.720140	0.360070	+	0.932925i	$0.382753\pi$
$840$	−3.79763e62	−0.509927
$841$	−7.05608e62	−0.923527
$842$	−1.37826e62	−0.175841
$843$	−5.45087e61	−0.0677912
$844$	−5.63236e62	−0.682854
$845$	−9.41244e62	−1.11246
$846$	−4.00800e60	−0.00461812
$847$	8.48610e62	0.953267
$848$	1.17772e62	0.128982
$849$	1.24128e63	1.32542
$850$	−4.77805e62	−0.497443
$851$	2.19383e61	0.0222699
$852$	−4.99351e62	−0.494259
$853$	3.48905e62	0.336747	0.168373	−	0.985723i	$-0.446149\pi$
$853$	3.48905e62	0.336747	0.168373	+	0.985723i	$0.446149\pi$
$854$	−2.38315e62	−0.224289
$855$	−7.68560e60	−0.00705352
$856$	1.36472e63	1.22140
$857$	5.09487e62	0.444678	0.222339	−	0.974969i	$-0.428631\pi$
$857$	5.09487e62	0.444678	0.222339	+	0.974969i	$0.428631\pi$
$858$	3.37141e62	0.286969
$859$	−1.66852e63	−1.38509	−0.692546	−	0.721374i	$-0.743511\pi$
$859$	−1.66852e63	−1.38509	−0.692546	+	0.721374i	$0.743511\pi$
$860$	5.82343e62	0.471479
$861$	2.32321e63	1.83452
$862$	−6.99411e62	−0.538674
$863$	6.32017e62	0.474785	0.237392	−	0.971414i	$-0.423707\pi$
$863$	6.32017e62	0.474785	0.237392	+	0.971414i	$0.423707\pi$
$864$	−1.31242e63	−0.961672
$865$	5.86541e62	0.419230
$866$	−2.26384e62	−0.157838
$867$	−4.05693e63	−2.75922
$868$	1.38055e62	0.0915960
$869$	4.07598e62	0.263819
$870$	1.03794e62	0.0655403
$871$	1.38258e63	0.851728
$872$	1.10047e63	0.661414
$873$	7.44579e60	0.00436621
$874$	1.76709e62	0.101103
$875$	−2.05916e63	−1.14952
$876$	−1.25407e63	−0.683098
$877$	−2.16093e63	−1.14855	−0.574274	−	0.818664i	$-0.694715\pi$
$877$	−2.16093e63	−1.14855	−0.574274	+	0.818664i	$0.694715\pi$
$878$	1.44126e63	0.747500
$879$	1.36185e63	0.689236
$880$	−2.85417e62	−0.140962
$881$	−1.77705e63	−0.856481	−0.428241	−	0.903665i	$-0.640866\pi$
$881$	−1.77705e63	−0.856481	−0.428241	+	0.903665i	$0.640866\pi$
$882$	5.70732e60	0.00268446
$883$	−2.16218e63	−0.992515	−0.496258	−	0.868175i	$-0.665293\pi$
$883$	−2.16218e63	−0.992515	−0.496258	+	0.868175i	$0.665293\pi$
$884$	6.17000e63	2.76415
$885$	1.99462e63	0.872128
$886$	−3.42700e62	−0.146248
$887$	9.41993e62	0.392365	0.196182	−	0.980567i	$-0.437146\pi$
$887$	9.41993e62	0.392365	0.196182	+	0.980567i	$0.437146\pi$
$888$	−1.00817e62	−0.0409878
$889$	3.86725e63	1.53467
$890$	6.85290e62	0.265454
$891$	−1.11455e63	−0.421435
$892$	−2.08037e63	−0.767883
$893$	1.12015e63	0.403619
$894$	−1.88131e63	−0.661765
$895$	−1.20466e63	−0.413684
$896$	−3.55565e63	−1.19206
$897$	−2.02288e63	−0.662113
$898$	8.73155e61	0.0279030
$899$	−8.26118e61	−0.0257756
$900$	−3.24783e61	−0.00989416
$901$	−1.54062e63	−0.458261
$902$	−9.34791e62	−0.271503
$903$	3.82031e63	1.08346
$904$	−1.31158e63	−0.363223
$905$	6.51163e61	0.0176094
$906$	1.81455e63	0.479195
$907$	4.24432e63	1.09459	0.547295	−	0.836940i	$-0.315658\pi$
$907$	4.24432e63	1.09459	0.547295	+	0.836940i	$0.315658\pi$
$908$	−3.50953e63	−0.883901
$909$	−5.63272e60	−0.00138546
$910$	−1.96700e63	−0.472513
$911$	−1.73895e63	−0.407983	−0.203991	−	0.978973i	$-0.565391\pi$
$911$	−1.73895e63	−0.407983	−0.203991	+	0.978973i	$0.565391\pi$
$912$	1.51681e63	0.347570
$913$	1.47014e63	0.329031
$914$	1.86079e63	0.406776
$915$	−1.33734e63	−0.285555
$916$	1.28459e63	0.267923
$917$	−5.07084e63	−1.03309
$918$	3.93624e63	0.783364
$919$	8.49800e63	1.65209	0.826044	−	0.563606i	$-0.190586\pi$
$919$	8.49800e63	1.65209	0.826044	+	0.563606i	$0.190586\pi$
$920$	−9.16846e62	−0.174124
$921$	5.70343e63	1.05817
$922$	−5.55847e62	−0.100749
$923$	−5.66276e63	−1.00275
$924$	−2.41698e63	−0.418145
$925$	−2.13471e62	−0.0360821
$926$	4.09296e62	0.0675929
$927$	1.63788e62	0.0264281
$928$	1.67179e63	0.263573
$929$	−6.41656e63	−0.988472	−0.494236	−	0.869328i	$-0.664552\pi$
$929$	−6.41656e63	−0.988472	−0.494236	+	0.869328i	$0.664552\pi$
$930$	−1.46756e62	−0.0220908
$931$	−1.59508e63	−0.234619
$932$	2.85734e63	0.410695
$933$	−1.10372e64	−1.55026
$934$	−4.11950e63	−0.565440
$935$	3.73365e63	0.500823
$936$	−1.73945e62	−0.0228024
$937$	4.22960e63	0.541874	0.270937	−	0.962597i	$-0.412666\pi$
$937$	4.22960e63	0.541874	0.270937	+	0.962597i	$0.412666\pi$
$938$	1.87761e63	0.235096
$939$	−6.14504e63	−0.751994
$940$	−2.65451e63	−0.317493
$941$	5.97856e63	0.698907	0.349454	−	0.936954i	$-0.386367\pi$
$941$	5.97856e63	0.698907	0.349454	+	0.936954i	$0.386367\pi$
$942$	−1.34524e63	−0.153711
$943$	5.60885e63	0.626429
$944$	7.36589e63	0.804132
$945$	6.62442e63	0.706910
$946$	−1.53718e63	−0.160348
$947$	−3.09116e63	−0.315208	−0.157604	−	0.987502i	$-0.550377\pi$
$947$	−3.09116e63	−0.315208	−0.157604	+	0.987502i	$0.550377\pi$
$948$	5.13322e63	0.511694
$949$	−1.42215e64	−1.38586
$950$	−1.71947e63	−0.163809
$951$	1.07519e64	1.00139
$952$	1.83456e64	1.67046
$953$	−8.78118e62	−0.0781727	−0.0390864	−	0.999236i	$-0.512445\pi$
$953$	−8.78118e62	−0.0781727	−0.0390864	+	0.999236i	$0.512445\pi$
$954$	1.98376e61	0.00172663
$955$	−5.39419e63	−0.459044
$956$	−1.13860e64	−0.947389
$957$	1.44632e63	0.117668
$958$	−3.71016e62	−0.0295144
$959$	−2.62411e63	−0.204119
$960$	−1.30555e63	−0.0993028
$961$	−1.33279e64	−0.991312
$962$	−5.22186e62	−0.0379805
$963$	−4.29371e62	−0.0305399
$964$	−1.25204e64	−0.870891
$965$	1.36590e64	0.929138
$966$	−2.74716e63	−0.182758
$967$	1.67955e63	0.109275	0.0546377	−	0.998506i	$-0.482600\pi$
$967$	1.67955e63	0.109275	0.0546377	+	0.998506i	$0.482600\pi$
$968$	−9.41505e63	−0.599104
$969$	−1.98420e64	−1.23488
$970$	−9.34155e62	−0.0568626
$971$	2.39350e64	1.42502	0.712508	−	0.701664i	$-0.247559\pi$
$971$	2.39350e64	1.42502	0.712508	+	0.701664i	$0.247559\pi$
$972$	5.30297e62	0.0308812
$973$	−1.13181e63	−0.0644682
$974$	9.92288e63	0.552866
$975$	1.96836e64	1.07277
$976$	−4.93864e63	−0.263291
$977$	1.55784e64	0.812438	0.406219	−	0.913776i	$-0.366847\pi$
$977$	1.55784e64	0.812438	0.406219	+	0.913776i	$0.366847\pi$
$978$	−5.14942e63	−0.262708
$979$	9.54921e63	0.476584
$980$	3.77997e63	0.184556
$981$	−3.46233e62	−0.0165381
$982$	6.85781e63	0.320471
$983$	8.28128e63	0.378614	0.189307	−	0.981918i	$-0.439376\pi$
$983$	8.28128e63	0.378614	0.189307	+	0.981918i	$0.439376\pi$
$984$	−2.57753e64	−1.15295
$985$	−1.22851e64	−0.537650
$986$	−5.01408e63	−0.214703
$987$	−1.74142e64	−0.729599
$988$	2.22039e64	0.910239
$989$	9.22322e63	0.369966
$990$	−4.80760e61	−0.00188700
$991$	−1.98538e64	−0.762537	−0.381269	−	0.924464i	$-0.624513\pi$
$991$	−1.98538e64	−0.762537	−0.381269	+	0.924464i	$0.624513\pi$
$992$	−2.36377e63	−0.0888390
$993$	−2.39574e64	−0.881112
$994$	−7.69029e63	−0.276781
$995$	−2.12207e64	−0.747418
$996$	1.85147e64	0.638177
$997$	5.32681e64	1.79689	0.898444	−	0.439088i	$-0.144698\pi$
$997$	5.32681e64	1.79689	0.898444	+	0.439088i	$0.144698\pi$
$998$	−7.90108e62	−0.0260844
$999$	1.75861e63	0.0568213

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1.44.a.a.1.2	✓	3
3.2	odd	2		9.44.a.b.1.2		3
4.3	odd	2		16.44.a.c.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.44.a.a.1.2	✓	3	1.1	even	1	trivial
9.44.a.b.1.2		3	3.2	odd	2
16.44.a.c.1.3		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)

\(f(q)\)	\(=\)	\(q-1.18359e6 q^{2} -1.79507e10 q^{3} -7.39521e12 q^{4} -6.39116e14 q^{5} +2.12463e16 q^{6} -1.72730e18 q^{7} +1.91639e19 q^{8} -6.02939e18 q^{9} +O(q^{10})\)	\(q-1.18359e6 q^{2} -1.79507e10 q^{3} -7.39521e12 q^{4} -6.39116e14 q^{5} +2.12463e16 q^{6} -1.72730e18 q^{7} +1.91639e19 q^{8} -6.02939e18 q^{9} +7.56451e20 q^{10} +1.05408e22 q^{11} +1.32749e23 q^{12} +1.50541e24 q^{13} +2.04442e24 q^{14} +1.14726e25 q^{15} +4.23668e25 q^{16} -5.54217e26 q^{17} +7.13632e24 q^{18} -1.99446e27 q^{19} +4.72640e27 q^{20} +3.10063e28 q^{21} -1.24760e28 q^{22} +7.48572e28 q^{23} -3.44005e29 q^{24} -7.28399e29 q^{25} -1.78179e30 q^{26} +6.00067e30 q^{27} +1.27738e31 q^{28} -7.64381e30 q^{29} -1.35788e31 q^{30} +1.08077e31 q^{31} -2.18712e32 q^{32} -1.89215e32 q^{33} +6.55966e32 q^{34} +1.10395e33 q^{35} +4.45886e31 q^{36} +2.93069e32 q^{37} +2.36062e33 q^{38} -2.70232e34 q^{39} -1.22479e34 q^{40} +7.49273e34 q^{41} -3.66987e34 q^{42} +1.23211e35 q^{43} -7.79515e34 q^{44} +3.85348e33 q^{45} -8.86002e34 q^{46} -5.61634e35 q^{47} -7.60514e35 q^{48} +7.99756e35 q^{49} +8.62125e35 q^{50} +9.94859e36 q^{51} -1.11328e37 q^{52} +2.77981e36 q^{53} -7.10233e36 q^{54} -6.73680e36 q^{55} -3.31018e37 q^{56} +3.58019e37 q^{57} +9.04713e36 q^{58} +1.73860e38 q^{59} -8.48422e37 q^{60} -1.16569e38 q^{61} -1.27918e37 q^{62} +1.04146e37 q^{63} -1.13797e38 q^{64} -9.62132e38 q^{65} +2.23953e38 q^{66} +9.18410e38 q^{67} +4.09855e39 q^{68} -1.34374e39 q^{69} -1.30662e39 q^{70} -3.76161e39 q^{71} -1.15546e38 q^{72} -9.44690e39 q^{73} -3.46873e38 q^{74} +1.30753e40 q^{75} +1.47494e40 q^{76} -1.82072e40 q^{77} +3.19843e40 q^{78} +3.86685e40 q^{79} -2.70773e40 q^{80} -1.05737e41 q^{81} -8.86831e40 q^{82} +1.39471e41 q^{83} -2.29298e41 q^{84} +3.54209e41 q^{85} -1.45831e41 q^{86} +1.37212e41 q^{87} +2.02002e41 q^{88} +9.05928e41 q^{89} -4.56094e39 q^{90} -2.60030e42 q^{91} -5.53585e41 q^{92} -1.94005e41 q^{93} +6.64744e41 q^{94} +1.27469e42 q^{95} +3.92603e42 q^{96} -1.23492e42 q^{97} -9.46583e41 q^{98} -6.35546e40 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 2209944 q^{2} + 24401437812 q^{3} + 9822618421824 q^{4} + 535205380774170 q^{5} - 91\!\cdots\!24 q^{6}+ \cdots + 47\!\cdots\!31 q^{9}+O(q^{10}) \) 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

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