LMFDB - Embedded newform 1.44.a.a.1.3

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			1.3
Root			$-91450.2$ 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)

$f(q)$	$=$	$q+3.62707e6 q^{2} +1.01494e10 q^{3} +4.35955e12 q^{4} +6.19839e14 q^{5} +3.68127e16 q^{6} +2.58688e18 q^{7} -1.60917e19 q^{8} -2.25246e20 q^{9} +O(q^{10})$	\(q+3.62707e6 q^{2} +1.01494e10 q^{3} +4.35955e12 q^{4} +6.19839e14 q^{5} +3.68127e16 q^{6} +2.58688e18 q^{7} -1.60917e19 q^{8} -2.25246e20 q^{9} +2.24820e21 q^{10} +2.74302e22 q^{11} +4.42469e22 q^{12} +6.62621e23 q^{13} +9.38279e24 q^{14} +6.29101e24 q^{15} -9.67126e25 q^{16} +5.82021e25 q^{17} -8.16984e26 q^{18} -1.98043e27 q^{19} +2.70222e27 q^{20} +2.62553e28 q^{21} +9.94913e28 q^{22} -2.61209e29 q^{23} -1.63321e29 q^{24} -7.52667e29 q^{25} +2.40337e30 q^{26} -5.61774e30 q^{27} +1.12776e31 q^{28} +2.27846e31 q^{29} +2.28180e31 q^{30} -1.73342e32 q^{31} -2.09240e32 q^{32} +2.78401e32 q^{33} +2.11103e32 q^{34} +1.60345e33 q^{35} -9.81972e32 q^{36} +5.95565e32 q^{37} -7.18317e33 q^{38} +6.72522e33 q^{39} -9.97424e33 q^{40} -5.56734e34 q^{41} +9.52299e34 q^{42} +1.13992e35 q^{43} +1.19583e35 q^{44} -1.39616e35 q^{45} -9.47425e35 q^{46} +2.48937e35 q^{47} -9.81577e35 q^{48} +4.50812e36 q^{49} -2.72998e36 q^{50} +5.90718e35 q^{51} +2.88873e36 q^{52} +3.93516e36 q^{53} -2.03759e37 q^{54} +1.70023e37 q^{55} -4.16271e37 q^{56} -2.01003e37 q^{57} +8.26415e37 q^{58} +6.06171e37 q^{59} +2.74260e37 q^{60} +3.31999e38 q^{61} -6.28725e38 q^{62} -5.82684e38 q^{63} +9.17655e37 q^{64} +4.10719e38 q^{65} +1.00978e39 q^{66} +2.46431e38 q^{67} +2.53735e38 q^{68} -2.65112e39 q^{69} +5.81582e39 q^{70} -5.22282e39 q^{71} +3.62458e39 q^{72} -1.32868e40 q^{73} +2.16016e39 q^{74} -7.63914e39 q^{75} -8.63380e39 q^{76} +7.09585e40 q^{77} +2.43929e40 q^{78} -1.99325e40 q^{79} -5.99463e40 q^{80} +1.69218e40 q^{81} -2.01932e41 q^{82} -5.56384e39 q^{83} +1.14461e41 q^{84} +3.60760e40 q^{85} +4.13456e41 q^{86} +2.31251e41 q^{87} -4.41397e41 q^{88} -2.64137e41 q^{89} -5.06399e41 q^{90} +1.71412e42 q^{91} -1.13876e42 q^{92} -1.75933e42 q^{93} +9.02914e41 q^{94} -1.22755e42 q^{95} -2.12366e42 q^{96} +3.46950e42 q^{97} +1.63513e43 q^{98} -6.17855e42 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	3.62707e6	1.22296	0.611478	−	0.791261i	$-0.290575\pi$
$2$	3.62707e6	1.22296	0.611478	+	0.791261i	$0.290575\pi$
$3$	1.01494e10	0.560189	0.280094	−	0.959972i	$-0.409634\pi$
$3$	1.01494e10	0.560189	0.280094	+	0.959972i	$0.409634\pi$
$4$	4.35955e12	0.495624
$5$	6.19839e14	0.581332	0.290666	−	0.956825i	$-0.406123\pi$
$5$	6.19839e14	0.581332	0.290666	+	0.956825i	$0.406123\pi$
$6$	3.68127e16	0.685087
$7$	2.58688e18	1.75052	0.875262	−	0.483650i	$-0.160689\pi$
$7$	2.58688e18	1.75052	0.875262	+	0.483650i	$0.160689\pi$
$8$	−1.60917e19	−0.616831
$9$	−2.25246e20	−0.686188
$10$	2.24820e21	0.710944
$11$	2.74302e22	1.11760	0.558800	−	0.829303i	$-0.311262\pi$
$11$	2.74302e22	1.11760	0.558800	+	0.829303i	$0.311262\pi$
$12$	4.42469e22	0.277643
$13$	6.62621e23	0.743846	0.371923	−	0.928264i	$-0.378698\pi$
$13$	6.62621e23	0.743846	0.371923	+	0.928264i	$0.378698\pi$
$14$	9.38279e24	2.14081
$15$	6.29101e24	0.325656
$16$	−9.67126e25	−1.24998
$17$	5.82021e25	0.204309	0.102154	−	0.994769i	$-0.467426\pi$
$17$	5.82021e25	0.204309	0.102154	+	0.994769i	$0.467426\pi$
$18$	−8.16984e26	−0.839179
$19$	−1.98043e27	−0.636147	−0.318074	−	0.948066i	$-0.603036\pi$
$19$	−1.98043e27	−0.636147	−0.318074	+	0.948066i	$0.603036\pi$
$20$	2.70222e27	0.288122
$21$	2.62553e28	0.980624
$22$	9.94913e28	1.36678
$23$	−2.61209e29	−1.37988	−0.689938	−	0.723868i	$-0.742362\pi$
$23$	−2.61209e29	−1.37988	−0.689938	+	0.723868i	$0.742362\pi$
$24$	−1.63321e29	−0.345542
$25$	−7.52667e29	−0.662053
$26$	2.40337e30	0.909692
$27$	−5.61774e30	−0.944584
$28$	1.12776e31	0.867601
$29$	2.27846e31	0.824300	0.412150	−	0.911116i	$-0.364778\pi$
$29$	2.27846e31	0.824300	0.412150	+	0.911116i	$0.364778\pi$
$30$	2.28180e31	0.398263
$31$	−1.73342e32	−1.49496	−0.747478	−	0.664287i	$-0.768735\pi$
$31$	−1.73342e32	−1.49496	−0.747478	+	0.664287i	$0.768735\pi$
$32$	−2.09240e32	−0.911842
$33$	2.78401e32	0.626067
$34$	2.11103e32	0.249861
$35$	1.60345e33	1.01763
$36$	−9.81972e32	−0.340091
$37$	5.95565e32	0.114444	0.0572218	−	0.998361i	$-0.481776\pi$
$37$	5.95565e32	0.114444	0.0572218	+	0.998361i	$0.481776\pi$
$38$	−7.18317e33	−0.777981
$39$	6.72522e33	0.416694
$40$	−9.97424e33	−0.358583
$41$	−5.56734e34	−1.17705	−0.588525	−	0.808479i	$-0.700291\pi$
$41$	−5.56734e34	−1.17705	−0.588525	+	0.808479i	$0.700291\pi$
$42$	9.52299e34	1.19926
$43$	1.13992e35	0.865568	0.432784	−	0.901498i	$-0.357531\pi$
$43$	1.13992e35	0.865568	0.432784	+	0.901498i	$0.357531\pi$
$44$	1.19583e35	0.553909
$45$	−1.39616e35	−0.398903
$46$	−9.47425e35	−1.68753
$47$	2.48937e35	0.279246	0.139623	−	0.990205i	$-0.455411\pi$
$47$	2.48937e35	0.279246	0.139623	+	0.990205i	$0.455411\pi$
$48$	−9.81577e35	−0.700225
$49$	4.50812e36	2.06433
$50$	−2.72998e36	−0.809663
$51$	5.90718e35	0.114451
$52$	2.88873e36	0.368668
$53$	3.93516e36	0.333451	0.166725	−	0.986003i	$-0.446681\pi$
$53$	3.93516e36	0.333451	0.166725	+	0.986003i	$0.446681\pi$
$54$	−2.03759e37	−1.15519
$55$	1.70023e37	0.649696
$56$	−4.16271e37	−1.07978
$57$	−2.01003e37	−0.356363
$58$	8.26415e37	1.00808
$59$	6.06171e37	0.512009	0.256004	−	0.966676i	$-0.417594\pi$
$59$	6.06171e37	0.512009	0.256004	+	0.966676i	$0.417594\pi$
$60$	2.74260e37	0.161403
$61$	3.31999e38	1.36945	0.684724	−	0.728802i	$-0.259923\pi$
$61$	3.31999e38	1.36945	0.684724	+	0.728802i	$0.259923\pi$
$62$	−6.28725e38	−1.82827
$63$	−5.82684e38	−1.20119
$64$	9.17655e37	0.134837
$65$	4.10719e38	0.432422
$66$	1.00978e39	0.765653
$67$	2.46431e38	0.135234	0.0676172	−	0.997711i	$-0.478460\pi$
$67$	2.46431e38	0.135234	0.0676172	+	0.997711i	$0.478460\pi$
$68$	2.53735e38	0.101260
$69$	−2.65112e39	−0.772991
$70$	5.81582e39	1.24452
$71$	−5.22282e39	−0.823855	−0.411927	−	0.911217i	$-0.635144\pi$
$71$	−5.22282e39	−0.823855	−0.411927	+	0.911217i	$0.635144\pi$
$72$	3.62458e39	0.423262
$73$	−1.32868e40	−1.15340	−0.576699	−	0.816957i	$-0.695659\pi$
$73$	−1.32868e40	−1.15340	−0.576699	+	0.816957i	$0.695659\pi$
$74$	2.16016e39	0.139960
$75$	−7.63914e39	−0.370875
$76$	−8.63380e39	−0.315290
$77$	7.09585e40	1.95638
$78$	2.43929e40	0.509599
$79$	−1.99325e40	−0.316650	−0.158325	−	0.987387i	$-0.550609\pi$
$79$	−1.99325e40	−0.316650	−0.158325	+	0.987387i	$0.550609\pi$
$80$	−5.99463e40	−0.726654
$81$	1.69218e40	0.157043
$82$	−2.01932e41	−1.43948
$83$	−5.56384e39	−0.0305630	−0.0152815	−	0.999883i	$-0.504864\pi$
$83$	−5.56384e39	−0.0305630	−0.0152815	+	0.999883i	$0.504864\pi$
$84$	1.14461e41	0.486020
$85$	3.60760e40	0.118771
$86$	4.13456e41	1.05855
$87$	2.31251e41	0.461764
$88$	−4.41397e41	−0.689369
$89$	−2.64137e41	−0.323552	−0.161776	−	0.986827i	$-0.551722\pi$
$89$	−2.64137e41	−0.323552	−0.161776	+	0.986827i	$0.551722\pi$
$90$	−5.06399e41	−0.487841
$91$	1.71412e42	1.30212
$92$	−1.13876e42	−0.683899
$93$	−1.75933e42	−0.837458
$94$	9.02914e41	0.341505
$95$	−1.22755e42	−0.369813
$96$	−2.12366e42	−0.510804
$97$	3.46950e42	0.667844	0.333922	−	0.942601i	$-0.391628\pi$
$97$	3.46950e42	0.667844	0.333922	+	0.942601i	$0.391628\pi$
$98$	1.63513e43	2.52459
$99$	−6.17855e42	−0.766884
$100$	−3.28129e42	−0.328129
$101$	−1.33544e43	−1.07824	−0.539118	−	0.842230i	$-0.681242\pi$
$101$	−1.33544e43	−1.07824	−0.539118	+	0.842230i	$0.681242\pi$
$102$	2.14258e42	0.139969
$103$	−1.58698e43	−0.840567	−0.420283	−	0.907393i	$-0.638069\pi$
$103$	−1.58698e43	−0.840567	−0.420283	+	0.907393i	$0.638069\pi$
$104$	−1.06627e43	−0.458827
$105$	1.62741e43	0.570068
$106$	1.42731e43	0.407796
$107$	6.39702e43	1.49357	0.746786	−	0.665064i	$-0.231596\pi$
$107$	6.39702e43	1.49357	0.746786	+	0.665064i	$0.231596\pi$
$108$	−2.44908e43	−0.468158
$109$	−4.11078e43	−0.644547	−0.322274	−	0.946647i	$-0.604447\pi$
$109$	−4.11078e43	−0.644547	−0.322274	+	0.946647i	$0.604447\pi$
$110$	6.16686e43	0.794550
$111$	6.04464e42	0.0641101
$112$	−2.50184e44	−2.18812
$113$	2.52895e44	1.82706	0.913532	−	0.406766i	$-0.133343\pi$
$113$	2.52895e44	1.82706	0.913532	+	0.406766i	$0.133343\pi$
$114$	−7.29051e43	−0.435816
$115$	−1.61908e44	−0.802166
$116$	9.93308e43	0.408542
$117$	−1.49253e44	−0.510419
$118$	2.19863e44	0.626164
$119$	1.50562e44	0.357647
$120$	−1.01233e44	−0.200874
$121$	1.50015e44	0.249028
$122$	1.20418e45	1.67478
$123$	−5.65053e44	−0.659371
$124$	−7.55695e44	−0.740935
$125$	−1.17121e45	−0.966205
$126$	−2.11344e45	−1.46900
$127$	6.08493e44	0.356841	0.178421	−	0.983954i	$-0.442901\pi$
$127$	6.08493e44	0.356841	0.178421	+	0.983954i	$0.442901\pi$
$128$	2.17333e45	1.07674
$129$	1.15695e45	0.484882
$130$	1.48971e45	0.528833
$131$	1.63203e45	0.491356	0.245678	−	0.969351i	$-0.420989\pi$
$131$	1.63203e45	0.491356	0.245678	+	0.969351i	$0.420989\pi$
$132$	1.21370e45	0.310293
$133$	−5.12314e45	−1.11359
$134$	8.93823e44	0.165386
$135$	−3.48210e45	−0.549117
$136$	−9.36568e44	−0.126024
$137$	4.99784e45	0.574500	0.287250	−	0.957856i	$-0.407259\pi$
$137$	4.99784e45	0.574500	0.287250	+	0.957856i	$0.407259\pi$
$138$	−9.61582e45	−0.945335
$139$	7.86097e44	0.0661695	0.0330847	−	0.999453i	$-0.489467\pi$
$139$	7.86097e44	0.0661695	0.0330847	+	0.999453i	$0.489467\pi$
$140$	6.99032e45	0.504364
$141$	2.52657e45	0.156430
$142$	−1.89435e46	−1.00754
$143$	1.81758e46	0.831322
$144$	2.17841e46	0.857722
$145$	1.41228e46	0.479192
$146$	−4.81922e46	−1.41056
$147$	4.57548e46	1.15642
$148$	2.59639e45	0.0567210
$149$	−2.89598e46	−0.547382	−0.273691	−	0.961818i	$-0.588244\pi$
$149$	−2.89598e46	−0.547382	−0.273691	+	0.961818i	$0.588244\pi$
$150$	−2.77077e46	−0.453564
$151$	−1.31169e47	−1.86135	−0.930675	−	0.365847i	$-0.880779\pi$
$151$	−1.31169e47	−1.86135	−0.930675	+	0.365847i	$0.880779\pi$
$152$	3.18684e46	0.392395
$153$	−1.31098e46	−0.140194
$154$	2.57372e47	2.39257
$155$	−1.07444e47	−0.869066
$156$	2.93190e46	0.206524
$157$	2.40050e47	1.47387	0.736935	−	0.675964i	$-0.236272\pi$
$157$	2.40050e47	1.47387	0.736935	+	0.675964i	$0.236272\pi$
$158$	−7.22967e46	−0.387250
$159$	3.99396e46	0.186795
$160$	−1.29695e47	−0.530083
$161$	−6.75716e47	−2.41551
$162$	6.13766e46	0.192057
$163$	4.76715e47	1.30685	0.653425	−	0.756991i	$-0.273332\pi$
$163$	4.76715e47	1.30685	0.653425	+	0.756991i	$0.273332\pi$
$164$	−2.42711e47	−0.583374
$165$	1.72564e47	0.363953
$166$	−2.01805e46	−0.0373772
$167$	6.00740e47	0.977873	0.488936	−	0.872320i	$-0.337385\pi$
$167$	6.00740e47	0.977873	0.488936	+	0.872320i	$0.337385\pi$
$168$	−4.22491e47	−0.604879
$169$	−3.54465e47	−0.446693
$170$	1.30850e47	0.145252
$171$	4.46085e47	0.436517
$172$	4.96952e47	0.428996
$173$	5.43885e47	0.414491	0.207246	−	0.978289i	$-0.433550\pi$
$173$	5.43885e47	0.414491	0.207246	+	0.978289i	$0.433550\pi$
$174$	8.38764e47	0.564717
$175$	−1.94706e48	−1.15894
$176$	−2.65284e48	−1.39698
$177$	6.15229e47	0.286822
$178$	−9.58045e47	−0.395691
$179$	1.67643e48	0.613828	0.306914	−	0.951737i	$-0.400704\pi$
$179$	1.67643e48	0.613828	0.306914	+	0.951737i	$0.400704\pi$
$180$	−6.08665e47	−0.197706
$181$	−3.59480e48	−1.03654	−0.518269	−	0.855218i	$-0.673423\pi$
$181$	−3.59480e48	−1.03654	−0.518269	+	0.855218i	$0.673423\pi$
$182$	6.21723e48	1.59244
$183$	3.36960e48	0.767150
$184$	4.20329e48	0.851150
$185$	3.69154e47	0.0665298
$186$	−6.38120e48	−1.02417
$187$	1.59650e48	0.228335
$188$	1.08526e48	0.138401
$189$	−1.45324e49	−1.65352
$190$	−4.45241e48	−0.452265
$191$	5.26498e47	0.0477727	0.0238863	−	0.999715i	$-0.492396\pi$
$191$	5.26498e47	0.0477727	0.0238863	+	0.999715i	$0.492396\pi$
$192$	9.31367e47	0.0755343
$193$	1.27068e48	0.0921625	0.0460813	−	0.998938i	$-0.485327\pi$
$193$	1.27068e48	0.0921625	0.0460813	+	0.998938i	$0.485327\pi$
$194$	1.25841e49	0.816745
$195$	4.16856e48	0.242238
$196$	1.96534e49	1.02313
$197$	−5.67999e48	−0.265048	−0.132524	−	0.991180i	$-0.542308\pi$
$197$	−5.67999e48	−0.265048	−0.132524	+	0.991180i	$0.542308\pi$
$198$	−2.24100e49	−0.937866
$199$	4.85226e48	0.182223	0.0911115	−	0.995841i	$-0.470958\pi$
$199$	4.85226e48	0.182223	0.0911115	+	0.995841i	$0.470958\pi$
$200$	1.21117e49	0.408375
$201$	2.50113e48	0.0757568
$202$	−4.84372e49	−1.31864
$203$	5.89410e49	1.44296
$204$	2.57527e48	0.0567248
$205$	−3.45086e49	−0.684257
$206$	−5.75610e49	−1.02798
$207$	5.88364e49	0.946855
$208$	−6.40838e49	−0.929794
$209$	−5.43237e49	−0.710958
$210$	5.90272e49	0.697168
$211$	9.39783e49	1.00220	0.501101	−	0.865389i	$-0.332929\pi$
$211$	9.39783e49	1.00220	0.501101	+	0.865389i	$0.332929\pi$
$212$	1.71555e49	0.165266
$213$	−5.30086e49	−0.461514
$214$	2.32024e50	1.82657
$215$	7.06565e49	0.503182
$216$	9.03987e49	0.582648
$217$	−4.48415e50	−2.61695
$218$	−1.49101e50	−0.788254
$219$	−1.34853e50	−0.646120
$220$	7.41225e49	0.322005
$221$	3.85659e49	0.151974
$222$	2.19243e49	0.0784039
$223$	3.04735e50	0.989391	0.494695	−	0.869066i	$-0.335280\pi$
$223$	3.04735e50	0.989391	0.494695	+	0.869066i	$0.335280\pi$
$224$	−5.41277e50	−1.59620
$225$	1.69535e50	0.454293
$226$	9.17269e50	2.23442
$227$	−5.39198e49	−0.119452	−0.0597259	−	0.998215i	$-0.519023\pi$
$227$	−5.39198e49	−0.119452	−0.0597259	+	0.998215i	$0.519023\pi$
$228$	−8.76281e49	−0.176622
$229$	−7.10477e49	−0.130343	−0.0651714	−	0.997874i	$-0.520759\pi$
$229$	−7.10477e49	−0.130343	−0.0651714	+	0.997874i	$0.520759\pi$
$230$	−5.87251e50	−0.981015
$231$	7.20188e50	1.09594
$232$	−3.66642e50	−0.508453
$233$	−4.35161e50	−0.550171	−0.275086	−	0.961420i	$-0.588706\pi$
$233$	−4.35161e50	−0.550171	−0.275086	+	0.961420i	$0.588706\pi$
$234$	−5.41351e50	−0.624220
$235$	1.54301e50	0.162334
$236$	2.64264e50	0.253764
$237$	−2.02304e50	−0.177384
$238$	5.46098e50	0.437387
$239$	5.98898e50	0.438327	0.219164	−	0.975688i	$-0.429667\pi$
$239$	5.98898e50	0.438327	0.219164	+	0.975688i	$0.429667\pi$
$240$	−6.08420e50	−0.407063
$241$	−2.41674e51	−1.47864	−0.739320	−	0.673354i	$-0.764853\pi$
$241$	−2.41674e51	−1.47864	−0.739320	+	0.673354i	$0.764853\pi$
$242$	5.44114e50	0.304551
$243$	2.01581e51	1.03256
$244$	1.44737e51	0.678731
$245$	2.79431e51	1.20006
$246$	−2.04949e51	−0.806382
$247$	−1.31228e51	−0.473196
$248$	2.78937e51	0.922135
$249$	−5.64698e49	−0.0171210
$250$	−4.24806e51	−1.18163
$251$	−1.10770e51	−0.282774	−0.141387	−	0.989954i	$-0.545156\pi$
$251$	−1.10770e51	−0.282774	−0.141387	+	0.989954i	$0.545156\pi$
$252$	−2.54024e51	−0.595337
$253$	−7.16502e51	−1.54215
$254$	2.20705e51	0.436402
$255$	3.66150e50	0.0665343
$256$	7.07565e51	1.18197
$257$	5.71497e51	0.877914	0.438957	−	0.898508i	$-0.355348\pi$
$257$	5.71497e51	0.877914	0.438957	+	0.898508i	$0.355348\pi$
$258$	4.19634e51	0.592989
$259$	1.54065e51	0.200336
$260$	1.79055e51	0.214318
$261$	−5.13215e51	−0.565625
$262$	5.91951e51	0.600908
$263$	−8.60748e51	−0.805058	−0.402529	−	0.915407i	$-0.631869\pi$
$263$	−8.60748e51	−0.805058	−0.402529	+	0.915407i	$0.631869\pi$
$264$	−4.47993e51	−0.386177
$265$	2.43917e51	0.193845
$266$	−1.85820e52	−1.36187
$267$	−2.68084e51	−0.181250
$268$	1.07433e51	0.0670254
$269$	3.31536e52	1.90922	0.954612	−	0.297853i	$-0.0962705\pi$
$269$	3.31536e52	1.90922	0.954612	+	0.297853i	$0.0962705\pi$
$270$	−1.26298e52	−0.671546
$271$	−1.65260e52	−0.811575	−0.405787	−	0.913968i	$-0.633003\pi$
$271$	−1.65260e52	−0.811575	−0.405787	+	0.913968i	$0.633003\pi$
$272$	−5.62888e51	−0.255382
$273$	1.73973e52	0.729433
$274$	1.81275e52	0.702589
$275$	−2.06458e52	−0.739910
$276$	−1.15577e52	−0.383113
$277$	3.44644e52	1.05695	0.528476	−	0.848948i	$-0.322763\pi$
$277$	3.44644e52	1.05695	0.528476	+	0.848948i	$0.322763\pi$
$278$	2.85123e51	0.0809224
$279$	3.90447e52	1.02582
$280$	−2.58021e52	−0.627708
$281$	−1.84357e52	−0.415406	−0.207703	−	0.978192i	$-0.566599\pi$
$281$	−1.84357e52	−0.415406	−0.207703	+	0.978192i	$0.566599\pi$
$282$	9.16406e51	0.191307
$283$	−2.27219e52	−0.439579	−0.219790	−	0.975547i	$-0.570537\pi$
$283$	−2.27219e52	−0.439579	−0.219790	+	0.975547i	$0.570537\pi$
$284$	−2.27692e52	−0.408322
$285$	−1.24589e52	−0.207165
$286$	6.59250e52	1.01667
$287$	−1.44020e53	−2.06045
$288$	4.71304e52	0.625696
$289$	−7.77653e52	−0.958258
$290$	5.12245e52	0.586031
$291$	3.52135e52	0.374119
$292$	−5.79245e52	−0.571651
$293$	2.15060e53	1.97200	0.985999	−	0.166752i	$-0.0533278\pi$
$293$	2.15060e53	1.97200	0.985999	+	0.166752i	$0.0533278\pi$
$294$	1.65956e53	1.41425
$295$	3.75729e52	0.297647
$296$	−9.58362e51	−0.0705924
$297$	−1.54096e53	−1.05567
$298$	−1.05039e53	−0.669424
$299$	−1.73083e53	−1.02642
$300$	−3.33032e52	−0.183814
$301$	2.94882e53	1.51520
$302$	−4.75761e53	−2.27635
$303$	−1.35539e53	−0.604015
$304$	1.91533e53	0.795172
$305$	2.05786e53	0.796104
$306$	−4.75502e52	−0.171452
$307$	2.45017e53	0.823609	0.411804	−	0.911272i	$-0.364899\pi$
$307$	2.45017e53	0.823609	0.411804	+	0.911272i	$0.364899\pi$
$308$	3.09347e53	0.969630
$309$	−1.61070e53	−0.470876
$310$	−3.89709e53	−1.06283
$311$	2.63881e53	0.671522	0.335761	−	0.941947i	$-0.391007\pi$
$311$	2.63881e53	0.671522	0.335761	+	0.941947i	$0.391007\pi$
$312$	−1.08220e53	−0.257030
$313$	−1.59181e53	−0.352930	−0.176465	−	0.984307i	$-0.556466\pi$
$313$	−1.59181e53	−0.352930	−0.176465	+	0.984307i	$0.556466\pi$
$314$	8.70678e53	1.80248
$315$	−3.61171e53	−0.698289
$316$	−8.68969e52	−0.156939
$317$	−6.66397e53	−1.12450	−0.562249	−	0.826968i	$-0.690064\pi$
$317$	−6.66397e53	−1.12450	−0.562249	+	0.826968i	$0.690064\pi$
$318$	1.44864e53	0.228443
$319$	6.24987e53	0.921237
$320$	5.68799e52	0.0783852
$321$	6.49260e53	0.836683
$322$	−2.45087e54	−2.95406
$323$	−1.15265e53	−0.129970
$324$	7.37715e52	0.0778342
$325$	−4.98733e53	−0.492466
$326$	1.72908e54	1.59822
$327$	−4.17221e53	−0.361068
$328$	8.95878e53	0.726041
$329$	6.43971e53	0.488826
$330$	6.25901e53	0.445098
$331$	−1.10752e53	−0.0737991	−0.0368996	−	0.999319i	$-0.511748\pi$
$331$	−1.10752e53	−0.0737991	−0.0368996	+	0.999319i	$0.511748\pi$
$332$	−2.42559e52	−0.0151477
$333$	−1.34149e53	−0.0785299
$334$	2.17893e54	1.19590
$335$	1.52748e53	0.0786161
$336$	−2.53922e54	−1.22576
$337$	−4.25604e54	−1.92736	−0.963680	−	0.267061i	$-0.913948\pi$
$337$	−4.25604e54	−1.92736	−0.963680	+	0.267061i	$0.913948\pi$
$338$	−1.28567e54	−0.546286
$339$	2.56674e54	1.02350
$340$	1.57275e53	0.0588658
$341$	−4.75482e54	−1.67076
$342$	1.61798e54	0.533841
$343$	6.01268e54	1.86314
$344$	−1.83431e54	−0.533909
$345$	−1.64327e54	−0.449365
$346$	1.97271e54	0.506905
$347$	4.53734e54	1.09577	0.547883	−	0.836555i	$-0.315434\pi$
$347$	4.53734e54	1.09577	0.547883	+	0.836555i	$0.315434\pi$
$348$	1.00815e54	0.228861
$349$	8.33491e54	1.77891	0.889455	−	0.457022i	$-0.151084\pi$
$349$	8.33491e54	1.77891	0.889455	+	0.457022i	$0.151084\pi$
$350$	−7.06212e54	−1.41733
$351$	−3.72243e54	−0.702625
$352$	−5.73949e54	−1.01907
$353$	−2.09801e53	−0.0350471	−0.0175235	−	0.999846i	$-0.505578\pi$
$353$	−2.09801e53	−0.0350471	−0.0175235	+	0.999846i	$0.505578\pi$
$354$	2.23148e54	0.350770
$355$	−3.23731e54	−0.478933
$356$	−1.15152e54	−0.160360
$357$	1.52811e54	0.200350
$358$	6.08055e54	0.750685
$359$	4.45690e53	0.0518206	0.0259103	−	0.999664i	$-0.491752\pi$
$359$	4.45690e53	0.0518206	0.0259103	+	0.999664i	$0.491752\pi$
$360$	2.24666e54	0.246056
$361$	−5.76969e54	−0.595317
$362$	−1.30386e55	−1.26764
$363$	1.52256e54	0.139503
$364$	7.47279e54	0.645362
$365$	−8.23569e54	−0.670507
$366$	1.22218e55	0.938191
$367$	−1.43102e55	−1.03591	−0.517957	−	0.855406i	$-0.673307\pi$
$367$	−1.43102e55	−1.03591	−0.517957	+	0.855406i	$0.673307\pi$
$368$	2.52622e55	1.72482
$369$	1.25402e55	0.807679
$370$	1.33895e54	0.0813630
$371$	1.01798e55	0.583713
$372$	−7.66987e54	−0.415064
$373$	−1.98870e55	−1.01585	−0.507925	−	0.861401i	$-0.669587\pi$
$373$	−1.98870e55	−1.01585	−0.507925	+	0.861401i	$0.669587\pi$
$374$	5.79060e54	0.279244
$375$	−1.18871e55	−0.541257
$376$	−4.00582e54	−0.172247
$377$	1.50976e55	0.613152
$378$	−5.27100e55	−2.02218
$379$	−1.23931e55	−0.449197	−0.224599	−	0.974451i	$-0.572107\pi$
$379$	−1.23931e55	−0.449197	−0.224599	+	0.974451i	$0.572107\pi$
$380$	−5.35157e54	−0.183288
$381$	6.17585e54	0.199899
$382$	1.90965e54	0.0584239
$383$	3.56358e55	1.03066	0.515328	−	0.856993i	$-0.327670\pi$
$383$	3.56358e55	1.03066	0.515328	+	0.856993i	$0.327670\pi$
$384$	2.20581e55	0.603179
$385$	4.39829e55	1.13731
$386$	4.60885e54	0.112711
$387$	−2.56762e55	−0.593943
$388$	1.51255e55	0.330999
$389$	1.74666e55	0.361653	0.180827	−	0.983515i	$-0.442123\pi$
$389$	1.74666e55	0.361653	0.180827	+	0.983515i	$0.442123\pi$
$390$	1.51197e55	0.296246
$391$	−1.52029e55	−0.281921
$392$	−7.25430e55	−1.27334
$393$	1.65642e55	0.275252
$394$	−2.06017e55	−0.324142
$395$	−1.23550e55	−0.184079
$396$	−2.69357e55	−0.380086
$397$	−3.61165e55	−0.482736	−0.241368	−	0.970434i	$-0.577596\pi$
$397$	−3.61165e55	−0.482736	−0.241368	+	0.970434i	$0.577596\pi$
$398$	1.75995e55	0.222851
$399$	−5.19969e55	−0.623821
$400$	7.27924e55	0.827554
$401$	1.08123e56	1.16497	0.582483	−	0.812843i	$-0.302081\pi$
$401$	1.08123e56	1.16497	0.582483	+	0.812843i	$0.302081\pi$
$402$	9.07179e54	0.0926473
$403$	−1.14860e56	−1.11202
$404$	−5.82190e55	−0.534399
$405$	1.04888e55	0.0912941
$406$	2.13783e56	1.76467
$407$	1.63365e55	0.127902
$408$	−9.50563e54	−0.0705972
$409$	−4.80971e55	−0.338897	−0.169448	−	0.985539i	$-0.554199\pi$
$409$	−4.80971e55	−0.338897	−0.169448	+	0.985539i	$0.554199\pi$
$410$	−1.25165e56	−0.836817
$411$	5.07252e55	0.321829
$412$	−6.91854e55	−0.416605
$413$	1.56809e56	0.896283
$414$	2.13404e56	1.15796
$415$	−3.44869e54	−0.0177672
$416$	−1.38647e56	−0.678270
$417$	7.97843e54	0.0370674
$418$	−1.97036e56	−0.869471
$419$	−4.52052e56	−1.89490	−0.947451	−	0.319900i	$-0.896351\pi$
$419$	−4.52052e56	−1.89490	−0.947451	+	0.319900i	$0.896351\pi$
$420$	7.09477e55	0.282539
$421$	−1.37281e56	−0.519453	−0.259727	−	0.965682i	$-0.583632\pi$
$421$	−1.37281e56	−0.519453	−0.259727	+	0.965682i	$0.583632\pi$
$422$	3.40866e56	1.22565
$423$	−5.60722e55	−0.191615
$424$	−6.33233e55	−0.205682
$425$	−4.38068e55	−0.135263
$426$	−1.92266e56	−0.564412
$427$	8.58841e56	2.39725
$428$	2.78881e56	0.740250
$429$	1.84474e56	0.465697
$430$	2.56276e56	0.615370
$431$	−1.97671e56	−0.451524	−0.225762	−	0.974182i	$-0.572487\pi$
$431$	−1.97671e56	−0.451524	−0.225762	+	0.974182i	$0.572487\pi$
$432$	5.43306e56	1.18071
$433$	−5.20903e56	−1.07713	−0.538563	−	0.842585i	$-0.681033\pi$
$433$	−5.20903e56	−1.07713	−0.538563	+	0.842585i	$0.681033\pi$
$434$	−1.62643e57	−3.20042
$435$	1.43338e56	0.268438
$436$	−1.79212e56	−0.319453
$437$	5.17307e56	0.877805
$438$	−4.89123e56	−0.790177
$439$	8.78281e56	1.35097	0.675486	−	0.737373i	$-0.263934\pi$
$439$	8.78281e56	1.35097	0.675486	+	0.737373i	$0.263934\pi$
$440$	−2.73595e56	−0.400752
$441$	−1.01544e57	−1.41652
$442$	1.39881e56	0.185858
$443$	7.62338e56	0.964867	0.482433	−	0.875933i	$-0.339753\pi$
$443$	7.62338e56	0.964867	0.482433	+	0.875933i	$0.339753\pi$
$444$	2.63519e55	0.0317745
$445$	−1.63723e56	−0.188091
$446$	1.10530e57	1.20998
$447$	−2.93925e56	−0.306637
$448$	2.37386e56	0.236036
$449$	3.22300e56	0.305467	0.152734	−	0.988267i	$-0.451192\pi$
$449$	3.22300e56	0.305467	0.152734	+	0.988267i	$0.451192\pi$
$450$	6.14917e56	0.555581
$451$	−1.52713e57	−1.31547
$452$	1.10251e57	0.905537
$453$	−1.33129e57	−1.04271
$454$	−1.95571e56	−0.146084
$455$	1.06248e57	0.756964
$456$	3.23446e56	0.219815
$457$	−3.49540e56	−0.226620	−0.113310	−	0.993560i	$-0.536145\pi$
$457$	−3.49540e56	−0.226620	−0.113310	+	0.993560i	$0.536145\pi$
$458$	−2.57695e56	−0.159404
$459$	−3.26964e56	−0.192987
$460$	−7.05846e56	−0.397572
$461$	−1.01829e57	−0.547397	−0.273699	−	0.961816i	$-0.588247\pi$
$461$	−1.01829e57	−0.547397	−0.273699	+	0.961816i	$0.588247\pi$
$462$	2.61217e57	1.34029
$463$	−1.12662e57	−0.551807	−0.275903	−	0.961185i	$-0.588977\pi$
$463$	−1.12662e57	−0.551807	−0.275903	+	0.961185i	$0.588977\pi$
$464$	−2.20356e57	−1.03036
$465$	−1.09050e57	−0.486841
$466$	−1.57836e57	−0.672835
$467$	4.32781e57	1.76180	0.880898	−	0.473307i	$-0.156940\pi$
$467$	4.32781e57	1.76180	0.880898	+	0.473307i	$0.156940\pi$
$468$	−6.50675e56	−0.252976
$469$	6.37487e56	0.236731
$470$	5.59662e56	0.198528
$471$	2.43637e57	0.825645
$472$	−9.75430e56	−0.315823
$473$	3.12681e57	0.967358
$474$	−7.33770e56	−0.216933
$475$	1.49061e57	0.421163
$476$	6.56381e56	0.177258
$477$	−8.86380e56	−0.228810
$478$	2.17225e57	0.536055
$479$	−5.08788e57	−1.20039	−0.600196	−	0.799853i	$-0.704911\pi$
$479$	−5.08788e57	−1.20039	−0.600196	+	0.799853i	$0.704911\pi$
$480$	−1.31633e57	−0.296947
$481$	3.94634e56	0.0851285
$482$	−8.76567e57	−1.80831
$483$	−6.85813e57	−1.35314
$484$	6.53997e56	0.123424
$485$	2.15054e57	0.388239
$486$	7.31148e57	1.26277
$487$	1.44042e57	0.238022	0.119011	−	0.992893i	$-0.462028\pi$
$487$	1.44042e57	0.238022	0.119011	+	0.992893i	$0.462028\pi$
$488$	−5.34242e57	−0.844718
$489$	4.83839e57	0.732083
$490$	1.01352e58	1.46762
$491$	5.96607e57	0.826868	0.413434	−	0.910534i	$-0.364329\pi$
$491$	5.96607e57	0.826868	0.413434	+	0.910534i	$0.364329\pi$
$492$	−2.46338e57	−0.326800
$493$	1.32611e57	0.168412
$494$	−4.75972e57	−0.578698
$495$	−3.82971e57	−0.445814
$496$	1.67644e58	1.86867
$497$	−1.35108e58	−1.44218
$498$	−2.04820e56	−0.0209383
$499$	−1.54904e58	−1.51670	−0.758350	−	0.651848i	$-0.773994\pi$
$499$	−1.54904e58	−1.51670	−0.758350	+	0.651848i	$0.773994\pi$
$500$	−5.10595e57	−0.478874
$501$	6.09716e57	0.547793
$502$	−4.01772e57	−0.345820
$503$	2.17882e58	1.79684	0.898420	−	0.439137i	$-0.144716\pi$
$503$	2.17882e58	1.79684	0.898420	+	0.439137i	$0.144716\pi$
$504$	9.37635e57	0.740930
$505$	−8.27756e57	−0.626813
$506$	−2.59880e58	−1.88598
$507$	−3.59761e57	−0.250232
$508$	2.65275e57	0.176859
$509$	2.00199e58	1.27947	0.639734	−	0.768596i	$-0.279044\pi$
$509$	2.00199e58	1.27947	0.639734	+	0.768596i	$0.279044\pi$
$510$	1.32805e57	0.0813686
$511$	−3.43713e58	−2.01905
$512$	6.54706e57	0.368759
$513$	1.11256e58	0.600895
$514$	2.07286e58	1.07365
$515$	−9.83675e57	−0.488648
$516$	5.04378e57	0.240319
$517$	6.82840e57	0.312085
$518$	5.58806e57	0.245003
$519$	5.52012e57	0.232193
$520$	−6.60914e57	−0.266731
$521$	4.15960e58	1.61080	0.805398	−	0.592735i	$-0.201952\pi$
$521$	4.15960e58	1.61080	0.805398	+	0.592735i	$0.201952\pi$
$522$	−1.86147e58	−0.691735
$523$	−1.32108e58	−0.471131	−0.235565	−	0.971858i	$-0.575694\pi$
$523$	−1.32108e58	−0.471131	−0.235565	+	0.971858i	$0.575694\pi$
$524$	7.11494e57	0.243528
$525$	−1.97615e58	−0.649225
$526$	−3.12199e58	−0.984552
$527$	−1.00889e58	−0.305433
$528$	−2.69249e58	−0.782571
$529$	3.23962e58	0.904059
$530$	8.84704e57	0.237065
$531$	−1.36538e58	−0.351334
$532$	−2.23346e58	−0.551922
$533$	−3.68904e58	−0.875545
$534$	−9.72360e57	−0.221661
$535$	3.96512e58	0.868261
$536$	−3.96548e57	−0.0834167
$537$	1.70149e58	0.343859
$538$	1.20250e59	2.33490
$539$	1.23659e59	2.30710
$540$	−1.51804e58	−0.272155
$541$	−6.56868e58	−1.13171	−0.565857	−	0.824503i	$-0.691455\pi$
$541$	−6.56868e58	−1.13171	−0.565857	+	0.824503i	$0.691455\pi$
$542$	−5.99410e58	−0.992521
$543$	−3.64851e58	−0.580657
$544$	−1.21782e58	−0.186297
$545$	−2.54803e58	−0.374696
$546$	6.31013e58	0.892065
$547$	−3.35920e58	−0.456571	−0.228286	−	0.973594i	$-0.573312\pi$
$547$	−3.35920e58	−0.456571	−0.228286	+	0.973594i	$0.573312\pi$
$548$	2.17883e58	0.284736
$549$	−7.47815e58	−0.939699
$550$	−7.48838e58	−0.904878
$551$	−4.51234e58	−0.524376
$552$	4.26610e58	0.476805
$553$	−5.15630e58	−0.554304
$554$	1.25005e59	1.29261
$555$	3.74671e57	0.0372692
$556$	3.42703e57	0.0327952
$557$	−7.51741e57	−0.0692120	−0.0346060	−	0.999401i	$-0.511018\pi$
$557$	−7.51741e57	−0.0692120	−0.0346060	+	0.999401i	$0.511018\pi$
$558$	1.41618e59	1.25454
$559$	7.55333e58	0.643850
$560$	−1.55074e59	−1.27202
$561$	1.62035e58	0.127911
$562$	−6.68675e58	−0.508024
$563$	−3.08360e58	−0.225490	−0.112745	−	0.993624i	$-0.535964\pi$
$563$	−3.08360e58	−0.225490	−0.112745	+	0.993624i	$0.535964\pi$
$564$	1.10147e58	0.0775305
$565$	1.56754e59	1.06213
$566$	−8.24141e58	−0.537586
$567$	4.37746e58	0.274907
$568$	8.40438e58	0.508179
$569$	−1.05318e59	−0.613179	−0.306590	−	0.951842i	$-0.599188\pi$
$569$	−1.05318e59	−0.613179	−0.306590	+	0.951842i	$0.599188\pi$
$570$	−4.51894e58	−0.253354
$571$	2.73679e59	1.47763	0.738814	−	0.673910i	$-0.235386\pi$
$571$	2.73679e59	1.47763	0.738814	+	0.673910i	$0.235386\pi$
$572$	7.92384e58	0.412023
$573$	5.34365e57	0.0267617
$574$	−5.22372e59	−2.51985
$575$	1.96604e59	0.913552
$576$	−2.06698e58	−0.0925238
$577$	−2.69178e59	−1.16081	−0.580403	−	0.814330i	$-0.697105\pi$
$577$	−2.69178e59	−1.16081	−0.580403	+	0.814330i	$0.697105\pi$
$578$	−2.82060e59	−1.17191
$579$	1.28967e58	0.0516284
$580$	6.15691e58	0.237499
$581$	−1.43930e58	−0.0535012
$582$	1.27722e59	0.457531
$583$	1.07942e59	0.372664
$584$	2.13807e59	0.711451
$585$	−9.25128e58	−0.296723
$586$	7.80039e59	2.41167
$587$	−5.77693e59	−1.72178	−0.860890	−	0.508790i	$-0.830093\pi$
$587$	−5.77693e59	−1.72178	−0.860890	+	0.508790i	$0.830093\pi$
$588$	1.99470e59	0.573147
$589$	3.43293e59	0.951012
$590$	1.36280e59	0.364009
$591$	−5.76487e58	−0.148477
$592$	−5.75986e58	−0.143052
$593$	−2.43327e58	−0.0582793	−0.0291396	−	0.999575i	$-0.509277\pi$
$593$	−2.43327e58	−0.0582793	−0.0291396	+	0.999575i	$0.509277\pi$
$594$	−5.58916e59	−1.29103
$595$	9.33241e58	0.207912
$596$	−1.26252e59	−0.271295
$597$	4.92477e58	0.102079
$598$	−6.27784e59	−1.25526
$599$	−3.96268e59	−0.764386	−0.382193	−	0.924083i	$-0.624831\pi$
$599$	−3.96268e59	−0.764386	−0.382193	+	0.924083i	$0.624831\pi$
$600$	1.22926e59	0.228767
$601$	−3.77157e59	−0.677207	−0.338603	−	0.940929i	$-0.609954\pi$
$601$	−3.77157e59	−0.677207	−0.338603	+	0.940929i	$0.609954\pi$
$602$	1.06956e60	1.85302
$603$	−5.55077e58	−0.0927963
$604$	−5.71839e59	−0.922529
$605$	9.29851e58	0.144768
$606$	−4.91610e59	−0.738685
$607$	7.51902e59	1.09045	0.545223	−	0.838291i	$-0.316445\pi$
$607$	7.51902e59	1.09045	0.545223	+	0.838291i	$0.316445\pi$
$608$	4.14385e59	0.580066
$609$	5.98218e59	0.808328
$610$	7.46401e59	0.973601
$611$	1.64951e59	0.207716
$612$	−5.71528e58	−0.0694836
$613$	−1.39353e60	−1.63575	−0.817876	−	0.575395i	$-0.804848\pi$
$613$	−1.39353e60	−1.63575	−0.817876	+	0.575395i	$0.804848\pi$
$614$	8.88693e59	1.00724
$615$	−3.50242e59	−0.383313
$616$	−1.14184e60	−1.20676
$617$	1.43273e60	1.46229	0.731146	−	0.682221i	$-0.238986\pi$
$617$	1.43273e60	1.46229	0.731146	+	0.682221i	$0.238986\pi$
$618$	−5.84212e59	−0.575861
$619$	−1.09264e60	−1.04022	−0.520112	−	0.854098i	$-0.674110\pi$
$619$	−1.09264e60	−1.04022	−0.520112	+	0.854098i	$0.674110\pi$
$620$	−4.68410e59	−0.430729
$621$	1.46741e60	1.30341
$622$	9.57116e59	0.821242
$623$	−6.83291e59	−0.566386
$624$	−6.50414e59	−0.520860
$625$	1.29722e59	0.100368
$626$	−5.77361e59	−0.431618
$627$	−5.51354e59	−0.398271
$628$	1.04651e60	0.730485
$629$	3.46631e58	0.0233818
$630$	−1.30999e60	−0.853978
$631$	−5.43638e59	−0.342514	−0.171257	−	0.985226i	$-0.554783\pi$
$631$	−5.43638e59	−0.342514	−0.171257	+	0.985226i	$0.554783\pi$
$632$	3.20747e59	0.195320
$633$	9.53826e59	0.561422
$634$	−2.41707e60	−1.37521
$635$	3.77168e59	0.207443
$636$	1.74119e59	0.0925801
$637$	2.98717e60	1.53555
$638$	2.26687e60	1.12663
$639$	1.17642e60	0.565320
$640$	1.34712e60	0.625945
$641$	−3.34810e60	−1.50436	−0.752179	−	0.658959i	$-0.770997\pi$
$641$	−3.34810e60	−1.50436	−0.752179	+	0.658959i	$0.770997\pi$
$642$	2.35491e60	1.02323
$643$	7.77539e59	0.326728	0.163364	−	0.986566i	$-0.447766\pi$
$643$	7.77539e59	0.326728	0.163364	+	0.986566i	$0.447766\pi$
$644$	−2.94582e60	−1.19718
$645$	7.17123e59	0.281877
$646$	−4.18076e59	−0.158948
$647$	−3.09018e60	−1.13643	−0.568214	−	0.822881i	$-0.692365\pi$
$647$	−3.09018e60	−1.13643	−0.568214	+	0.822881i	$0.692365\pi$
$648$	−2.72300e59	−0.0968689
$649$	1.66274e60	0.572220
$650$	−1.80894e60	−0.602265
$651$	−4.55116e60	−1.46599
$652$	2.07826e60	0.647706
$653$	−6.18136e60	−1.86402	−0.932010	−	0.362433i	$-0.881946\pi$
$653$	−6.18136e60	−1.86402	−0.932010	+	0.362433i	$0.881946\pi$
$654$	−1.51329e60	−0.441571
$655$	1.01160e60	0.285641
$656$	5.38432e60	1.47129
$657$	2.99280e60	0.791448
$658$	2.33573e60	0.597813
$659$	6.32794e60	1.56757	0.783784	−	0.621034i	$-0.213287\pi$
$659$	6.32794e60	1.56757	0.783784	+	0.621034i	$0.213287\pi$
$660$	7.52300e59	0.180383
$661$	−1.18734e60	−0.275577	−0.137789	−	0.990462i	$-0.543999\pi$
$661$	−1.18734e60	−0.275577	−0.137789	+	0.990462i	$0.543999\pi$
$662$	−4.01707e59	−0.0902531
$663$	3.91422e59	0.0851343
$664$	8.95314e58	0.0188522
$665$	−3.17552e60	−0.647366
$666$	−4.86567e59	−0.0960387
$667$	−5.95156e60	−1.13743
$668$	2.61896e60	0.484657
$669$	3.09289e60	0.554246
$670$	5.54027e59	0.0961441
$671$	9.10680e60	1.53049
$672$	−5.49365e60	−0.894174
$673$	−5.49460e60	−0.866188	−0.433094	−	0.901349i	$-0.642578\pi$
$673$	−5.49460e60	−0.866188	−0.433094	+	0.901349i	$0.642578\pi$
$674$	−1.54370e61	−2.35708
$675$	4.22829e60	0.625365
$676$	−1.54531e60	−0.221391
$677$	−5.42453e59	−0.0752845	−0.0376423	−	0.999291i	$-0.511985\pi$
$677$	−5.42453e59	−0.0752845	−0.0376423	+	0.999291i	$0.511985\pi$
$678$	9.30975e60	1.25170
$679$	8.97518e60	1.16908
$680$	−5.80522e59	−0.0732617
$681$	−5.47255e59	−0.0669156
$682$	−1.72461e61	−2.04327
$683$	−2.55176e60	−0.292951	−0.146475	−	0.989214i	$-0.546793\pi$
$683$	−2.55176e60	−0.292951	−0.146475	+	0.989214i	$0.546793\pi$
$684$	1.94473e60	0.216348
$685$	3.09786e60	0.333975
$686$	2.18084e61	2.27854
$687$	−7.21094e59	−0.0730166
$688$	−1.10244e61	−1.08194
$689$	2.60752e60	0.248036
$690$	−5.96026e60	−0.549553
$691$	1.08476e61	0.969518	0.484759	−	0.874648i	$-0.338907\pi$
$691$	1.08476e61	0.969518	0.484759	+	0.874648i	$0.338907\pi$
$692$	2.37109e60	0.205432
$693$	−1.59831e61	−1.34245
$694$	1.64573e61	1.34007
$695$	4.87254e59	0.0384664
$696$	−3.72121e60	−0.284830
$697$	−3.24031e60	−0.240482
$698$	3.02313e61	2.17553
$699$	−4.41663e60	−0.308200
$700$	−8.48830e60	−0.574398
$701$	−2.44763e61	−1.60623	−0.803116	−	0.595822i	$-0.796826\pi$
$701$	−2.44763e61	−1.60623	−0.803116	+	0.595822i	$0.796826\pi$
$702$	−1.35015e61	−0.859281
$703$	−1.17948e60	−0.0728030
$704$	2.51714e60	0.150694
$705$	1.56607e60	0.0909379
$706$	−7.60964e59	−0.0428610
$707$	−3.45461e61	−1.88748
$708$	2.68212e60	0.142156
$709$	1.87862e61	0.965929	0.482965	−	0.875640i	$-0.339560\pi$
$709$	1.87862e61	0.965929	0.482965	+	0.875640i	$0.339560\pi$
$710$	−1.17420e61	−0.585715
$711$	4.48973e60	0.217282
$712$	4.25041e60	0.199577
$713$	4.52786e61	2.06285
$714$	5.54258e60	0.245019
$715$	1.12661e61	0.483274
$716$	7.30850e60	0.304228
$717$	6.07847e60	0.245546
$718$	1.61655e60	0.0633744
$719$	2.37257e61	0.902710	0.451355	−	0.892345i	$-0.350941\pi$
$719$	2.37257e61	0.902710	0.451355	+	0.892345i	$0.350941\pi$
$720$	1.35027e61	0.498621
$721$	−4.10533e61	−1.47143
$722$	−2.09271e61	−0.728047
$723$	−2.45285e61	−0.828318
$724$	−1.56717e61	−0.513732
$725$	−1.71493e61	−0.545730
$726$	5.52245e60	0.170606
$727$	1.81553e61	0.544518	0.272259	−	0.962224i	$-0.412229\pi$
$727$	1.81553e61	0.544518	0.272259	+	0.962224i	$0.412229\pi$
$728$	−2.75830e61	−0.803188
$729$	1.49046e61	0.421384
$730$	−2.98714e61	−0.820001
$731$	6.63455e60	0.176843
$732$	1.46899e61	0.380217
$733$	1.31563e61	0.330672	0.165336	−	0.986237i	$-0.447129\pi$
$733$	1.31563e61	0.330672	0.165336	+	0.986237i	$0.447129\pi$
$734$	−5.19040e61	−1.26688
$735$	2.83606e61	0.672261
$736$	5.46554e61	1.25823
$737$	6.75965e60	0.151138
$738$	4.54843e61	0.987756
$739$	−5.98405e61	−1.26223	−0.631117	−	0.775688i	$-0.717403\pi$
$739$	−5.98405e61	−1.26223	−0.631117	+	0.775688i	$0.717403\pi$
$740$	1.60935e60	0.0329737
$741$	−1.33189e61	−0.265079
$742$	3.69228e61	0.713856
$743$	−5.00463e60	−0.0939967	−0.0469983	−	0.998895i	$-0.514966\pi$
$743$	−5.00463e60	−0.0939967	−0.0469983	+	0.998895i	$0.514966\pi$
$744$	2.83105e61	0.516570
$745$	−1.79504e61	−0.318210
$746$	−7.21316e61	−1.24234
$747$	1.25323e60	0.0209720
$748$	6.96000e60	0.113168
$749$	1.65483e62	2.61453
$750$	−4.31153e61	−0.661934
$751$	−3.12943e61	−0.466881	−0.233441	−	0.972371i	$-0.574998\pi$
$751$	−3.12943e61	−0.466881	−0.233441	+	0.972371i	$0.574998\pi$
$752$	−2.40754e61	−0.349052
$753$	−1.12426e61	−0.158407
$754$	5.47600e61	0.749859
$755$	−8.13039e61	−1.08206
$756$	−6.33547e61	−0.819522
$757$	1.08176e62	1.36010	0.680048	−	0.733167i	$-0.261959\pi$
$757$	1.08176e62	1.36010	0.680048	+	0.733167i	$0.261959\pi$
$758$	−4.49507e61	−0.549349
$759$	−7.27209e61	−0.863895
$760$	1.97533e61	0.228112
$761$	−6.63216e61	−0.744535	−0.372268	−	0.928125i	$-0.621420\pi$
$761$	−6.63216e61	−0.744535	−0.372268	+	0.928125i	$0.621420\pi$
$762$	2.24002e61	0.244467
$763$	−1.06341e62	−1.12830
$764$	2.29530e60	0.0236773
$765$	−8.12597e60	−0.0814994
$766$	1.29254e62	1.26045
$767$	4.01662e61	0.380856
$768$	7.18138e61	0.662128
$769$	−6.68870e61	−0.599688	−0.299844	−	0.953988i	$-0.596935\pi$
$769$	−6.68870e61	−0.599688	−0.299844	+	0.953988i	$0.596935\pi$
$770$	1.59529e62	1.39088
$771$	5.80037e61	0.491797
$772$	5.53960e60	0.0456779
$773$	−4.99608e61	−0.400655	−0.200327	−	0.979729i	$-0.564201\pi$
$773$	−4.99608e61	−0.400655	−0.200327	+	0.979729i	$0.564201\pi$
$774$	−9.31293e61	−0.726366
$775$	1.30469e62	0.989740
$776$	−5.58301e61	−0.411947
$777$	1.56367e61	0.112226
$778$	6.33526e61	0.442286
$779$	1.10258e62	0.748778
$780$	1.81730e61	0.120059
$781$	−1.43263e62	−0.920740
$782$	−5.51421e61	−0.344777
$783$	−1.27998e62	−0.778620
$784$	−4.35992e62	−2.58037
$785$	1.48792e62	0.856807
$786$	6.00796e61	0.336622
$787$	−2.83453e62	−1.54534	−0.772671	−	0.634806i	$-0.781080\pi$
$787$	−2.83453e62	−1.54534	−0.772671	+	0.634806i	$0.781080\pi$
$788$	−2.47622e61	−0.131364
$789$	−8.73610e61	−0.450985
$790$	−4.48124e61	−0.225121
$791$	6.54209e62	3.19832
$792$	9.94230e61	0.473037
$793$	2.19990e62	1.01866
$794$	−1.30997e62	−0.590365
$795$	2.47562e61	0.108590
$796$	2.11537e61	0.0903140
$797$	4.08442e61	0.169737	0.0848685	−	0.996392i	$-0.472953\pi$
$797$	4.08442e61	0.169737	0.0848685	+	0.996392i	$0.472953\pi$
$798$	−1.88596e62	−0.762906
$799$	1.44887e61	0.0570523
$800$	1.57488e62	0.603688
$801$	5.94959e61	0.222018
$802$	3.92169e62	1.42470
$803$	−3.64460e62	−1.28904
$804$	1.09038e61	0.0375469
$805$	−4.18836e62	−1.40421
$806$	−4.16607e62	−1.35995
$807$	3.36490e62	1.06953
$808$	2.14894e62	0.665089
$809$	−2.70018e62	−0.813765	−0.406882	−	0.913481i	$-0.633384\pi$
$809$	−2.70018e62	−0.813765	−0.406882	+	0.913481i	$0.633384\pi$
$810$	3.80436e61	0.111649
$811$	4.07164e61	0.116365	0.0581823	−	0.998306i	$-0.481470\pi$
$811$	4.07164e61	0.116365	0.0581823	+	0.998306i	$0.481470\pi$
$812$	2.56957e62	0.715163
$813$	−1.67730e62	−0.454635
$814$	5.92535e61	0.156419
$815$	2.95487e62	0.759713
$816$	−5.71299e61	−0.143062
$817$	−2.25753e62	−0.550629
$818$	−1.74451e62	−0.414456
$819$	−3.86099e62	−0.893500
$820$	−1.50442e62	−0.339134
$821$	−4.97093e62	−1.09159	−0.545795	−	0.837919i	$-0.683772\pi$
$821$	−4.97093e62	−1.09159	−0.545795	+	0.837919i	$0.683772\pi$
$822$	1.83984e62	0.393582
$823$	7.87730e62	1.64165	0.820826	−	0.571179i	$-0.193514\pi$
$823$	7.87730e62	1.64165	0.820826	+	0.571179i	$0.193514\pi$
$824$	2.55372e62	0.518487
$825$	−2.09543e62	−0.414489
$826$	5.68758e62	1.09612
$827$	−7.36002e62	−1.38201	−0.691004	−	0.722851i	$-0.742831\pi$
$827$	−7.36002e62	−1.38201	−0.691004	+	0.722851i	$0.742831\pi$
$828$	2.56500e62	0.469284
$829$	3.97702e62	0.708983	0.354491	−	0.935059i	$-0.384654\pi$
$829$	3.97702e62	0.708983	0.354491	+	0.935059i	$0.384654\pi$
$830$	−1.25086e61	−0.0217286
$831$	3.49794e62	0.592093
$832$	6.08058e61	0.100298
$833$	2.62382e62	0.421761
$834$	2.89383e61	0.0453318
$835$	3.72362e62	0.568468
$836$	−2.36827e62	−0.352367
$837$	9.73792e62	1.41211
$838$	−1.63962e63	−2.31738
$839$	−6.29957e62	−0.867818	−0.433909	−	0.900957i	$-0.642866\pi$
$839$	−6.29957e62	−0.867818	−0.433909	+	0.900957i	$0.642866\pi$
$840$	−2.61877e62	−0.351635
$841$	−2.44896e62	−0.320530
$842$	−4.97929e62	−0.635269
$843$	−1.87111e62	−0.232706
$844$	4.09703e62	0.496715
$845$	−2.19711e62	−0.259677
$846$	−2.03378e62	−0.234337
$847$	3.88070e62	0.435930
$848$	−3.80580e62	−0.416807
$849$	−2.30615e62	−0.246247
$850$	−1.58890e62	−0.165421
$851$	−1.55567e62	−0.157918
$852$	−2.31094e62	−0.228737
$853$	1.37710e63	1.32911	0.664557	−	0.747238i	$-0.268620\pi$
$853$	1.37710e63	1.32911	0.664557	+	0.747238i	$0.268620\pi$
$854$	3.11508e63	2.93173
$855$	2.76501e62	0.253761
$856$	−1.02939e63	−0.921281
$857$	6.27513e62	0.547690	0.273845	−	0.961774i	$-0.411704\pi$
$857$	6.27513e62	0.547690	0.273845	+	0.961774i	$0.411704\pi$
$858$	6.69101e62	0.569528
$859$	−1.57268e63	−1.30553	−0.652767	−	0.757559i	$-0.726392\pi$
$859$	−1.57268e63	−1.30553	−0.652767	+	0.757559i	$0.726392\pi$
$860$	3.08031e62	0.249389
$861$	−1.46172e63	−1.15424
$862$	−7.16966e62	−0.552195
$863$	1.77472e63	1.33321	0.666603	−	0.745413i	$-0.267748\pi$
$863$	1.77472e63	1.33321	0.666603	+	0.745413i	$0.267748\pi$
$864$	1.17545e63	0.861311
$865$	3.37121e62	0.240957
$866$	−1.88935e63	−1.31728
$867$	−7.89273e62	−0.536805
$868$	−1.95489e63	−1.29702
$869$	−5.46753e62	−0.353888
$870$	5.19899e62	0.328288
$871$	1.63290e62	0.100594
$872$	6.61493e62	0.397577
$873$	−7.81492e62	−0.458267
$874$	1.87631e63	1.07352
$875$	−3.02977e63	−1.69136
$876$	−5.87900e62	−0.320233
$877$	1.15736e62	0.0615147	0.0307573	−	0.999527i	$-0.490208\pi$
$877$	1.15736e62	0.0615147	0.0307573	+	0.999527i	$0.490208\pi$
$878$	3.18559e63	1.65218
$879$	2.18274e63	1.10469
$880$	−1.64434e63	−0.812108
$881$	3.96934e63	1.91310	0.956548	−	0.291576i	$-0.0941798\pi$
$881$	3.96934e63	1.91310	0.956548	+	0.291576i	$0.0941798\pi$
$882$	−3.68306e63	−1.73234
$883$	−1.37793e63	−0.632515	−0.316258	−	0.948673i	$-0.602426\pi$
$883$	−1.37793e63	−0.632515	−0.316258	+	0.948673i	$0.602426\pi$
$884$	1.68130e62	0.0753220
$885$	3.81343e62	0.166738
$886$	2.76505e63	1.17999
$887$	−3.36758e63	−1.40268	−0.701341	−	0.712826i	$-0.747415\pi$
$887$	−3.36758e63	−1.40268	−0.701341	+	0.712826i	$0.747415\pi$
$888$	−9.72682e61	−0.0395451
$889$	1.57410e63	0.624659
$890$	−5.93834e62	−0.230028
$891$	4.64168e62	0.175511
$892$	1.32851e63	0.490365
$893$	−4.93004e62	−0.177641
$894$	−1.06609e63	−0.375004
$895$	1.03912e63	0.356838
$896$	5.62214e63	1.88486
$897$	−1.75669e63	−0.574987
$898$	1.16901e63	0.373573
$899$	−3.94954e63	−1.23229
$900$	7.39098e62	0.225158
$901$	2.29035e62	0.0681268
$902$	−5.53902e63	−1.60876
$903$	2.99289e63	0.848796
$904$	−4.06950e63	−1.12699
$905$	−2.22820e63	−0.602572
$906$	−4.82870e63	−1.27519
$907$	−3.22814e63	−0.832522	−0.416261	−	0.909245i	$-0.636660\pi$
$907$	−3.22814e63	−0.832522	−0.416261	+	0.909245i	$0.636660\pi$
$908$	−2.35066e62	−0.0592031
$909$	3.00802e63	0.739873
$910$	3.85369e63	0.925734
$911$	6.66803e63	1.56442	0.782208	−	0.623017i	$-0.214093\pi$
$911$	6.66803e63	1.56442	0.782208	+	0.623017i	$0.214093\pi$
$912$	1.94395e63	0.445446
$913$	−1.52617e62	−0.0341572
$914$	−1.26781e63	−0.277147
$915$	2.08861e63	0.445969
$916$	−3.09736e62	−0.0646010
$917$	4.22187e63	0.860131
$918$	−1.18592e63	−0.236014
$919$	3.12159e63	0.606866	0.303433	−	0.952853i	$-0.401867\pi$
$919$	3.12159e63	0.606866	0.303433	+	0.952853i	$0.401867\pi$
$920$	2.60536e63	0.494801
$921$	2.48678e63	0.461376
$922$	−3.69342e63	−0.669443
$923$	−3.46075e63	−0.612822
$924$	3.13970e63	0.543176
$925$	−4.48262e62	−0.0757678
$926$	−4.08634e63	−0.674836
$927$	3.57462e63	0.576787
$928$	−4.76745e63	−0.751631
$929$	−1.01789e64	−1.56806	−0.784028	−	0.620725i	$-0.786838\pi$
$929$	−1.01789e64	−1.56806	−0.784028	+	0.620725i	$0.786838\pi$
$930$	−3.95532e63	−0.595385
$931$	−8.92802e63	−1.31322
$932$	−1.89711e63	−0.272678
$933$	2.67824e63	0.376179
$934$	1.56973e64	2.15460
$935$	9.89571e62	0.132739
$936$	2.40173e63	0.314842
$937$	−5.70526e63	−0.730928	−0.365464	−	0.930826i	$-0.619090\pi$
$937$	−5.70526e63	−0.730928	−0.365464	+	0.930826i	$0.619090\pi$
$938$	2.31221e63	0.289512
$939$	−1.61560e63	−0.197707
$940$	6.72684e62	0.0804567
$941$	−1.04360e64	−1.22000	−0.609999	−	0.792402i	$-0.708830\pi$
$941$	−1.04360e64	−1.22000	−0.609999	+	0.792402i	$0.708830\pi$
$942$	8.83688e63	1.00973
$943$	1.45424e64	1.62418
$944$	−5.86244e63	−0.640001
$945$	−9.00775e63	−0.961242
$946$	1.13412e64	1.18304
$947$	1.40457e64	1.43225	0.716124	−	0.697973i	$-0.245914\pi$
$947$	1.40457e64	1.43225	0.716124	+	0.697973i	$0.245914\pi$
$948$	−8.81954e62	−0.0879157
$949$	−8.80412e63	−0.857951
$950$	5.40654e63	0.515065
$951$	−6.76354e63	−0.629931
$952$	−2.42279e63	−0.220608
$953$	−5.00331e63	−0.445410	−0.222705	−	0.974886i	$-0.571489\pi$
$953$	−5.00331e63	−0.445410	−0.222705	+	0.974886i	$0.571489\pi$
$954$	−3.21496e63	−0.279825
$955$	3.26344e62	0.0277718
$956$	2.61093e63	0.217245
$957$	6.34326e63	0.516067
$958$	−1.84541e64	−1.46803
$959$	1.29288e64	1.00568
$960$	5.77298e62	0.0439105
$961$	1.66028e64	1.23489
$962$	1.43136e63	0.104109
$963$	−1.44090e64	−1.02487
$964$	−1.05359e64	−0.732849
$965$	7.87618e62	0.0535770
$966$	−2.48749e64	−1.65483
$967$	1.23774e64	0.805307	0.402654	−	0.915352i	$-0.368088\pi$
$967$	1.23774e64	0.805307	0.402654	+	0.915352i	$0.368088\pi$
$968$	−2.41399e63	−0.153608
$969$	−1.16988e63	−0.0728080
$970$	7.80015e63	0.474800
$971$	−6.90009e63	−0.410810	−0.205405	−	0.978677i	$-0.565851\pi$
$971$	−6.90009e63	−0.410810	−0.205405	+	0.978677i	$0.565851\pi$
$972$	8.78802e63	0.511760
$973$	2.03353e63	0.115831
$974$	5.22452e63	0.291091
$975$	−5.06186e63	−0.275874
$976$	−3.21085e64	−1.71178
$977$	2.22048e64	1.15801	0.579006	−	0.815323i	$-0.303441\pi$
$977$	2.22048e64	1.15801	0.579006	+	0.815323i	$0.303441\pi$
$978$	1.75492e64	0.895306
$979$	−7.24534e63	−0.361602
$980$	1.21819e64	0.594779
$981$	9.25938e63	0.442281
$982$	2.16394e64	1.01122
$983$	8.17397e63	0.373708	0.186854	−	0.982388i	$-0.440171\pi$
$983$	8.17397e63	0.373708	0.186854	+	0.982388i	$0.440171\pi$
$984$	9.09264e63	0.406720
$985$	−3.52068e63	−0.154081
$986$	4.80991e63	0.205960
$987$	6.53593e63	0.273835
$988$	−5.72094e63	−0.234527
$989$	−2.97757e64	−1.19438
$990$	−1.38906e64	−0.545211
$991$	−3.43882e64	−1.32077	−0.660383	−	0.750929i	$-0.729606\pi$
$991$	−3.43882e64	−1.32077	−0.660383	+	0.750929i	$0.729606\pi$
$992$	3.62701e64	1.36316
$993$	−1.12407e63	−0.0413414
$994$	−4.90046e64	−1.76372
$995$	3.00762e63	0.105932
$996$	−2.46183e62	−0.00848560
$997$	−2.06533e64	−0.696697	−0.348349	−	0.937365i	$-0.613257\pi$
$997$	−2.06533e64	−0.696697	−0.348349	+	0.937365i	$0.613257\pi$
$998$	−5.61846e64	−1.85486
$999$	−3.34573e63	−0.108102

Twists

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

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

\(f(q)\)	\(=\)	\(q+3.62707e6 q^{2} +1.01494e10 q^{3} +4.35955e12 q^{4} +6.19839e14 q^{5} +3.68127e16 q^{6} +2.58688e18 q^{7} -1.60917e19 q^{8} -2.25246e20 q^{9} +O(q^{10})\)	\(q+3.62707e6 q^{2} +1.01494e10 q^{3} +4.35955e12 q^{4} +6.19839e14 q^{5} +3.68127e16 q^{6} +2.58688e18 q^{7} -1.60917e19 q^{8} -2.25246e20 q^{9} +2.24820e21 q^{10} +2.74302e22 q^{11} +4.42469e22 q^{12} +6.62621e23 q^{13} +9.38279e24 q^{14} +6.29101e24 q^{15} -9.67126e25 q^{16} +5.82021e25 q^{17} -8.16984e26 q^{18} -1.98043e27 q^{19} +2.70222e27 q^{20} +2.62553e28 q^{21} +9.94913e28 q^{22} -2.61209e29 q^{23} -1.63321e29 q^{24} -7.52667e29 q^{25} +2.40337e30 q^{26} -5.61774e30 q^{27} +1.12776e31 q^{28} +2.27846e31 q^{29} +2.28180e31 q^{30} -1.73342e32 q^{31} -2.09240e32 q^{32} +2.78401e32 q^{33} +2.11103e32 q^{34} +1.60345e33 q^{35} -9.81972e32 q^{36} +5.95565e32 q^{37} -7.18317e33 q^{38} +6.72522e33 q^{39} -9.97424e33 q^{40} -5.56734e34 q^{41} +9.52299e34 q^{42} +1.13992e35 q^{43} +1.19583e35 q^{44} -1.39616e35 q^{45} -9.47425e35 q^{46} +2.48937e35 q^{47} -9.81577e35 q^{48} +4.50812e36 q^{49} -2.72998e36 q^{50} +5.90718e35 q^{51} +2.88873e36 q^{52} +3.93516e36 q^{53} -2.03759e37 q^{54} +1.70023e37 q^{55} -4.16271e37 q^{56} -2.01003e37 q^{57} +8.26415e37 q^{58} +6.06171e37 q^{59} +2.74260e37 q^{60} +3.31999e38 q^{61} -6.28725e38 q^{62} -5.82684e38 q^{63} +9.17655e37 q^{64} +4.10719e38 q^{65} +1.00978e39 q^{66} +2.46431e38 q^{67} +2.53735e38 q^{68} -2.65112e39 q^{69} +5.81582e39 q^{70} -5.22282e39 q^{71} +3.62458e39 q^{72} -1.32868e40 q^{73} +2.16016e39 q^{74} -7.63914e39 q^{75} -8.63380e39 q^{76} +7.09585e40 q^{77} +2.43929e40 q^{78} -1.99325e40 q^{79} -5.99463e40 q^{80} +1.69218e40 q^{81} -2.01932e41 q^{82} -5.56384e39 q^{83} +1.14461e41 q^{84} +3.60760e40 q^{85} +4.13456e41 q^{86} +2.31251e41 q^{87} -4.41397e41 q^{88} -2.64137e41 q^{89} -5.06399e41 q^{90} +1.71412e42 q^{91} -1.13876e42 q^{92} -1.75933e42 q^{93} +9.02914e41 q^{94} -1.22755e42 q^{95} -2.12366e42 q^{96} +3.46950e42 q^{97} +1.63513e43 q^{98} -6.17855e42 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 2209944 q^{2} + 24401437812 q^{3} + 9822618421824 q^{4} + 535205380774170 q^{5} - 91\!\cdots\!24 q^{6}+ \cdots + 47\!\cdots\!31 q^{9}+O(q^{10}) \) 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

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