LMFDB - Embedded newform 3.30.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3,30,Mod(1,3)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 30, names="a")

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

chi := DirichletCharacter("3.1");

S:= CuspForms(chi, 30);

N := Newforms(S);

Level:	$ N $	$=$	$ 3 $
Weight:	$ k $	$=$	$ 30 $
Character orbit:	$[\chi]$	$=$	3.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:	$15.9834127149$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{77089}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 19272 $ x^2 - x - 19272
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 2^{2}\cdot 3\cdot 7 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$139.325$ of defining polynomial
Character	$\chi$	$=$	3.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-34179.3 q^{2} -4.78297e6 q^{3} +6.31351e8 q^{4} -2.18126e10 q^{5} +1.63478e11 q^{6} +3.31488e12 q^{7} -3.22926e12 q^{8} +2.28768e13 q^{9} +O(q^{10})$	\(q-34179.3 q^{2} -4.78297e6 q^{3} +6.31351e8 q^{4} -2.18126e10 q^{5} +1.63478e11 q^{6} +3.31488e12 q^{7} -3.22926e12 q^{8} +2.28768e13 q^{9} +7.45538e14 q^{10} -8.29004e13 q^{11} -3.01973e15 q^{12} +2.34198e15 q^{13} -1.13300e17 q^{14} +1.04329e17 q^{15} -2.28580e17 q^{16} +3.59403e17 q^{17} -7.81912e17 q^{18} -2.93337e18 q^{19} -1.37714e19 q^{20} -1.58550e19 q^{21} +2.83348e18 q^{22} +1.39110e19 q^{23} +1.54454e19 q^{24} +2.89524e20 q^{25} -8.00473e19 q^{26} -1.09419e20 q^{27} +2.09285e21 q^{28} -1.94885e21 q^{29} -3.56588e21 q^{30} +3.97886e21 q^{31} +9.54640e21 q^{32} +3.96510e20 q^{33} -1.22841e22 q^{34} -7.23060e22 q^{35} +1.44433e22 q^{36} -2.25333e22 q^{37} +1.00260e23 q^{38} -1.12016e22 q^{39} +7.04384e22 q^{40} +2.66746e23 q^{41} +5.41911e23 q^{42} -5.53027e23 q^{43} -5.23393e22 q^{44} -4.99002e23 q^{45} -4.75467e23 q^{46} -2.44770e24 q^{47} +1.09329e24 q^{48} +7.76851e24 q^{49} -9.89571e24 q^{50} -1.71901e24 q^{51} +1.47861e24 q^{52} +1.63222e24 q^{53} +3.73986e24 q^{54} +1.80827e24 q^{55} -1.07046e25 q^{56} +1.40302e25 q^{57} +6.66103e25 q^{58} -3.27794e25 q^{59} +6.58681e25 q^{60} -3.87903e25 q^{61} -1.35994e26 q^{62} +7.58338e25 q^{63} -2.03571e26 q^{64} -5.10847e25 q^{65} -1.35524e25 q^{66} -5.10980e26 q^{67} +2.26909e26 q^{68} -6.65358e25 q^{69} +2.47137e27 q^{70} -5.71879e26 q^{71} -7.38750e25 q^{72} -3.88369e26 q^{73} +7.70171e26 q^{74} -1.38478e27 q^{75} -1.85198e27 q^{76} -2.74805e26 q^{77} +3.82864e26 q^{78} +2.83632e26 q^{79} +4.98592e27 q^{80} +5.23348e26 q^{81} -9.11720e27 q^{82} +2.80690e27 q^{83} -1.00100e28 q^{84} -7.83950e27 q^{85} +1.89020e28 q^{86} +9.32129e27 q^{87} +2.67707e26 q^{88} -1.94592e28 q^{89} +1.70555e28 q^{90} +7.76339e27 q^{91} +8.78271e27 q^{92} -1.90307e28 q^{93} +8.36605e28 q^{94} +6.39843e28 q^{95} -4.56601e28 q^{96} -9.79243e28 q^{97} -2.65522e29 q^{98} -1.89650e27 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 45036 q^{2} - 9565938 q^{3} + 212348816 q^{4} + 187613820 q^{5} + 215405791884 q^{6} + 2643976121248 q^{7} + 7148407194432 q^{8} + 45753584909922 q^{9}+O(q^{10}) $ 2 * q - 45036 * q^2 - 9565938 * q^3 + 212348816 * q^4 + 187613820 * q^5 + 215405791884 * q^6 + 2643976121248 * q^7 + 7148407194432 * q^8 + 45753584909922 * q^9	$ 2 q - 45036 q^{2} - 9565938 q^{3} + 212348816 q^{4} + 187613820 q^{5} + 215405791884 q^{6} + 2643976121248 q^{7} + 7148407194432 q^{8} + 45753584909922 q^{9} + 506687260172760 q^{10} + 11\!\cdots\!28 q^{11}+ \cdots + 27\!\cdots\!08 q^{99}+O(q^{100}) $ 2 * q - 45036 * q^2 - 9565938 * q^3 + 212348816 * q^4 + 187613820 * q^5 + 215405791884 * q^6 + 2643976121248 * q^7 + 7148407194432 * q^8 + 45753584909922 * q^9 + 506687260172760 * q^10 + 1183469847829128 * q^11 - 1015657804114704 * q^12 - 21620888448148964 * q^13 - 106016273372995776 * q^14 - 897351085031580 * q^15 - 116297875935973120 * q^16 - 303436852359947964 * q^17 - 1030279225001623596 * q^18 - 7827889308240559496 * q^19 - 22989510711581456160 * q^20 - 12646055824669425312 * q^21 - 10915176904366508208 * q^22 - 1116121153769543376 * q^23 - 34190610010345228608 * q^24 + 587267318983626701150 * q^25 + 180111376423529552664 * q^26 - 218837978263024718418 * q^27 + 2373960709689332060416 * q^28 - 1549485579134315167092 * q^29 - 2423469458101245724440 * q^30 + 5185371205472693880112 * q^31 + 2755913283673324950528 * q^32 - 5660499594601436521032 * q^33 - 5087847547502785153368 * q^34 - 87065978554982950367040 * q^35 + 4857859791688701676176 * q^36 - 119610541537944992870612 * q^37 + 153398867521954218331824 * q^38 + 103412039199954602194116 * q^39 + 298748936011672856304000 * q^40 + 328159280597938698745332 * q^41 + 507072549038564233738944 * q^42 - 445450142806590533867000 * q^43 - 582951091424778866423232 * q^44 + 4292002421822411161020 * q^45 - 312321856572855528664608 * q^46 - 3462042915003644476983360 * q^47 + 556249135367605417793280 * q^48 + 4998714551689832609432370 * q^49 - 13128231346593205174089300 * q^50 + 1451329058295207953425116 * q^51 + 11519108423346209889919456 * q^52 - 14708457881668639138246596 * q^53 + 4927793594526790609336524 * q^54 + 29668651008250805659776240 * q^55 - 17666989638946946010639360 * q^56 + 37440551896746040612023624 * q^57 + 62274468648513136429575288 * q^58 - 48644338512234214893804984 * q^59 + 109958117058662045788139040 * q^60 - 74065165362970768623670820 * q^61 - 149093160585184069121258784 * q^62 + 60485692981663296515111328 * q^63 - 190129418691127176875831296 * q^64 - 578272316465227808767070520 * q^65 + 52206952763100973397109552 * q^66 - 366723705229906233436453064 * q^67 + 504640651326985312676536608 * q^68 + 5338372878723959111563344 * q^69 + 2631611128693389613002449280 * q^70 - 127322506876819543969204656 * q^71 + 163532627770570907729977152 * q^72 - 731571978572366031601976876 * q^73 + 1824113482985542836781172664 * q^74 - 2808881381411798019172714350 * q^75 + 198831266834486833097469376 * q^76 - 1124415098711978092688640384 * q^77 - 861467129981072720975779416 * q^78 - 5200098584837687939224496240 * q^79 + 7456159068548324050900753920 * q^80 + 1046695266054721074427023042 * q^81 - 9783939716187695677162489464 * q^82 + 7969015649847556259120597112 * q^83 - 11354580481662074875675855104 * q^84 - 22422099301146829036391554440 * q^85 + 17734112012711861680386446928 * q^86 + 7411141490946476280430856148 * q^87 + 13409672678850676246787849472 * q^88 + 12871942448610625249661939124 * q^89 + 11591379290545057161379062360 * q^90 + 23840130434649524469770109632 * q^91 + 15079105137564640323695392128 * q^92 - 24801469729268525175065412528 * q^93 + 94672981437665362714609762176 * q^94 - 43696120536074431524731727600 * q^95 - 13181447802497719365301957632 * q^96 - 92696268103775509741340043644 * q^97 - 235450999642801088400974721036 * q^98 + 27073994085491238235563904008 * 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 $

$2$	−34179.3	−1.47512	−0.737561	−	0.675281i	$-0.764022\pi$
$2$	−34179.3	−1.47512	−0.737561	+	0.675281i	$0.764022\pi$
$3$	−4.78297e6	−0.577350
$3$	−4.78297e6	−0.577350
$4$	6.31351e8	1.17598
$5$	−2.18126e10	−1.59824	−0.799120	−	0.601172i	$-0.794701\pi$
$5$	−2.18126e10	−1.59824	−0.799120	+	0.601172i	$0.794701\pi$
$6$	1.63478e11	0.851662
$7$	3.31488e12	1.84734	0.923668	−	0.383193i	$-0.125176\pi$
$7$	3.31488e12	1.84734	0.923668	+	0.383193i	$0.125176\pi$
$8$	−3.22926e12	−0.259596
$9$	2.28768e13	0.333333
$10$	7.45538e14	2.35760
$11$	−8.29004e13	−0.0658208	−0.0329104	−	0.999458i	$-0.510478\pi$
$11$	−8.29004e13	−0.0658208	−0.0329104	+	0.999458i	$0.510478\pi$
$12$	−3.01973e15	−0.678954
$13$	2.34198e15	0.164970	0.0824851	−	0.996592i	$-0.473714\pi$
$13$	2.34198e15	0.164970	0.0824851	+	0.996592i	$0.473714\pi$
$14$	−1.13300e17	−2.72505
$15$	1.04329e17	0.922744
$16$	−2.28580e17	−0.793047
$17$	3.59403e17	0.517693	0.258846	−	0.965918i	$-0.416658\pi$
$17$	3.59403e17	0.517693	0.258846	+	0.965918i	$0.416658\pi$
$18$	−7.81912e17	−0.491707
$19$	−2.93337e18	−0.842246	−0.421123	−	0.907003i	$-0.638364\pi$
$19$	−2.93337e18	−0.842246	−0.421123	+	0.907003i	$0.638364\pi$
$20$	−1.37714e19	−1.87950
$21$	−1.58550e19	−1.06656
$22$	2.83348e18	0.0970936
$23$	1.39110e19	0.250210	0.125105	−	0.992144i	$-0.460073\pi$
$23$	1.39110e19	0.250210	0.125105	+	0.992144i	$0.460073\pi$
$24$	1.54454e19	0.149878
$25$	2.89524e20	1.55437
$26$	−8.00473e19	−0.243351
$27$	−1.09419e20	−0.192450
$28$	2.09285e21	2.17244
$29$	−1.94885e21	−1.21621	−0.608104	−	0.793858i	$-0.708069\pi$
$29$	−1.94885e21	−1.21621	−0.608104	+	0.793858i	$0.708069\pi$
$30$	−3.56588e21	−1.36116
$31$	3.97886e21	0.944090	0.472045	−	0.881574i	$-0.343516\pi$
$31$	3.97886e21	0.944090	0.472045	+	0.881574i	$0.343516\pi$
$32$	9.54640e21	1.42944
$33$	3.96510e20	0.0380016
$34$	−1.22841e22	−0.763660
$35$	−7.23060e22	−2.95249
$36$	1.44433e22	0.391994
$37$	−2.25333e22	−0.411055	−0.205527	−	0.978651i	$-0.565891\pi$
$37$	−2.25333e22	−0.411055	−0.205527	+	0.978651i	$0.565891\pi$
$38$	1.00260e23	1.24242
$39$	−1.12016e22	−0.0952456
$40$	7.04384e22	0.414896
$41$	2.66746e23	1.09833	0.549165	−	0.835714i	$-0.314946\pi$
$41$	2.66746e23	1.09833	0.549165	+	0.835714i	$0.314946\pi$
$42$	5.41911e23	1.57331
$43$	−5.53027e23	−1.14144	−0.570720	−	0.821144i	$-0.693336\pi$
$43$	−5.53027e23	−1.14144	−0.570720	+	0.821144i	$0.693336\pi$
$44$	−5.23393e22	−0.0774041
$45$	−4.99002e23	−0.532746
$46$	−4.75467e23	−0.369090
$47$	−2.44770e24	−1.39104	−0.695519	−	0.718508i	$-0.744825\pi$
$47$	−2.44770e24	−1.39104	−0.695519	+	0.718508i	$0.744825\pi$
$48$	1.09329e24	0.457866
$49$	7.76851e24	2.41265
$50$	−9.89571e24	−2.29288
$51$	−1.71901e24	−0.298890
$52$	1.47861e24	0.194002
$53$	1.63222e24	0.162472	0.0812361	−	0.996695i	$-0.474113\pi$
$53$	1.63222e24	0.162472	0.0812361	+	0.996695i	$0.474113\pi$
$54$	3.73986e24	0.283887
$55$	1.80827e24	0.105197
$56$	−1.07046e25	−0.479561
$57$	1.40302e25	0.486271
$58$	6.66103e25	1.79405
$59$	−3.27794e25	−0.689043	−0.344521	−	0.938778i	$-0.611959\pi$
$59$	−3.27794e25	−0.689043	−0.344521	+	0.938778i	$0.611959\pi$
$60$	6.58681e25	1.08513
$61$	−3.87903e25	−0.502853	−0.251426	−	0.967876i	$-0.580900\pi$
$61$	−3.87903e25	−0.502853	−0.251426	+	0.967876i	$0.580900\pi$
$62$	−1.35994e26	−1.39265
$63$	7.58338e25	0.615779
$64$	−2.03571e26	−1.31555
$65$	−5.10847e25	−0.263662
$66$	−1.35524e25	−0.0560570
$67$	−5.10980e26	−1.69949	−0.849746	−	0.527192i	$-0.823245\pi$
$67$	−5.10980e26	−1.69949	−0.849746	+	0.527192i	$0.823245\pi$
$68$	2.26909e26	0.608798
$69$	−6.65358e25	−0.144459
$70$	2.47137e27	4.35527
$71$	−5.71879e26	−0.820462	−0.410231	−	0.911982i	$-0.634552\pi$
$71$	−5.71879e26	−0.820462	−0.410231	+	0.911982i	$0.634552\pi$
$72$	−7.38750e25	−0.0865320
$73$	−3.88369e26	−0.372445	−0.186223	−	0.982508i	$-0.559625\pi$
$73$	−3.88369e26	−0.372445	−0.186223	+	0.982508i	$0.559625\pi$
$74$	7.70171e26	0.606355
$75$	−1.38478e27	−0.897415
$76$	−1.85198e27	−0.990467
$77$	−2.74805e26	−0.121593
$78$	3.82864e26	0.140499
$79$	2.83632e26	0.0865292	0.0432646	−	0.999064i	$-0.486224\pi$
$79$	2.83632e26	0.0865292	0.0432646	+	0.999064i	$0.486224\pi$
$80$	4.98592e27	1.26748
$81$	5.23348e26	0.111111
$82$	−9.11720e27	−1.62017
$83$	2.80690e27	0.418403	0.209201	−	0.977873i	$-0.432914\pi$
$83$	2.80690e27	0.418403	0.209201	+	0.977873i	$0.432914\pi$
$84$	−1.00100e28	−1.25426
$85$	−7.83950e27	−0.827397
$86$	1.89020e28	1.68376
$87$	9.32129e27	0.702178
$88$	2.67707e26	0.0170868
$89$	−1.94592e28	−1.05431	−0.527157	−	0.849768i	$-0.676742\pi$
$89$	−1.94592e28	−1.05431	−0.527157	+	0.849768i	$0.676742\pi$
$90$	1.70555e28	0.785866
$91$	7.76339e27	0.304755
$92$	8.78271e27	0.294242
$93$	−1.90307e28	−0.545071
$94$	8.36605e28	2.05195
$95$	6.39843e28	1.34611
$96$	−4.56601e28	−0.825286
$97$	−9.79243e28	−1.52300	−0.761501	−	0.648164i	$-0.775537\pi$
$97$	−9.79243e28	−1.52300	−0.761501	+	0.648164i	$0.775537\pi$
$98$	−2.65522e29	−3.55895
$99$	−1.89650e27	−0.0219403
$100$	1.82791e29	1.82791
$101$	−4.48482e28	−0.388226	−0.194113	−	0.980979i	$-0.562183\pi$
$101$	−4.48482e28	−0.388226	−0.194113	+	0.980979i	$0.562183\pi$
$102$	5.87546e28	0.440899
$103$	−1.54050e29	−1.00351	−0.501754	−	0.865010i	$-0.667312\pi$
$103$	−1.54050e29	−1.00351	−0.501754	+	0.865010i	$0.667312\pi$
$104$	−7.56287e27	−0.0428256
$105$	3.45837e29	1.70462
$106$	−5.57881e28	−0.239666
$107$	2.04368e29	0.766210	0.383105	−	0.923705i	$-0.374855\pi$
$107$	2.04368e29	0.766210	0.383105	+	0.923705i	$0.374855\pi$
$108$	−6.90818e28	−0.226318
$109$	4.98278e29	1.42820	0.714098	−	0.700046i	$-0.246837\pi$
$109$	4.98278e29	1.42820	0.714098	+	0.700046i	$0.246837\pi$
$110$	−6.18054e28	−0.155179
$111$	1.07776e29	0.237322
$112$	−7.57716e29	−1.46503
$113$	4.26815e29	0.725442	0.362721	−	0.931898i	$-0.381848\pi$
$113$	4.26815e29	0.725442	0.362721	+	0.931898i	$0.381848\pi$
$114$	−4.79542e29	−0.717309
$115$	−3.03434e29	−0.399895
$116$	−1.23041e30	−1.43024
$117$	5.35771e28	0.0549900
$118$	1.12037e30	1.01642
$119$	1.19138e30	0.956353
$120$	−3.36905e29	−0.239541
$121$	−1.57944e30	−0.995668
$122$	1.32582e30	0.741769
$123$	−1.27584e30	−0.634121
$124$	2.51205e30	1.11023
$125$	−2.25235e30	−0.886014
$126$	−2.59194e30	−0.908348
$127$	−9.24923e29	−0.289036	−0.144518	−	0.989502i	$-0.546163\pi$
$127$	−9.24923e29	−0.289036	−0.144518	+	0.989502i	$0.546163\pi$
$128$	1.83271e30	0.511152
$129$	2.64511e30	0.659011
$130$	1.74604e30	0.388933
$131$	6.38172e30	1.27205	0.636025	−	0.771669i	$-0.280578\pi$
$131$	6.38172e30	1.27205	0.636025	+	0.771669i	$0.280578\pi$
$132$	2.50337e29	0.0446893
$133$	−9.72375e30	−1.55591
$134$	1.74649e31	2.50696
$135$	2.38671e30	0.307581
$136$	−1.16060e30	−0.134391
$137$	−1.40882e31	−1.46692	−0.733461	−	0.679731i	$-0.762096\pi$
$137$	−1.40882e31	−1.46692	−0.733461	+	0.679731i	$0.762096\pi$
$138$	2.27415e30	0.213094
$139$	−1.49816e31	−1.26428	−0.632140	−	0.774854i	$-0.717823\pi$
$139$	−1.49816e31	−1.26428	−0.632140	+	0.774854i	$0.717823\pi$
$140$	−4.56505e31	−3.47207
$141$	1.17073e31	0.803116
$142$	1.95464e31	1.21028
$143$	−1.94151e29	−0.0108585
$144$	−5.22918e30	−0.264349
$145$	4.25094e31	1.94379
$146$	1.32742e31	0.549402
$147$	−3.71565e31	−1.39295
$148$	−1.42264e31	−0.483393
$149$	1.20894e31	0.372568	0.186284	−	0.982496i	$-0.440356\pi$
$149$	1.20894e31	0.372568	0.186284	+	0.982496i	$0.440356\pi$
$150$	4.73309e31	1.32380
$151$	4.36447e31	1.10858	0.554289	−	0.832325i	$-0.312990\pi$
$151$	4.36447e31	1.10858	0.554289	+	0.832325i	$0.312990\pi$
$152$	9.47260e30	0.218644
$153$	8.22199e30	0.172564
$154$	9.39263e30	0.179365
$155$	−8.67891e31	−1.50888
$156$	−7.07216e30	−0.112007
$157$	−2.01617e29	−0.00291060	−0.00145530	−	0.999999i	$-0.500463\pi$
$157$	−2.01617e29	−0.00291060	−0.00145530	+	0.999999i	$0.500463\pi$
$158$	−9.69434e30	−0.127641
$159$	−7.80686e30	−0.0938033
$160$	−2.08232e32	−2.28458
$161$	4.61132e31	0.462222
$162$	−1.78876e31	−0.163902
$163$	7.56962e31	0.634387	0.317193	−	0.948361i	$-0.397260\pi$
$163$	7.56962e31	0.634387	0.317193	+	0.948361i	$0.397260\pi$
$164$	1.68411e32	1.29162
$165$	−8.64891e30	−0.0607357
$166$	−9.59377e31	−0.617195
$167$	6.19364e31	0.365222	0.182611	−	0.983185i	$-0.441545\pi$
$167$	6.19364e31	0.365222	0.182611	+	0.983185i	$0.441545\pi$
$168$	5.11997e31	0.276875
$169$	−1.96053e32	−0.972785
$170$	2.67948e32	1.22051
$171$	−6.71060e31	−0.280749
$172$	−3.49154e32	−1.34231
$173$	−2.57773e31	−0.0911107	−0.0455553	−	0.998962i	$-0.514506\pi$
$173$	−2.57773e31	−0.0911107	−0.0455553	+	0.998962i	$0.514506\pi$
$174$	−3.18595e32	−1.03580
$175$	9.59736e32	2.87144
$176$	1.89494e31	0.0521990
$177$	1.56783e32	0.397819
$178$	6.65102e32	1.55524
$179$	−4.32471e32	−0.932369	−0.466185	−	0.884687i	$-0.654372\pi$
$179$	−4.32471e32	−0.932369	−0.466185	+	0.884687i	$0.654372\pi$
$180$	−3.15045e32	−0.626501
$181$	−4.06703e32	−0.746342	−0.373171	−	0.927763i	$-0.621729\pi$
$181$	−4.06703e32	−0.746342	−0.373171	+	0.927763i	$0.621729\pi$
$182$	−2.65347e32	−0.449551
$183$	1.85533e32	0.290322
$184$	−4.49222e31	−0.0649534
$185$	4.91509e32	0.656964
$186$	6.50457e32	0.804046
$187$	−2.97947e31	−0.0340749
$188$	−1.54536e33	−1.63584
$189$	−3.62711e32	−0.355520
$190$	−2.18694e33	−1.98568
$191$	−1.26944e33	−1.06814	−0.534072	−	0.845439i	$-0.679339\pi$
$191$	−1.26944e33	−1.06814	−0.534072	+	0.845439i	$0.679339\pi$
$192$	9.73673e32	0.759530
$193$	−1.71482e33	−1.24062	−0.620308	−	0.784358i	$-0.712993\pi$
$193$	−1.71482e33	−1.24062	−0.620308	+	0.784358i	$0.712993\pi$
$194$	3.34698e33	2.24661
$195$	2.44337e32	0.152225
$196$	4.90466e33	2.83724
$197$	−2.35275e31	−0.0126420	−0.00632100	−	0.999980i	$-0.502012\pi$
$197$	−2.35275e31	−0.0126420	−0.00632100	+	0.999980i	$0.502012\pi$
$198$	6.48208e31	0.0323645
$199$	1.93244e33	0.896882	0.448441	−	0.893812i	$-0.351979\pi$
$199$	1.93244e33	0.896882	0.448441	+	0.893812i	$0.351979\pi$
$200$	−9.34947e32	−0.403508
$201$	2.44400e33	0.981202
$202$	1.53288e33	0.572681
$203$	−6.46020e33	−2.24674
$204$	−1.08530e33	−0.351490
$205$	−5.81843e33	−1.75539
$206$	5.26530e33	1.48030
$207$	3.18239e32	0.0834033
$208$	−5.35332e32	−0.130829
$209$	2.43177e32	0.0554373
$210$	−1.18205e34	−2.51452
$211$	2.44326e33	0.485147	0.242574	−	0.970133i	$-0.422008\pi$
$211$	2.44326e33	0.485147	0.242574	+	0.970133i	$0.422008\pi$
$212$	1.03050e33	0.191064
$213$	2.73528e33	0.473694
$214$	−6.98514e33	−1.13025
$215$	1.20629e34	1.82430
$216$	3.53342e32	0.0499593
$217$	1.31894e34	1.74405
$218$	−1.70308e34	−2.10676
$219$	1.85756e33	0.215031
$220$	1.14165e33	0.123710
$221$	8.41716e32	0.0854039
$222$	−3.68370e33	−0.350079
$223$	−1.54974e34	−1.37987	−0.689933	−	0.723873i	$-0.742360\pi$
$223$	−1.54974e34	−1.37987	−0.689933	+	0.723873i	$0.742360\pi$
$224$	3.16452e34	2.64065
$225$	6.62337e33	0.518123
$226$	−1.45882e34	−1.07011
$227$	1.30973e33	0.0901167	0.0450583	−	0.998984i	$-0.485653\pi$
$227$	1.30973e33	0.0901167	0.0450583	+	0.998984i	$0.485653\pi$
$228$	8.85798e33	0.571847
$229$	−1.15385e34	−0.699090	−0.349545	−	0.936919i	$-0.613664\pi$
$229$	−1.15385e34	−0.699090	−0.349545	+	0.936919i	$0.613664\pi$
$230$	1.03712e34	0.589894
$231$	1.31438e33	0.0702018
$232$	6.29334e33	0.315722
$233$	−2.81873e34	−1.32859	−0.664297	−	0.747468i	$-0.731269\pi$
$233$	−2.81873e34	−1.32859	−0.664297	+	0.747468i	$0.731269\pi$
$234$	−1.83123e33	−0.0811170
$235$	5.33906e34	2.22321
$236$	−2.06953e34	−0.810302
$237$	−1.35660e33	−0.0499577
$238$	−4.07204e34	−1.41074
$239$	−3.11157e34	−1.01440	−0.507200	−	0.861828i	$-0.669320\pi$
$239$	−3.11157e34	−1.01440	−0.507200	+	0.861828i	$0.669320\pi$
$240$	−2.38475e34	−0.731780
$241$	6.24749e34	1.80492	0.902461	−	0.430772i	$-0.141759\pi$
$241$	6.24749e34	1.80492	0.902461	+	0.430772i	$0.141759\pi$
$242$	5.39840e34	1.46873
$243$	−2.50316e33	−0.0641500
$244$	−2.44903e34	−0.591346
$245$	−1.69451e35	−3.85599
$246$	4.36073e34	0.935405
$247$	−6.86990e33	−0.138946
$248$	−1.28487e34	−0.245082
$249$	−1.34253e34	−0.241565
$250$	7.69836e34	1.30698
$251$	1.21741e35	1.95061	0.975303	−	0.220873i	$-0.0708907\pi$
$251$	1.21741e35	1.95061	0.975303	+	0.220873i	$0.0708907\pi$
$252$	4.78777e34	0.724145
$253$	−1.15323e33	−0.0164690
$254$	3.16132e34	0.426363
$255$	3.74961e34	0.477698
$256$	4.66504e34	0.561534
$257$	1.18845e35	1.35192	0.675958	−	0.736940i	$-0.263730\pi$
$257$	1.18845e35	1.35192	0.675958	+	0.736940i	$0.263730\pi$
$258$	−9.04079e34	−0.972122
$259$	−7.46951e34	−0.759356
$260$	−3.22524e34	−0.310062
$261$	−4.45834e34	−0.405402
$262$	−2.18122e35	−1.87643
$263$	−1.28323e35	−1.04459	−0.522297	−	0.852764i	$-0.674925\pi$
$263$	−1.28323e35	−1.04459	−0.522297	+	0.852764i	$0.674925\pi$
$264$	−1.28043e33	−0.00986507
$265$	−3.56029e34	−0.259669
$266$	3.32351e35	2.29516
$267$	9.30728e34	0.608709
$268$	−3.22608e35	−1.99857
$269$	−1.69731e35	−0.996218	−0.498109	−	0.867114i	$-0.665972\pi$
$269$	−1.69731e35	−0.996218	−0.498109	+	0.867114i	$0.665972\pi$
$270$	−8.15760e34	−0.453720
$271$	9.75843e34	0.514429	0.257214	−	0.966354i	$-0.417195\pi$
$271$	9.75843e34	0.514429	0.257214	+	0.966354i	$0.417195\pi$
$272$	−8.21524e34	−0.410555
$273$	−3.71321e34	−0.175951
$274$	4.81524e35	2.16389
$275$	−2.40016e34	−0.102310
$276$	−4.20075e34	−0.169881
$277$	1.31257e34	0.0503695	0.0251847	−	0.999683i	$-0.491983\pi$
$277$	1.31257e34	0.0503695	0.0251847	+	0.999683i	$0.491983\pi$
$278$	5.12060e35	1.86497
$279$	9.10234e34	0.314697
$280$	2.33495e35	0.766453
$281$	−1.84417e35	−0.574856	−0.287428	−	0.957802i	$-0.592800\pi$
$281$	−1.84417e35	−0.574856	−0.287428	+	0.957802i	$0.592800\pi$
$282$	−4.00146e35	−1.18469
$283$	1.03663e35	0.291555	0.145778	−	0.989317i	$-0.453432\pi$
$283$	1.03663e35	0.291555	0.145778	+	0.989317i	$0.453432\pi$
$284$	−3.61057e35	−0.964849
$285$	−3.06035e35	−0.777178
$286$	6.63595e33	0.0160175
$287$	8.84232e35	2.02898
$288$	2.18391e35	0.476479
$289$	−3.52798e35	−0.731994
$290$	−1.45294e36	−2.86733
$291$	4.68369e35	0.879305
$292$	−2.45197e35	−0.437989
$293$	1.04263e35	0.177235	0.0886176	−	0.996066i	$-0.471755\pi$
$293$	1.04263e35	0.177235	0.0886176	+	0.996066i	$0.471755\pi$
$294$	1.26998e36	2.05476
$295$	7.15002e35	1.10126
$296$	7.27658e34	0.106708
$297$	9.07088e33	0.0126672
$298$	−4.13208e35	−0.549582
$299$	3.25793e34	0.0412771
$300$	−8.74284e35	−1.05534
$301$	−1.83322e36	−2.10863
$302$	−1.49174e36	−1.63529
$303$	2.14507e35	0.224142
$304$	6.70510e35	0.667941
$305$	8.46116e35	0.803679
$306$	−2.81021e35	−0.254553
$307$	1.57406e35	0.135992	0.0679961	−	0.997686i	$-0.478339\pi$
$307$	1.57406e35	0.135992	0.0679961	+	0.997686i	$0.478339\pi$
$308$	−1.73498e35	−0.142991
$309$	7.36814e35	0.579376
$310$	2.96639e36	2.22578
$311$	3.84085e35	0.275044	0.137522	−	0.990499i	$-0.456086\pi$
$311$	3.84085e35	0.275044	0.137522	+	0.990499i	$0.456086\pi$
$312$	3.61730e34	0.0247254
$313$	−4.72696e35	−0.308453	−0.154226	−	0.988036i	$-0.549289\pi$
$313$	−4.72696e35	−0.308453	−0.154226	+	0.988036i	$0.549289\pi$
$314$	6.89113e33	0.00429349
$315$	−1.65413e36	−0.984162
$316$	1.79071e35	0.101757
$317$	1.01252e36	0.549598	0.274799	−	0.961502i	$-0.411389\pi$
$317$	1.01252e36	0.549598	0.274799	+	0.961502i	$0.411389\pi$
$318$	2.66833e35	0.138371
$319$	1.61561e35	0.0800517
$320$	4.44040e36	2.10256
$321$	−9.77485e35	−0.442371
$322$	−1.57612e36	−0.681833
$323$	−1.05426e36	−0.436025
$324$	3.30416e35	0.130665
$325$	6.78060e35	0.256424
$326$	−2.58724e36	−0.935797
$327$	−2.38325e36	−0.824569
$328$	−8.61393e35	−0.285122
$329$	−8.11382e36	−2.56971
$330$	2.95613e35	0.0895925
$331$	−6.92814e35	−0.200960	−0.100480	−	0.994939i	$-0.532038\pi$
$331$	−6.92814e35	−0.200960	−0.100480	+	0.994939i	$0.532038\pi$
$332$	1.77214e36	0.492034
$333$	−5.15489e35	−0.137018
$334$	−2.11694e36	−0.538747
$335$	1.11458e37	2.71619
$336$	3.62413e36	0.845833
$337$	−8.43275e36	−1.88511	−0.942553	−	0.334056i	$-0.891582\pi$
$337$	−8.43275e36	−1.88511	−0.942553	+	0.334056i	$0.891582\pi$
$338$	6.70095e36	1.43498
$339$	−2.04144e36	−0.418834
$340$	−4.94948e36	−0.973005
$341$	−3.29849e35	−0.0621407
$342$	2.29363e36	0.414139
$343$	1.50781e37	2.60964
$344$	1.78587e36	0.296313
$345$	1.45132e36	0.230880
$346$	8.81050e35	0.134399
$347$	5.80275e36	0.848900	0.424450	−	0.905451i	$-0.360467\pi$
$347$	5.80275e36	0.848900	0.424450	+	0.905451i	$0.360467\pi$
$348$	5.88501e36	0.825749
$349$	−5.03015e35	−0.0677037	−0.0338518	−	0.999427i	$-0.510777\pi$
$349$	−5.03015e35	−0.0677037	−0.0338518	+	0.999427i	$0.510777\pi$
$350$	−3.28031e37	−4.23572
$351$	−2.56258e35	−0.0317485
$352$	−7.91401e35	−0.0940866
$353$	8.86210e35	0.101112	0.0505561	−	0.998721i	$-0.483901\pi$
$353$	8.86210e35	0.101112	0.0505561	+	0.998721i	$0.483901\pi$
$354$	−5.35871e36	−0.586831
$355$	1.24742e37	1.31129
$356$	−1.22856e37	−1.23986
$357$	−5.69832e36	−0.552151
$358$	1.47815e37	1.37536
$359$	−9.54709e36	−0.853103	−0.426551	−	0.904463i	$-0.640272\pi$
$359$	−9.54709e36	−0.853103	−0.426551	+	0.904463i	$0.640272\pi$
$360$	1.61140e36	0.138299
$361$	−3.52518e36	−0.290621
$362$	1.39008e37	1.10094
$363$	7.55440e36	0.574849
$364$	4.90143e36	0.358387
$365$	8.47132e36	0.595257
$366$	−6.34138e36	−0.428260
$367$	−2.69909e37	−1.75210	−0.876052	−	0.482217i	$-0.839832\pi$
$367$	−2.69909e37	−1.75210	−0.876052	+	0.482217i	$0.839832\pi$
$368$	−3.17978e36	−0.198428
$369$	6.10230e36	0.366110
$370$	−1.67994e37	−0.969101
$371$	5.41061e36	0.300141
$372$	−1.20151e37	−0.640994
$373$	1.26607e37	0.649653	0.324826	−	0.945774i	$-0.394694\pi$
$373$	1.26607e37	0.649653	0.324826	+	0.945774i	$0.394694\pi$
$374$	1.01836e36	0.0502647
$375$	1.07729e37	0.511540
$376$	7.90425e36	0.361108
$377$	−4.56418e36	−0.200638
$378$	1.23972e37	0.524435
$379$	−3.49141e37	−1.42145	−0.710726	−	0.703469i	$-0.751634\pi$
$379$	−3.49141e37	−1.42145	−0.710726	+	0.703469i	$0.751634\pi$
$380$	4.03965e37	1.58300
$381$	4.42388e36	0.166875
$382$	4.33887e37	1.57564
$383$	−3.44611e37	−1.20489	−0.602444	−	0.798161i	$-0.705806\pi$
$383$	−3.44611e37	−1.20489	−0.602444	+	0.798161i	$0.705806\pi$
$384$	−8.76582e36	−0.295114
$385$	5.99420e36	0.194335
$386$	5.86113e37	1.83006
$387$	−1.26515e37	−0.380480
$388$	−6.18246e37	−1.79102
$389$	5.97197e37	1.66666	0.833332	−	0.552772i	$-0.186430\pi$
$389$	5.97197e37	1.66666	0.833332	+	0.552772i	$0.186430\pi$
$390$	−8.35124e36	−0.224551
$391$	4.99965e36	0.129532
$392$	−2.50865e37	−0.626314
$393$	−3.05236e37	−0.734418
$394$	8.04153e35	0.0186485
$395$	−6.18675e36	−0.138294
$396$	−1.19735e36	−0.0258014
$397$	−1.64443e37	−0.341628	−0.170814	−	0.985303i	$-0.554640\pi$
$397$	−1.64443e37	−0.341628	−0.170814	+	0.985303i	$0.554640\pi$
$398$	−6.60492e37	−1.32301
$399$	4.65084e37	0.898306
$400$	−6.61794e37	−1.23269
$401$	−6.35087e37	−1.14088	−0.570440	−	0.821339i	$-0.693227\pi$
$401$	−6.35087e37	−1.14088	−0.570440	+	0.821339i	$0.693227\pi$
$402$	−8.35341e37	−1.44739
$403$	9.31842e36	0.155747
$404$	−2.83149e37	−0.456547
$405$	−1.14156e37	−0.177582
$406$	2.20805e38	3.31422
$407$	1.86802e36	0.0270559
$408$	5.55114e36	0.0775907
$409$	1.29243e38	1.74349	0.871746	−	0.489958i	$-0.162988\pi$
$409$	1.29243e38	1.74349	0.871746	+	0.489958i	$0.162988\pi$
$410$	1.98869e38	2.58942
$411$	6.73834e37	0.846928
$412$	−9.72593e37	−1.18011
$413$	−1.08660e38	−1.27289
$414$	−1.08772e37	−0.123030
$415$	−6.12257e37	−0.668707
$416$	2.23575e37	0.235814
$417$	7.16565e37	0.729932
$418$	−8.31162e36	−0.0817767
$419$	−1.95207e38	−1.85520	−0.927601	−	0.373573i	$-0.878133\pi$
$419$	−1.95207e38	−1.85520	−0.927601	+	0.373573i	$0.878133\pi$
$420$	2.18345e38	2.00460
$421$	−1.98023e37	−0.175641	−0.0878203	−	0.996136i	$-0.527990\pi$
$421$	−1.98023e37	−0.175641	−0.0878203	+	0.996136i	$0.527990\pi$
$422$	−8.35087e37	−0.715651
$423$	−5.59955e37	−0.463679
$424$	−5.27086e36	−0.0421771
$425$	1.04056e38	0.804686
$426$	−9.34899e37	−0.698756
$427$	−1.28585e38	−0.928938
$428$	1.29028e38	0.901049
$429$	9.28621e35	0.00626913
$430$	−4.12302e38	−2.69106
$431$	2.60608e38	1.64462	0.822312	−	0.569037i	$-0.192684\pi$
$431$	2.60608e38	1.64462	0.822312	+	0.569037i	$0.192684\pi$
$432$	2.50110e37	0.152622
$433$	1.69736e38	1.00161	0.500807	−	0.865559i	$-0.333037\pi$
$433$	1.69736e38	1.00161	0.500807	+	0.865559i	$0.333037\pi$
$434$	−4.50805e38	−2.57269
$435$	−2.03321e38	−1.12225
$436$	3.14588e38	1.67953
$437$	−4.08060e37	−0.210738
$438$	−6.34899e37	−0.317198
$439$	2.79719e38	1.35203	0.676015	−	0.736888i	$-0.263705\pi$
$439$	2.79719e38	1.35203	0.676015	+	0.736888i	$0.263705\pi$
$440$	−5.83937e36	−0.0273088
$441$	1.77719e38	0.804217
$442$	−2.87692e37	−0.125981
$443$	−2.43951e38	−1.03383	−0.516915	−	0.856037i	$-0.672919\pi$
$443$	−2.43951e38	−1.03383	−0.516915	+	0.856037i	$0.672919\pi$
$444$	6.80445e37	0.279087
$445$	4.24456e38	1.68505
$446$	5.29688e38	2.03547
$447$	−5.78234e37	−0.215102
$448$	−6.74812e38	−2.43025
$449$	4.38823e37	0.153009	0.0765045	−	0.997069i	$-0.475624\pi$
$449$	4.38823e37	0.153009	0.0765045	+	0.997069i	$0.475624\pi$
$450$	−2.26382e38	−0.764294
$451$	−2.21134e37	−0.0722929
$452$	2.69470e38	0.853107
$453$	−2.08751e38	−0.640037
$454$	−4.47654e37	−0.132933
$455$	−1.69340e38	−0.487072
$456$	−4.53071e37	−0.126234
$457$	1.82946e38	0.493785	0.246893	−	0.969043i	$-0.420590\pi$
$457$	1.82946e38	0.493785	0.246893	+	0.969043i	$0.420590\pi$
$458$	3.94376e38	1.03124
$459$	−3.93255e37	−0.0996301
$460$	−1.91574e38	−0.470270
$461$	3.29567e38	0.783935	0.391967	−	0.919979i	$-0.371795\pi$
$461$	3.29567e38	0.783935	0.391967	+	0.919979i	$0.371795\pi$
$462$	−4.49246e37	−0.103556
$463$	−1.85461e38	−0.414312	−0.207156	−	0.978308i	$-0.566421\pi$
$463$	−1.85461e38	−0.414312	−0.207156	+	0.978308i	$0.566421\pi$
$464$	4.45469e38	0.964510
$465$	4.15109e38	0.871154
$466$	9.63421e38	1.95984
$467$	−2.97079e37	−0.0585838	−0.0292919	−	0.999571i	$-0.509325\pi$
$467$	−2.97079e37	−0.0585838	−0.0292919	+	0.999571i	$0.509325\pi$
$468$	3.38259e37	0.0646674
$469$	−1.69384e39	−3.13953
$470$	−1.82485e39	−3.27951
$471$	9.64330e35	0.00168044
$472$	1.05853e38	0.178873
$473$	4.58461e37	0.0751305
$474$	4.63677e37	0.0736936
$475$	−8.49279e38	−1.30916
$476$	7.52177e38	1.12465
$477$	3.73400e37	0.0541574
$478$	1.06351e39	1.49636
$479$	−3.48703e38	−0.475983	−0.237991	−	0.971267i	$-0.576489\pi$
$479$	−3.48703e38	−0.475983	−0.237991	+	0.971267i	$0.576489\pi$
$480$	9.95965e38	1.31900
$481$	−5.27726e37	−0.0678117
$482$	−2.13535e39	−2.66248
$483$	−2.20558e38	−0.266864
$484$	−9.97179e38	−1.17089
$485$	2.13598e39	2.43412
$486$	8.55560e37	0.0946291
$487$	5.58774e38	0.599883	0.299942	−	0.953958i	$-0.403033\pi$
$487$	5.58774e38	0.599883	0.299942	+	0.953958i	$0.403033\pi$
$488$	1.25264e38	0.130538
$489$	−3.62053e38	−0.366263
$490$	5.79172e39	5.68806
$491$	−9.57783e37	−0.0913241	−0.0456621	−	0.998957i	$-0.514540\pi$
$491$	−9.57783e37	−0.0913241	−0.0456621	+	0.998957i	$0.514540\pi$
$492$	−8.05503e38	−0.745715
$493$	−7.00423e38	−0.629622
$494$	2.34808e38	0.204961
$495$	4.13675e37	0.0350658
$496$	−9.09488e38	−0.748708
$497$	−1.89571e39	−1.51567
$498$	4.58867e38	0.356337
$499$	1.19177e39	0.898950	0.449475	−	0.893293i	$-0.351611\pi$
$499$	1.19177e39	0.898950	0.449475	+	0.893293i	$0.351611\pi$
$500$	−1.42202e39	−1.04194
$501$	−2.96240e38	−0.210861
$502$	−4.16103e39	−2.87738
$503$	−3.16763e38	−0.212813	−0.106407	−	0.994323i	$-0.533935\pi$
$503$	−3.16763e38	−0.212813	−0.106407	+	0.994323i	$0.533935\pi$
$504$	−2.44887e38	−0.159854
$505$	9.78254e38	0.620478
$506$	3.94164e37	0.0242938
$507$	9.37717e38	0.561638
$508$	−5.83951e38	−0.339901
$509$	3.42453e39	1.93728	0.968641	−	0.248463i	$-0.0799254\pi$
$509$	3.42453e39	1.93728	0.968641	+	0.248463i	$0.0799254\pi$
$510$	−1.28159e39	−0.704662
$511$	−1.28739e39	−0.688032
$512$	−2.57841e39	−1.33948
$513$	3.20966e38	0.162090
$514$	−4.06203e39	−1.99424
$515$	3.36022e39	1.60385
$516$	1.66999e39	0.774986
$517$	2.02915e38	0.0915591
$518$	2.55302e39	1.12014
$519$	1.23292e38	0.0526028
$520$	1.64966e38	0.0684455
$521$	−2.91827e39	−1.17755	−0.588773	−	0.808298i	$-0.700389\pi$
$521$	−2.91827e39	−1.17755	−0.588773	+	0.808298i	$0.700389\pi$
$522$	1.52383e39	0.598018
$523$	3.47823e39	1.32765	0.663826	−	0.747887i	$-0.268931\pi$
$523$	3.47823e39	1.32765	0.663826	+	0.747887i	$0.268931\pi$
$524$	4.02911e39	1.49591
$525$	−4.59039e39	−1.65783
$526$	4.38600e39	1.54090
$527$	1.43001e39	0.488749
$528$	−9.06344e37	−0.0301371
$529$	−2.89754e39	−0.937395
$530$	1.21688e39	0.383044
$531$	−7.49886e38	−0.229681
$532$	−6.13910e39	−1.82973
$533$	6.24716e38	0.181192
$534$	−3.18116e39	−0.897919
$535$	−4.45779e39	−1.22459
$536$	1.65009e39	0.441181
$537$	2.06850e39	0.538304
$538$	5.80130e39	1.46954
$539$	−6.44013e38	−0.158803
$540$	1.50685e39	0.361710
$541$	6.83902e39	1.59821	0.799105	−	0.601192i	$-0.205307\pi$
$541$	6.83902e39	1.59821	0.799105	+	0.601192i	$0.205307\pi$
$542$	−3.33536e39	−0.758845
$543$	1.94525e39	0.430901
$544$	3.43100e39	0.740009
$545$	−1.08687e40	−2.28260
$546$	1.26915e39	0.259548
$547$	1.73726e39	0.345979	0.172989	−	0.984924i	$-0.444657\pi$
$547$	1.73726e39	0.345979	0.172989	+	0.984924i	$0.444657\pi$
$548$	−8.89460e39	−1.72508
$549$	−8.87398e38	−0.167618
$550$	8.20358e38	0.150919
$551$	5.71669e39	1.02435
$552$	2.14861e38	0.0375009
$553$	9.40206e38	0.159849
$554$	−4.48628e38	−0.0743011
$555$	−2.35087e39	−0.379298
$556$	−9.45864e39	−1.48677
$557$	−9.12669e39	−1.39770	−0.698848	−	0.715270i	$-0.746304\pi$
$557$	−9.12669e39	−1.39770	−0.698848	+	0.715270i	$0.746304\pi$
$558$	−3.11111e39	−0.464216
$559$	−1.29518e39	−0.188304
$560$	1.65277e40	2.34146
$561$	1.42507e38	0.0196732
$562$	6.30323e39	0.847982
$563$	1.92419e39	0.252276	0.126138	−	0.992013i	$-0.459742\pi$
$563$	1.92419e39	0.252276	0.126138	+	0.992013i	$0.459742\pi$
$564$	7.39139e39	0.944450
$565$	−9.30994e39	−1.15943
$566$	−3.54313e39	−0.430079
$567$	1.73483e39	0.205260
$568$	1.84675e39	0.212988
$569$	−5.68019e39	−0.638609	−0.319305	−	0.947652i	$-0.603449\pi$
$569$	−5.68019e39	−0.638609	−0.319305	+	0.947652i	$0.603449\pi$
$570$	1.04600e40	1.14643
$571$	1.50459e40	1.60766	0.803829	−	0.594861i	$-0.202793\pi$
$571$	1.50459e40	1.60766	0.803829	+	0.594861i	$0.202793\pi$
$572$	−1.22578e38	−0.0127694
$573$	6.07171e39	0.616693
$574$	−3.02224e40	−2.99300
$575$	4.02756e39	0.388918
$576$	−4.65705e39	−0.438515
$577$	4.17395e39	0.383264	0.191632	−	0.981467i	$-0.438622\pi$
$577$	4.17395e39	0.383264	0.191632	+	0.981467i	$0.438622\pi$
$578$	1.20584e40	1.07978
$579$	8.20193e39	0.716271
$580$	2.68384e40	2.28586
$581$	9.30453e39	0.772930
$582$	−1.60085e40	−1.29708
$583$	−1.35312e38	−0.0106940
$584$	1.25414e39	0.0966853
$585$	−1.16865e39	−0.0878873
$586$	−3.56363e39	−0.261443
$587$	−1.90083e40	−1.36047	−0.680236	−	0.732993i	$-0.738123\pi$
$587$	−1.90083e40	−1.36047	−0.680236	+	0.732993i	$0.738123\pi$
$588$	−2.34588e40	−1.63808
$589$	−1.16714e40	−0.795157
$590$	−2.44382e40	−1.62449
$591$	1.12531e38	0.00729886
$592$	5.15067e39	0.325986
$593$	−3.50059e39	−0.216196	−0.108098	−	0.994140i	$-0.534476\pi$
$593$	−3.50059e39	−0.216196	−0.108098	+	0.994140i	$0.534476\pi$
$594$	−3.10036e38	−0.0186857
$595$	−2.59870e40	−1.52848
$596$	7.63268e39	0.438133
$597$	−9.24278e39	−0.517815
$598$	−1.11354e39	−0.0608888
$599$	−2.83667e39	−0.151398	−0.0756990	−	0.997131i	$-0.524119\pi$
$599$	−2.83667e39	−0.151398	−0.0756990	+	0.997131i	$0.524119\pi$
$600$	4.47182e39	0.232965
$601$	1.73580e40	0.882711	0.441356	−	0.897332i	$-0.354498\pi$
$601$	1.73580e40	0.882711	0.441356	+	0.897332i	$0.354498\pi$
$602$	6.26580e40	3.11048
$603$	−1.16896e40	−0.566497
$604$	2.75551e40	1.30367
$605$	3.44516e40	1.59132
$606$	−7.33170e39	−0.330637
$607$	1.57654e40	0.694175	0.347088	−	0.937833i	$-0.387171\pi$
$607$	1.57654e40	0.694175	0.347088	+	0.937833i	$0.387171\pi$
$608$	−2.80031e40	−1.20394
$609$	3.08989e40	1.29716
$610$	−2.89196e40	−1.18552
$611$	−5.73247e39	−0.229480
$612$	5.19096e39	0.202933
$613$	−4.66699e40	−1.78180	−0.890902	−	0.454196i	$-0.849927\pi$
$613$	−4.66699e40	−1.78180	−0.890902	+	0.454196i	$0.849927\pi$
$614$	−5.38001e39	−0.200605
$615$	2.78294e40	1.01348
$616$	8.87415e38	0.0315651
$617$	5.06170e40	1.75858	0.879289	−	0.476288i	$-0.158018\pi$
$617$	5.06170e40	1.75858	0.879289	+	0.476288i	$0.158018\pi$
$618$	−2.51838e40	−0.854649
$619$	4.64467e40	1.53972	0.769858	−	0.638216i	$-0.220327\pi$
$619$	4.64467e40	1.53972	0.769858	+	0.638216i	$0.220327\pi$
$620$	−5.47944e40	−1.77442
$621$	−1.52213e39	−0.0481529
$622$	−1.31278e40	−0.405723
$623$	−6.45049e40	−1.94767
$624$	2.56047e39	0.0755342
$625$	−4.79848e39	−0.138307
$626$	1.61564e40	0.455005
$627$	−1.16311e39	−0.0320067
$628$	−1.27291e38	−0.00342282
$629$	−8.09853e39	−0.212800
$630$	5.65369e40	1.45176
$631$	−3.73359e39	−0.0936918	−0.0468459	−	0.998902i	$-0.514917\pi$
$631$	−3.73359e39	−0.0936918	−0.0468459	+	0.998902i	$0.514917\pi$
$632$	−9.15921e38	−0.0224626
$633$	−1.16860e40	−0.280100
$634$	−3.46072e40	−0.810723
$635$	2.01749e40	0.461948
$636$	−4.92887e39	−0.110311
$637$	1.81937e40	0.398016
$638$	−5.52202e39	−0.118086
$639$	−1.30828e40	−0.273487
$640$	−3.99762e40	−0.816943
$641$	−7.41713e40	−1.48182	−0.740908	−	0.671607i	$-0.765604\pi$
$641$	−7.41713e40	−1.48182	−0.740908	+	0.671607i	$0.765604\pi$
$642$	3.34097e40	0.652551
$643$	9.07810e40	1.73355	0.866774	−	0.498701i	$-0.166190\pi$
$643$	9.07810e40	1.73355	0.866774	+	0.498701i	$0.166190\pi$
$644$	2.91136e40	0.543565
$645$	−5.76966e40	−1.05326
$646$	3.60339e40	0.643190
$647$	1.41458e40	0.246897	0.123449	−	0.992351i	$-0.460605\pi$
$647$	1.41458e40	0.246897	0.123449	+	0.992351i	$0.460605\pi$
$648$	−1.69002e39	−0.0288440
$649$	2.71742e39	0.0453533
$650$	−2.31756e40	−0.378257
$651$	−6.30846e40	−1.00693
$652$	4.77909e40	0.746028
$653$	−3.46789e40	−0.529448	−0.264724	−	0.964324i	$-0.585281\pi$
$653$	−3.46789e40	−0.529448	−0.264724	+	0.964324i	$0.585281\pi$
$654$	8.14577e40	1.21634
$655$	−1.39202e41	−2.03304
$656$	−6.09730e40	−0.871027
$657$	−8.88463e39	−0.124148
$658$	2.77324e41	3.79064
$659$	−4.40657e40	−0.589199	−0.294600	−	0.955621i	$-0.595186\pi$
$659$	−4.40657e40	−0.589199	−0.294600	+	0.955621i	$0.595186\pi$
$660$	−5.46050e39	−0.0714241
$661$	2.13853e40	0.273649	0.136825	−	0.990595i	$-0.456310\pi$
$661$	2.13853e40	0.273649	0.136825	+	0.990595i	$0.456310\pi$
$662$	2.36799e40	0.296441
$663$	−4.02590e39	−0.0493080
$664$	−9.06420e39	−0.108616
$665$	2.12100e41	2.48672
$666$	1.76190e40	0.202118
$667$	−2.71104e40	−0.304307
$668$	3.91036e40	0.429495
$669$	7.41234e40	0.796666
$670$	−3.80955e41	−4.00672
$671$	3.21573e39	0.0330981
$672$	−1.51358e41	−1.52458
$673$	3.93184e40	0.387595	0.193797	−	0.981042i	$-0.437920\pi$
$673$	3.93184e40	0.387595	0.193797	+	0.981042i	$0.437920\pi$
$674$	2.88225e41	2.78076
$675$	−3.16794e40	−0.299138
$676$	−1.23778e41	−1.14398
$677$	5.14234e40	0.465184	0.232592	−	0.972574i	$-0.425279\pi$
$677$	5.14234e40	0.465184	0.232592	+	0.972574i	$0.425279\pi$
$678$	6.97751e40	0.617831
$679$	−3.24607e41	−2.81350
$680$	2.53158e40	0.214789
$681$	−6.26437e39	−0.0520289
$682$	1.12740e40	0.0916651
$683$	−9.75495e40	−0.776470	−0.388235	−	0.921560i	$-0.626915\pi$
$683$	−9.75495e40	−0.776470	−0.388235	+	0.921560i	$0.626915\pi$
$684$	−4.23675e40	−0.330156
$685$	3.07300e41	2.34449
$686$	−5.15357e41	−3.84954
$687$	5.51881e40	0.403620
$688$	1.26411e41	0.905217
$689$	3.82264e39	0.0268031
$690$	−4.96050e40	−0.340575
$691$	2.28890e40	0.153885	0.0769424	−	0.997036i	$-0.475484\pi$
$691$	2.28890e40	0.153885	0.0769424	+	0.997036i	$0.475484\pi$
$692$	−1.62745e40	−0.107145
$693$	−6.28665e39	−0.0405310
$694$	−1.98334e41	−1.25223
$695$	3.26787e41	2.02062
$696$	−3.01008e40	−0.182282
$697$	9.58695e40	0.568598
$698$	1.71927e40	0.0998711
$699$	1.34819e41	0.767065
$700$	6.05930e41	3.37677
$701$	1.71553e41	0.936454	0.468227	−	0.883608i	$-0.344893\pi$
$701$	1.71553e41	0.936454	0.468227	+	0.883608i	$0.344893\pi$
$702$	8.75869e39	0.0468329
$703$	6.60984e40	0.346209
$704$	1.68761e40	0.0865902
$705$	−2.55365e41	−1.28357
$706$	−3.02900e40	−0.149153
$707$	−1.48666e41	−0.717184
$708$	9.89849e40	0.467828
$709$	−2.53704e41	−1.17478	−0.587390	−	0.809304i	$-0.699845\pi$
$709$	−2.53704e41	−1.17478	−0.587390	+	0.809304i	$0.699845\pi$
$710$	−4.26357e41	−1.93432
$711$	6.48860e39	0.0288431
$712$	6.28388e40	0.273696
$713$	5.53498e40	0.236221
$714$	1.94764e41	0.814489
$715$	4.23494e39	0.0173544
$716$	−2.73041e41	−1.09645
$717$	1.48825e41	0.585665
$718$	3.26312e41	1.25843
$719$	1.11329e41	0.420766	0.210383	−	0.977619i	$-0.432529\pi$
$719$	1.11329e41	0.420766	0.210383	+	0.977619i	$0.432529\pi$
$720$	1.14062e41	0.422493
$721$	−5.10656e41	−1.85382
$722$	1.20488e41	0.428701
$723$	−2.98815e41	−1.04207
$724$	−2.56772e41	−0.877685
$725$	−5.64238e41	−1.89043
$726$	−2.58204e41	−0.847972
$727$	2.82458e41	0.909296	0.454648	−	0.890671i	$-0.349765\pi$
$727$	2.82458e41	0.909296	0.454648	+	0.890671i	$0.349765\pi$
$728$	−2.50700e40	−0.0791132
$729$	1.19725e40	0.0370370
$730$	−2.89543e41	−0.878076
$731$	−1.98759e41	−0.590916
$732$	1.17136e41	0.341414
$733$	6.93277e40	0.198107	0.0990534	−	0.995082i	$-0.468419\pi$
$733$	6.93277e40	0.198107	0.0990534	+	0.995082i	$0.468419\pi$
$734$	9.22530e41	2.58457
$735$	8.10480e41	2.22626
$736$	1.32800e41	0.357659
$737$	4.23604e40	0.111862
$738$	−2.08572e41	−0.540057
$739$	9.44578e40	0.239824	0.119912	−	0.992785i	$-0.461739\pi$
$739$	9.44578e40	0.239824	0.119912	+	0.992785i	$0.461739\pi$
$740$	3.10315e41	0.772578
$741$	3.28585e40	0.0802202
$742$	−1.84931e41	−0.442744
$743$	−3.24456e41	−0.761760	−0.380880	−	0.924625i	$-0.624379\pi$
$743$	−3.24456e41	−0.761760	−0.380880	+	0.924625i	$0.624379\pi$
$744$	6.14552e40	0.141498
$745$	−2.63702e41	−0.595452
$746$	−4.32735e41	−0.958317
$747$	6.42128e40	0.139468
$748$	−1.88109e40	−0.0400715
$749$	6.77454e41	1.41545
$750$	−3.68210e41	−0.754584
$751$	−4.42662e41	−0.889801	−0.444900	−	0.895580i	$-0.646761\pi$
$751$	−4.42662e41	−0.889801	−0.444900	+	0.895580i	$0.646761\pi$
$752$	5.59496e41	1.10316
$753$	−5.82285e41	−1.12618
$754$	1.56000e41	0.295965
$755$	−9.52004e41	−1.77177
$756$	−2.28998e41	−0.418085
$757$	1.46733e41	0.262808	0.131404	−	0.991329i	$-0.458052\pi$
$757$	1.46733e41	0.262808	0.131404	+	0.991329i	$0.458052\pi$
$758$	1.19334e42	2.09681
$759$	5.51585e39	0.00950838
$760$	−2.06622e41	−0.349445
$761$	1.05264e42	1.74664	0.873320	−	0.487147i	$-0.161962\pi$
$761$	1.05264e42	1.74664	0.873320	+	0.487147i	$0.161962\pi$
$762$	−1.51205e41	−0.246161
$763$	1.65173e42	2.63836
$764$	−8.01465e41	−1.25612
$765$	−1.79343e41	−0.275799
$766$	1.17785e42	1.77736
$767$	−7.67687e40	−0.113671
$768$	−2.23128e41	−0.324202
$769$	−9.61195e41	−1.37050	−0.685251	−	0.728307i	$-0.740308\pi$
$769$	−9.61195e41	−1.37050	−0.685251	+	0.728307i	$0.740308\pi$
$770$	−2.04877e41	−0.286667
$771$	−5.68431e41	−0.780530
$772$	−1.08265e42	−1.45894
$773$	−1.18429e42	−1.56622	−0.783112	−	0.621880i	$-0.786369\pi$
$773$	−1.18429e42	−1.56622	−0.783112	+	0.621880i	$0.786369\pi$
$774$	4.32418e41	0.561255
$775$	1.15197e42	1.46746
$776$	3.16223e41	0.395365
$777$	3.57264e41	0.438414
$778$	−2.04117e42	−2.45853
$779$	−7.82465e41	−0.925064
$780$	1.54262e41	0.179014
$781$	4.74090e40	0.0540034
$782$	−1.70884e41	−0.191075
$783$	2.13241e41	0.234059
$784$	−1.77573e42	−1.91335
$785$	4.39779e39	0.00465184
$786$	1.04327e42	1.08336
$787$	1.19776e42	1.22106	0.610530	−	0.791993i	$-0.290956\pi$
$787$	1.19776e42	1.22106	0.610530	+	0.791993i	$0.290956\pi$
$788$	−1.48541e40	−0.0148668
$789$	6.13767e41	0.603097
$790$	2.11458e41	0.204001
$791$	1.41484e42	1.34013
$792$	6.12427e39	0.00569560
$793$	−9.08463e40	−0.0829557
$794$	5.62054e41	0.503942
$795$	1.70288e41	0.149920
$796$	1.22005e42	1.05472
$797$	−1.98756e42	−1.68723	−0.843617	−	0.536945i	$-0.819578\pi$
$797$	−1.98756e42	−1.68723	−0.843617	+	0.536945i	$0.819578\pi$
$798$	−1.58962e42	−1.32511
$799$	−8.79710e41	−0.720130
$800$	2.76391e42	2.22187
$801$	−4.45164e41	−0.351438
$802$	2.17068e42	1.68294
$803$	3.21959e40	0.0245146
$804$	1.54302e42	1.15388
$805$	−1.00585e42	−0.738741
$806$	−3.18497e41	−0.229745
$807$	8.11820e41	0.575167
$808$	1.44826e41	0.100782
$809$	1.12159e42	0.766621	0.383310	−	0.923620i	$-0.374784\pi$
$809$	1.12159e42	0.766621	0.383310	+	0.923620i	$0.374784\pi$
$810$	3.90175e41	0.261955
$811$	1.75250e42	1.15573	0.577866	−	0.816132i	$-0.303886\pi$
$811$	1.75250e42	1.15573	0.577866	+	0.816132i	$0.303886\pi$
$812$	−4.07865e42	−2.64213
$813$	−4.66743e41	−0.297006
$814$	−6.38475e40	−0.0399108
$815$	−1.65113e42	−1.01390
$816$	3.92933e41	0.237034
$817$	1.62223e42	0.961375
$818$	−4.41744e42	−2.57186
$819$	1.77602e41	0.101585
$820$	−3.67347e42	−2.06431
$821$	6.24559e41	0.344824	0.172412	−	0.985025i	$-0.444844\pi$
$821$	6.24559e41	0.344824	0.172412	+	0.985025i	$0.444844\pi$
$822$	−2.30311e42	−1.24932
$823$	−1.33927e42	−0.713788	−0.356894	−	0.934145i	$-0.616164\pi$
$823$	−1.33927e42	−0.713788	−0.356894	+	0.934145i	$0.616164\pi$
$824$	4.97466e41	0.260507
$825$	1.14799e41	0.0590685
$826$	3.71390e42	1.87767
$827$	2.09164e42	1.03910	0.519550	−	0.854440i	$-0.326100\pi$
$827$	2.09164e42	1.03910	0.519550	+	0.854440i	$0.326100\pi$
$828$	2.00920e41	0.0980808
$829$	−3.02903e42	−1.45299	−0.726496	−	0.687171i	$-0.758852\pi$
$829$	−3.02903e42	−1.45299	−0.726496	+	0.687171i	$0.758852\pi$
$830$	2.09265e42	0.986425
$831$	−6.27801e40	−0.0290808
$832$	−4.76760e41	−0.217026
$833$	2.79203e42	1.24901
$834$	−2.44916e42	−1.07674
$835$	−1.35099e42	−0.583712
$836$	1.53530e41	0.0651933
$837$	−4.35362e41	−0.181690
$838$	6.67202e42	2.73665
$839$	−1.39735e42	−0.563324	−0.281662	−	0.959514i	$-0.590886\pi$
$839$	−1.39735e42	−0.563324	−0.281662	+	0.959514i	$0.590886\pi$
$840$	−1.11680e42	−0.442512
$841$	1.23033e42	0.479160
$842$	6.76828e41	0.259091
$843$	8.82060e41	0.331893
$844$	1.54255e42	0.570525
$845$	4.27643e42	1.55474
$846$	1.91388e42	0.683983
$847$	−5.23564e42	−1.83933
$848$	−3.73094e41	−0.128848
$849$	−4.95817e41	−0.168329
$850$	−3.55655e42	−1.18701
$851$	−3.13460e41	−0.102850
$852$	1.72692e42	0.557056
$853$	−3.59749e42	−1.14088	−0.570438	−	0.821341i	$-0.693227\pi$
$853$	−3.59749e42	−1.14088	−0.570438	+	0.821341i	$0.693227\pi$
$854$	4.39495e42	1.37030
$855$	1.46375e42	0.448704
$856$	−6.59956e41	−0.198905
$857$	−2.08139e42	−0.616783	−0.308392	−	0.951260i	$-0.599791\pi$
$857$	−2.08139e42	−0.616783	−0.308392	+	0.951260i	$0.599791\pi$
$858$	−3.17396e40	−0.00924773
$859$	1.48591e42	0.425689	0.212845	−	0.977086i	$-0.431727\pi$
$859$	1.48591e42	0.425689	0.212845	+	0.977086i	$0.431727\pi$
$860$	7.61594e42	2.14534
$861$	−4.22925e42	−1.17143
$862$	−8.90738e42	−2.42602
$863$	−1.35024e42	−0.361621	−0.180811	−	0.983518i	$-0.557872\pi$
$863$	−1.35024e42	−0.361621	−0.180811	+	0.983518i	$0.557872\pi$
$864$	−1.04456e42	−0.275095
$865$	5.62270e41	0.145617
$866$	−5.80146e42	−1.47750
$867$	1.68742e42	0.422617
$868$	8.32715e42	2.05098
$869$	−2.35132e40	−0.00569542
$870$	6.94937e42	1.65545
$871$	−1.19671e42	−0.280365
$872$	−1.60907e42	−0.370754
$873$	−2.24019e42	−0.507667
$874$	1.39472e42	0.310865
$875$	−7.46626e42	−1.63677
$876$	1.17277e42	0.252873
$877$	7.15530e42	1.51752	0.758759	−	0.651371i	$-0.225806\pi$
$877$	7.15530e42	1.51752	0.758759	+	0.651371i	$0.225806\pi$
$878$	−9.56059e42	−1.99441
$879$	−4.98687e41	−0.102327
$880$	−4.13335e41	−0.0834264
$881$	8.13095e42	1.61432	0.807162	−	0.590331i	$-0.201003\pi$
$881$	8.13095e42	1.61432	0.807162	+	0.590331i	$0.201003\pi$
$882$	−6.07429e42	−1.18632
$883$	8.88454e41	0.170689	0.0853444	−	0.996352i	$-0.472801\pi$
$883$	8.88454e41	0.170689	0.0853444	+	0.996352i	$0.472801\pi$
$884$	5.31418e41	0.100433
$885$	−3.41983e42	−0.635810
$886$	8.33807e42	1.52502
$887$	1.26168e42	0.227016	0.113508	−	0.993537i	$-0.463791\pi$
$887$	1.26168e42	0.227016	0.113508	+	0.993537i	$0.463791\pi$
$888$	−3.48036e41	−0.0616079
$889$	−3.06601e42	−0.533946
$890$	−1.45076e43	−2.48565
$891$	−4.33857e40	−0.00731342
$892$	−9.78427e42	−1.62270
$893$	7.18000e42	1.17160
$894$	1.97636e42	0.317302
$895$	9.43330e42	1.49015
$896$	6.07522e42	0.944270
$897$	−1.55826e41	−0.0238314
$898$	−1.49986e42	−0.225707
$899$	−7.75419e42	−1.14821
$900$	4.18167e42	0.609304
$901$	5.86625e41	0.0841107
$902$	7.55820e41	0.106641
$903$	8.76822e42	1.21742
$904$	−1.37830e42	−0.188322
$905$	8.87123e42	1.19283
$906$	7.13497e42	0.944133
$907$	6.96676e42	0.907246	0.453623	−	0.891194i	$-0.350131\pi$
$907$	6.96676e42	0.907246	0.453623	+	0.891194i	$0.350131\pi$
$908$	8.26896e41	0.105976
$909$	−1.02598e42	−0.129409
$910$	5.78790e42	0.718490
$911$	−1.28869e43	−1.57446	−0.787232	−	0.616657i	$-0.788486\pi$
$911$	−1.28869e43	−1.57446	−0.787232	+	0.616657i	$0.788486\pi$
$912$	−3.20703e42	−0.385636
$913$	−2.32693e41	−0.0275396
$914$	−6.25296e42	−0.728393
$915$	−4.04695e42	−0.464004
$916$	−7.28482e42	−0.822118
$917$	2.11546e43	2.34990
$918$	1.34412e42	0.146966
$919$	−3.22703e41	−0.0347318	−0.0173659	−	0.999849i	$-0.505528\pi$
$919$	−3.22703e41	−0.0347318	−0.0173659	+	0.999849i	$0.505528\pi$
$920$	9.79868e41	0.103811
$921$	−7.52867e41	−0.0785152
$922$	−1.12643e43	−1.15640
$923$	−1.33933e42	−0.135352
$924$	8.29837e41	0.0825561
$925$	−6.52392e42	−0.638930
$926$	6.33891e42	0.611160
$927$	−3.52416e42	−0.334503
$928$	−1.86045e43	−1.73849
$929$	−1.01081e43	−0.929913	−0.464956	−	0.885334i	$-0.653930\pi$
$929$	−1.01081e43	−0.929913	−0.464956	+	0.885334i	$0.653930\pi$
$930$	−1.41881e43	−1.28506
$931$	−2.27879e43	−2.03205
$932$	−1.77961e43	−1.56240
$933$	−1.83707e42	−0.158797
$934$	1.01539e42	0.0864182
$935$	6.49898e41	0.0544599
$936$	−1.73014e41	−0.0142752
$937$	7.71372e42	0.626671	0.313336	−	0.949642i	$-0.398554\pi$
$937$	7.71372e42	0.626671	0.313336	+	0.949642i	$0.398554\pi$
$938$	5.78941e43	4.63119
$939$	2.26089e42	0.178085
$940$	3.37082e43	2.61446
$941$	−6.76953e42	−0.517022	−0.258511	−	0.966008i	$-0.583232\pi$
$941$	−6.76953e42	−0.517022	−0.258511	+	0.966008i	$0.583232\pi$
$942$	−3.29601e40	−0.00247885
$943$	3.71071e42	0.274813
$944$	7.49272e42	0.546444
$945$	7.91165e42	0.568206
$946$	−1.56699e42	−0.110827
$947$	−1.37113e43	−0.955004	−0.477502	−	0.878631i	$-0.658458\pi$
$947$	−1.37113e43	−0.955004	−0.477502	+	0.878631i	$0.658458\pi$
$948$	−8.56493e41	−0.0587494
$949$	−9.09553e41	−0.0614424
$950$	2.90277e43	1.93117
$951$	−4.84286e42	−0.317310
$952$	−3.84726e42	−0.248265
$953$	−2.19117e43	−1.39261	−0.696304	−	0.717747i	$-0.745173\pi$
$953$	−2.19117e43	−1.39261	−0.696304	+	0.717747i	$0.745173\pi$
$954$	−1.27625e42	−0.0798887
$955$	2.76898e43	1.70715
$956$	−1.96449e43	−1.19292
$957$	−7.72739e41	−0.0462179
$958$	1.19184e43	0.702132
$959$	−4.67007e43	−2.70990
$960$	−2.12383e43	−1.21391
$961$	−1.93060e42	−0.108693
$962$	1.80373e42	0.100031
$963$	4.67528e42	0.255403
$964$	3.94436e43	2.12256
$965$	3.74046e43	1.98280
$966$	7.53851e42	0.393656
$967$	1.25188e43	0.643988	0.321994	−	0.946742i	$-0.395647\pi$
$967$	1.25188e43	0.643988	0.321994	+	0.946742i	$0.395647\pi$
$968$	5.10041e42	0.258471
$969$	5.04250e42	0.251739
$970$	−7.30063e43	−3.59062
$971$	2.66485e43	1.29120	0.645601	−	0.763675i	$-0.276607\pi$
$971$	2.66485e43	1.29120	0.645601	+	0.763675i	$0.276607\pi$
$972$	−1.58037e42	−0.0754393
$973$	−4.96621e43	−2.33555
$974$	−1.90985e43	−0.884900
$975$	−3.24314e42	−0.148047
$976$	8.86670e42	0.398786
$977$	2.04494e43	0.906167	0.453084	−	0.891468i	$-0.350324\pi$
$977$	2.04494e43	0.906167	0.453084	+	0.891468i	$0.350324\pi$
$978$	1.23747e43	0.540283
$979$	1.61318e42	0.0693958
$980$	−1.06983e44	−4.53458
$981$	1.13990e43	0.476065
$982$	3.27363e42	0.134714
$983$	3.10913e43	1.26071	0.630353	−	0.776309i	$-0.282910\pi$
$983$	3.10913e43	1.26071	0.630353	+	0.776309i	$0.282910\pi$
$984$	4.12002e42	0.164615
$985$	5.13195e41	0.0202049
$986$	2.39399e43	0.928769
$987$	3.88081e43	1.48363
$988$	−4.33732e42	−0.163398
$989$	−7.69315e42	−0.285600
$990$	−1.41391e42	−0.0517263
$991$	−1.36776e43	−0.493108	−0.246554	−	0.969129i	$-0.579298\pi$
$991$	−1.36776e43	−0.493108	−0.246554	+	0.969129i	$0.579298\pi$
$992$	3.79837e43	1.34952
$993$	3.31371e42	0.116025
$994$	6.47940e43	2.23580
$995$	−4.21514e43	−1.43343
$996$	−8.47608e42	−0.284076
$997$	−3.89685e43	−1.28716	−0.643581	−	0.765378i	$-0.722552\pi$
$997$	−3.89685e43	−1.28716	−0.643581	+	0.765378i	$0.722552\pi$
$998$	−4.07339e43	−1.32606
$999$	2.46557e42	0.0791075

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3.30.a.a.1.1	✓	2
3.2	odd	2		9.30.a.b.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.30.a.a.1.1	✓	2	1.1	even	1	trivial
9.30.a.b.1.2		2	3.2	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:	\( N \)	\(=\)	\( 3 \)
Weight:	\( k \)	\(=\)	\( 30 \)
Character orbit:	\([\chi]\)	\(=\)	3.a (trivial)

\(f(q)\)	\(=\)	\(q-34179.3 q^{2} -4.78297e6 q^{3} +6.31351e8 q^{4} -2.18126e10 q^{5} +1.63478e11 q^{6} +3.31488e12 q^{7} -3.22926e12 q^{8} +2.28768e13 q^{9} +O(q^{10})\)	\(q-34179.3 q^{2} -4.78297e6 q^{3} +6.31351e8 q^{4} -2.18126e10 q^{5} +1.63478e11 q^{6} +3.31488e12 q^{7} -3.22926e12 q^{8} +2.28768e13 q^{9} +7.45538e14 q^{10} -8.29004e13 q^{11} -3.01973e15 q^{12} +2.34198e15 q^{13} -1.13300e17 q^{14} +1.04329e17 q^{15} -2.28580e17 q^{16} +3.59403e17 q^{17} -7.81912e17 q^{18} -2.93337e18 q^{19} -1.37714e19 q^{20} -1.58550e19 q^{21} +2.83348e18 q^{22} +1.39110e19 q^{23} +1.54454e19 q^{24} +2.89524e20 q^{25} -8.00473e19 q^{26} -1.09419e20 q^{27} +2.09285e21 q^{28} -1.94885e21 q^{29} -3.56588e21 q^{30} +3.97886e21 q^{31} +9.54640e21 q^{32} +3.96510e20 q^{33} -1.22841e22 q^{34} -7.23060e22 q^{35} +1.44433e22 q^{36} -2.25333e22 q^{37} +1.00260e23 q^{38} -1.12016e22 q^{39} +7.04384e22 q^{40} +2.66746e23 q^{41} +5.41911e23 q^{42} -5.53027e23 q^{43} -5.23393e22 q^{44} -4.99002e23 q^{45} -4.75467e23 q^{46} -2.44770e24 q^{47} +1.09329e24 q^{48} +7.76851e24 q^{49} -9.89571e24 q^{50} -1.71901e24 q^{51} +1.47861e24 q^{52} +1.63222e24 q^{53} +3.73986e24 q^{54} +1.80827e24 q^{55} -1.07046e25 q^{56} +1.40302e25 q^{57} +6.66103e25 q^{58} -3.27794e25 q^{59} +6.58681e25 q^{60} -3.87903e25 q^{61} -1.35994e26 q^{62} +7.58338e25 q^{63} -2.03571e26 q^{64} -5.10847e25 q^{65} -1.35524e25 q^{66} -5.10980e26 q^{67} +2.26909e26 q^{68} -6.65358e25 q^{69} +2.47137e27 q^{70} -5.71879e26 q^{71} -7.38750e25 q^{72} -3.88369e26 q^{73} +7.70171e26 q^{74} -1.38478e27 q^{75} -1.85198e27 q^{76} -2.74805e26 q^{77} +3.82864e26 q^{78} +2.83632e26 q^{79} +4.98592e27 q^{80} +5.23348e26 q^{81} -9.11720e27 q^{82} +2.80690e27 q^{83} -1.00100e28 q^{84} -7.83950e27 q^{85} +1.89020e28 q^{86} +9.32129e27 q^{87} +2.67707e26 q^{88} -1.94592e28 q^{89} +1.70555e28 q^{90} +7.76339e27 q^{91} +8.78271e27 q^{92} -1.90307e28 q^{93} +8.36605e28 q^{94} +6.39843e28 q^{95} -4.56601e28 q^{96} -9.79243e28 q^{97} -2.65522e29 q^{98} -1.89650e27 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 45036 q^{2} - 9565938 q^{3} + 212348816 q^{4} + 187613820 q^{5} + 215405791884 q^{6} + 2643976121248 q^{7} + 7148407194432 q^{8} + 45753584909922 q^{9}+O(q^{10}) \) 2 * q - 45036 * q^2 - 9565938 * q^3 + 212348816 * q^4 + 187613820 * q^5 + 215405791884 * q^6 + 2643976121248 * q^7 + 7148407194432 * q^8 + 45753584909922 * q^9	\( 2 q - 45036 q^{2} - 9565938 q^{3} + 212348816 q^{4} + 187613820 q^{5} + 215405791884 q^{6} + 2643976121248 q^{7} + 7148407194432 q^{8} + 45753584909922 q^{9} + 506687260172760 q^{10} + 11\!\cdots\!28 q^{11}+ \cdots + 27\!\cdots\!08 q^{99}+O(q^{100}) \) 2 * q - 45036 * q^2 - 9565938 * q^3 + 212348816 * q^4 + 187613820 * q^5 + 215405791884 * q^6 + 2643976121248 * q^7 + 7148407194432 * q^8 + 45753584909922 * q^9 + 506687260172760 * q^10 + 1183469847829128 * q^11 - 1015657804114704 * q^12 - 21620888448148964 * q^13 - 106016273372995776 * q^14 - 897351085031580 * q^15 - 116297875935973120 * q^16 - 303436852359947964 * q^17 - 1030279225001623596 * q^18 - 7827889308240559496 * q^19 - 22989510711581456160 * q^20 - 12646055824669425312 * q^21 - 10915176904366508208 * q^22 - 1116121153769543376 * q^23 - 34190610010345228608 * q^24 + 587267318983626701150 * q^25 + 180111376423529552664 * q^26 - 218837978263024718418 * q^27 + 2373960709689332060416 * q^28 - 1549485579134315167092 * q^29 - 2423469458101245724440 * q^30 + 5185371205472693880112 * q^31 + 2755913283673324950528 * q^32 - 5660499594601436521032 * q^33 - 5087847547502785153368 * q^34 - 87065978554982950367040 * q^35 + 4857859791688701676176 * q^36 - 119610541537944992870612 * q^37 + 153398867521954218331824 * q^38 + 103412039199954602194116 * q^39 + 298748936011672856304000 * q^40 + 328159280597938698745332 * q^41 + 507072549038564233738944 * q^42 - 445450142806590533867000 * q^43 - 582951091424778866423232 * q^44 + 4292002421822411161020 * q^45 - 312321856572855528664608 * q^46 - 3462042915003644476983360 * q^47 + 556249135367605417793280 * q^48 + 4998714551689832609432370 * q^49 - 13128231346593205174089300 * q^50 + 1451329058295207953425116 * q^51 + 11519108423346209889919456 * q^52 - 14708457881668639138246596 * q^53 + 4927793594526790609336524 * q^54 + 29668651008250805659776240 * q^55 - 17666989638946946010639360 * q^56 + 37440551896746040612023624 * q^57 + 62274468648513136429575288 * q^58 - 48644338512234214893804984 * q^59 + 109958117058662045788139040 * q^60 - 74065165362970768623670820 * q^61 - 149093160585184069121258784 * q^62 + 60485692981663296515111328 * q^63 - 190129418691127176875831296 * q^64 - 578272316465227808767070520 * q^65 + 52206952763100973397109552 * q^66 - 366723705229906233436453064 * q^67 + 504640651326985312676536608 * q^68 + 5338372878723959111563344 * q^69 + 2631611128693389613002449280 * q^70 - 127322506876819543969204656 * q^71 + 163532627770570907729977152 * q^72 - 731571978572366031601976876 * q^73 + 1824113482985542836781172664 * q^74 - 2808881381411798019172714350 * q^75 + 198831266834486833097469376 * q^76 - 1124415098711978092688640384 * q^77 - 861467129981072720975779416 * q^78 - 5200098584837687939224496240 * q^79 + 7456159068548324050900753920 * q^80 + 1046695266054721074427023042 * q^81 - 9783939716187695677162489464 * q^82 + 7969015649847556259120597112 * q^83 - 11354580481662074875675855104 * q^84 - 22422099301146829036391554440 * q^85 + 17734112012711861680386446928 * q^86 + 7411141490946476280430856148 * q^87 + 13409672678850676246787849472 * q^88 + 12871942448610625249661939124 * q^89 + 11591379290545057161379062360 * q^90 + 23840130434649524469770109632 * q^91 + 15079105137564640323695392128 * q^92 - 24801469729268525175065412528 * q^93 + 94672981437665362714609762176 * q^94 - 43696120536074431524731727600 * q^95 - 13181447802497719365301957632 * q^96 - 92696268103775509741340043644 * q^97 - 235450999642801088400974721036 * q^98 + 27073994085491238235563904008 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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