LMFDB - Embedded newform 49.26.a.d.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [49,26,Mod(1,49)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(49, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 26, names="a")

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

chi := DirichletCharacter("49.1");

S:= CuspForms(chi, 26);

N := Newforms(S);

Level:	$ N $	$=$	$ 49 = 7^{2} $
Weight:	$ k $	$=$	$ 26 $
Character orbit:	$[\chi]$	$=$	49.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:	$194.038422177$
Analytic rank:	$0$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - x^{6} - 212249190 x^{5} + 97966970896 x^{4} + \cdots + 48\!\cdots\!56 $ x^7 - x^6 - 212249190x^5 + 97966970896x^4 + 13490510525162432x^3 - 12908535655668027648x^2 - 247876261380147473323520*x + 486739593081059559316115456
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{13}\cdot 3^{10}\cdot 5^{4}\cdot 7^{4} $
Twist minimal:	no (minimal twist has level 7)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$10105.3$ of defining polynomial
Character	$\chi$	$=$	49.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+11301.3 q^{2} -634140. q^{3} +9.41649e7 q^{4} -5.29471e8 q^{5} -7.16660e9 q^{6} +6.84977e11 q^{8} -4.45155e11 q^{9} +O(q^{10})$	\(q+11301.3 q^{2} -634140. q^{3} +9.41649e7 q^{4} -5.29471e8 q^{5} -7.16660e9 q^{6} +6.84977e11 q^{8} -4.45155e11 q^{9} -5.98371e12 q^{10} -1.21153e13 q^{11} -5.97137e13 q^{12} +1.33738e14 q^{13} +3.35758e14 q^{15} +4.58148e15 q^{16} -8.48253e14 q^{17} -5.03083e15 q^{18} +3.46660e15 q^{19} -4.98575e16 q^{20} -1.36918e17 q^{22} -2.00601e16 q^{23} -4.34371e17 q^{24} -1.76841e16 q^{25} +1.51141e18 q^{26} +8.19590e17 q^{27} +6.10906e17 q^{29} +3.79451e18 q^{30} -6.65067e18 q^{31} +2.87926e19 q^{32} +7.68278e18 q^{33} -9.58636e18 q^{34} -4.19180e19 q^{36} +9.20488e17 q^{37} +3.91771e19 q^{38} -8.48086e19 q^{39} -3.62675e20 q^{40} +1.01791e20 q^{41} +3.45500e20 q^{43} -1.14083e21 q^{44} +2.35697e20 q^{45} -2.26706e20 q^{46} -3.45236e19 q^{47} -2.90530e21 q^{48} -1.99853e20 q^{50} +5.37911e20 q^{51} +1.25934e22 q^{52} +5.24544e21 q^{53} +9.26243e21 q^{54} +6.41468e21 q^{55} -2.19831e21 q^{57} +6.90403e21 q^{58} +1.34542e22 q^{59} +3.16167e22 q^{60} +2.79568e22 q^{61} -7.51612e22 q^{62} +1.71665e23 q^{64} -7.08104e22 q^{65} +8.68254e22 q^{66} -9.11798e22 q^{67} -7.98757e22 q^{68} +1.27209e22 q^{69} +1.20768e23 q^{71} -3.04921e23 q^{72} +1.71355e23 q^{73} +1.04027e22 q^{74} +1.12142e22 q^{75} +3.26432e23 q^{76} -9.58448e23 q^{78} +4.35071e23 q^{79} -2.42576e24 q^{80} -1.42560e23 q^{81} +1.15037e24 q^{82} +9.54510e23 q^{83} +4.49125e23 q^{85} +3.90459e24 q^{86} -3.87400e23 q^{87} -8.29868e24 q^{88} -1.50044e24 q^{89} +2.66368e24 q^{90} -1.88896e24 q^{92} +4.21746e24 q^{93} -3.90162e23 q^{94} -1.83546e24 q^{95} -1.82586e25 q^{96} -1.28050e25 q^{97} +5.39318e24 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q + 8373 q^{2} + 599172 q^{3} + 199632661 q^{4} - 485320794 q^{5} - 548762130 q^{6} + 679913241639 q^{8} + 2499178495563 q^{9}+O(q^{10}) $ 7 * q + 8373 * q^2 + 599172 * q^3 + 199632661 * q^4 - 485320794 * q^5 - 548762130 * q^6 + 679913241639 * q^8 + 2499178495563 * q^9	$ 7 q + 8373 q^{2} + 599172 q^{3} + 199632661 q^{4} - 485320794 q^{5} - 548762130 q^{6} + 679913241639 q^{8} + 2499178495563 q^{9} + 876704815140 q^{10} - 7845139606524 q^{11} + 83731581305106 q^{12} + 75871445642734 q^{13} + 12\!\cdots\!84 q^{15}+ \cdots + 29\!\cdots\!00 q^{99}+O(q^{100}) $ 7 * q + 8373 * q^2 + 599172 * q^3 + 199632661 * q^4 - 485320794 * q^5 - 548762130 * q^6 + 679913241639 * q^8 + 2499178495563 * q^9 + 876704815140 * q^10 - 7845139606524 * q^11 + 83731581305106 * q^12 + 75871445642734 * q^13 + 1250450093573784 * q^15 + 2533333214129041 * q^16 - 4930179049331550 * q^17 + 6108218172751149 * q^18 + 8822108307937204 * q^19 + 35797888210439208 * q^20 + 122308015837411896 * q^22 + 260380318250119992 * q^23 - 280838923324398306 * q^24 + 442974124902943561 * q^25 - 525030062154247104 * q^26 + 508138451607400488 * q^27 + 3074121146906357394 * q^29 + 20693674849314206160 * q^30 - 17867964278742490304 * q^31 + 41524963168122393471 * q^32 - 18631713362079899088 * q^33 - 76530595013021124150 * q^34 + 120686738791924632357 * q^36 + 37537195275383667242 * q^37 - 133898980332930749790 * q^38 + 160680068588101330968 * q^39 - 260261018010811048560 * q^40 - 349555665716732087718 * q^41 - 188918130006461199484 * q^43 - 866635019544130150704 * q^44 + 2875914312455481795918 * q^45 - 1056444907691638473648 * q^46 + 577519309883773958064 * q^47 + 1705636002072738200514 * q^48 - 3108044078925178785 * q^50 - 8568497654252614793448 * q^51 + 21223967127059853562252 * q^52 + 724118360265623334330 * q^53 + 23525683999565788877508 * q^54 + 3874297214249814234792 * q^55 + 21002099147408968606176 * q^57 - 6571075616758407948534 * q^58 + 29388013065202679743548 * q^59 + 131210151872269358361312 * q^60 - 24863323230677092393442 * q^61 - 178098511159147000538004 * q^62 + 185730465159694629378817 * q^64 - 28642507689771657088260 * q^65 + 182488465275344339797728 * q^66 + 87288896332559907446444 * q^67 - 236561584649915083645422 * q^68 + 38736311524504328113344 * q^69 + 507749245951454445426264 * q^71 - 136846012456831244000985 * q^72 + 384451815193432683470074 * q^73 - 180156332882615168418510 * q^74 + 917728597534517928543804 * q^75 + 1802955096706900507996366 * q^76 - 2701299412149008608565208 * q^78 - 512089643024553543168400 * q^79 - 1072829383400652355143456 * q^80 - 1711055088184234765637889 * q^81 + 328793973025384284153498 * q^82 - 683613625271699866065420 * q^83 - 4106127272649214828366668 * q^85 + 6352668961585470034751760 * q^86 - 6810779334667612471104168 * q^87 - 1678346430445345786597824 * q^88 - 7785138614078665124468694 * q^89 + 6907385334351120772566420 * q^90 + 4229143913695999872649632 * q^92 + 9311007684860974346150688 * q^93 - 16094575705640558287782684 * q^94 + 8670853765297953493275288 * q^95 - 20458763379770390869400514 * q^96 - 16735236191051483252826350 * q^97 + 29494988134999515624453300 * 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 $

$2$	11301.3	1.95098	0.975491	−	0.220038i	$-0.0706182\pi$
$2$	11301.3	1.95098	0.975491	+	0.220038i	$0.0706182\pi$
$3$	−634140.	−0.688921	−0.344460	−	0.938801i	$-0.611938\pi$
$3$	−634140.	−0.688921	−0.344460	+	0.938801i	$0.611938\pi$
$4$	9.41649e7	2.80633
$5$	−5.29471e8	−0.969877	−0.484939	−	0.874548i	$-0.661158\pi$
$5$	−5.29471e8	−0.969877	−0.484939	+	0.874548i	$0.661158\pi$
$6$	−7.16660e9	−1.34407
$7$	0	0
$7$	0	0
$8$	6.84977e11	3.52412
$9$	−4.45155e11	−0.525388
$10$	−5.98371e12	−1.89221
$11$	−1.21153e13	−1.16392	−0.581962	−	0.813216i	$-0.697715\pi$
$11$	−1.21153e13	−1.16392	−0.581962	+	0.813216i	$0.697715\pi$
$12$	−5.97137e13	−1.93334
$13$	1.33738e14	1.59207	0.796037	−	0.605248i	$-0.206926\pi$
$13$	1.33738e14	1.59207	0.796037	+	0.605248i	$0.206926\pi$
$14$	0	0
$15$	3.35758e14	0.668169
$16$	4.58148e15	4.06917
$17$	−8.48253e14	−0.353113	−0.176557	−	0.984290i	$-0.556496\pi$
$17$	−8.48253e14	−0.353113	−0.176557	+	0.984290i	$0.556496\pi$
$18$	−5.03083e15	−1.02502
$19$	3.46660e15	0.359322	0.179661	−	0.983729i	$-0.442500\pi$
$19$	3.46660e15	0.359322	0.179661	+	0.983729i	$0.442500\pi$
$20$	−4.98575e16	−2.72180
$21$	0	0
$22$	−1.36918e17	−2.27080
$23$	−2.00601e16	−0.190869	−0.0954346	−	0.995436i	$-0.530424\pi$
$23$	−2.00601e16	−0.190869	−0.0954346	+	0.995436i	$0.530424\pi$
$24$	−4.34371e17	−2.42784
$25$	−1.76841e16	−0.0593380
$26$	1.51141e18	3.10611
$27$	8.19590e17	1.05087
$28$	0	0
$29$	6.10906e17	0.320627	0.160313	−	0.987066i	$-0.448750\pi$
$29$	6.10906e17	0.320627	0.160313	+	0.987066i	$0.448750\pi$
$30$	3.79451e18	1.30359
$31$	−6.65067e18	−1.51651	−0.758254	−	0.651960i	$-0.773947\pi$
$31$	−6.65067e18	−1.51651	−0.758254	+	0.651960i	$0.773947\pi$
$32$	2.87926e19	4.41476
$33$	7.68278e18	0.801852
$34$	−9.58636e18	−0.688918
$35$	0	0
$36$	−4.19180e19	−1.47441
$37$	9.20488e17	0.0229878	0.0114939	−	0.999934i	$-0.496341\pi$
$37$	9.20488e17	0.0229878	0.0114939	+	0.999934i	$0.496341\pi$
$38$	3.91771e19	0.701031
$39$	−8.48086e19	−1.09681
$40$	−3.62675e20	−3.41797
$41$	1.01791e20	0.704549	0.352274	−	0.935897i	$-0.385408\pi$
$41$	1.01791e20	0.704549	0.352274	+	0.935897i	$0.385408\pi$
$42$	0	0
$43$	3.45500e20	1.31854	0.659268	−	0.751908i	$-0.270866\pi$
$43$	3.45500e20	1.31854	0.659268	+	0.751908i	$0.270866\pi$
$44$	−1.14083e21	−3.26636
$45$	2.35697e20	0.509562
$46$	−2.26706e20	−0.372383
$47$	−3.45236e19	−0.0433404	−0.0216702	−	0.999765i	$-0.506898\pi$
$47$	−3.45236e19	−0.0433404	−0.0216702	+	0.999765i	$0.506898\pi$
$48$	−2.90530e21	−2.80334
$49$	0	0
$50$	−1.99853e20	−0.115767
$51$	5.37911e20	0.243267
$52$	1.25934e22	4.46789
$53$	5.24544e21	1.46667	0.733337	−	0.679866i	$-0.237962\pi$
$53$	5.24544e21	1.46667	0.733337	+	0.679866i	$0.237962\pi$
$54$	9.26243e21	2.05023
$55$	6.41468e21	1.12886
$56$	0	0
$57$	−2.19831e21	−0.247544
$58$	6.90403e21	0.625537
$59$	1.34542e22	0.984480	0.492240	−	0.870460i	$-0.336178\pi$
$59$	1.34542e22	0.984480	0.492240	+	0.870460i	$0.336178\pi$
$60$	3.16167e22	1.87510
$61$	2.79568e22	1.34854	0.674272	−	0.738483i	$-0.264457\pi$
$61$	2.79568e22	1.34854	0.674272	+	0.738483i	$0.264457\pi$
$62$	−7.51612e22	−2.95868
$63$	0	0
$64$	1.71665e23	4.54394
$65$	−7.08104e22	−1.54412
$66$	8.68254e22	1.56440
$67$	−9.11798e22	−1.36133	−0.680665	−	0.732595i	$-0.738309\pi$
$67$	−9.11798e22	−1.36133	−0.680665	+	0.732595i	$0.738309\pi$
$68$	−7.98757e22	−0.990953
$69$	1.27209e22	0.131494
$70$	0	0
$71$	1.20768e23	0.873418	0.436709	−	0.899603i	$-0.356144\pi$
$71$	1.20768e23	0.873418	0.436709	+	0.899603i	$0.356144\pi$
$72$	−3.04921e23	−1.85153
$73$	1.71355e23	0.875713	0.437857	−	0.899045i	$-0.355738\pi$
$73$	1.71355e23	0.875713	0.437857	+	0.899045i	$0.355738\pi$
$74$	1.04027e22	0.0448487
$75$	1.12142e22	0.0408792
$76$	3.26432e23	1.00838
$77$	0	0
$78$	−9.58448e23	−2.13986
$79$	4.35071e23	0.828364	0.414182	−	0.910194i	$-0.364068\pi$
$79$	4.35071e23	0.828364	0.414182	+	0.910194i	$0.364068\pi$
$80$	−2.42576e24	−3.94660
$81$	−1.42560e23	−0.198580
$82$	1.15037e24	1.37456
$83$	9.54510e23	0.980176	0.490088	−	0.871673i	$-0.336965\pi$
$83$	9.54510e23	0.980176	0.490088	+	0.871673i	$0.336965\pi$
$84$	0	0
$85$	4.49125e23	0.342476
$86$	3.90459e24	2.57244
$87$	−3.87400e23	−0.220886
$88$	−8.29868e24	−4.10181
$89$	−1.50044e24	−0.643937	−0.321969	−	0.946750i	$-0.604345\pi$
$89$	−1.50044e24	−0.643937	−0.321969	+	0.946750i	$0.604345\pi$
$90$	2.66368e24	0.994146
$91$	0	0
$92$	−1.88896e24	−0.535643
$93$	4.21746e24	1.04475
$94$	−3.90162e23	−0.0845564
$95$	−1.83546e24	−0.348498
$96$	−1.82586e25	−3.04142
$97$	−1.28050e25	−1.87384	−0.936920	−	0.349545i	$-0.886336\pi$
$97$	−1.28050e25	−1.87384	−0.936920	+	0.349545i	$0.886336\pi$
$98$	0	0
$99$	5.39318e24	0.611512
$100$	−1.66522e24	−0.166522
$101$	−1.66990e24	−0.147459	−0.0737297	−	0.997278i	$-0.523490\pi$
$101$	−1.66990e24	−0.147459	−0.0737297	+	0.997278i	$0.523490\pi$
$102$	6.07909e24	0.474610
$103$	4.73718e24	0.327381	0.163691	−	0.986512i	$-0.447660\pi$
$103$	4.73718e24	0.327381	0.163691	+	0.986512i	$0.447660\pi$
$104$	9.16075e25	5.61066
$105$	0	0
$106$	5.92803e25	2.86145
$107$	2.30452e25	0.989197	0.494598	−	0.869122i	$-0.335315\pi$
$107$	2.30452e25	0.989197	0.494598	+	0.869122i	$0.335315\pi$
$108$	7.71766e25	2.94910
$109$	5.50785e24	0.187565	0.0937824	−	0.995593i	$-0.470104\pi$
$109$	5.50785e24	0.187565	0.0937824	+	0.995593i	$0.470104\pi$
$110$	7.24942e25	2.20239
$111$	−5.83718e23	−0.0158368
$112$	0	0
$113$	−1.22036e25	−0.264855	−0.132428	−	0.991193i	$-0.542277\pi$
$113$	−1.22036e25	−0.264855	−0.132428	+	0.991193i	$0.542277\pi$
$114$	−2.48437e25	−0.482955
$115$	1.06213e25	0.185120
$116$	5.75259e25	0.899785
$117$	−5.95342e25	−0.836456
$118$	1.52050e26	1.92070
$119$	0	0
$120$	2.29987e26	2.35471
$121$	3.84328e25	0.354719
$122$	3.15949e26	2.63099
$123$	−6.45497e25	−0.485378
$124$	−6.26260e26	−4.25582
$125$	1.67158e26	1.02743
$126$	0	0
$127$	2.83965e26	1.43126	0.715630	−	0.698480i	$-0.246140\pi$
$127$	2.83965e26	1.43126	0.715630	+	0.698480i	$0.246140\pi$
$128$	9.73920e26	4.45040
$129$	−2.19095e26	−0.908366
$130$	−8.00249e26	−3.01254
$131$	3.83863e26	1.31306	0.656530	−	0.754300i	$-0.272024\pi$
$131$	3.83863e26	1.31306	0.656530	+	0.754300i	$0.272024\pi$
$132$	7.23448e26	2.25026
$133$	0	0
$134$	−1.03045e27	−2.65593
$135$	−4.33949e26	−1.01922
$136$	−5.81034e26	−1.24441
$137$	4.01352e26	0.784364	0.392182	−	0.919888i	$-0.371720\pi$
$137$	4.01352e26	0.784364	0.392182	+	0.919888i	$0.371720\pi$
$138$	1.43763e26	0.256542
$139$	−7.02258e25	−0.114502	−0.0572508	−	0.998360i	$-0.518233\pi$
$139$	−7.02258e25	−0.114502	−0.0572508	+	0.998360i	$0.518233\pi$
$140$	0	0
$141$	2.18928e25	0.0298581
$142$	1.36483e27	1.70402
$143$	−1.62027e27	−1.85305
$144$	−2.03947e27	−2.13789
$145$	−3.23457e26	−0.310968
$146$	1.93654e27	1.70850
$147$	0	0
$148$	8.66777e25	0.0645113
$149$	−4.22072e26	−0.288774	−0.144387	−	0.989521i	$-0.546121\pi$
$149$	−4.22072e26	−0.288774	−0.144387	+	0.989521i	$0.546121\pi$
$150$	1.26735e26	0.0797545
$151$	1.56693e27	0.907482	0.453741	−	0.891133i	$-0.350089\pi$
$151$	1.56693e27	0.907482	0.453741	+	0.891133i	$0.350089\pi$
$152$	2.37454e27	1.26629
$153$	3.77604e26	0.185521
$154$	0	0
$155$	3.52134e27	1.47083
$156$	−7.98600e27	−3.07802
$157$	1.76240e27	0.627133	0.313567	−	0.949566i	$-0.398476\pi$
$157$	1.76240e27	0.627133	0.313567	+	0.949566i	$0.398476\pi$
$158$	4.91687e27	1.61612
$159$	−3.32634e27	−1.01042
$160$	−1.52449e28	−4.28177
$161$	0	0
$162$	−1.61111e27	−0.387425
$163$	9.09664e26	0.202552	0.101276	−	0.994858i	$-0.467708\pi$
$163$	9.09664e26	0.202552	0.101276	+	0.994858i	$0.467708\pi$
$164$	9.58514e27	1.97720
$165$	−4.06781e27	−0.777698
$166$	1.07872e28	1.91231
$167$	−6.57959e27	−1.08204	−0.541020	−	0.841010i	$-0.681962\pi$
$167$	−6.57959e27	−1.08204	−0.541020	+	0.841010i	$0.681962\pi$
$168$	0	0
$169$	1.08295e28	1.53470
$170$	5.07570e27	0.668166
$171$	−1.54317e27	−0.188783
$172$	3.25339e28	3.70025
$173$	1.25506e28	1.32766	0.663831	−	0.747882i	$-0.268929\pi$
$173$	1.25506e28	1.32766	0.663831	+	0.747882i	$0.268929\pi$
$174$	−4.37812e27	−0.430945
$175$	0	0
$176$	−5.55059e28	−4.73621
$177$	−8.53183e27	−0.678229
$178$	−1.69569e28	−1.25631
$179$	−1.46782e28	−1.01394	−0.506969	−	0.861964i	$-0.669234\pi$
$179$	−1.46782e28	−1.01394	−0.506969	+	0.861964i	$0.669234\pi$
$180$	2.21943e28	1.43000
$181$	−4.34483e27	−0.261210	−0.130605	−	0.991434i	$-0.541692\pi$
$181$	−4.34483e27	−0.261210	−0.130605	+	0.991434i	$0.541692\pi$
$182$	0	0
$183$	−1.77285e28	−0.929040
$184$	−1.37407e28	−0.672647
$185$	−4.87372e26	−0.0222953
$186$	4.76627e28	2.03830
$187$	1.02768e28	0.410997
$188$	−3.25092e27	−0.121628
$189$	0	0
$190$	−2.07431e28	−0.679914
$191$	4.04639e27	0.124208	0.0621042	−	0.998070i	$-0.480219\pi$
$191$	4.04639e27	0.124208	0.0621042	+	0.998070i	$0.480219\pi$
$192$	−1.08860e29	−3.13042
$193$	−4.00210e28	−1.07850	−0.539251	−	0.842145i	$-0.681293\pi$
$193$	−4.00210e28	−1.07850	−0.539251	+	0.842145i	$0.681293\pi$
$194$	−1.44713e29	−3.65583
$195$	4.49037e28	1.06377
$196$	0	0
$197$	4.92771e27	0.102758	0.0513792	−	0.998679i	$-0.483638\pi$
$197$	4.92771e27	0.102758	0.0513792	+	0.998679i	$0.483638\pi$
$198$	6.09499e28	1.19305
$199$	−1.01292e28	−0.186171	−0.0930855	−	0.995658i	$-0.529673\pi$
$199$	−1.01292e28	−0.186171	−0.0930855	+	0.995658i	$0.529673\pi$
$200$	−1.21132e28	−0.209114
$201$	5.78207e28	0.937849
$202$	−1.88720e28	−0.287691
$203$	0	0
$204$	5.06523e28	0.682688
$205$	−5.38953e28	−0.683326
$206$	5.35362e28	0.638716
$207$	8.92988e27	0.100280
$208$	6.12718e29	6.47842
$209$	−4.19988e28	−0.418223
$210$	0	0
$211$	3.06311e28	0.270789	0.135395	−	0.990792i	$-0.456770\pi$
$211$	3.06311e28	0.270789	0.135395	+	0.990792i	$0.456770\pi$
$212$	4.93936e29	4.11597
$213$	−7.65837e28	−0.601716
$214$	2.60440e29	1.92991
$215$	−1.82932e29	−1.27882
$216$	5.61400e29	3.70340
$217$	0	0
$218$	6.22459e28	0.365936
$219$	−1.08663e29	−0.603297
$220$	6.04038e29	3.16797
$221$	−1.13444e29	−0.562182
$222$	−6.59678e27	−0.0308972
$223$	−1.21791e29	−0.539268	−0.269634	−	0.962963i	$-0.586903\pi$
$223$	−1.21791e29	−0.539268	−0.269634	+	0.962963i	$0.586903\pi$
$224$	0	0
$225$	7.87216e27	0.0311754
$226$	−1.37917e29	−0.516728
$227$	9.87281e28	0.350040	0.175020	−	0.984565i	$-0.444001\pi$
$227$	9.87281e28	0.350040	0.175020	+	0.984565i	$0.444001\pi$
$228$	−2.07004e29	−0.694692
$229$	−4.93548e29	−1.56814	−0.784071	−	0.620671i	$-0.786860\pi$
$229$	−4.93548e29	−1.56814	−0.784071	+	0.620671i	$0.786860\pi$
$230$	1.20034e29	0.361165
$231$	0	0
$232$	4.18457e29	1.12993
$233$	−1.60794e29	−0.411453	−0.205727	−	0.978610i	$-0.565956\pi$
$233$	−1.60794e29	−0.411453	−0.205727	+	0.978610i	$0.565956\pi$
$234$	−6.72814e29	−1.63191
$235$	1.82793e28	0.0420349
$236$	1.26691e30	2.76278
$237$	−2.75896e29	−0.570677
$238$	0	0
$239$	−5.32243e29	−0.991143	−0.495572	−	0.868567i	$-0.665041\pi$
$239$	−5.32243e29	−0.991143	−0.495572	+	0.868567i	$0.665041\pi$
$240$	1.53827e30	2.71889
$241$	6.61841e29	1.11056	0.555278	−	0.831665i	$-0.312612\pi$
$241$	6.61841e29	1.11056	0.555278	+	0.831665i	$0.312612\pi$
$242$	4.34340e29	0.692051
$243$	−6.04027e29	−0.914066
$244$	2.63255e30	3.78446
$245$	0	0
$246$	−7.29496e29	−0.946965
$247$	4.63616e29	0.572067
$248$	−4.55556e30	−5.34436
$249$	−6.05293e29	−0.675264
$250$	1.88910e30	2.00449
$251$	9.83103e29	0.992379	0.496190	−	0.868214i	$-0.334732\pi$
$251$	9.83103e29	0.992379	0.496190	+	0.868214i	$0.334732\pi$
$252$	0	0
$253$	2.43034e29	0.222157
$254$	3.20917e30	2.79236
$255$	−2.84808e29	−0.235939
$256$	5.24643e30	4.13870
$257$	9.37783e29	0.704593	0.352297	−	0.935888i	$-0.385401\pi$
$257$	9.37783e29	0.704593	0.352297	+	0.935888i	$0.385401\pi$
$258$	−2.47606e30	−1.77221
$259$	0	0
$260$	−6.66785e30	−4.33330
$261$	−2.71948e29	−0.168453
$262$	4.33814e30	2.56176
$263$	−3.05716e29	−0.172136	−0.0860679	−	0.996289i	$-0.527430\pi$
$263$	−3.05716e29	−0.172136	−0.0860679	+	0.996289i	$0.527430\pi$
$264$	5.26253e30	2.82582
$265$	−2.77731e30	−1.42249
$266$	0	0
$267$	9.51489e29	0.443622
$268$	−8.58594e30	−3.82035
$269$	−2.36859e30	−1.00597	−0.502986	−	0.864295i	$-0.667765\pi$
$269$	−2.36859e30	−1.00597	−0.502986	+	0.864295i	$0.667765\pi$
$270$	−4.90419e30	−1.98847
$271$	−2.69397e30	−1.04298	−0.521491	−	0.853256i	$-0.674624\pi$
$271$	−2.69397e30	−1.04298	−0.521491	+	0.853256i	$0.674624\pi$
$272$	−3.88625e30	−1.43688
$273$	0	0
$274$	4.53579e30	1.53028
$275$	2.14248e29	0.0690649
$276$	1.19787e30	0.369015
$277$	4.96833e30	1.46290	0.731448	−	0.681898i	$-0.238845\pi$
$277$	4.96833e30	1.46290	0.731448	+	0.681898i	$0.238845\pi$
$278$	−7.93642e29	−0.223391
$279$	2.96058e30	0.796755
$280$	0	0
$281$	3.00264e30	0.739052	0.369526	−	0.929220i	$-0.379520\pi$
$281$	3.00264e30	0.739052	0.369526	+	0.929220i	$0.379520\pi$
$282$	2.47417e29	0.0582527
$283$	3.81397e30	0.859105	0.429553	−	0.903042i	$-0.358671\pi$
$283$	3.81397e30	0.859105	0.429553	+	0.903042i	$0.358671\pi$
$284$	1.13721e31	2.45110
$285$	1.16394e30	0.240088
$286$	−1.83112e31	−3.61527
$287$	0	0
$288$	−1.28172e31	−2.31946
$289$	−5.05109e30	−0.875311
$290$	−3.65548e30	−0.606694
$291$	8.12015e30	1.29093
$292$	1.61357e31	2.45754
$293$	4.44140e30	0.648149	0.324074	−	0.946032i	$-0.394947\pi$
$293$	4.44140e30	0.648149	0.324074	+	0.946032i	$0.394947\pi$
$294$	0	0
$295$	−7.12359e30	−0.954825
$296$	6.30513e29	0.0810117
$297$	−9.92956e30	−1.22313
$298$	−4.76996e30	−0.563393
$299$	−2.68280e30	−0.303878
$300$	1.05598e30	0.114721
$301$	0	0
$302$	1.77084e31	1.77048
$303$	1.05895e30	0.101588
$304$	1.58821e31	1.46214
$305$	−1.48023e31	−1.30792
$306$	4.26742e30	0.361949
$307$	2.06199e31	1.67902	0.839511	−	0.543343i	$-0.182842\pi$
$307$	2.06199e31	1.67902	0.839511	+	0.543343i	$0.182842\pi$
$308$	0	0
$309$	−3.00403e30	−0.225540
$310$	3.97957e31	2.86956
$311$	−8.01414e30	−0.555076	−0.277538	−	0.960715i	$-0.589518\pi$
$311$	−8.01414e30	−0.555076	−0.277538	+	0.960715i	$0.589518\pi$
$312$	−5.80920e31	−3.86530
$313$	−5.99501e30	−0.383253	−0.191627	−	0.981468i	$-0.561376\pi$
$313$	−5.99501e30	−0.383253	−0.191627	+	0.981468i	$0.561376\pi$
$314$	1.99175e31	1.22353
$315$	0	0
$316$	4.09684e31	2.32467
$317$	−2.14631e31	−1.17072	−0.585358	−	0.810775i	$-0.699046\pi$
$317$	−2.14631e31	−1.17072	−0.585358	+	0.810775i	$0.699046\pi$
$318$	−3.75920e31	−1.97132
$319$	−7.40129e30	−0.373185
$320$	−9.08917e31	−4.40707
$321$	−1.46139e31	−0.681478
$322$	0	0
$323$	−2.94055e30	−0.126881
$324$	−1.34241e31	−0.557280
$325$	−2.36504e30	−0.0944704
$326$	1.02804e31	0.395175
$327$	−3.49275e30	−0.129217
$328$	6.97245e31	2.48292
$329$	0	0
$330$	−4.59715e31	−1.51727
$331$	−4.65863e30	−0.148050	−0.0740250	−	0.997256i	$-0.523584\pi$
$331$	−4.65863e30	−0.148050	−0.0740250	+	0.997256i	$0.523584\pi$
$332$	8.98813e31	2.75070
$333$	−4.09760e29	−0.0120775
$334$	−7.43580e31	−2.11104
$335$	4.82770e31	1.32032
$336$	0	0
$337$	−5.05197e31	−1.28259	−0.641294	−	0.767295i	$-0.721602\pi$
$337$	−5.05197e31	−1.28259	−0.641294	+	0.767295i	$0.721602\pi$
$338$	1.22387e32	2.99417
$339$	7.73881e30	0.182464
$340$	4.22918e31	0.961103
$341$	8.05747e31	1.76510
$342$	−1.74399e31	−0.368313
$343$	0	0
$344$	2.36659e32	4.64668
$345$	−6.73536e30	−0.127533
$346$	1.41838e32	2.59025
$347$	3.75194e31	0.660903	0.330451	−	0.943823i	$-0.392799\pi$
$347$	3.75194e31	0.660903	0.330451	+	0.943823i	$0.392799\pi$
$348$	−3.64795e31	−0.619880
$349$	−8.45885e31	−1.38673	−0.693367	−	0.720584i	$-0.743874\pi$
$349$	−8.45885e31	−1.38673	−0.693367	+	0.720584i	$0.743874\pi$
$350$	0	0
$351$	1.09610e32	1.67306
$352$	−3.48831e32	−5.13844
$353$	−1.04589e32	−1.48697	−0.743486	−	0.668751i	$-0.766829\pi$
$353$	−1.04589e32	−1.48697	−0.743486	+	0.668751i	$0.766829\pi$
$354$	−9.64207e31	−1.32321
$355$	−6.39430e31	−0.847108
$356$	−1.41289e32	−1.80710
$357$	0	0
$358$	−1.65883e32	−1.97818
$359$	1.11128e32	1.27980	0.639902	−	0.768456i	$-0.278975\pi$
$359$	1.11128e32	1.27980	0.639902	+	0.768456i	$0.278975\pi$
$360$	1.61447e32	1.79576
$361$	−8.10592e31	−0.870888
$362$	−4.91022e31	−0.509617
$363$	−2.43718e31	−0.244373
$364$	0	0
$365$	−9.07276e31	−0.849334
$366$	−2.00356e32	−1.81254
$367$	−4.59064e31	−0.401373	−0.200686	−	0.979656i	$-0.564317\pi$
$367$	−4.59064e31	−0.401373	−0.200686	+	0.979656i	$0.564317\pi$
$368$	−9.19051e31	−0.776680
$369$	−4.53128e31	−0.370162
$370$	−5.50793e30	−0.0434978
$371$	0	0
$372$	3.97136e32	2.93193
$373$	2.19124e32	1.56433	0.782166	−	0.623070i	$-0.214115\pi$
$373$	2.19124e32	1.56433	0.782166	+	0.623070i	$0.214115\pi$
$374$	1.16141e32	0.801848
$375$	−1.06001e32	−0.707817
$376$	−2.36479e31	−0.152737
$377$	8.17014e31	0.510461
$378$	0	0
$379$	−2.98752e32	−1.74711	−0.873555	−	0.486726i	$-0.838191\pi$
$379$	−2.98752e32	−1.74711	−0.873555	+	0.486726i	$0.838191\pi$
$380$	−1.72836e32	−0.978002
$381$	−1.80074e32	−0.986024
$382$	4.57295e31	0.242328
$383$	−8.44157e30	−0.0432951	−0.0216475	−	0.999766i	$-0.506891\pi$
$383$	−8.44157e30	−0.0432951	−0.0216475	+	0.999766i	$0.506891\pi$
$384$	−6.17602e32	−3.06597
$385$	0	0
$386$	−4.52289e32	−2.10414
$387$	−1.53801e32	−0.692743
$388$	−1.20578e33	−5.25862
$389$	3.97269e32	1.67770	0.838850	−	0.544362i	$-0.183228\pi$
$389$	3.97269e32	1.67770	0.838850	+	0.544362i	$0.183228\pi$
$390$	5.07470e32	2.07540
$391$	1.70161e31	0.0673984
$392$	0	0
$393$	−2.43423e32	−0.904594
$394$	5.56896e31	0.200480
$395$	−2.30357e32	−0.803412
$396$	5.07848e32	1.71611
$397$	−1.84348e32	−0.603611	−0.301806	−	0.953370i	$-0.597589\pi$
$397$	−1.84348e32	−0.603611	−0.301806	+	0.953370i	$0.597589\pi$
$398$	−1.14473e32	−0.363216
$399$	0	0
$400$	−8.10193e31	−0.241456
$401$	−1.37008e32	−0.395768	−0.197884	−	0.980225i	$-0.563407\pi$
$401$	−1.37008e32	−0.395768	−0.197884	+	0.980225i	$0.563407\pi$
$402$	6.53450e32	1.82973
$403$	−8.89448e32	−2.41439
$404$	−1.57246e32	−0.413820
$405$	7.54813e31	0.192598
$406$	0	0
$407$	−1.11520e31	−0.0267560
$408$	3.68457e32	0.857303
$409$	−4.24058e32	−0.956938	−0.478469	−	0.878104i	$-0.658808\pi$
$409$	−4.24058e32	−0.956938	−0.478469	+	0.878104i	$0.658808\pi$
$410$	−6.09087e32	−1.33316
$411$	−2.54513e32	−0.540365
$412$	4.46076e32	0.918741
$413$	0	0
$414$	1.00919e32	0.195645
$415$	−5.05385e32	−0.950651
$416$	3.85067e33	7.02862
$417$	4.45330e31	0.0788825
$418$	−4.74641e32	−0.815946
$419$	5.24921e32	0.875827	0.437914	−	0.899017i	$-0.355718\pi$
$419$	5.24921e32	0.875827	0.437914	+	0.899017i	$0.355718\pi$
$420$	0	0
$421$	3.91883e32	0.616070	0.308035	−	0.951375i	$-0.400329\pi$
$421$	3.91883e32	0.616070	0.308035	+	0.951375i	$0.400329\pi$
$422$	3.46171e32	0.528305
$423$	1.53684e31	0.0227705
$424$	3.59300e33	5.16874
$425$	1.50006e31	0.0209530
$426$	−8.65495e32	−1.17394
$427$	0	0
$428$	2.17005e33	2.77602
$429$	1.02748e33	1.27661
$430$	−2.06737e33	−2.49495
$431$	−6.62790e32	−0.776980	−0.388490	−	0.921453i	$-0.627003\pi$
$431$	−6.62790e32	−0.776980	−0.388490	+	0.921453i	$0.627003\pi$
$432$	3.75493e33	4.27618
$433$	5.49355e32	0.607791	0.303895	−	0.952705i	$-0.401713\pi$
$433$	5.49355e32	0.607791	0.303895	+	0.952705i	$0.401713\pi$
$434$	0	0
$435$	2.05117e32	0.214233
$436$	5.18647e32	0.526369
$437$	−6.95405e31	−0.0685835
$438$	−1.22804e33	−1.17702
$439$	7.59659e32	0.707640	0.353820	−	0.935314i	$-0.384883\pi$
$439$	7.59659e32	0.707640	0.353820	+	0.935314i	$0.384883\pi$
$440$	4.39391e33	3.97825
$441$	0	0
$442$	−1.28206e33	−1.09681
$443$	1.99474e33	1.65897	0.829485	−	0.558528i	$-0.188634\pi$
$443$	1.99474e33	1.65897	0.829485	+	0.558528i	$0.188634\pi$
$444$	−5.49658e31	−0.0444432
$445$	7.94439e32	0.624540
$446$	−1.37640e33	−1.05210
$447$	2.67653e32	0.198942
$448$	0	0
$449$	−5.83519e32	−0.410181	−0.205091	−	0.978743i	$-0.565749\pi$
$449$	−5.83519e32	−0.410181	−0.205091	+	0.978743i	$0.565749\pi$
$450$	8.89657e31	0.0608228
$451$	−1.23323e33	−0.820041
$452$	−1.14915e33	−0.743272
$453$	−9.93654e32	−0.625184
$454$	1.11576e33	0.682921
$455$	0	0
$456$	−1.50579e33	−0.872377
$457$	9.81014e32	0.552997	0.276498	−	0.961014i	$-0.410826\pi$
$457$	9.81014e32	0.552997	0.276498	+	0.961014i	$0.410826\pi$
$458$	−5.57773e33	−3.05942
$459$	−6.95220e32	−0.371077
$460$	1.00015e33	0.519508
$461$	9.66010e32	0.488337	0.244169	−	0.969733i	$-0.421485\pi$
$461$	9.66010e32	0.488337	0.244169	+	0.969733i	$0.421485\pi$
$462$	0	0
$463$	−1.79149e33	−0.857929	−0.428965	−	0.903321i	$-0.641122\pi$
$463$	−1.79149e33	−0.857929	−0.428965	+	0.903321i	$0.641122\pi$
$464$	2.79885e33	1.30468
$465$	−2.23302e33	−1.01328
$466$	−1.81718e33	−0.802738
$467$	−6.33478e32	−0.272440	−0.136220	−	0.990679i	$-0.543495\pi$
$467$	−6.33478e32	−0.272440	−0.136220	+	0.990679i	$0.543495\pi$
$468$	−5.60603e33	−2.34737
$469$	0	0
$470$	2.06579e32	0.0820094
$471$	−1.11761e33	−0.432045
$472$	9.21580e33	3.46943
$473$	−4.18582e33	−1.53467
$474$	−3.11798e33	−1.11338
$475$	−6.13036e31	−0.0213214
$476$	0	0
$477$	−2.33503e33	−0.770572
$478$	−6.01504e33	−1.93370
$479$	−1.94791e33	−0.610064	−0.305032	−	0.952342i	$-0.598667\pi$
$479$	−1.94791e33	−0.610064	−0.305032	+	0.952342i	$0.598667\pi$
$480$	9.66737e33	2.94980
$481$	1.23104e32	0.0365982
$482$	7.47966e33	2.16668
$483$	0	0
$484$	3.61902e33	0.995460
$485$	6.77986e33	1.81739
$486$	−6.82628e33	−1.78333
$487$	−5.59193e33	−1.42380	−0.711901	−	0.702280i	$-0.752166\pi$
$487$	−5.59193e33	−1.42380	−0.711901	+	0.702280i	$0.752166\pi$
$488$	1.91498e34	4.75244
$489$	−5.76854e32	−0.139542
$490$	0	0
$491$	−4.80596e33	−1.10474	−0.552372	−	0.833598i	$-0.686277\pi$
$491$	−4.80596e33	−1.10474	−0.552372	+	0.833598i	$0.686277\pi$
$492$	−6.07832e33	−1.36213
$493$	−5.18203e32	−0.113217
$494$	5.23946e33	1.11609
$495$	−2.85553e33	−0.593091
$496$	−3.04699e34	−6.17093
$497$	0	0
$498$	−6.84059e33	−1.31743
$499$	−3.77817e33	−0.709617	−0.354809	−	0.934939i	$-0.615454\pi$
$499$	−3.77817e33	−0.709617	−0.354809	+	0.934939i	$0.615454\pi$
$500$	1.57404e34	2.88330
$501$	4.17238e33	0.745440
$502$	1.11103e34	1.93611
$503$	9.34696e32	0.158880	0.0794402	−	0.996840i	$-0.474687\pi$
$503$	9.34696e32	0.158880	0.0794402	+	0.996840i	$0.474687\pi$
$504$	0	0
$505$	8.84161e32	0.143017
$506$	2.74660e33	0.433425
$507$	−6.86739e33	−1.05729
$508$	2.67395e34	4.01659
$509$	−9.83451e33	−1.44139	−0.720693	−	0.693254i	$-0.756176\pi$
$509$	−9.83451e33	−1.44139	−0.720693	+	0.693254i	$0.756176\pi$
$510$	−3.21870e33	−0.460313
$511$	0	0
$512$	2.66121e34	3.62414
$513$	2.84119e33	0.377601
$514$	1.05982e34	1.37465
$515$	−2.50820e33	−0.317520
$516$	−2.06311e34	−2.54918
$517$	4.18263e32	0.0504450
$518$	0	0
$519$	−7.95883e33	−0.914655
$520$	−4.85035e34	−5.44165
$521$	−1.75879e34	−1.92638	−0.963192	−	0.268814i	$-0.913368\pi$
$521$	−1.75879e34	−1.92638	−0.963192	+	0.268814i	$0.913368\pi$
$522$	−3.07337e33	−0.328649
$523$	4.83097e33	0.504387	0.252193	−	0.967677i	$-0.418848\pi$
$523$	4.83097e33	0.504387	0.252193	+	0.967677i	$0.418848\pi$
$524$	3.61464e34	3.68488
$525$	0	0
$526$	−3.45499e33	−0.335834
$527$	5.64145e33	0.535499
$528$	3.51985e34	3.26287
$529$	−1.06434e34	−0.963569
$530$	−3.13872e34	−2.77526
$531$	−5.98920e33	−0.517234
$532$	0	0
$533$	1.36133e34	1.12169
$534$	1.07531e34	0.865498
$535$	−1.22017e34	−0.959399
$536$	−6.24561e34	−4.79750
$537$	9.30806e33	0.698523
$538$	−2.67681e34	−1.96263
$539$	0	0
$540$	−4.08628e34	−2.86026
$541$	1.72050e34	1.17676	0.588382	−	0.808583i	$-0.299765\pi$
$541$	1.72050e34	1.17676	0.588382	+	0.808583i	$0.299765\pi$
$542$	−3.04454e34	−2.03484
$543$	2.75523e33	0.179953
$544$	−2.44234e34	−1.55891
$545$	−2.91625e33	−0.181915
$546$	0	0
$547$	−2.66275e34	−1.58668	−0.793338	−	0.608781i	$-0.791659\pi$
$547$	−2.66275e34	−1.58668	−0.793338	+	0.608781i	$0.791659\pi$
$548$	3.77932e34	2.20119
$549$	−1.24451e34	−0.708509
$550$	2.42128e33	0.134744
$551$	2.11777e33	0.115208
$552$	8.71355e33	0.463400
$553$	0	0
$554$	5.61486e34	2.85408
$555$	3.09062e32	0.0153597
$556$	−6.61280e33	−0.321329
$557$	−2.57932e34	−1.22551	−0.612753	−	0.790275i	$-0.709938\pi$
$557$	−2.57932e34	−1.22551	−0.612753	+	0.790275i	$0.709938\pi$
$558$	3.34584e34	1.55445
$559$	4.62064e34	2.09920
$560$	0	0
$561$	−6.51694e33	−0.283144
$562$	3.39338e34	1.44188
$563$	3.74307e34	1.55551	0.777756	−	0.628566i	$-0.216358\pi$
$563$	3.74307e34	1.55551	0.777756	+	0.628566i	$0.216358\pi$
$564$	2.06153e33	0.0837919
$565$	6.46147e33	0.256877
$566$	4.31028e34	1.67610
$567$	0	0
$568$	8.27232e34	3.07803
$569$	1.51380e34	0.551018	0.275509	−	0.961298i	$-0.411154\pi$
$569$	1.51380e34	0.551018	0.275509	+	0.961298i	$0.411154\pi$
$570$	1.31540e34	0.468407
$571$	1.08075e34	0.376508	0.188254	−	0.982120i	$-0.439717\pi$
$571$	1.08075e34	0.376508	0.188254	+	0.982120i	$0.439717\pi$
$572$	−1.52573e35	−5.20028
$573$	−2.56598e33	−0.0855697
$574$	0	0
$575$	3.54745e32	0.0113258
$576$	−7.64177e34	−2.38733
$577$	−7.50297e33	−0.229369	−0.114685	−	0.993402i	$-0.536586\pi$
$577$	−7.50297e33	−0.229369	−0.114685	+	0.993402i	$0.536586\pi$
$578$	−5.70839e34	−1.70772
$579$	2.53789e34	0.743003
$580$	−3.04583e34	−0.872681
$581$	0	0
$582$	9.17682e34	2.51858
$583$	−6.35499e34	−1.70710
$584$	1.17374e35	3.08612
$585$	3.15216e34	0.811260
$586$	5.01936e34	1.26453
$587$	4.30323e34	1.06125	0.530625	−	0.847607i	$-0.321957\pi$
$587$	4.30323e34	1.06125	0.530625	+	0.847607i	$0.321957\pi$
$588$	0	0
$589$	−2.30552e34	−0.544914
$590$	−8.05058e34	−1.86285
$591$	−3.12486e33	−0.0707925
$592$	4.21720e33	0.0935411
$593$	−4.05228e34	−0.880068	−0.440034	−	0.897981i	$-0.645034\pi$
$593$	−4.05228e34	−0.880068	−0.440034	+	0.897981i	$0.645034\pi$
$594$	−1.12217e35	−2.38631
$595$	0	0
$596$	−3.97444e34	−0.810396
$597$	6.42333e33	0.128257
$598$	−3.03192e34	−0.592860
$599$	2.60491e34	0.498835	0.249418	−	0.968396i	$-0.419761\pi$
$599$	2.60491e34	0.498835	0.249418	+	0.968396i	$0.419761\pi$
$600$	7.68146e33	0.144063
$601$	−4.79733e34	−0.881188	−0.440594	−	0.897706i	$-0.645232\pi$
$601$	−4.79733e34	−0.881188	−0.440594	+	0.897706i	$0.645232\pi$
$602$	0	0
$603$	4.05892e34	0.715227
$604$	1.47550e35	2.54670
$605$	−2.03490e34	−0.344034
$606$	1.19675e34	0.198196
$607$	1.33129e34	0.215980	0.107990	−	0.994152i	$-0.465559\pi$
$607$	1.33129e34	0.215980	0.107990	+	0.994152i	$0.465559\pi$
$608$	9.98125e34	1.58632
$609$	0	0
$610$	−1.67286e35	−2.55173
$611$	−4.61712e33	−0.0690012
$612$	3.55571e34	0.520635
$613$	−2.38883e34	−0.342712	−0.171356	−	0.985209i	$-0.554815\pi$
$613$	−2.38883e34	−0.342712	−0.171356	+	0.985209i	$0.554815\pi$
$614$	2.33031e35	3.27574
$615$	3.41772e34	0.470758
$616$	0	0
$617$	1.25303e35	1.65728	0.828642	−	0.559779i	$-0.189114\pi$
$617$	1.25303e35	1.65728	0.828642	+	0.559779i	$0.189114\pi$
$618$	−3.39495e34	−0.440025
$619$	−6.31972e34	−0.802722	−0.401361	−	0.915920i	$-0.631463\pi$
$619$	−6.31972e34	−0.802722	−0.401361	+	0.915920i	$0.631463\pi$
$620$	3.31586e35	4.12763
$621$	−1.64411e34	−0.200579
$622$	−9.05702e34	−1.08294
$623$	0	0
$624$	−3.88549e35	−4.46312
$625$	−8.32348e34	−0.937141
$626$	−6.77514e34	−0.747720
$627$	2.66331e34	0.288123
$628$	1.65957e35	1.75994
$629$	−7.80807e32	−0.00811728
$630$	0	0
$631$	−1.00326e35	−1.00241	−0.501207	−	0.865327i	$-0.667110\pi$
$631$	−1.00326e35	−1.00241	−0.501207	+	0.865327i	$0.667110\pi$
$632$	2.98013e35	2.91926
$633$	−1.94244e34	−0.186552
$634$	−2.42561e35	−2.28405
$635$	−1.50351e35	−1.38815
$636$	−3.13225e35	−2.83558
$637$	0	0
$638$	−8.36442e34	−0.728077
$639$	−5.37604e34	−0.458883
$640$	−5.15662e35	−4.31634
$641$	1.84385e35	1.51356	0.756781	−	0.653668i	$-0.226771\pi$
$641$	1.84385e35	1.51356	0.756781	+	0.653668i	$0.226771\pi$
$642$	−1.65156e35	−1.32955
$643$	7.33037e34	0.578747	0.289373	−	0.957216i	$-0.406553\pi$
$643$	7.33037e34	0.578747	0.289373	+	0.957216i	$0.406553\pi$
$644$	0	0
$645$	1.16004e35	0.881004
$646$	−3.32321e34	−0.247543
$647$	2.19935e35	1.60691	0.803453	−	0.595368i	$-0.202994\pi$
$647$	2.19935e35	1.60691	0.803453	+	0.595368i	$0.202994\pi$
$648$	−9.76502e34	−0.699819
$649$	−1.63001e35	−1.14586
$650$	−2.67280e34	−0.184310
$651$	0	0
$652$	8.56584e34	0.568428
$653$	1.62784e35	1.05974	0.529869	−	0.848080i	$-0.322241\pi$
$653$	1.62784e35	1.05974	0.529869	+	0.848080i	$0.322241\pi$
$654$	−3.94726e34	−0.252101
$655$	−2.03244e35	−1.27351
$656$	4.66353e35	2.86693
$657$	−7.62797e34	−0.460089
$658$	0	0
$659$	7.54818e34	0.438303	0.219151	−	0.975691i	$-0.429671\pi$
$659$	7.54818e34	0.438303	0.219151	+	0.975691i	$0.429671\pi$
$660$	−3.83044e35	−2.18248
$661$	3.32721e35	1.86021	0.930106	−	0.367292i	$-0.119715\pi$
$661$	3.32721e35	1.86021	0.930106	+	0.367292i	$0.119715\pi$
$662$	−5.26486e34	−0.288843
$663$	7.19392e34	0.387299
$664$	6.53817e35	3.45426
$665$	0	0
$666$	−4.63082e33	−0.0235630
$667$	−1.22549e34	−0.0611977
$668$	−6.19567e35	−3.03656
$669$	7.72326e34	0.371513
$670$	5.45593e35	2.57593
$671$	−3.38705e35	−1.56960
$672$	0	0
$673$	−2.51254e35	−1.12182	−0.560912	−	0.827875i	$-0.689549\pi$
$673$	−2.51254e35	−1.12182	−0.560912	+	0.827875i	$0.689549\pi$
$674$	−5.70939e35	−2.50231
$675$	−1.44937e34	−0.0623566
$676$	1.01975e36	4.30687
$677$	3.66408e35	1.51917	0.759586	−	0.650407i	$-0.225401\pi$
$677$	3.66408e35	1.51917	0.759586	+	0.650407i	$0.225401\pi$
$678$	8.74586e34	0.355985
$679$	0	0
$680$	3.07640e35	1.20693
$681$	−6.26074e34	−0.241150
$682$	9.10599e35	3.44368
$683$	5.95674e34	0.221182	0.110591	−	0.993866i	$-0.464726\pi$
$683$	5.95674e34	0.221182	0.110591	+	0.993866i	$0.464726\pi$
$684$	−1.45313e35	−0.529789
$685$	−2.12504e35	−0.760737
$686$	0	0
$687$	3.12978e35	1.08033
$688$	1.58290e36	5.36534
$689$	7.01515e35	2.33505
$690$	−7.61183e34	−0.248814
$691$	1.74504e35	0.560182	0.280091	−	0.959973i	$-0.409635\pi$
$691$	1.74504e35	0.560182	0.280091	+	0.959973i	$0.409635\pi$
$692$	1.18182e36	3.72586
$693$	0	0
$694$	4.24018e35	1.28941
$695$	3.71825e34	0.111052
$696$	−2.65360e35	−0.778431
$697$	−8.63445e34	−0.248786
$698$	−9.55960e35	−2.70550
$699$	1.01966e35	0.283459
$700$	0	0
$701$	1.50148e35	0.402759	0.201379	−	0.979513i	$-0.435458\pi$
$701$	1.50148e35	0.402759	0.201379	+	0.979513i	$0.435458\pi$
$702$	1.23874e36	3.26412
$703$	3.19096e33	0.00826001
$704$	−2.07977e36	−5.28880
$705$	−1.15916e34	−0.0289587
$706$	−1.18199e36	−2.90106
$707$	0	0
$708$	−8.03399e35	−1.90334
$709$	−1.96379e35	−0.457105	−0.228553	−	0.973532i	$-0.573399\pi$
$709$	−1.96379e35	−0.457105	−0.228553	+	0.973532i	$0.573399\pi$
$710$	−7.22639e35	−1.65269
$711$	−1.93674e35	−0.435213
$712$	−1.02777e36	−2.26931
$713$	1.33413e35	0.289455
$714$	0	0
$715$	8.57887e35	1.79723
$716$	−1.38218e36	−2.84545
$717$	3.37517e35	0.682819
$718$	1.25589e36	2.49688
$719$	−1.81504e35	−0.354629	−0.177314	−	0.984154i	$-0.556741\pi$
$719$	−1.81504e35	−0.354629	−0.177314	+	0.984154i	$0.556741\pi$
$720$	1.07984e36	2.07349
$721$	0	0
$722$	−9.16074e35	−1.69909
$723$	−4.19700e35	−0.765086
$724$	−4.09130e35	−0.733043
$725$	−1.08033e34	−0.0190253
$726$	−2.75432e35	−0.476768
$727$	1.01706e36	1.73048	0.865241	−	0.501356i	$-0.167165\pi$
$727$	1.01706e36	1.73048	0.865241	+	0.501356i	$0.167165\pi$
$728$	0	0
$729$	5.03827e35	0.828299
$730$	−1.02534e36	−1.65704
$731$	−2.93071e35	−0.465592
$732$	−1.66941e36	−2.60720
$733$	2.47070e35	0.379332	0.189666	−	0.981849i	$-0.439259\pi$
$733$	2.47070e35	0.379332	0.189666	+	0.981849i	$0.439259\pi$
$734$	−5.18802e35	−0.783071
$735$	0	0
$736$	−5.77584e35	−0.842641
$737$	1.10467e36	1.58449
$738$	−5.12093e35	−0.722179
$739$	5.19115e35	0.719793	0.359897	−	0.932992i	$-0.382812\pi$
$739$	5.19115e35	0.719793	0.359897	+	0.932992i	$0.382812\pi$
$740$	−4.58933e34	−0.0625681
$741$	−2.93997e35	−0.394109
$742$	0	0
$743$	−2.96481e35	−0.384270	−0.192135	−	0.981369i	$-0.561541\pi$
$743$	−2.96481e35	−0.384270	−0.192135	+	0.981369i	$0.561541\pi$
$744$	2.88886e36	3.68184
$745$	2.23475e35	0.280075
$746$	2.47638e36	3.05199
$747$	−4.24905e35	−0.514973
$748$	9.67715e35	1.15339
$749$	0	0
$750$	−1.19795e36	−1.38094
$751$	−1.21244e36	−1.37456	−0.687278	−	0.726395i	$-0.741195\pi$
$751$	−1.21244e36	−1.37456	−0.687278	+	0.726395i	$0.741195\pi$
$752$	−1.58169e35	−0.176360
$753$	−6.23425e35	−0.683671
$754$	9.23332e35	0.995900
$755$	−8.29644e35	−0.880147
$756$	0	0
$757$	1.02920e36	1.05634	0.528169	−	0.849139i	$-0.322879\pi$
$757$	1.02920e36	1.05634	0.528169	+	0.849139i	$0.322879\pi$
$758$	−3.37628e36	−3.40858
$759$	−1.54118e35	−0.153049
$760$	−1.25725e36	−1.22815
$761$	1.67665e36	1.61114	0.805571	−	0.592499i	$-0.201859\pi$
$761$	1.67665e36	1.61114	0.805571	+	0.592499i	$0.201859\pi$
$762$	−2.03506e36	−1.92372
$763$	0	0
$764$	3.81028e35	0.348570
$765$	−1.99930e35	−0.179933
$766$	−9.54007e34	−0.0844680
$767$	1.79933e36	1.56736
$768$	−3.32697e36	−2.85124
$769$	5.51316e35	0.464859	0.232429	−	0.972613i	$-0.425333\pi$
$769$	5.51316e35	0.464859	0.232429	+	0.972613i	$0.425333\pi$
$770$	0	0
$771$	−5.94686e35	−0.485409
$772$	−3.76857e36	−3.02664
$773$	1.17252e36	0.926566	0.463283	−	0.886210i	$-0.346671\pi$
$773$	1.17252e36	0.926566	0.463283	+	0.886210i	$0.346671\pi$
$774$	−1.73815e36	−1.35153
$775$	1.17611e35	0.0899864
$776$	−8.77112e36	−6.60364
$777$	0	0
$778$	4.48965e36	3.27316
$779$	3.52869e35	0.253160
$780$	4.22835e36	2.98530
$781$	−1.46314e36	−1.01659
$782$	1.92304e35	0.131493
$783$	5.00693e35	0.336937
$784$	0	0
$785$	−9.33141e35	−0.608242
$786$	−2.75099e36	−1.76485
$787$	1.22061e36	0.770713	0.385357	−	0.922768i	$-0.374078\pi$
$787$	1.22061e36	0.770713	0.385357	+	0.922768i	$0.374078\pi$
$788$	4.64018e35	0.288374
$789$	1.93867e35	0.118588
$790$	−2.60334e36	−1.56744
$791$	0	0
$792$	3.69420e36	2.15504
$793$	3.73889e36	2.14698
$794$	−2.08337e36	−1.17763
$795$	1.76120e36	0.979985
$796$	−9.53816e35	−0.522458
$797$	2.58450e36	1.39363	0.696815	−	0.717251i	$-0.254600\pi$
$797$	2.58450e36	1.39363	0.696815	+	0.717251i	$0.254600\pi$
$798$	0	0
$799$	2.92848e34	0.0153041
$800$	−5.09172e35	−0.261963
$801$	6.67929e35	0.338317
$802$	−1.54837e36	−0.772137
$803$	−2.07602e36	−1.01926
$804$	5.44469e36	2.63192
$805$	0	0
$806$	−1.00519e37	−4.71043
$807$	1.50201e36	0.693035
$808$	−1.14384e36	−0.519665
$809$	7.30168e35	0.326638	0.163319	−	0.986573i	$-0.447780\pi$
$809$	7.30168e35	0.326638	0.163319	+	0.986573i	$0.447780\pi$
$810$	8.53036e35	0.375755
$811$	7.76161e34	0.0336660	0.0168330	−	0.999858i	$-0.494642\pi$
$811$	7.76161e34	0.0336660	0.0168330	+	0.999858i	$0.494642\pi$
$812$	0	0
$813$	1.70836e36	0.718533
$814$	−1.26032e35	−0.0522005
$815$	−4.81640e35	−0.196450
$816$	2.46443e36	0.989895
$817$	1.19771e36	0.473778
$818$	−4.79241e36	−1.86697
$819$	0	0
$820$	−5.07505e36	−1.91764
$821$	2.44681e35	0.0910563	0.0455281	−	0.998963i	$-0.485503\pi$
$821$	2.44681e35	0.0910563	0.0455281	+	0.998963i	$0.485503\pi$
$822$	−2.87633e36	−1.05424
$823$	−1.02598e36	−0.370374	−0.185187	−	0.982703i	$-0.559289\pi$
$823$	−1.02598e36	−0.370374	−0.185187	+	0.982703i	$0.559289\pi$
$824$	3.24486e36	1.15373
$825$	−1.35863e35	−0.0475802
$826$	0	0
$827$	2.08230e36	0.707497	0.353749	−	0.935340i	$-0.384907\pi$
$827$	2.08230e36	0.707497	0.353749	+	0.935340i	$0.384907\pi$
$828$	8.40881e35	0.281420
$829$	−5.20139e36	−1.71470	−0.857350	−	0.514734i	$-0.827891\pi$
$829$	−5.20139e36	−1.71470	−0.857350	+	0.514734i	$0.827891\pi$
$830$	−5.71150e36	−1.85470
$831$	−3.15062e36	−1.00782
$832$	2.29582e37	7.23429
$833$	0	0
$834$	5.03280e35	0.153898
$835$	3.48370e36	1.04945
$836$	−3.95481e36	−1.17367
$837$	−5.45083e36	−1.59365
$838$	5.93229e36	1.70872
$839$	1.43469e36	0.407132	0.203566	−	0.979061i	$-0.434747\pi$
$839$	1.43469e36	0.407132	0.203566	+	0.979061i	$0.434747\pi$
$840$	0	0
$841$	−3.25716e36	−0.897199
$842$	4.42879e36	1.20194
$843$	−1.90410e36	−0.509148
$844$	2.88437e36	0.759925
$845$	−5.73388e36	−1.48847
$846$	1.73683e35	0.0444249
$847$	0	0
$848$	2.40319e37	5.96814
$849$	−2.41859e36	−0.591856
$850$	1.69526e35	0.0408790
$851$	−1.84651e34	−0.00438766
$852$	−7.21150e36	−1.68861
$853$	2.42386e36	0.559300	0.279650	−	0.960102i	$-0.409782\pi$
$853$	2.42386e36	0.559300	0.279650	+	0.960102i	$0.409782\pi$
$854$	0	0
$855$	8.17066e35	0.183097
$856$	1.57854e37	3.48605
$857$	6.13430e36	1.33507	0.667536	−	0.744577i	$-0.267349\pi$
$857$	6.13430e36	1.33507	0.667536	+	0.744577i	$0.267349\pi$
$858$	1.16119e37	2.49064
$859$	−6.92554e36	−1.46399	−0.731997	−	0.681308i	$-0.761411\pi$
$859$	−6.92554e36	−1.46399	−0.731997	+	0.681308i	$0.761411\pi$
$860$	−1.72258e37	−3.58879
$861$	0	0
$862$	−7.49039e36	−1.51588
$863$	−8.22038e36	−1.63967	−0.819836	−	0.572598i	$-0.805936\pi$
$863$	−8.22038e36	−1.63967	−0.819836	+	0.572598i	$0.805936\pi$
$864$	2.35982e37	4.63934
$865$	−6.64517e36	−1.28767
$866$	6.20842e36	1.18579
$867$	3.20310e36	0.603020
$868$	0	0
$869$	−5.27100e36	−0.964153
$870$	2.31809e36	0.417964
$871$	−1.21942e37	−2.16734
$872$	3.77275e36	0.661001
$873$	5.70021e36	0.984493
$874$	−7.85897e35	−0.133805
$875$	0	0
$876$	−1.02323e37	−1.69305
$877$	7.07453e36	1.15399	0.576996	−	0.816747i	$-0.304225\pi$
$877$	7.07453e36	1.15399	0.576996	+	0.816747i	$0.304225\pi$
$878$	8.58514e36	1.38059
$879$	−2.81647e36	−0.446523
$880$	2.93887e37	4.59354
$881$	1.05926e37	1.63231	0.816153	−	0.577835i	$-0.196102\pi$
$881$	1.05926e37	1.63231	0.816153	+	0.577835i	$0.196102\pi$
$882$	0	0
$883$	−3.12974e36	−0.468813	−0.234407	−	0.972139i	$-0.575315\pi$
$883$	−3.12974e36	−0.468813	−0.234407	+	0.972139i	$0.575315\pi$
$884$	−1.06824e37	−1.57767
$885$	4.51735e36	0.657799
$886$	2.25431e37	3.23662
$887$	−1.85304e36	−0.262324	−0.131162	−	0.991361i	$-0.541871\pi$
$887$	−1.85304e36	−0.262324	−0.131162	+	0.991361i	$0.541871\pi$
$888$	−3.99834e35	−0.0558107
$889$	0	0
$890$	8.97819e36	1.21847
$891$	1.72715e36	0.231132
$892$	−1.14684e37	−1.51337
$893$	−1.19680e35	−0.0155732
$894$	3.02482e36	0.388133
$895$	7.77170e36	0.983395
$896$	0	0
$897$	1.70127e36	0.209348
$898$	−6.59452e36	−0.800256
$899$	−4.06294e36	−0.486232
$900$	7.41282e35	0.0874887
$901$	−4.44946e36	−0.517902
$902$	−1.39371e37	−1.59989
$903$	0	0
$904$	−8.35921e36	−0.933383
$905$	2.30046e36	0.253342
$906$	−1.12296e37	−1.21972
$907$	−1.38911e37	−1.48814	−0.744072	−	0.668100i	$-0.767108\pi$
$907$	−1.38911e37	−1.48814	−0.744072	+	0.668100i	$0.767108\pi$
$908$	9.29672e36	0.982328
$909$	7.43363e35	0.0774734
$910$	0	0
$911$	1.16883e36	0.118514	0.0592570	−	0.998243i	$-0.481127\pi$
$911$	1.16883e36	0.118514	0.0592570	+	0.998243i	$0.481127\pi$
$912$	−1.00715e37	−1.00730
$913$	−1.15641e37	−1.14085
$914$	1.10867e37	1.07889
$915$	9.38675e36	0.901055
$916$	−4.64749e37	−4.40073
$917$	0	0
$918$	−7.85689e36	−0.723964
$919$	4.96428e35	0.0451245	0.0225623	−	0.999745i	$-0.492818\pi$
$919$	4.96428e35	0.0451245	0.0225623	+	0.999745i	$0.492818\pi$
$920$	7.27531e36	0.652385
$921$	−1.30759e37	−1.15671
$922$	1.09172e37	0.952738
$923$	1.61513e37	1.39054
$924$	0	0
$925$	−1.62780e34	−0.00136405
$926$	−2.02461e37	−1.67381
$927$	−2.10878e36	−0.172002
$928$	1.75896e37	1.41549
$929$	−1.62945e37	−1.29373	−0.646867	−	0.762603i	$-0.723921\pi$
$929$	−1.62945e37	−1.29373	−0.646867	+	0.762603i	$0.723921\pi$
$930$	−2.52360e37	−1.97690
$931$	0	0
$932$	−1.51411e37	−1.15467
$933$	5.08209e36	0.382403
$934$	−7.15912e36	−0.531525
$935$	−5.44127e36	−0.398617
$936$	−4.07795e37	−2.94777
$937$	−1.84405e37	−1.31531	−0.657655	−	0.753319i	$-0.728452\pi$
$937$	−1.84405e37	−1.31531	−0.657655	+	0.753319i	$0.728452\pi$
$938$	0	0
$939$	3.80167e36	0.264031
$940$	1.72126e36	0.117964
$941$	−1.70060e37	−1.15009	−0.575044	−	0.818122i	$-0.695015\pi$
$941$	−1.70060e37	−1.15009	−0.575044	+	0.818122i	$0.695015\pi$
$942$	−1.26305e37	−0.842913
$943$	−2.04194e36	−0.134477
$944$	6.16400e37	4.00602
$945$	0	0
$946$	−4.73052e37	−2.99412
$947$	3.00075e37	1.87437	0.937186	−	0.348830i	$-0.113421\pi$
$947$	3.00075e37	1.87437	0.937186	+	0.348830i	$0.113421\pi$
$948$	−2.59797e37	−1.60151
$949$	2.29167e37	1.39420
$950$	−6.92811e35	−0.0415977
$951$	1.36106e37	0.806531
$952$	0	0
$953$	1.53331e37	0.885051	0.442525	−	0.896756i	$-0.354083\pi$
$953$	1.53331e37	0.885051	0.442525	+	0.896756i	$0.354083\pi$
$954$	−2.63889e37	−1.50337
$955$	−2.14245e36	−0.120467
$956$	−5.01186e37	−2.78148
$957$	4.69345e36	0.257095
$958$	−2.20140e37	−1.19023
$959$	0	0
$960$	5.76381e37	3.03612
$961$	2.49987e37	1.29979
$962$	1.39124e36	0.0714025
$963$	−1.02587e37	−0.519712
$964$	6.23222e37	3.11659
$965$	2.11899e37	1.04602
$966$	0	0
$967$	2.57114e37	1.23679	0.618393	−	0.785869i	$-0.287784\pi$
$967$	2.57114e37	1.23679	0.618393	+	0.785869i	$0.287784\pi$
$968$	2.63256e37	1.25007
$969$	1.86472e36	0.0874112
$970$	7.66212e37	3.54570
$971$	8.64809e36	0.395075	0.197538	−	0.980295i	$-0.436706\pi$
$971$	8.64809e36	0.395075	0.197538	+	0.980295i	$0.436706\pi$
$972$	−5.68781e37	−2.56517
$973$	0	0
$974$	−6.31961e37	−2.77781
$975$	1.49976e36	0.0650826
$976$	1.28084e38	5.48746
$977$	2.38611e37	1.00927	0.504637	−	0.863332i	$-0.331626\pi$
$977$	2.38611e37	1.00927	0.504637	+	0.863332i	$0.331626\pi$
$978$	−6.51920e36	−0.272244
$979$	1.81782e37	0.749494
$980$	0	0
$981$	−2.45185e36	−0.0985443
$982$	−5.43136e37	−2.15533
$983$	−3.49272e36	−0.136850	−0.0684250	−	0.997656i	$-0.521797\pi$
$983$	−3.49272e36	−0.136850	−0.0684250	+	0.997656i	$0.521797\pi$
$984$	−4.42151e37	−1.71053
$985$	−2.60908e36	−0.0996631
$986$	−5.85637e36	−0.220885
$987$	0	0
$988$	4.36564e37	1.60541
$989$	−6.93077e36	−0.251668
$990$	−3.22712e37	−1.15711
$991$	−3.11489e37	−1.10286	−0.551432	−	0.834220i	$-0.685918\pi$
$991$	−3.11489e37	−1.10286	−0.551432	+	0.834220i	$0.685918\pi$
$992$	−1.91490e38	−6.69501
$993$	2.95422e36	0.101995
$994$	0	0
$995$	5.36312e36	0.180563
$996$	−5.69973e37	−1.89502
$997$	5.60061e37	1.83885	0.919424	−	0.393267i	$-0.128655\pi$
$997$	5.60061e37	1.83885	0.919424	+	0.393267i	$0.128655\pi$
$998$	−4.26982e37	−1.38445
$999$	7.54423e35	0.0241572

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	49.26.a.d.1.7		7
7.6	odd	2		7.26.a.b.1.7	✓	7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7.26.a.b.1.7	✓	7	7.6	odd	2
49.26.a.d.1.7		7	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:	\( N \)	\(=\)	\( 49 = 7^{2} \)
Weight:	\( k \)	\(=\)	\( 26 \)
Character orbit:	\([\chi]\)	\(=\)	49.a (trivial)

\(f(q)\)	\(=\)	\(q+11301.3 q^{2} -634140. q^{3} +9.41649e7 q^{4} -5.29471e8 q^{5} -7.16660e9 q^{6} +6.84977e11 q^{8} -4.45155e11 q^{9} +O(q^{10})\)	\(q+11301.3 q^{2} -634140. q^{3} +9.41649e7 q^{4} -5.29471e8 q^{5} -7.16660e9 q^{6} +6.84977e11 q^{8} -4.45155e11 q^{9} -5.98371e12 q^{10} -1.21153e13 q^{11} -5.97137e13 q^{12} +1.33738e14 q^{13} +3.35758e14 q^{15} +4.58148e15 q^{16} -8.48253e14 q^{17} -5.03083e15 q^{18} +3.46660e15 q^{19} -4.98575e16 q^{20} -1.36918e17 q^{22} -2.00601e16 q^{23} -4.34371e17 q^{24} -1.76841e16 q^{25} +1.51141e18 q^{26} +8.19590e17 q^{27} +6.10906e17 q^{29} +3.79451e18 q^{30} -6.65067e18 q^{31} +2.87926e19 q^{32} +7.68278e18 q^{33} -9.58636e18 q^{34} -4.19180e19 q^{36} +9.20488e17 q^{37} +3.91771e19 q^{38} -8.48086e19 q^{39} -3.62675e20 q^{40} +1.01791e20 q^{41} +3.45500e20 q^{43} -1.14083e21 q^{44} +2.35697e20 q^{45} -2.26706e20 q^{46} -3.45236e19 q^{47} -2.90530e21 q^{48} -1.99853e20 q^{50} +5.37911e20 q^{51} +1.25934e22 q^{52} +5.24544e21 q^{53} +9.26243e21 q^{54} +6.41468e21 q^{55} -2.19831e21 q^{57} +6.90403e21 q^{58} +1.34542e22 q^{59} +3.16167e22 q^{60} +2.79568e22 q^{61} -7.51612e22 q^{62} +1.71665e23 q^{64} -7.08104e22 q^{65} +8.68254e22 q^{66} -9.11798e22 q^{67} -7.98757e22 q^{68} +1.27209e22 q^{69} +1.20768e23 q^{71} -3.04921e23 q^{72} +1.71355e23 q^{73} +1.04027e22 q^{74} +1.12142e22 q^{75} +3.26432e23 q^{76} -9.58448e23 q^{78} +4.35071e23 q^{79} -2.42576e24 q^{80} -1.42560e23 q^{81} +1.15037e24 q^{82} +9.54510e23 q^{83} +4.49125e23 q^{85} +3.90459e24 q^{86} -3.87400e23 q^{87} -8.29868e24 q^{88} -1.50044e24 q^{89} +2.66368e24 q^{90} -1.88896e24 q^{92} +4.21746e24 q^{93} -3.90162e23 q^{94} -1.83546e24 q^{95} -1.82586e25 q^{96} -1.28050e25 q^{97} +5.39318e24 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q + 8373 q^{2} + 599172 q^{3} + 199632661 q^{4} - 485320794 q^{5} - 548762130 q^{6} + 679913241639 q^{8} + 2499178495563 q^{9}+O(q^{10}) \) 7 * q + 8373 * q^2 + 599172 * q^3 + 199632661 * q^4 - 485320794 * q^5 - 548762130 * q^6 + 679913241639 * q^8 + 2499178495563 * q^9	\( 7 q + 8373 q^{2} + 599172 q^{3} + 199632661 q^{4} - 485320794 q^{5} - 548762130 q^{6} + 679913241639 q^{8} + 2499178495563 q^{9} + 876704815140 q^{10} - 7845139606524 q^{11} + 83731581305106 q^{12} + 75871445642734 q^{13} + 12\!\cdots\!84 q^{15}+ \cdots + 29\!\cdots\!00 q^{99}+O(q^{100}) \) 7 * q + 8373 * q^2 + 599172 * q^3 + 199632661 * q^4 - 485320794 * q^5 - 548762130 * q^6 + 679913241639 * q^8 + 2499178495563 * q^9 + 876704815140 * q^10 - 7845139606524 * q^11 + 83731581305106 * q^12 + 75871445642734 * q^13 + 1250450093573784 * q^15 + 2533333214129041 * q^16 - 4930179049331550 * q^17 + 6108218172751149 * q^18 + 8822108307937204 * q^19 + 35797888210439208 * q^20 + 122308015837411896 * q^22 + 260380318250119992 * q^23 - 280838923324398306 * q^24 + 442974124902943561 * q^25 - 525030062154247104 * q^26 + 508138451607400488 * q^27 + 3074121146906357394 * q^29 + 20693674849314206160 * q^30 - 17867964278742490304 * q^31 + 41524963168122393471 * q^32 - 18631713362079899088 * q^33 - 76530595013021124150 * q^34 + 120686738791924632357 * q^36 + 37537195275383667242 * q^37 - 133898980332930749790 * q^38 + 160680068588101330968 * q^39 - 260261018010811048560 * q^40 - 349555665716732087718 * q^41 - 188918130006461199484 * q^43 - 866635019544130150704 * q^44 + 2875914312455481795918 * q^45 - 1056444907691638473648 * q^46 + 577519309883773958064 * q^47 + 1705636002072738200514 * q^48 - 3108044078925178785 * q^50 - 8568497654252614793448 * q^51 + 21223967127059853562252 * q^52 + 724118360265623334330 * q^53 + 23525683999565788877508 * q^54 + 3874297214249814234792 * q^55 + 21002099147408968606176 * q^57 - 6571075616758407948534 * q^58 + 29388013065202679743548 * q^59 + 131210151872269358361312 * q^60 - 24863323230677092393442 * q^61 - 178098511159147000538004 * q^62 + 185730465159694629378817 * q^64 - 28642507689771657088260 * q^65 + 182488465275344339797728 * q^66 + 87288896332559907446444 * q^67 - 236561584649915083645422 * q^68 + 38736311524504328113344 * q^69 + 507749245951454445426264 * q^71 - 136846012456831244000985 * q^72 + 384451815193432683470074 * q^73 - 180156332882615168418510 * q^74 + 917728597534517928543804 * q^75 + 1802955096706900507996366 * q^76 - 2701299412149008608565208 * q^78 - 512089643024553543168400 * q^79 - 1072829383400652355143456 * q^80 - 1711055088184234765637889 * q^81 + 328793973025384284153498 * q^82 - 683613625271699866065420 * q^83 - 4106127272649214828366668 * q^85 + 6352668961585470034751760 * q^86 - 6810779334667612471104168 * q^87 - 1678346430445345786597824 * q^88 - 7785138614078665124468694 * q^89 + 6907385334351120772566420 * q^90 + 4229143913695999872649632 * q^92 + 9311007684860974346150688 * q^93 - 16094575705640558287782684 * q^94 + 8670853765297953493275288 * q^95 - 20458763379770390869400514 * q^96 - 16735236191051483252826350 * q^97 + 29494988134999515624453300 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more