LMFDB - Embedded newform 2.52.a.a.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2,52,Mod(1,2)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2, base_ring=CyclotomicField(1))

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

N = Newforms(chi, 52, names="a")

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

chi := DirichletCharacter("2.1");

S:= CuspForms(chi, 52);

N := Newforms(S);

Level:	$ N $	$=$	$ 2 $
Weight:	$ k $	$=$	$ 52 $
Character orbit:	$[\chi]$	$=$	2.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$32.9462706828$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\mathbb{Q}[x]/(x^{2} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 126606928812 $ x^2 - x - 126606928812
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{8}\cdot 3\cdot 5^{2}\cdot 17 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-355818.$ of defining polynomial
Character	$\chi$	$=$	2.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.35544e7 q^{2} +2.06801e12 q^{3} +1.12590e15 q^{4} -1.04818e18 q^{5} -6.93910e19 q^{6} -3.66463e21 q^{7} -3.77789e22 q^{8} +2.12298e24 q^{9} +O(q^{10})$	\(q-3.35544e7 q^{2} +2.06801e12 q^{3} +1.12590e15 q^{4} -1.04818e18 q^{5} -6.93910e19 q^{6} -3.66463e21 q^{7} -3.77789e22 q^{8} +2.12298e24 q^{9} +3.51711e25 q^{10} +1.59060e25 q^{11} +2.32837e27 q^{12} +3.56652e28 q^{13} +1.22965e29 q^{14} -2.16765e30 q^{15} +1.26765e30 q^{16} -2.66976e31 q^{17} -7.12354e31 q^{18} +5.44923e32 q^{19} -1.18015e33 q^{20} -7.57851e33 q^{21} -5.33716e32 q^{22} +9.27808e34 q^{23} -7.81273e34 q^{24} +6.54592e35 q^{25} -1.19672e36 q^{26} -6.35188e34 q^{27} -4.12601e36 q^{28} -1.09592e37 q^{29} +7.27342e37 q^{30} +1.02630e38 q^{31} -4.25353e37 q^{32} +3.28937e37 q^{33} +8.95823e38 q^{34} +3.84120e39 q^{35} +2.39026e39 q^{36} +6.63338e39 q^{37} -1.82846e40 q^{38} +7.37560e40 q^{39} +3.95991e40 q^{40} +1.12343e41 q^{41} +2.54292e41 q^{42} -4.52684e41 q^{43} +1.79085e40 q^{44} -2.22526e42 q^{45} -3.11321e42 q^{46} +2.08213e42 q^{47} +2.62152e42 q^{48} +8.40282e41 q^{49} -2.19645e43 q^{50} -5.52110e43 q^{51} +4.01554e43 q^{52} +9.74215e43 q^{53} +2.13134e42 q^{54} -1.66723e43 q^{55} +1.38446e44 q^{56} +1.12691e45 q^{57} +3.67729e44 q^{58} -8.85579e44 q^{59} -2.44056e45 q^{60} +5.77115e45 q^{61} -3.44370e45 q^{62} -7.77994e45 q^{63} +1.42725e45 q^{64} -3.73835e46 q^{65} -1.10373e45 q^{66} +3.60128e46 q^{67} -3.00588e46 q^{68} +1.91872e47 q^{69} -1.28889e47 q^{70} -1.74751e46 q^{71} -8.02039e46 q^{72} +1.78289e47 q^{73} -2.22579e47 q^{74} +1.35370e48 q^{75} +6.13529e47 q^{76} -5.82896e46 q^{77} -2.47484e48 q^{78} -4.78329e47 q^{79} -1.32873e48 q^{80} -4.70360e48 q^{81} -3.76961e48 q^{82} +6.61867e47 q^{83} -8.53264e48 q^{84} +2.79839e49 q^{85} +1.51895e49 q^{86} -2.26637e49 q^{87} -6.00911e47 q^{88} +3.82364e49 q^{89} +7.46675e49 q^{90} -1.30700e50 q^{91} +1.04462e50 q^{92} +2.12240e50 q^{93} -6.98646e49 q^{94} -5.71178e50 q^{95} -8.79635e49 q^{96} +2.27864e49 q^{97} -2.81952e49 q^{98} +3.37681e49 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 67108864 q^{2} + 187290382776 q^{3} + 22\!\cdots\!48 q^{4}+ \cdots + 35\!\cdots\!94 q^{9}+O(q^{10}) $ 2 * q - 67108864 * q^2 + 187290382776 * q^3 + 2251799813685248 * q^4 - 1222737445852282500 * q^5 - 6284422413111263232 * q^6 - 4100377271642428803152 * q^7 - 75557863725914323419136 * q^8 + 3506398323112132655391594 * q^9	$ 2 q - 67108864 q^{2} + 187290382776 q^{3} + 22\!\cdots\!48 q^{4}+ \cdots - 69\!\cdots\!12 q^{99}+O(q^{100}) $ 2 * q - 67108864 * q^2 + 187290382776 * q^3 + 2251799813685248 * q^4 - 1222737445852282500 * q^5 - 6284422413111263232 * q^6 - 4100377271642428803152 * q^7 - 75557863725914323419136 * q^8 + 3506398323112132655391594 * q^9 + 41028260480704095191040000 * q^10 - 511916859296118812642710296 * q^11 + 210870224520017790552244224 * q^12 + 2389767980887171723586110636 * q^13 + 137585830335671405590205169664 * q^14 - 1839354430187803812510967110000 * q^15 + 2535301200456458802993406410752 * q^16 - 38170755374707224218983245478812 * q^17 - 117655204097780083560316674244608 * q^18 - 136117369289850199022410411314920 * q^19 - 1376679976378072874209278689280000 * q^20 - 6758992101020073667714498669814976 * q^21 + 17177079444905186562740562922831872 * q^22 + 82360875483744207844699244747978256 * q^23 - 7075630609481669591875521261600768 * q^24 + 240973064028364917488157674630468750 * q^25 - 80187307210455903271392945480138752 * q^26 + 1385153336120426710614208934265178800 * q^27 - 4616614388161823353220959231539150848 * q^28 - 33433848941184296370650849380528607220 * q^29 + 61718493151635410256239995146731520000 * q^30 + 308835076169577443464575338477040889024 * q^31 - 85070591730234615865843651857942052864 * q^32 + 1025581489016605768622275037376245389152 * q^33 + 1280798015609248074964626419558104694784 * q^34 + 3917257457400276775841278728681725220000 * q^35 + 3947853545345083164778963744406850502656 * q^36 + 10523630739281458197095845856733483317308 * q^37 + 4567341011855166793283936622558513725440 * q^38 + 136337774481417941078653256910482131362768 * q^39 + 46193714653139652548699795548494888960000 * q^40 + 196921516461268471750199128431445042148724 * q^41 + 226794140842215192518316741030397064773632 * q^42 - 436185332310493098065395196254952050932824 * q^43 - 576367144192668828966791952235883296456704 * q^44 - 2466750259163950296521489332322761530652500 * q^45 - 2763572395879762127518827368347393528430592 * q^46 - 5071937001112410134266285842260710712524512 * q^47 + 237418766142971237567054930636937181003776 * q^48 - 11559100479246355218990053936704271423429934 * q^49 - 8085714290771416695041997498666188800000000 * q^50 - 33633211699677626929831102056190930239511056 * q^51 + 2690639547056352295318532134393023104548864 * q^52 + 105529315512706056254590899937168095592592796 * q^53 - 46478033426426001872288151918593412012441600 * q^54 + 75463119614657853791897301419452272509310000 * q^55 + 154907873557797506701664657509452692466958336 * q^56 + 2407756071827149822022303793221962598517371040 * q^57 + 1121853810795240472036850721281189275018199040 * q^58 - 1105487952975610110465550699194488821613128440 * q^59 - 2070928981599016062235107492831332810096640000 * q^60 + 2174583020587510252529691078631554971127524044 * q^61 - 10362785562546906795465937603804852071975354368 * q^62 - 8382756336243902670051269559132648323046912144 * q^63 + 2854495385411919762116571938898990272765493248 * q^64 - 31575047397398129139930605639711933367031335000 * q^65 - 34412804333666445134043861426938684325614321664 * q^66 + 52980256222774625688459101408623680382039369528 * q^67 - 42976449920495453102531459600465894030010482688 * q^68 + 211468773409731513422661817504083539452351739328 * q^69 - 131441348980830483856145429894597398537175040000 * q^70 + 71838794922889018513950754051538223712457615664 * q^71 - 132467983333240509586920533992165045525536571392 * q^72 + 633989662758328739460390107342060538497732058676 * q^73 - 353114452034329417935295157282245408093745709056 * q^74 + 2131605811399349017290662875234578991549903125000 * q^75 - 153254533403105388013903908093949314821343150080 * q^76 + 171706038038113743094982498894497703297304386496 * q^77 - 4574736582868073567503677360581302764027066187776 * q^78 + 1987694552793370941077747858308362884236649620960 * q^79 - 1550003857156178057948973978145874453955870720000 * q^80 - 10407615343628609253811192857082917170490174846318 * q^81 - 6607589633436513569085977641412189328516493344768 * q^82 - 7294964975412571318915019371395141945504236734824 * q^83 - 7609948576888532406722767841366068242946430337024 * q^84 + 29986629004292497369543490180442720795343506195000 * q^85 + 14635951072409843545504634665863443256285979475968 * q^86 + 19604850482371457136774548808933025198099393538640 * q^87 + 19339672146847101120085850819446194030892315312128 * q^88 + 76584790355821941738982505226510313491919750326420 * q^89 + 82770403832099147076010150340149503832495226880000 * q^90 - 116200228922371894653439828143865282695294601882336 * q^91 + 92730102034624558484005821650951568526964365983744 * q^92 - 175573684530170608392805003946795499445900778834688 * q^93 + 170185965212110290206348958186699743875075286237184 * q^94 - 452296986866245785230138918380370612312622071550000 * q^95 - 7966451844068230668899590110321825328262893535232 * q^96 - 299203660839571973887426598893507965282463766755772 * q^97 + 387859051012039237443446873495475779587022927167488 * q^98 - 696432229055306535317133838555495031791652116305912 * 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 $

$2$	−3.35544e7	−0.707107
$2$	−3.35544e7	−0.707107
$3$	2.06801e12	1.40916	0.704581	−	0.709623i	$-0.251135\pi$
$3$	2.06801e12	1.40916	0.704581	+	0.709623i	$0.251135\pi$
$4$	1.12590e15	0.500000
$5$	−1.04818e18	−1.57290	−0.786449	−	0.617655i	$-0.788083\pi$
$5$	−1.04818e18	−1.57290	−0.786449	+	0.617655i	$0.788083\pi$
$6$	−6.93910e19	−0.996428
$7$	−3.66463e21	−1.03283	−0.516417	−	0.856337i	$-0.672735\pi$
$7$	−3.66463e21	−1.03283	−0.516417	+	0.856337i	$0.672735\pi$
$8$	−3.77789e22	−0.353553
$9$	2.12298e24	0.985738
$10$	3.51711e25	1.11221
$11$	1.59060e25	0.0442636	0.0221318	−	0.999755i	$-0.492955\pi$
$11$	1.59060e25	0.0442636	0.0221318	+	0.999755i	$0.492955\pi$
$12$	2.32837e27	0.704581
$13$	3.56652e28	1.40181	0.700905	−	0.713255i	$-0.252780\pi$
$13$	3.56652e28	1.40181	0.700905	+	0.713255i	$0.252780\pi$
$14$	1.22965e29	0.730324
$15$	−2.16765e30	−2.21647
$16$	1.26765e30	0.250000
$17$	−2.66976e31	−1.12208	−0.561042	−	0.827788i	$-0.689599\pi$
$17$	−2.66976e31	−1.12208	−0.561042	+	0.827788i	$0.689599\pi$
$18$	−7.12354e31	−0.697022
$19$	5.44923e32	1.34313	0.671566	−	0.740945i	$-0.265622\pi$
$19$	5.44923e32	1.34313	0.671566	+	0.740945i	$0.265622\pi$
$20$	−1.18015e33	−0.786449
$21$	−7.57851e33	−1.45543
$22$	−5.33716e32	−0.0312991
$23$	9.27808e34	1.75145	0.875726	−	0.482808i	$-0.160383\pi$
$23$	9.27808e34	1.75145	0.875726	+	0.482808i	$0.160383\pi$
$24$	−7.81273e34	−0.498214
$25$	6.54592e35	1.47401
$26$	−1.19672e36	−0.991229
$27$	−6.35188e34	−0.0200968
$28$	−4.12601e36	−0.516417
$29$	−1.09592e37	−0.560569	−0.280285	−	0.959917i	$-0.590429\pi$
$29$	−1.09592e37	−0.560569	−0.280285	+	0.959917i	$0.590429\pi$
$30$	7.27342e37	1.56728
$31$	1.02630e38	0.958411	0.479205	−	0.877703i	$-0.340925\pi$
$31$	1.02630e38	0.958411	0.479205	+	0.877703i	$0.340925\pi$
$32$	−4.25353e37	−0.176777
$33$	3.28937e37	0.0623746
$34$	8.95823e38	0.793433
$35$	3.84120e39	1.62454
$36$	2.39026e39	0.492869
$37$	6.63338e39	0.680128	0.340064	−	0.940402i	$-0.389551\pi$
$37$	6.63338e39	0.680128	0.340064	+	0.940402i	$0.389551\pi$
$38$	−1.82846e40	−0.949738
$39$	7.37560e40	1.97538
$40$	3.95991e40	0.556104
$41$	1.12343e41	0.840539	0.420270	−	0.907399i	$-0.361936\pi$
$41$	1.12343e41	0.840539	0.420270	+	0.907399i	$0.361936\pi$
$42$	2.54292e41	1.02914
$43$	−4.52684e41	−1.00542	−0.502712	−	0.864454i	$-0.667664\pi$
$43$	−4.52684e41	−1.00542	−0.502712	+	0.864454i	$0.667664\pi$
$44$	1.79085e40	0.0221318
$45$	−2.22526e42	−1.55047
$46$	−3.11321e42	−1.23846
$47$	2.08213e42	0.478643	0.239322	−	0.970940i	$-0.423075\pi$
$47$	2.08213e42	0.478643	0.239322	+	0.970940i	$0.423075\pi$
$48$	2.62152e42	0.352291
$49$	8.40282e41	0.0667460
$50$	−2.19645e43	−1.04228
$51$	−5.52110e43	−1.58120
$52$	4.01554e43	0.700905
$53$	9.74215e43	1.04621	0.523106	−	0.852267i	$-0.324773\pi$
$53$	9.74215e43	1.04621	0.523106	+	0.852267i	$0.324773\pi$
$54$	2.13134e42	0.0142106
$55$	−1.66723e43	−0.0696222
$56$	1.38446e44	0.365162
$57$	1.12691e45	1.89269
$58$	3.67729e44	0.396382
$59$	−8.85579e44	−0.617307	−0.308653	−	0.951175i	$-0.599878\pi$
$59$	−8.85579e44	−0.617307	−0.308653	+	0.951175i	$0.599878\pi$
$60$	−2.44056e45	−1.10823
$61$	5.77115e45	1.71930	0.859650	−	0.510883i	$-0.170682\pi$
$61$	5.77115e45	1.71930	0.859650	+	0.510883i	$0.170682\pi$
$62$	−3.44370e45	−0.677699
$63$	−7.77994e45	−1.01810
$64$	1.42725e45	0.125000
$65$	−3.73835e46	−2.20490
$66$	−1.10373e45	−0.0441055
$67$	3.60128e46	0.980730	0.490365	−	0.871517i	$-0.336863\pi$
$67$	3.60128e46	0.980730	0.490365	+	0.871517i	$0.336863\pi$
$68$	−3.00588e46	−0.561042
$69$	1.91872e47	2.46808
$70$	−1.28889e47	−1.14873
$71$	−1.74751e46	−0.108475	−0.0542377	−	0.998528i	$-0.517273\pi$
$71$	−1.74751e46	−0.108475	−0.0542377	+	0.998528i	$0.517273\pi$
$72$	−8.02039e46	−0.348511
$73$	1.78289e47	0.544993	0.272497	−	0.962157i	$-0.412151\pi$
$73$	1.78289e47	0.544993	0.272497	+	0.962157i	$0.412151\pi$
$74$	−2.22579e47	−0.480923
$75$	1.35370e48	2.07712
$76$	6.13529e47	0.671566
$77$	−5.82896e46	−0.0457170
$78$	−2.47484e48	−1.39680
$79$	−4.78329e47	−0.195090	−0.0975451	−	0.995231i	$-0.531099\pi$
$79$	−4.78329e47	−0.195090	−0.0975451	+	0.995231i	$0.531099\pi$
$80$	−1.32873e48	−0.393225
$81$	−4.70360e48	−1.01406
$82$	−3.76961e48	−0.594351
$83$	6.61867e47	0.0766089	0.0383045	−	0.999266i	$-0.487804\pi$
$83$	6.61867e47	0.0766089	0.0383045	+	0.999266i	$0.487804\pi$
$84$	−8.53264e48	−0.727715
$85$	2.79839e49	1.76492
$86$	1.51895e49	0.710942
$87$	−2.26637e49	−0.789933
$88$	−6.00911e47	−0.0156496
$89$	3.82364e49	0.746503	0.373252	−	0.927730i	$-0.378243\pi$
$89$	3.82364e49	0.746503	0.373252	+	0.927730i	$0.378243\pi$
$90$	7.46675e49	1.09635
$91$	−1.30700e50	−1.44784
$92$	1.04462e50	0.875726
$93$	2.12240e50	1.35056
$94$	−6.98646e49	−0.338452
$95$	−5.71178e50	−2.11261
$96$	−8.79635e49	−0.249107
$97$	2.27864e49	0.0495446	0.0247723	−	0.999693i	$-0.492114\pi$
$97$	2.27864e49	0.0495446	0.0247723	+	0.999693i	$0.492114\pi$
$98$	−2.81952e49	−0.0471965
$99$	3.37681e49	0.0436323
$100$	7.37005e50	0.737005
$101$	−2.14712e51	−1.66594	−0.832972	−	0.553315i	$-0.813363\pi$
$101$	−2.14712e51	−1.66594	−0.832972	+	0.553315i	$0.813363\pi$
$102$	1.85257e51	1.11808
$103$	−2.02109e51	−0.951122	−0.475561	−	0.879683i	$-0.657755\pi$
$103$	−2.02109e51	−0.951122	−0.475561	+	0.879683i	$0.657755\pi$
$104$	−1.34739e51	−0.495614
$105$	7.94364e51	2.28924
$106$	−3.26892e51	−0.739784
$107$	3.19036e51	0.568268	0.284134	−	0.958785i	$-0.408294\pi$
$107$	3.19036e51	0.568268	0.284134	+	0.958785i	$0.408294\pi$
$108$	−7.15158e49	−0.0100484
$109$	7.41841e51	0.824015	0.412007	−	0.911180i	$-0.364828\pi$
$109$	7.41841e51	0.824015	0.412007	+	0.911180i	$0.364828\pi$
$110$	5.59430e50	0.0492303
$111$	1.37179e52	0.958411
$112$	−4.64547e51	−0.258208
$113$	−8.79642e51	−0.389767	−0.194884	−	0.980826i	$-0.562433\pi$
$113$	−8.79642e51	−0.389767	−0.194884	+	0.980826i	$0.562433\pi$
$114$	−3.78128e52	−1.33833
$115$	−9.72510e52	−2.75486
$116$	−1.23389e52	−0.280285
$117$	7.57164e52	1.38182
$118$	2.97151e52	0.436502
$119$	9.78370e52	1.15893
$120$	8.18914e52	0.783640
$121$	−1.28877e53	−0.998041
$122$	−1.93648e53	−1.21573
$123$	2.32327e53	1.18446
$124$	1.15551e53	0.479205
$125$	−2.20645e53	−0.745570
$126$	2.61051e53	0.719908
$127$	5.10035e53	1.14975	0.574877	−	0.818240i	$-0.305050\pi$
$127$	5.10035e53	1.14975	0.574877	+	0.818240i	$0.305050\pi$
$128$	−4.78905e52	−0.0883883
$129$	−9.36155e53	−1.41681
$130$	1.25438e54	1.55910
$131$	−6.47085e53	−0.661521	−0.330760	−	0.943715i	$-0.607305\pi$
$131$	−6.47085e53	−0.661521	−0.330760	+	0.943715i	$0.607305\pi$
$132$	3.70351e52	0.0311873
$133$	−1.99694e54	−1.38723
$134$	−1.20839e54	−0.693481
$135$	6.65791e52	0.0316102
$136$	1.00861e54	0.396716
$137$	2.74968e54	0.897238	0.448619	−	0.893723i	$-0.351916\pi$
$137$	2.74968e54	0.897238	0.448619	+	0.893723i	$0.351916\pi$
$138$	−6.43815e54	−1.74520
$139$	−5.44884e52	−0.0122864	−0.00614322	−	0.999981i	$-0.501955\pi$
$139$	−5.44884e52	−0.0122864	−0.00614322	+	0.999981i	$0.501955\pi$
$140$	4.32480e54	0.812272
$141$	4.30586e54	0.674486
$142$	5.86366e53	0.0767037
$143$	5.67289e53	0.0620491
$144$	2.69120e54	0.246435
$145$	1.14872e55	0.881719
$146$	−5.98238e54	−0.385368
$147$	1.73771e54	0.0940559
$148$	7.46852e54	0.340064
$149$	3.76168e55	1.44255	0.721276	−	0.692648i	$-0.243556\pi$
$149$	3.76168e55	1.44255	0.721276	+	0.692648i	$0.243556\pi$
$150$	−4.54228e55	−1.46875
$151$	−3.23926e55	−0.884166	−0.442083	−	0.896974i	$-0.645760\pi$
$151$	−3.23926e55	−0.884166	−0.442083	+	0.896974i	$0.645760\pi$
$152$	−2.05866e55	−0.474869
$153$	−5.66785e55	−1.10608
$154$	1.95587e54	0.0323268
$155$	−1.07575e56	−1.50748
$156$	8.30419e55	0.987688
$157$	9.66686e55	0.976887	0.488444	−	0.872595i	$-0.337565\pi$
$157$	9.66686e55	0.976887	0.488444	+	0.872595i	$0.337565\pi$
$158$	1.60500e55	0.137950
$159$	2.01469e56	1.47428
$160$	4.45846e55	0.278052
$161$	−3.40008e56	−1.80896
$162$	1.57827e56	0.717047
$163$	7.49906e55	0.291221	0.145611	−	0.989342i	$-0.453485\pi$
$163$	7.49906e55	0.291221	0.145611	+	0.989342i	$0.453485\pi$
$164$	1.26487e56	0.420270
$165$	−3.44786e55	−0.0981090
$166$	−2.22086e55	−0.0541707
$167$	−3.41560e56	−0.714821	−0.357411	−	0.933947i	$-0.616340\pi$
$167$	−3.41560e56	−0.714821	−0.357411	+	0.933947i	$0.616340\pi$
$168$	2.86308e56	0.514572
$169$	6.24697e56	0.965069
$170$	−9.38984e56	−1.24799
$171$	1.15686e57	1.32398
$172$	−5.09676e56	−0.502712
$173$	−1.00275e57	−0.853130	−0.426565	−	0.904457i	$-0.640276\pi$
$173$	−1.00275e57	−0.853130	−0.426565	+	0.904457i	$0.640276\pi$
$174$	7.60469e56	0.558567
$175$	−2.39884e57	−1.52241
$176$	2.01632e55	0.0110659
$177$	−1.83139e57	−0.869885
$178$	−1.28300e57	−0.527858
$179$	1.65195e57	0.589175	0.294587	−	0.955625i	$-0.404818\pi$
$179$	1.65195e57	0.589175	0.294587	+	0.955625i	$0.404818\pi$
$180$	−2.50542e57	−0.775233
$181$	6.54541e57	1.75846	0.879231	−	0.476396i	$-0.158057\pi$
$181$	6.54541e57	1.75846	0.879231	+	0.476396i	$0.158057\pi$
$182$	4.38556e57	1.02377
$183$	1.19348e58	2.42277
$184$	−3.50516e57	−0.619232
$185$	−6.95297e57	−1.06977
$186$	−7.12160e57	−0.954988
$187$	−4.24652e56	−0.0496675
$188$	2.34427e57	0.239322
$189$	2.32773e56	0.0207566
$190$	1.91655e58	1.49384
$191$	−1.29166e58	−0.880638	−0.440319	−	0.897841i	$-0.645135\pi$
$191$	−1.29166e58	−0.880638	−0.440319	+	0.897841i	$0.645135\pi$
$192$	2.95157e57	0.176145
$193$	−1.98221e57	−0.103619	−0.0518095	−	0.998657i	$-0.516499\pi$
$193$	−1.98221e57	−0.103619	−0.0518095	+	0.998657i	$0.516499\pi$
$194$	−7.64584e56	−0.0350333
$195$	−7.73096e58	−3.10707
$196$	9.46073e56	0.0333730
$197$	2.64545e58	0.819616	0.409808	−	0.912172i	$-0.365596\pi$
$197$	2.64545e58	0.819616	0.409808	+	0.912172i	$0.365596\pi$
$198$	−1.13307e57	−0.0308527
$199$	−9.08242e56	−0.0217494	−0.0108747	−	0.999941i	$-0.503462\pi$
$199$	−9.08242e56	−0.0217494	−0.0108747	+	0.999941i	$0.503462\pi$
$200$	−2.47298e58	−0.521141
$201$	7.44749e58	1.38201
$202$	7.20453e58	1.17800
$203$	4.01614e58	0.578975
$204$	−6.21620e58	−0.790599
$205$	−1.17756e59	−1.32208
$206$	6.78165e58	0.672545
$207$	1.96972e59	1.72647
$208$	4.52110e58	0.350452
$209$	8.66754e57	0.0594519
$210$	−2.66544e59	−1.61874
$211$	−1.54685e59	−0.832234	−0.416117	−	0.909311i	$-0.636609\pi$
$211$	−1.54685e59	−0.832234	−0.416117	+	0.909311i	$0.636609\pi$
$212$	1.09687e59	0.523106
$213$	−3.61387e58	−0.152859
$214$	−1.07051e59	−0.401826
$215$	4.74494e59	1.58143
$216$	2.39967e57	0.00710528
$217$	−3.76102e59	−0.989879
$218$	−2.48920e59	−0.582666
$219$	3.68703e59	0.767984
$220$	−1.87714e58	−0.0348111
$221$	−9.52175e59	−1.57295
$222$	−4.60297e59	−0.677699
$223$	−7.00614e58	−0.0919825	−0.0459912	−	0.998942i	$-0.514645\pi$
$223$	−7.00614e58	−0.0919825	−0.0459912	+	0.998942i	$0.514645\pi$
$224$	1.55876e59	0.182581
$225$	1.38968e60	1.45299
$226$	2.95159e59	0.275607
$227$	−1.31783e60	−1.09951	−0.549757	−	0.835324i	$-0.685280\pi$
$227$	−1.31783e60	−1.09951	−0.549757	+	0.835324i	$0.685280\pi$
$228$	1.26879e60	0.946345
$229$	1.55766e60	1.03912	0.519562	−	0.854432i	$-0.326095\pi$
$229$	1.55766e60	1.03912	0.519562	+	0.854432i	$0.326095\pi$
$230$	3.26320e60	1.94798
$231$	−1.20544e59	−0.0644226
$232$	4.14026e59	0.198191
$233$	−1.77057e60	−0.759515	−0.379757	−	0.925086i	$-0.623993\pi$
$233$	−1.77057e60	−0.759515	−0.379757	+	0.925086i	$0.623993\pi$
$234$	−2.54062e60	−0.977092
$235$	−2.18244e60	−0.752857
$236$	−9.97073e59	−0.308653
$237$	−9.89189e59	−0.274914
$238$	−3.28286e60	−0.819484
$239$	3.87218e60	0.868579	0.434290	−	0.900773i	$-0.356999\pi$
$239$	3.87218e60	0.868579	0.434290	+	0.900773i	$0.356999\pi$
$240$	−2.74782e60	−0.554117
$241$	−5.07953e59	−0.0921275	−0.0460638	−	0.998939i	$-0.514668\pi$
$241$	−5.07953e59	−0.0921275	−0.0460638	+	0.998939i	$0.514668\pi$
$242$	4.32439e60	0.705721
$243$	−9.59031e60	−1.40888
$244$	6.49774e60	0.859650
$245$	−8.80767e59	−0.104985
$246$	−7.79559e60	−0.837537
$247$	1.94348e61	1.88281
$248$	−3.87726e60	−0.338849
$249$	1.36875e60	0.107954
$250$	7.40361e60	0.527197
$251$	−1.64293e59	−0.0105667	−0.00528335	−	0.999986i	$-0.501682\pi$
$251$	−1.64293e59	−0.0105667	−0.00528335	+	0.999986i	$0.501682\pi$
$252$	−8.75943e60	−0.509052
$253$	1.47577e60	0.0775256
$254$	−1.71139e61	−0.812999
$255$	5.78711e61	2.48706
$256$	1.60694e60	0.0625000
$257$	−1.73968e61	−0.612598	−0.306299	−	0.951935i	$-0.599091\pi$
$257$	−1.73968e61	−0.612598	−0.306299	+	0.951935i	$0.599091\pi$
$258$	3.14122e61	1.00183
$259$	−2.43089e61	−0.702460
$260$	−4.20901e61	−1.10245
$261$	−2.32661e61	−0.552575
$262$	2.17126e61	0.467766
$263$	−5.35000e61	−1.04588	−0.522941	−	0.852369i	$-0.675165\pi$
$263$	−5.35000e61	−1.04588	−0.522941	+	0.852369i	$0.675165\pi$
$264$	−1.24269e60	−0.0220528
$265$	−1.02115e62	−1.64559
$266$	6.70063e61	0.980921
$267$	7.90733e61	1.05194
$268$	4.05468e61	0.490365
$269$	−2.03191e61	−0.223471	−0.111735	−	0.993738i	$-0.535641\pi$
$269$	−2.03191e61	−0.223471	−0.111735	+	0.993738i	$0.535641\pi$
$270$	−2.23403e60	−0.0223518
$271$	1.04229e62	0.949009	0.474505	−	0.880253i	$-0.342627\pi$
$271$	1.04229e62	0.949009	0.474505	+	0.880253i	$0.342627\pi$
$272$	−3.38433e61	−0.280521
$273$	−2.70289e62	−2.04024
$274$	−9.22639e61	−0.634443
$275$	1.04119e61	0.0652450
$276$	2.16028e62	1.23404
$277$	2.56003e62	1.33355	0.666776	−	0.745258i	$-0.267674\pi$
$277$	2.56003e62	1.33355	0.666776	+	0.745258i	$0.267674\pi$
$278$	1.82833e60	0.00868783
$279$	2.17882e62	0.944743
$280$	−1.45116e62	−0.574363
$281$	4.94167e62	1.78592	0.892961	−	0.450134i	$-0.148624\pi$
$281$	4.94167e62	1.78592	0.892961	+	0.450134i	$0.148624\pi$
$282$	−1.44481e62	−0.476934
$283$	2.97737e62	0.898004	0.449002	−	0.893531i	$-0.351780\pi$
$283$	2.97737e62	0.898004	0.449002	+	0.893531i	$0.351780\pi$
$284$	−1.96752e61	−0.0542377
$285$	−1.18120e63	−2.97701
$286$	−1.90351e61	−0.0438754
$287$	−4.11696e62	−0.868137
$288$	−9.03015e61	−0.174256
$289$	1.46660e62	0.259070
$290$	−3.85446e62	−0.623469
$291$	4.71225e61	0.0698163
$292$	2.00735e62	0.272497
$293$	−4.51171e62	−0.561328	−0.280664	−	0.959806i	$-0.590555\pi$
$293$	−4.51171e62	−0.561328	−0.280664	+	0.959806i	$0.590555\pi$
$294$	−5.83080e61	−0.0665076
$295$	9.28246e62	0.970961
$296$	−2.50602e62	−0.240462
$297$	−1.01033e60	−0.000889556 0
$298$	−1.26221e63	−1.02004
$299$	3.30904e63	2.45520
$300$	1.52414e63	1.03856
$301$	1.65892e63	1.03844
$302$	1.08692e63	0.625200
$303$	−4.44026e63	−2.34759
$304$	6.90772e62	0.335783
$305$	−6.04920e63	−2.70428
$306$	1.90181e63	0.782117
$307$	3.92099e63	1.48377	0.741886	−	0.670526i	$-0.233932\pi$
$307$	3.92099e63	1.48377	0.741886	+	0.670526i	$0.233932\pi$
$308$	−6.56282e61	−0.0228585
$309$	−4.17964e63	−1.34029
$310$	3.60961e63	1.06595
$311$	6.67797e63	1.81658	0.908289	−	0.418342i	$-0.137389\pi$
$311$	6.67797e63	1.81658	0.908289	+	0.418342i	$0.137389\pi$
$312$	−2.78642e63	−0.698401
$313$	−6.27841e63	−1.45034	−0.725168	−	0.688572i	$-0.758238\pi$
$313$	−6.27841e63	−1.45034	−0.725168	+	0.688572i	$0.758238\pi$
$314$	−3.24366e63	−0.690764
$315$	8.15478e63	1.60137
$316$	−5.38550e62	−0.0975451
$317$	−1.01021e64	−1.68811	−0.844054	−	0.536259i	$-0.819837\pi$
$317$	−1.01021e64	−1.68811	−0.844054	+	0.536259i	$0.819837\pi$
$318$	−6.76017e63	−1.04248
$319$	−1.74317e62	−0.0248128
$320$	−1.49601e63	−0.196612
$321$	6.59770e63	0.800782
$322$	1.14088e64	1.27913
$323$	−1.45482e64	−1.50711
$324$	−5.29579e63	−0.507029
$325$	2.33461e64	2.06628
$326$	−2.51627e63	−0.205924
$327$	1.53414e64	1.16117
$328$	−4.24420e63	−0.297175
$329$	−7.63023e63	−0.494359
$330$	1.15691e63	0.0693735
$331$	1.20224e64	0.667389	0.333694	−	0.942681i	$-0.391705\pi$
$331$	1.20224e64	0.667389	0.333694	+	0.942681i	$0.391705\pi$
$332$	7.45196e62	0.0383045
$333$	1.40825e64	0.670429
$334$	1.14609e64	0.505455
$335$	−3.77479e64	−1.54259
$336$	−9.60690e63	−0.363858
$337$	2.04266e64	0.717189	0.358595	−	0.933493i	$-0.383256\pi$
$337$	2.04266e64	0.717189	0.358595	+	0.933493i	$0.383256\pi$
$338$	−2.09613e64	−0.682407
$339$	−1.81911e64	−0.549245
$340$	3.15071e64	0.882461
$341$	1.63243e63	0.0424227
$342$	−3.88178e64	−0.936193
$343$	4.30557e64	0.963896
$344$	1.71019e64	0.355471
$345$	−2.01116e65	−3.88204
$346$	3.36466e64	0.603254
$347$	1.95556e64	0.325739	0.162870	−	0.986648i	$-0.447925\pi$
$347$	1.95556e64	0.325739	0.162870	+	0.986648i	$0.447925\pi$
$348$	−2.55171e64	−0.394967
$349$	3.04085e64	0.437469	0.218734	−	0.975784i	$-0.429807\pi$
$349$	3.04085e64	0.437469	0.218734	+	0.975784i	$0.429807\pi$
$350$	8.04917e64	1.07650
$351$	−2.26541e63	−0.0281718
$352$	−6.76565e62	−0.00782478
$353$	1.22631e64	0.131931	0.0659654	−	0.997822i	$-0.478987\pi$
$353$	1.22631e64	0.131931	0.0659654	+	0.997822i	$0.478987\pi$
$354$	6.14512e64	0.615102
$355$	1.83170e64	0.170621
$356$	4.30504e64	0.373252
$357$	2.02328e65	1.63311
$358$	−5.54302e64	−0.416610
$359$	4.18244e64	0.292767	0.146383	−	0.989228i	$-0.453237\pi$
$359$	4.18244e64	0.292767	0.146383	+	0.989228i	$0.453237\pi$
$360$	8.40681e64	0.548173
$361$	1.32340e65	0.804003
$362$	−2.19627e65	−1.24342
$363$	−2.66519e65	−1.40640
$364$	−1.47155e65	−0.723918
$365$	−1.86879e65	−0.857219
$366$	−4.00466e65	−1.71316
$367$	2.23984e65	0.893782	0.446891	−	0.894588i	$-0.352531\pi$
$367$	2.23984e65	0.893782	0.446891	+	0.894588i	$0.352531\pi$
$368$	1.17614e65	0.437863
$369$	2.38502e65	0.828552
$370$	2.33303e65	0.756444
$371$	−3.57014e65	−1.08056
$372$	2.38961e65	0.675278
$373$	4.52272e65	1.19351	0.596753	−	0.802425i	$-0.296457\pi$
$373$	4.52272e65	1.19351	0.596753	+	0.802425i	$0.296457\pi$
$374$	1.42489e64	0.0351202
$375$	−4.56296e65	−1.05063
$376$	−7.86606e64	−0.169226
$377$	−3.90861e65	−0.785811
$378$	−7.81057e63	−0.0146772
$379$	−7.03989e65	−1.23670	−0.618352	−	0.785901i	$-0.712200\pi$
$379$	−7.03989e65	−1.23670	−0.618352	+	0.785901i	$0.712200\pi$
$380$	−6.43089e65	−1.05631
$381$	1.05476e66	1.62019
$382$	4.33409e65	0.622705
$383$	1.31094e66	1.76204	0.881019	−	0.473081i	$-0.156858\pi$
$383$	1.31094e66	1.76204	0.881019	+	0.473081i	$0.156858\pi$
$384$	−9.90381e64	−0.124554
$385$	6.10980e64	0.0719082
$386$	6.65121e64	0.0732697
$387$	−9.61038e65	−0.991085
$388$	2.56552e64	0.0247723
$389$	1.70530e66	1.54201	0.771004	−	0.636831i	$-0.219755\pi$
$389$	1.70530e66	1.54201	0.771004	+	0.636831i	$0.219755\pi$
$390$	2.59408e66	2.19703
$391$	−2.47703e66	−1.96527
$392$	−3.17450e64	−0.0235983
$393$	−1.33818e66	−0.932190
$394$	−8.87665e65	−0.579556
$395$	5.01374e65	0.306857
$396$	3.80195e64	0.0218162
$397$	1.75181e66	0.942603	0.471302	−	0.881972i	$-0.343784\pi$
$397$	1.75181e66	0.942603	0.471302	+	0.881972i	$0.343784\pi$
$398$	3.04755e64	0.0153792
$399$	−4.12970e66	−1.95484
$400$	8.29794e65	0.368503
$401$	−4.60572e66	−1.91918	−0.959591	−	0.281398i	$-0.909202\pi$
$401$	−4.60572e66	−1.91918	−0.959591	+	0.281398i	$0.909202\pi$
$402$	−2.49896e66	−0.977227
$403$	3.66032e66	1.34351
$404$	−2.41744e66	−0.832972
$405$	4.93022e66	1.59501
$406$	−1.34759e66	−0.409397
$407$	1.05510e65	0.0301049
$408$	2.08581e66	0.559038
$409$	−1.85477e65	−0.0467030	−0.0233515	−	0.999727i	$-0.507434\pi$
$409$	−1.85477e65	−0.0467030	−0.0233515	+	0.999727i	$0.507434\pi$
$410$	3.95123e66	0.934854
$411$	5.68637e66	1.26435
$412$	−2.27554e66	−0.475561
$413$	3.24532e66	0.637575
$414$	−6.60927e66	−1.22080
$415$	−6.93756e65	−0.120498
$416$	−1.51703e66	−0.247807
$417$	−1.12683e65	−0.0173136
$418$	−2.90834e65	−0.0420388
$419$	7.10134e66	0.965790	0.482895	−	0.875678i	$-0.339585\pi$
$419$	7.10134e66	0.965790	0.482895	+	0.875678i	$0.339585\pi$
$420$	8.94374e66	1.14462
$421$	−3.97611e66	−0.478922	−0.239461	−	0.970906i	$-0.576971\pi$
$421$	−3.97611e66	−0.478922	−0.239461	+	0.970906i	$0.576971\pi$
$422$	5.19036e66	0.588478
$423$	4.42031e66	0.471817
$424$	−3.68048e66	−0.369892
$425$	−1.74760e67	−1.65396
$426$	1.21261e66	0.108088
$427$	−2.11492e67	−1.77575
$428$	3.59202e66	0.284134
$429$	1.17316e66	0.0874373
$430$	−1.59214e67	−1.11824
$431$	6.23308e65	0.0412603	0.0206301	−	0.999787i	$-0.493433\pi$
$431$	6.23308e65	0.0412603	0.0206301	+	0.999787i	$0.493433\pi$
$432$	−8.05197e64	−0.00502419
$433$	−1.91154e67	−1.12445	−0.562226	−	0.826984i	$-0.690055\pi$
$433$	−1.91154e67	−1.12445	−0.562226	+	0.826984i	$0.690055\pi$
$434$	1.26199e67	0.699950
$435$	2.37557e67	1.24248
$436$	8.35239e66	0.412007
$437$	5.05584e67	2.35243
$438$	−1.23716e67	−0.543046
$439$	−4.30961e67	−1.78481	−0.892406	−	0.451234i	$-0.850984\pi$
$439$	−4.30961e67	−1.78481	−0.892406	+	0.451234i	$0.850984\pi$
$440$	6.29863e65	0.0246152
$441$	1.78390e66	0.0657941
$442$	3.19497e67	1.11224
$443$	−1.10016e67	−0.361544	−0.180772	−	0.983525i	$-0.557860\pi$
$443$	−1.10016e67	−0.361544	−0.180772	+	0.983525i	$0.557860\pi$
$444$	1.54450e67	0.479206
$445$	−4.00786e67	−1.17417
$446$	2.35087e66	0.0650414
$447$	7.77919e67	2.03279
$448$	−5.23034e66	−0.129104
$449$	−1.55367e67	−0.362308	−0.181154	−	0.983455i	$-0.557983\pi$
$449$	−1.55367e67	−0.362308	−0.181154	+	0.983455i	$0.557983\pi$
$450$	−4.66301e67	−1.02742
$451$	1.78693e66	0.0372053
$452$	−9.90388e66	−0.194884
$453$	−6.69883e67	−1.24593
$454$	4.42191e67	0.777474
$455$	1.36997e68	2.27730
$456$	−4.25734e67	−0.669167
$457$	9.49329e67	1.41109	0.705544	−	0.708666i	$-0.250703\pi$
$457$	9.49329e67	1.41109	0.705544	+	0.708666i	$0.250703\pi$
$458$	−5.22664e67	−0.734772
$459$	1.69580e66	0.0225502
$460$	−1.09495e68	−1.37743
$461$	−7.18592e67	−0.855280	−0.427640	−	0.903949i	$-0.640655\pi$
$461$	−7.18592e67	−0.855280	−0.427640	+	0.903949i	$0.640655\pi$
$462$	4.04477e66	0.0455537
$463$	−2.17111e67	−0.231402	−0.115701	−	0.993284i	$-0.536911\pi$
$463$	−2.17111e67	−0.231402	−0.115701	+	0.993284i	$0.536911\pi$
$464$	−1.38924e67	−0.140142
$465$	−2.22466e68	−2.12429
$466$	5.94103e67	0.537058
$467$	−2.67357e67	−0.228829	−0.114415	−	0.993433i	$-0.536499\pi$
$467$	−2.67357e67	−0.228829	−0.114415	+	0.993433i	$0.536499\pi$
$468$	8.52491e67	0.690909
$469$	−1.31974e68	−1.01293
$470$	7.32307e67	0.532351
$471$	1.99912e68	1.37659
$472$	3.34562e67	0.218251
$473$	−7.20037e66	−0.0445037
$474$	3.31917e67	0.194393
$475$	3.56702e68	1.97979
$476$	1.10155e68	0.579463
$477$	2.06824e68	1.03129
$478$	−1.29929e68	−0.614178
$479$	−2.33770e68	−1.04769	−0.523846	−	0.851813i	$-0.675503\pi$
$479$	−2.33770e68	−1.04769	−0.523846	+	0.851813i	$0.675503\pi$
$480$	9.22016e67	0.391820
$481$	2.36581e68	0.953410
$482$	1.70441e67	0.0651440
$483$	−7.03140e68	−2.54912
$484$	−1.45103e68	−0.499020
$485$	−2.38842e67	−0.0779286
$486$	3.21797e68	0.996226
$487$	−2.07120e68	−0.608461	−0.304231	−	0.952598i	$-0.598399\pi$
$487$	−2.07120e68	−0.608461	−0.304231	+	0.952598i	$0.598399\pi$
$488$	−2.18028e68	−0.607864
$489$	1.55081e68	0.410378
$490$	2.95536e67	0.0742354
$491$	−2.77262e68	−0.661168	−0.330584	−	0.943777i	$-0.607246\pi$
$491$	−2.77262e68	−0.661168	−0.330584	+	0.943777i	$0.607246\pi$
$492$	2.61577e68	0.592228
$493$	2.92584e68	0.629005
$494$	−6.52123e68	−1.33135
$495$	−3.53950e67	−0.0686293
$496$	1.30099e68	0.239603
$497$	6.40397e67	0.112037
$498$	−4.59276e67	−0.0763353
$499$	−1.52829e68	−0.241346	−0.120673	−	0.992692i	$-0.538505\pi$
$499$	−1.52829e68	−0.241346	−0.120673	+	0.992692i	$0.538505\pi$
$500$	−2.48424e68	−0.372785
$501$	−7.06351e68	−1.00730
$502$	5.51276e66	0.00747178
$503$	1.28813e68	0.165950	0.0829750	−	0.996552i	$-0.473558\pi$
$503$	1.28813e68	0.165950	0.0829750	+	0.996552i	$0.473558\pi$
$504$	2.93918e68	0.359954
$505$	2.25056e69	2.62036
$506$	−4.95186e67	−0.0548189
$507$	1.29188e69	1.35994
$508$	5.74248e68	0.574877
$509$	−5.81158e68	−0.553339	−0.276669	−	0.960965i	$-0.589231\pi$
$509$	−5.81158e68	−0.553339	−0.276669	+	0.960965i	$0.589231\pi$
$510$	−1.94183e69	−1.75862
$511$	−6.53363e68	−0.562887
$512$	−5.39199e67	−0.0441942
$513$	−3.46129e67	−0.0269926
$514$	5.83741e68	0.433172
$515$	2.11847e69	1.49602
$516$	−1.05402e69	−0.708403
$517$	3.31183e67	0.0211865
$518$	8.15671e68	0.496714
$519$	−2.07369e69	−1.20220
$520$	1.41231e69	0.779551
$521$	3.94936e68	0.207570	0.103785	−	0.994600i	$-0.466905\pi$
$521$	3.94936e68	0.207570	0.103785	+	0.994600i	$0.466905\pi$
$522$	7.80682e68	0.390729
$523$	−3.08603e69	−1.47098	−0.735491	−	0.677534i	$-0.763049\pi$
$523$	−3.08603e69	−1.47098	−0.735491	+	0.677534i	$0.763049\pi$
$524$	−7.28553e68	−0.330760
$525$	−4.96083e69	−2.14532
$526$	1.79516e69	0.739550
$527$	−2.73998e69	−1.07542
$528$	4.16978e67	0.0155937
$529$	5.80207e69	2.06758
$530$	3.42642e69	1.16361
$531$	−1.88007e69	−0.608503
$532$	−2.24836e69	−0.693616
$533$	4.00673e69	1.17828
$534$	−2.65326e69	−0.743837
$535$	−3.34407e69	−0.893828
$536$	−1.36053e69	−0.346740
$537$	3.41625e69	0.830243
$538$	6.81794e68	0.158018
$539$	1.33655e67	0.00295442
$540$	7.49614e67	0.0158051
$541$	−5.66988e69	−1.14036	−0.570182	−	0.821518i	$-0.693127\pi$
$541$	−5.66988e69	−1.14036	−0.570182	+	0.821518i	$0.693127\pi$
$542$	−3.49733e69	−0.671051
$543$	1.35360e70	2.47796
$544$	1.13559e69	0.198358
$545$	−7.77583e69	−1.29609
$546$	9.06938e69	1.44266
$547$	8.02401e69	1.21819	0.609095	−	0.793098i	$-0.291533\pi$
$547$	8.02401e69	1.21819	0.609095	+	0.793098i	$0.291533\pi$
$548$	3.09586e69	0.448619
$549$	1.22520e70	1.69478
$550$	−3.49366e68	−0.0461352
$551$	−5.97192e69	−0.752919
$552$	−7.24871e69	−0.872598
$553$	1.75290e69	0.201496
$554$	−8.59002e69	−0.942964
$555$	−1.43788e70	−1.50748
$556$	−6.13484e67	−0.00614322
$557$	−5.53278e69	−0.529220	−0.264610	−	0.964356i	$-0.585243\pi$
$557$	−5.53278e69	−0.529220	−0.264610	+	0.964356i	$0.585243\pi$
$558$	−7.31089e69	−0.668034
$559$	−1.61450e70	−1.40941
$560$	4.86929e69	0.406136
$561$	−8.78185e68	−0.0699895
$562$	−1.65815e70	−1.26284
$563$	2.17899e70	1.58596	0.792978	−	0.609250i	$-0.208529\pi$
$563$	2.17899e70	1.58596	0.792978	+	0.609250i	$0.208529\pi$
$564$	4.84797e69	0.337243
$565$	9.22023e69	0.613064
$566$	−9.99039e69	−0.634985
$567$	1.72370e70	1.04735
$568$	6.60190e68	0.0383518
$569$	−3.21653e69	−0.178659	−0.0893295	−	0.996002i	$-0.528472\pi$
$569$	−3.21653e69	−0.178659	−0.0893295	+	0.996002i	$0.528472\pi$
$570$	3.96346e70	2.10506
$571$	−2.61263e70	−1.32696	−0.663479	−	0.748195i	$-0.730921\pi$
$571$	−2.61263e70	−1.32696	−0.663479	+	0.748195i	$0.730921\pi$
$572$	6.38711e68	0.0310246
$573$	−2.67117e70	−1.24096
$574$	1.38142e70	0.613866
$575$	6.07336e70	2.58166
$576$	3.03002e69	0.123217
$577$	−3.12401e70	−1.21543	−0.607714	−	0.794156i	$-0.707913\pi$
$577$	−3.12401e70	−1.21543	−0.607714	+	0.794156i	$0.707913\pi$
$578$	−4.92111e69	−0.183190
$579$	−4.09924e69	−0.146016
$580$	1.29334e70	0.440859
$581$	−2.42550e69	−0.0791243
$582$	−1.58117e69	−0.0493676
$583$	1.54958e69	0.0463092
$584$	−6.73556e69	−0.192684
$585$	−7.93644e70	−2.17346
$586$	1.51388e70	0.396919
$587$	4.11408e70	1.03276	0.516382	−	0.856359i	$-0.327279\pi$
$587$	4.11408e70	1.03276	0.516382	+	0.856359i	$0.327279\pi$
$588$	1.95649e69	0.0470280
$589$	5.59256e70	1.28727
$590$	−3.11468e70	−0.686573
$591$	5.47082e70	1.15497
$592$	8.40881e69	0.170032
$593$	−6.25875e70	−1.21225	−0.606126	−	0.795368i	$-0.707277\pi$
$593$	−6.25875e70	−1.21225	−0.606126	+	0.795368i	$0.707277\pi$
$594$	3.39010e67	0.000629011 0
$595$	−1.02551e71	−1.82287
$596$	4.23527e70	0.721276
$597$	−1.87825e69	−0.0306485
$598$	−1.11033e71	−1.73609
$599$	6.19303e70	0.927939	0.463969	−	0.885851i	$-0.346425\pi$
$599$	6.19303e70	0.927939	0.463969	+	0.885851i	$0.346425\pi$
$600$	−5.11415e70	−0.734373
$601$	−2.53959e70	−0.349514	−0.174757	−	0.984612i	$-0.555914\pi$
$601$	−2.53959e70	−0.349514	−0.174757	+	0.984612i	$0.555914\pi$
$602$	−5.56641e70	−0.734285
$603$	7.64544e70	0.966743
$604$	−3.64708e70	−0.442083
$605$	1.35086e71	1.56982
$606$	1.48990e71	1.65999
$607$	−1.47728e71	−1.57816	−0.789081	−	0.614290i	$-0.789443\pi$
$607$	−1.47728e71	−1.57816	−0.789081	+	0.614290i	$0.789443\pi$
$608$	−2.31785e70	−0.237434
$609$	8.30543e70	0.815870
$610$	2.02978e71	1.91222
$611$	7.42594e70	0.670966
$612$	−6.38143e70	−0.553040
$613$	−3.89520e70	−0.323808	−0.161904	−	0.986806i	$-0.551764\pi$
$613$	−3.89520e70	−0.323808	−0.161904	+	0.986806i	$0.551764\pi$
$614$	−1.31567e71	−1.04919
$615$	−2.43520e71	−1.86303
$616$	2.20212e69	0.0161634
$617$	2.31064e71	1.62727	0.813636	−	0.581375i	$-0.197485\pi$
$617$	2.31064e71	1.62727	0.813636	+	0.581375i	$0.197485\pi$
$618$	1.40245e71	0.947725
$619$	2.46632e71	1.59933	0.799664	−	0.600448i	$-0.205011\pi$
$619$	2.46632e71	1.59933	0.799664	+	0.600448i	$0.205011\pi$
$620$	−1.21119e71	−0.753742
$621$	−5.89333e69	−0.0351985
$622$	−2.24075e71	−1.28452
$623$	−1.40122e71	−0.771014
$624$	9.34968e70	0.493844
$625$	−5.94218e70	−0.301304
$626$	2.10668e71	1.02554
$627$	1.79246e70	0.0837773
$628$	1.08839e71	0.488444
$629$	−1.77095e71	−0.763160
$630$	−2.73629e71	−1.13234
$631$	−1.57409e71	−0.625575	−0.312788	−	0.949823i	$-0.601263\pi$
$631$	−1.57409e71	−0.625575	−0.312788	+	0.949823i	$0.601263\pi$
$632$	1.80707e70	0.0689748
$633$	−3.19890e71	−1.17275
$634$	3.38970e71	1.19367
$635$	−5.34608e71	−1.80845
$636$	2.26834e71	0.737142
$637$	2.99688e70	0.0935651
$638$	5.84909e69	0.0175453
$639$	−3.70992e70	−0.106928
$640$	5.01978e70	0.139026
$641$	−3.44895e71	−0.917925	−0.458963	−	0.888456i	$-0.651779\pi$
$641$	−3.44895e71	−0.917925	−0.458963	+	0.888456i	$0.651779\pi$
$642$	−2.21382e71	−0.566238
$643$	7.91762e71	1.94632	0.973162	−	0.230123i	$-0.0739128\pi$
$643$	7.91762e71	1.94632	0.973162	+	0.230123i	$0.0739128\pi$
$644$	−3.82815e71	−0.904480
$645$	9.81259e71	2.22849
$646$	4.88155e71	1.06568
$647$	6.42443e71	1.34827	0.674133	−	0.738610i	$-0.264518\pi$
$647$	6.42443e71	1.34827	0.674133	+	0.738610i	$0.264518\pi$
$648$	1.77697e71	0.358524
$649$	−1.40860e70	−0.0273242
$650$	−7.83366e71	−1.46108
$651$	−7.77783e71	−1.39490
$652$	8.44319e70	0.145611
$653$	7.30780e71	1.21199	0.605997	−	0.795467i	$-0.292774\pi$
$653$	7.30780e71	1.21199	0.605997	+	0.795467i	$0.292774\pi$
$654$	−5.14770e71	−0.821072
$655$	6.78262e71	1.04051
$656$	1.42412e71	0.210135
$657$	3.78503e71	0.537221
$658$	2.56028e71	0.349565
$659$	−6.68820e71	−0.878478	−0.439239	−	0.898370i	$-0.644752\pi$
$659$	−6.68820e71	−0.878478	−0.439239	+	0.898370i	$0.644752\pi$
$660$	−3.88194e70	−0.0490545
$661$	−1.31106e72	−1.59399	−0.796997	−	0.603983i	$-0.793579\pi$
$661$	−1.31106e72	−1.59399	−0.796997	+	0.603983i	$0.793579\pi$
$662$	−4.03406e71	−0.471915
$663$	−1.96911e72	−2.21654
$664$	−2.50046e70	−0.0270853
$665$	2.09316e72	2.18198
$666$	−4.72531e71	−0.474065
$667$	−1.01680e72	−0.981811
$668$	−3.84563e71	−0.357411
$669$	−1.44888e71	−0.129618
$670$	1.26661e72	1.09078
$671$	9.17958e70	0.0761024
$672$	3.22354e71	0.257286
$673$	2.25014e72	1.72912	0.864561	−	0.502528i	$-0.167597\pi$
$673$	2.25014e72	1.72912	0.864561	+	0.502528i	$0.167597\pi$
$674$	−6.85403e71	−0.507129
$675$	−4.15789e70	−0.0296228
$676$	7.03346e71	0.482534
$677$	−5.41995e71	−0.358084	−0.179042	−	0.983841i	$-0.557300\pi$
$677$	−5.41995e71	−0.358084	−0.179042	+	0.983841i	$0.557300\pi$
$678$	6.10392e71	0.388375
$679$	−8.35037e70	−0.0511713
$680$	−1.05720e72	−0.623994
$681$	−2.72529e72	−1.54939
$682$	−5.47754e70	−0.0299974
$683$	−2.36747e71	−0.124898	−0.0624491	−	0.998048i	$-0.519891\pi$
$683$	−2.36747e71	−0.124898	−0.0624491	+	0.998048i	$0.519891\pi$
$684$	1.30251e72	0.661988
$685$	−2.88216e72	−1.41126
$686$	−1.44471e72	−0.681578
$687$	3.22126e72	1.46430
$688$	−5.73845e71	−0.251356
$689$	3.47455e72	1.46659
$690$	6.74834e72	2.74502
$691$	2.27457e72	0.891679	0.445840	−	0.895113i	$-0.352905\pi$
$691$	2.27457e72	0.891679	0.445840	+	0.895113i	$0.352905\pi$
$692$	−1.12899e72	−0.426565
$693$	−1.23748e71	−0.0450650
$694$	−6.56178e71	−0.230332
$695$	5.71136e70	0.0193253
$696$	8.56211e71	0.279284
$697$	−2.99929e72	−0.943155
$698$	−1.02034e72	−0.309337
$699$	−3.66155e72	−1.07028
$700$	−2.70085e72	−0.761204
$701$	−3.31656e72	−0.901320	−0.450660	−	0.892696i	$-0.648811\pi$
$701$	−3.31656e72	−0.901320	−0.450660	+	0.892696i	$0.648811\pi$
$702$	7.60145e70	0.0199205
$703$	3.61468e72	0.913502
$704$	2.27018e70	0.00553295
$705$	−4.51332e72	−1.06090
$706$	−4.11482e71	−0.0932891
$707$	7.86839e72	1.72064
$708$	−2.06196e72	−0.434943
$709$	−9.46208e72	−1.92534	−0.962671	−	0.270675i	$-0.912753\pi$
$709$	−9.46208e72	−1.92534	−0.962671	+	0.270675i	$0.912753\pi$
$710$	−6.14617e71	−0.120647
$711$	−1.01548e72	−0.192308
$712$	−1.44453e72	−0.263929
$713$	9.52211e72	1.67861
$714$	−6.78900e72	−1.15479
$715$	−5.94621e71	−0.0975970
$716$	1.85993e72	0.294587
$717$	8.00772e72	1.22397
$718$	−1.40340e72	−0.207017
$719$	6.32315e72	0.900216	0.450108	−	0.892974i	$-0.351385\pi$
$719$	6.32315e72	0.900216	0.450108	+	0.892974i	$0.351385\pi$
$720$	−2.82086e72	−0.387617
$721$	7.40655e72	0.982351
$722$	−4.44060e72	−0.568516
$723$	−1.05045e72	−0.129823
$724$	7.36947e72	0.879231
$725$	−7.17380e72	−0.826285
$726$	8.94289e72	0.994476
$727$	−3.56008e72	−0.382237	−0.191118	−	0.981567i	$-0.561211\pi$
$727$	−3.56008e72	−0.382237	−0.191118	+	0.981567i	$0.561211\pi$
$728$	4.93770e72	0.511887
$729$	−9.70275e72	−0.971277
$730$	6.27061e72	0.606145
$731$	1.20856e73	1.12817
$732$	1.34374e73	1.21139
$733$	−1.61861e73	−1.40926	−0.704630	−	0.709575i	$-0.748887\pi$
$733$	−1.61861e73	−1.40926	−0.704630	+	0.709575i	$0.748887\pi$
$734$	−7.51565e72	−0.632000
$735$	−1.82144e72	−0.147940
$736$	−3.94646e72	−0.309616
$737$	5.72819e71	0.0434107
$738$	−8.00280e72	−0.585875
$739$	−6.36915e72	−0.450452	−0.225226	−	0.974307i	$-0.572312\pi$
$739$	−6.36915e72	−0.450452	−0.225226	+	0.974307i	$0.572312\pi$
$740$	−7.82835e72	−0.534886
$741$	4.01914e73	2.65319
$742$	1.19794e73	0.764074
$743$	−2.53184e73	−1.56035	−0.780173	−	0.625564i	$-0.784869\pi$
$743$	−2.53184e73	−1.56035	−0.780173	+	0.625564i	$0.784869\pi$
$744$	−8.01821e72	−0.477494
$745$	−3.94291e73	−2.26899
$746$	−1.51757e73	−0.843936
$747$	1.40513e72	0.0755164
$748$	−4.78115e71	−0.0248337
$749$	−1.16915e73	−0.586926
$750$	1.53108e73	0.742907
$751$	−5.80597e72	−0.272305	−0.136153	−	0.990688i	$-0.543474\pi$
$751$	−5.80597e72	−0.272305	−0.136153	+	0.990688i	$0.543474\pi$
$752$	2.63941e72	0.119661
$753$	−3.39760e71	−0.0148902
$754$	1.31151e73	0.555652
$755$	3.39533e73	1.39070
$756$	2.62079e71	0.0103783
$757$	2.56646e73	0.982628	0.491314	−	0.870982i	$-0.336517\pi$
$757$	2.56646e73	0.982628	0.491314	+	0.870982i	$0.336517\pi$
$758$	2.36220e73	0.874482
$759$	3.05191e72	0.109246
$760$	2.15785e73	0.746920
$761$	9.99441e72	0.334540	0.167270	−	0.985911i	$-0.446505\pi$
$761$	9.99441e72	0.334540	0.167270	+	0.985911i	$0.446505\pi$
$762$	−3.53918e73	−1.14565
$763$	−2.71857e73	−0.851071
$764$	−1.45428e73	−0.440319
$765$	5.94092e73	1.73975
$766$	−4.39880e73	−1.24595
$767$	−3.15843e73	−0.865346
$768$	3.32317e72	0.0880726
$769$	1.58088e73	0.405301	0.202651	−	0.979251i	$-0.435044\pi$
$769$	1.58088e73	0.405301	0.202651	+	0.979251i	$0.435044\pi$
$770$	−2.05011e72	−0.0508467
$771$	−3.59768e73	−0.863249
$772$	−2.23177e72	−0.0518095
$773$	3.90612e73	0.877342	0.438671	−	0.898648i	$-0.355449\pi$
$773$	3.90612e73	0.877342	0.438671	+	0.898648i	$0.355449\pi$
$774$	3.22471e73	0.700803
$775$	6.71809e73	1.41271
$776$	−8.60845e71	−0.0175166
$777$	−5.02711e73	−0.989880
$778$	−5.72204e73	−1.09036
$779$	6.12184e73	1.12895
$780$	−8.70428e73	−1.55353
$781$	−2.77958e71	−0.00480151
$782$	8.31152e73	1.38966
$783$	6.96114e71	0.0112656
$784$	1.06518e72	0.0166865
$785$	−1.01326e74	−1.53654
$786$	4.49019e73	0.659158
$787$	−6.95089e73	−0.987836	−0.493918	−	0.869508i	$-0.664436\pi$
$787$	−6.95089e73	−0.987836	−0.493918	+	0.869508i	$0.664436\pi$
$788$	2.97851e73	0.409808
$789$	−1.10639e74	−1.47382
$790$	−1.68233e73	−0.216981
$791$	3.22356e73	0.402565
$792$	−1.27572e72	−0.0154264
$793$	2.05829e74	2.41013
$794$	−5.87810e73	−0.666521
$795$	−2.11176e74	−2.31890
$796$	−1.02259e72	−0.0108747
$797$	−9.06131e73	−0.933262	−0.466631	−	0.884452i	$-0.654532\pi$
$797$	−9.06131e73	−0.933262	−0.466631	+	0.884452i	$0.654532\pi$
$798$	1.38570e74	1.38228
$799$	−5.55878e73	−0.537078
$800$	−2.78433e73	−0.260571
$801$	8.11751e73	0.735857
$802$	1.54542e74	1.35707
$803$	2.83586e72	0.0241234
$804$	8.38513e73	0.691004
$805$	3.56389e74	2.84531
$806$	−1.22820e74	−0.950004
$807$	−4.20200e73	−0.314906
$808$	8.11157e73	0.589000
$809$	−1.89657e73	−0.133439	−0.0667193	−	0.997772i	$-0.521253\pi$
$809$	−1.89657e73	−0.133439	−0.0667193	+	0.997772i	$0.521253\pi$
$810$	−1.65431e74	−1.12784
$811$	8.25544e73	0.545392	0.272696	−	0.962100i	$-0.412085\pi$
$811$	8.25544e73	0.545392	0.272696	+	0.962100i	$0.412085\pi$
$812$	4.52177e73	0.289488
$813$	2.15546e74	1.33731
$814$	−3.54034e72	−0.0212874
$815$	−7.86036e73	−0.458061
$816$	−6.99882e73	−0.395299
$817$	−2.46678e74	−1.35042
$818$	6.22356e72	0.0330240
$819$	−2.77473e74	−1.42719
$820$	−1.32581e74	−0.661041
$821$	−1.00216e74	−0.484379	−0.242189	−	0.970229i	$-0.577866\pi$
$821$	−1.00216e74	−0.484379	−0.242189	+	0.970229i	$0.577866\pi$
$822$	−1.90803e74	−0.894033
$823$	1.95186e74	0.886652	0.443326	−	0.896360i	$-0.353798\pi$
$823$	1.95186e74	0.886652	0.443326	+	0.896360i	$0.353798\pi$
$824$	7.63546e73	0.336272
$825$	2.15320e73	0.0919408
$826$	−1.08895e74	−0.450834
$827$	−5.86838e73	−0.235574	−0.117787	−	0.993039i	$-0.537580\pi$
$827$	−5.86838e73	−0.235574	−0.117787	+	0.993039i	$0.537580\pi$
$828$	2.21770e74	0.863237
$829$	−4.42553e74	−1.67042	−0.835209	−	0.549933i	$-0.814653\pi$
$829$	−4.42553e74	−1.67042	−0.835209	+	0.549933i	$0.814653\pi$
$830$	2.32786e73	0.0852050
$831$	5.29416e74	1.87919
$832$	5.09030e73	0.175226
$833$	−2.24335e73	−0.0748945
$834$	3.78100e72	0.0122426
$835$	3.58017e74	1.12434
$836$	9.75878e72	0.0297259
$837$	−6.51894e72	−0.0192610
$838$	−2.38281e74	−0.682916
$839$	−2.45206e74	−0.681712	−0.340856	−	0.940116i	$-0.610717\pi$
$839$	−2.45206e74	−0.681712	−0.340856	+	0.940116i	$0.610717\pi$
$840$	−3.00102e74	−0.809370
$841$	−2.62103e74	−0.685762
$842$	1.33416e74	0.338649
$843$	1.02194e75	2.51665
$844$	−1.74160e74	−0.416117
$845$	−6.54795e74	−1.51796
$846$	−1.48321e74	−0.333625
$847$	4.72287e74	1.03081
$848$	1.23496e74	0.261553
$849$	6.15723e74	1.26543
$850$	5.86399e74	1.16953
$851$	6.15450e74	1.19121
$852$	−4.06885e73	−0.0764297
$853$	−5.27771e72	−0.00962155	−0.00481078	−	0.999988i	$-0.501531\pi$
$853$	−5.27771e72	−0.00962155	−0.00481078	+	0.999988i	$0.501531\pi$
$854$	7.09648e74	1.25565
$855$	−1.21260e75	−2.08248
$856$	−1.20528e74	−0.200913
$857$	−7.34375e74	−1.18825	−0.594124	−	0.804373i	$-0.702501\pi$
$857$	−7.34375e74	−1.18825	−0.594124	+	0.804373i	$0.702501\pi$
$858$	−3.93648e73	−0.0618275
$859$	−1.04232e75	−1.58919	−0.794595	−	0.607140i	$-0.792317\pi$
$859$	−1.04232e75	−1.58919	−0.794595	+	0.607140i	$0.792317\pi$
$860$	5.34233e74	0.790715
$861$	−8.51392e74	−1.22335
$862$	−2.09147e73	−0.0291754
$863$	−8.89250e74	−1.20434	−0.602169	−	0.798369i	$-0.705697\pi$
$863$	−8.89250e74	−1.20434	−0.602169	+	0.798369i	$0.705697\pi$
$864$	2.70179e72	0.00355264
$865$	1.05106e75	1.34189
$866$	6.41405e74	0.795108
$867$	3.03295e74	0.365072
$868$	−4.23453e74	−0.494940
$869$	−7.60828e72	−0.00863540
$870$	−7.97108e74	−0.878570
$871$	1.28440e75	1.37480
$872$	−2.80260e74	−0.291333
$873$	4.83750e73	0.0488380
$874$	−1.69646e75	−1.66342
$875$	8.08582e74	0.770050
$876$	4.15123e74	0.383992
$877$	−1.31321e75	−1.17990	−0.589948	−	0.807441i	$-0.700852\pi$
$877$	−1.31321e75	−1.17990	−0.589948	+	0.807441i	$0.700852\pi$
$878$	1.44606e75	1.26205
$879$	−9.33027e74	−0.791003
$880$	−2.11347e73	−0.0174055
$881$	1.46560e75	1.17255	0.586274	−	0.810113i	$-0.300594\pi$
$881$	1.46560e75	1.17255	0.586274	+	0.810113i	$0.300594\pi$
$882$	−5.98578e73	−0.0465234
$883$	−1.17536e75	−0.887513	−0.443757	−	0.896147i	$-0.646354\pi$
$883$	−1.17536e75	−0.887513	−0.443757	+	0.896147i	$0.646354\pi$
$884$	−1.07205e75	−0.786473
$885$	1.91962e75	1.36824
$886$	3.69153e74	0.255650
$887$	2.17326e75	1.46237	0.731187	−	0.682177i	$-0.238967\pi$
$887$	2.17326e75	1.46237	0.731187	+	0.682177i	$0.238967\pi$
$888$	−5.18248e74	−0.338850
$889$	−1.86909e75	−1.18750
$890$	1.34482e75	0.830267
$891$	−7.48154e73	−0.0448859
$892$	−7.88822e73	−0.0459912
$893$	1.13460e75	0.642881
$894$	−2.61026e75	−1.43740
$895$	−1.73154e75	−0.926712
$896$	1.75501e74	0.0912905
$897$	6.84314e75	3.45978
$898$	5.21327e74	0.256191
$899$	−1.12474e75	−0.537256
$900$	1.56465e75	0.726494
$901$	−2.60092e75	−1.17394
$902$	−5.99593e73	−0.0263081
$903$	3.43066e75	1.46332
$904$	3.32319e74	0.137804
$905$	−6.86076e75	−2.76588
$906$	2.24775e75	0.881008
$907$	3.44327e75	1.31215	0.656077	−	0.754694i	$-0.272215\pi$
$907$	3.44327e75	1.31215	0.656077	+	0.754694i	$0.272215\pi$
$908$	−1.48375e75	−0.549757
$909$	−4.55828e75	−1.64219
$910$	−4.59685e75	−1.61029
$911$	−5.46662e74	−0.186209	−0.0931043	−	0.995656i	$-0.529679\pi$
$911$	−5.46662e74	−0.186209	−0.0931043	+	0.995656i	$0.529679\pi$
$912$	1.42853e75	0.473173
$913$	1.05276e73	0.00339099
$914$	−3.18542e75	−0.997789
$915$	−1.25098e76	−3.81078
$916$	1.75377e75	0.519562
$917$	2.37133e75	0.683241
$918$	−5.69016e73	−0.0159454
$919$	4.51848e75	1.23153	0.615767	−	0.787928i	$-0.288846\pi$
$919$	4.51848e75	1.23153	0.615767	+	0.787928i	$0.288846\pi$
$920$	3.67404e75	0.973989
$921$	8.10865e75	2.09088
$922$	2.41119e75	0.604775
$923$	−6.23252e74	−0.152062
$924$	−1.35720e74	−0.0322113
$925$	4.34216e75	1.00252
$926$	7.28503e74	0.163626
$927$	−4.29073e75	−0.937558
$928$	4.66152e74	0.0990956
$929$	−6.84179e75	−1.41504	−0.707521	−	0.706693i	$-0.750186\pi$
$929$	−6.84179e75	−1.41504	−0.707521	+	0.706693i	$0.750186\pi$
$930$	7.46472e75	1.50210
$931$	4.57889e74	0.0896486
$932$	−1.99348e75	−0.379757
$933$	1.38101e76	2.55985
$934$	8.97101e74	0.161807
$935$	4.45111e74	0.0781219
$936$	−2.86049e75	−0.488546
$937$	−8.17060e75	−1.35798	−0.678991	−	0.734146i	$-0.737583\pi$
$937$	−8.17060e75	−1.35798	−0.678991	+	0.734146i	$0.737583\pi$
$938$	4.42830e75	0.716251
$939$	−1.29838e76	−2.04376
$940$	−2.45721e75	−0.376429
$941$	2.86304e75	0.426867	0.213433	−	0.976958i	$-0.431535\pi$
$941$	2.86304e75	0.426867	0.213433	+	0.976958i	$0.431535\pi$
$942$	−6.70793e75	−0.973398
$943$	1.04233e76	1.47216
$944$	−1.12260e75	−0.154327
$945$	−2.43988e74	−0.0326481
$946$	2.41604e74	0.0314689
$947$	1.13481e76	1.43879	0.719396	−	0.694600i	$-0.244419\pi$
$947$	1.13481e76	1.43879	0.719396	+	0.694600i	$0.244419\pi$
$948$	−1.11373e75	−0.137457
$949$	6.35870e75	0.763976
$950$	−1.19689e76	−1.39992
$951$	−2.08912e76	−2.37882
$952$	−3.69618e75	−0.409742
$953$	3.10822e75	0.335462	0.167731	−	0.985833i	$-0.446356\pi$
$953$	3.10822e75	0.335462	0.167731	+	0.985833i	$0.446356\pi$
$954$	−6.93985e75	−0.729234
$955$	1.35389e76	1.38515
$956$	4.35969e75	0.434290
$957$	−3.60489e74	−0.0349653
$958$	7.84403e75	0.740830
$959$	−1.00766e76	−0.926698
$960$	−3.09377e75	−0.277059
$961$	−9.33963e74	−0.0814485
$962$	−7.93833e75	−0.674163
$963$	6.77306e75	0.560164
$964$	−5.71905e74	−0.0460638
$965$	2.07772e75	0.162982
$966$	2.35935e76	1.80250
$967$	−4.90527e75	−0.364996	−0.182498	−	0.983206i	$-0.558418\pi$
$967$	−4.90527e75	−0.364996	−0.182498	+	0.983206i	$0.558418\pi$
$968$	4.86883e75	0.352861
$969$	−3.00858e76	−2.12376
$970$	8.01421e74	0.0551038
$971$	−1.81139e76	−1.21317	−0.606586	−	0.795018i	$-0.707461\pi$
$971$	−1.81139e76	−1.21317	−0.606586	+	0.795018i	$0.707461\pi$
$972$	−1.07977e76	−0.704438
$973$	1.99680e74	0.0126899
$974$	6.94978e75	0.430247
$975$	4.82801e76	2.91172
$976$	7.31580e75	0.429825
$977$	2.03393e76	1.16419	0.582095	−	0.813120i	$-0.302233\pi$
$977$	2.03393e76	1.16419	0.582095	+	0.813120i	$0.302233\pi$
$978$	−5.20367e75	−0.290181
$979$	6.08187e74	0.0330429
$980$	−9.91655e74	−0.0524923
$981$	1.57491e76	0.812263
$982$	9.30336e75	0.467516
$983$	1.78546e76	0.874250	0.437125	−	0.899401i	$-0.355997\pi$
$983$	1.78546e76	0.874250	0.437125	+	0.899401i	$0.355997\pi$
$984$	−8.77706e75	−0.418768
$985$	−2.77291e76	−1.28917
$986$	−9.81750e75	−0.444774
$987$	−1.57794e76	−0.696632
$988$	2.18816e76	0.941407
$989$	−4.20003e76	−1.76095
$990$	1.18766e75	0.0485282
$991$	−1.12270e76	−0.447081	−0.223540	−	0.974695i	$-0.571761\pi$
$991$	−1.12270e76	−0.447081	−0.223540	+	0.974695i	$0.571761\pi$
$992$	−4.36540e75	−0.169425
$993$	2.48626e76	0.940459
$994$	−2.14882e75	−0.0792221
$995$	9.52001e74	0.0342097
$996$	1.54107e75	0.0539772
$997$	−4.17736e76	−1.42618	−0.713092	−	0.701070i	$-0.752706\pi$
$997$	−4.17736e76	−1.42618	−0.713092	+	0.701070i	$0.752706\pi$
$998$	5.12808e75	0.170658
$999$	−4.21344e74	−0.0136684

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2.52.a.a.1.2	✓	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2.52.a.a.1.2	✓	2	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 2 \)
Weight:	\( k \)	\(=\)	\( 52 \)
Character orbit:	\([\chi]\)	\(=\)	2.a (trivial)

\(f(q)\)	\(=\)	\(q-3.35544e7 q^{2} +2.06801e12 q^{3} +1.12590e15 q^{4} -1.04818e18 q^{5} -6.93910e19 q^{6} -3.66463e21 q^{7} -3.77789e22 q^{8} +2.12298e24 q^{9} +O(q^{10})\)	\(q-3.35544e7 q^{2} +2.06801e12 q^{3} +1.12590e15 q^{4} -1.04818e18 q^{5} -6.93910e19 q^{6} -3.66463e21 q^{7} -3.77789e22 q^{8} +2.12298e24 q^{9} +3.51711e25 q^{10} +1.59060e25 q^{11} +2.32837e27 q^{12} +3.56652e28 q^{13} +1.22965e29 q^{14} -2.16765e30 q^{15} +1.26765e30 q^{16} -2.66976e31 q^{17} -7.12354e31 q^{18} +5.44923e32 q^{19} -1.18015e33 q^{20} -7.57851e33 q^{21} -5.33716e32 q^{22} +9.27808e34 q^{23} -7.81273e34 q^{24} +6.54592e35 q^{25} -1.19672e36 q^{26} -6.35188e34 q^{27} -4.12601e36 q^{28} -1.09592e37 q^{29} +7.27342e37 q^{30} +1.02630e38 q^{31} -4.25353e37 q^{32} +3.28937e37 q^{33} +8.95823e38 q^{34} +3.84120e39 q^{35} +2.39026e39 q^{36} +6.63338e39 q^{37} -1.82846e40 q^{38} +7.37560e40 q^{39} +3.95991e40 q^{40} +1.12343e41 q^{41} +2.54292e41 q^{42} -4.52684e41 q^{43} +1.79085e40 q^{44} -2.22526e42 q^{45} -3.11321e42 q^{46} +2.08213e42 q^{47} +2.62152e42 q^{48} +8.40282e41 q^{49} -2.19645e43 q^{50} -5.52110e43 q^{51} +4.01554e43 q^{52} +9.74215e43 q^{53} +2.13134e42 q^{54} -1.66723e43 q^{55} +1.38446e44 q^{56} +1.12691e45 q^{57} +3.67729e44 q^{58} -8.85579e44 q^{59} -2.44056e45 q^{60} +5.77115e45 q^{61} -3.44370e45 q^{62} -7.77994e45 q^{63} +1.42725e45 q^{64} -3.73835e46 q^{65} -1.10373e45 q^{66} +3.60128e46 q^{67} -3.00588e46 q^{68} +1.91872e47 q^{69} -1.28889e47 q^{70} -1.74751e46 q^{71} -8.02039e46 q^{72} +1.78289e47 q^{73} -2.22579e47 q^{74} +1.35370e48 q^{75} +6.13529e47 q^{76} -5.82896e46 q^{77} -2.47484e48 q^{78} -4.78329e47 q^{79} -1.32873e48 q^{80} -4.70360e48 q^{81} -3.76961e48 q^{82} +6.61867e47 q^{83} -8.53264e48 q^{84} +2.79839e49 q^{85} +1.51895e49 q^{86} -2.26637e49 q^{87} -6.00911e47 q^{88} +3.82364e49 q^{89} +7.46675e49 q^{90} -1.30700e50 q^{91} +1.04462e50 q^{92} +2.12240e50 q^{93} -6.98646e49 q^{94} -5.71178e50 q^{95} -8.79635e49 q^{96} +2.27864e49 q^{97} -2.81952e49 q^{98} +3.37681e49 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 67108864 q^{2} + 187290382776 q^{3} + 22\!\cdots\!48 q^{4}+ \cdots + 35\!\cdots\!94 q^{9}+O(q^{10}) \) 2 * q - 67108864 * q^2 + 187290382776 * q^3 + 2251799813685248 * q^4 - 1222737445852282500 * q^5 - 6284422413111263232 * q^6 - 4100377271642428803152 * q^7 - 75557863725914323419136 * q^8 + 3506398323112132655391594 * q^9	\( 2 q - 67108864 q^{2} + 187290382776 q^{3} + 22\!\cdots\!48 q^{4}+ \cdots - 69\!\cdots\!12 q^{99}+O(q^{100}) \) 2 * q - 67108864 * q^2 + 187290382776 * q^3 + 2251799813685248 * q^4 - 1222737445852282500 * q^5 - 6284422413111263232 * q^6 - 4100377271642428803152 * q^7 - 75557863725914323419136 * q^8 + 3506398323112132655391594 * q^9 + 41028260480704095191040000 * q^10 - 511916859296118812642710296 * q^11 + 210870224520017790552244224 * q^12 + 2389767980887171723586110636 * q^13 + 137585830335671405590205169664 * q^14 - 1839354430187803812510967110000 * q^15 + 2535301200456458802993406410752 * q^16 - 38170755374707224218983245478812 * q^17 - 117655204097780083560316674244608 * q^18 - 136117369289850199022410411314920 * q^19 - 1376679976378072874209278689280000 * q^20 - 6758992101020073667714498669814976 * q^21 + 17177079444905186562740562922831872 * q^22 + 82360875483744207844699244747978256 * q^23 - 7075630609481669591875521261600768 * q^24 + 240973064028364917488157674630468750 * q^25 - 80187307210455903271392945480138752 * q^26 + 1385153336120426710614208934265178800 * q^27 - 4616614388161823353220959231539150848 * q^28 - 33433848941184296370650849380528607220 * q^29 + 61718493151635410256239995146731520000 * q^30 + 308835076169577443464575338477040889024 * q^31 - 85070591730234615865843651857942052864 * q^32 + 1025581489016605768622275037376245389152 * q^33 + 1280798015609248074964626419558104694784 * q^34 + 3917257457400276775841278728681725220000 * q^35 + 3947853545345083164778963744406850502656 * q^36 + 10523630739281458197095845856733483317308 * q^37 + 4567341011855166793283936622558513725440 * q^38 + 136337774481417941078653256910482131362768 * q^39 + 46193714653139652548699795548494888960000 * q^40 + 196921516461268471750199128431445042148724 * q^41 + 226794140842215192518316741030397064773632 * q^42 - 436185332310493098065395196254952050932824 * q^43 - 576367144192668828966791952235883296456704 * q^44 - 2466750259163950296521489332322761530652500 * q^45 - 2763572395879762127518827368347393528430592 * q^46 - 5071937001112410134266285842260710712524512 * q^47 + 237418766142971237567054930636937181003776 * q^48 - 11559100479246355218990053936704271423429934 * q^49 - 8085714290771416695041997498666188800000000 * q^50 - 33633211699677626929831102056190930239511056 * q^51 + 2690639547056352295318532134393023104548864 * q^52 + 105529315512706056254590899937168095592592796 * q^53 - 46478033426426001872288151918593412012441600 * q^54 + 75463119614657853791897301419452272509310000 * q^55 + 154907873557797506701664657509452692466958336 * q^56 + 2407756071827149822022303793221962598517371040 * q^57 + 1121853810795240472036850721281189275018199040 * q^58 - 1105487952975610110465550699194488821613128440 * q^59 - 2070928981599016062235107492831332810096640000 * q^60 + 2174583020587510252529691078631554971127524044 * q^61 - 10362785562546906795465937603804852071975354368 * q^62 - 8382756336243902670051269559132648323046912144 * q^63 + 2854495385411919762116571938898990272765493248 * q^64 - 31575047397398129139930605639711933367031335000 * q^65 - 34412804333666445134043861426938684325614321664 * q^66 + 52980256222774625688459101408623680382039369528 * q^67 - 42976449920495453102531459600465894030010482688 * q^68 + 211468773409731513422661817504083539452351739328 * q^69 - 131441348980830483856145429894597398537175040000 * q^70 + 71838794922889018513950754051538223712457615664 * q^71 - 132467983333240509586920533992165045525536571392 * q^72 + 633989662758328739460390107342060538497732058676 * q^73 - 353114452034329417935295157282245408093745709056 * q^74 + 2131605811399349017290662875234578991549903125000 * q^75 - 153254533403105388013903908093949314821343150080 * q^76 + 171706038038113743094982498894497703297304386496 * q^77 - 4574736582868073567503677360581302764027066187776 * q^78 + 1987694552793370941077747858308362884236649620960 * q^79 - 1550003857156178057948973978145874453955870720000 * q^80 - 10407615343628609253811192857082917170490174846318 * q^81 - 6607589633436513569085977641412189328516493344768 * q^82 - 7294964975412571318915019371395141945504236734824 * q^83 - 7609948576888532406722767841366068242946430337024 * q^84 + 29986629004292497369543490180442720795343506195000 * q^85 + 14635951072409843545504634665863443256285979475968 * q^86 + 19604850482371457136774548808933025198099393538640 * q^87 + 19339672146847101120085850819446194030892315312128 * q^88 + 76584790355821941738982505226510313491919750326420 * q^89 + 82770403832099147076010150340149503832495226880000 * q^90 - 116200228922371894653439828143865282695294601882336 * q^91 + 92730102034624558484005821650951568526964365983744 * q^92 - 175573684530170608392805003946795499445900778834688 * q^93 + 170185965212110290206348958186699743875075286237184 * q^94 - 452296986866245785230138918380370612312622071550000 * q^95 - 7966451844068230668899590110321825328262893535232 * q^96 - 299203660839571973887426598893507965282463766755772 * q^97 + 387859051012039237443446873495475779587022927167488 * q^98 - 696432229055306535317133838555495031791652116305912 * q^99

Introduction

L-functions

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